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Transcript
The Dynamic Earth
English edition
‘The Dynamic Earth’ was developed as an Advanced Integrated Science module for Dutch upper
secondary students (pre-university stream, vwo), within the course known as ‘Nature Life and
Technology’ (NLT). In 2008, the module received certification from the national NLT Steering
Commission.
The module was developed for Junior College Utrecht (www.uu.nl/jcu ) by a team headed by Dr.
M.L. Kloosterboer – van Hoeve (module coordinator) with contributions from:



Utrecht University, Faculty of Geosciences
o Prof. dr. R. Wortel
o Dr. P. Meijer
o Dr. H. Paulssen
o Dr. H. de Bresser
o Dr. M. van Bergen
o Dr. A. van den Berg
o T.S. van der Voort
Junior College Utrecht
o Dr. M.L. Kloosterboer-van Hoeve (module coordinator)
o Dr. A.E. van der Valk (curriculum coordinator)
o K.J. Kieviet MSc (layout)
Partner schools of JCU:
o Baarnsch Lyceum: Drs. W. Theulings and Drs. I. Rijnja
o Revius Lyceum Doorn: Drs. J. Hillebrand
o Leidsche Rijn College: Drs. P. Duifhuis and Drs. F. Valk
o Goois Lyceum Bussum: mw. M. Raaijmaakers
Translation: ms. Anne Glerum and ms. Nienke Blom, with thanks to ms. Kate Smith for editing
the English text. The translation was made possible by the PRIMAS Project (www.primasproject.eu and a SPRINT grant from the Faculty of Science and the Faculty of Geosciences,
Utrecht University.
© 2011 JCU/Utrecht University.
For this module a Creative Commons Attribution-NonCommercial-ShareAlike
3.0 Netherlands License applies http://creativecommons.org/licenses/by-ncsa/3.0/nl/deed.en
The authors’ copyrights remain with lie with Utrecht University and Junior College Utrecht, P.O. box
80 000, 3508TA Utrecht, The Netherlands. Altered versions of this module may only be distributed
if the fact that it is an altered version is clearly stated, along with the name of the authors who
made the modifications.
In the development of this material, the authors have used materials of others. If possible, the
source of the materials is mentioned and a similar or more open license is applicable. If material
has been used in which the source is mentioned incorrectly, please contact Junior College Utrecht
([email protected] ).
The module has been composed with care. Utrecht University and Junior College Utrecht do not
accept any responsibility for any damage that originates from this module or the use of this
module.
An
electronic
version
of
this
module
(pdf
format)
can
be
found
on
http://www.uu.nl/faculty/science/EN/vwo/juniorcollege. Teacher materials such as a teacher guide
as well as the module in MSWord format can be requested at [email protected].
The Dynamic Earth
Table of Contents
Table of Contents
Table of Contents
4
Introduction to the English edition
6
Introduction
8
An interdisciplinary course
8
Four kinds of exercises
8
Glossary
8
Chapter 1.
Basic Theory
10
1.1
Introduction
11
1.2
How to use maps and the atlas
11
1.3
Types of rock
11
1.4
Dating of rock
15
Chapter 2.
Plate Tectonics
21
2.1
The observations that led to plate tectonics theory
22
2.2
Three steps to plate tectonics.
24
2.3
Structure of the Earth
31
2.4
The engine driving plate motion
33
2.5
Types of motion at plate boundaries
33
2.6
Intraplate motion
34
2.7
Describing plate motions
35
Chapter 3.
Earthquakes and tsunamis
45
3.1
Earthquake waves
46
3.2
The relationship between plate tectonics and earthquakes.
51
3.3
The development of an earthquake
53
3.4
The motion of plates during an earthquake
56
3.5
The strength (magnitude) of an earthquake
60
3.6
The relation between earthquakes and tsunamis
62
Chapter 4.
Volcanoes
69
4.1
Volcano types and occurrences
70
4.2
Formation of different types of igneous rocks
72
4.3
Magma formation
74
4
Table of Contents
4.4
Volcanoes on Iceland
77
4.5
The quantity of gas emitted during the Laki eruption
79
4.6
Acid rain in Western Europe.
83
4.7
The consequences of acid rain
85
Chapter 5.
Mountain building
96
5.1
The relation between mountain formation and plate tectonics
97
5.2
Information about orogenesis: hidden in rocks
99
5.3
The relation between force, stress and deformation.
104
5.4
Fast deformation (brittle behaviour)
110
5.6 Slow deformation (ductile behaviour)
114
5.5
119
What different types of deformation tell us about orogenesis.
Chapter 6.
Convection: the Earth as an heat engine
125
6.1
Introduction
126
6.2
The interior structure and chemical composition of the Earth
126
6.3
A model for the Earth’s thermal state
133
6.4
The start of convection in a viscous medium
138
6.5
The internal temperature of the Earth
140
6.6
Liquid magma within solid mantle rock
144
6.7
Recent developments
144
6.8
What have we learnt?
146
Glossary
5
The Dynamic Earth
147
The Dynamic Earth
Introduction to the English edition
Introduction to the English edition
Junior College Utrecht, JCU, developed the original Dutch version of this module in cooperation
with the Department of Earth Sciences from the Faculty of Geoscience, Utrecht University
(http://www.uu.nl/faculty/geosciences/en/facultystructure/departments). JCU offers an enriched
science curriculum to select groups of talented and motivated secondary school students from the
Utrecht region of the Netherlands. The module was tested on JCU students as well as on students
from its partner schools and, as a result of evaluations, it has been revised several times.
This module can be chosen as a part of the new integrated, advanced science course Nature Life
and Technology (NLT) from the Dutch upper secondary curriculum. NLT was been introduced in
2007. It aims to expose students to modern science to encourage them to consider science studies
as part of their future secondary education. This module aims to orientate students towards
geology, geophysics and geochemistry, subjects that traditionally get little attention in the Dutch
upper secondary curriculum.
This module and the module ‘the Molecules of Life’ have been translated into English for two
reasons:
-
Many Dutch upper secondary schools have bilingual programs. With these English versions,
the modules can be taught in the English part of those programs
Teachers and scientists from countries other than the Netherlands are interested in NLT.
Using these two modules as examples, they can inform themselves about the pedagogy
and methods used for these subjects.
On http://www.uu.nl/faculty/science/EN/vwo/juniorcollege), the modules are available in pdf
format on the Internet.
For many parts of the module ‘The Dynamic Earth’, the context is Dutch (e.g. assignment 2.1
“when did the Netherlands lie on the equator?”) Someone from abroad who wants to use (parts of)
this module can adapt the context so that it is suitable for to his or her own location (under the
conditions of the creative commons licence). For this, a Word version of the student material is
available. In addition, teacher materials are available, including a teacher guide, outcomes of
assignments and PowerPoint presentations. Send a request to [email protected].
I would like to thank Anne Glerum and Nienke Blom for translating the module, Kate Smith for
editing the English text, the writing team for checking the chapters they have written, Krijn Kieviet
and Saskia Klaasing for the layout of the module.
Please feel free to use this lesson material in your classes. We would be very happy to hear from
you and to learn about your experience of this module!
Dr. Ton van der Valk
Curriculum Coordinator Junior College Utrecht, Utrecht University
[email protected]
6
Introduction to the English edition
7
The Dynamic Earth
The Dynamic Earth
Introduction
Introduction
The Dynamic Earth is a course intended for the last two years of upper secondary school education
(grades 11 and 12). It is centred on the theory of plate tectonics (see Figure I, front page).
Chapter 1 will provide you with all the tools earth scientists use to study the Earth. It is essential
you read this chapter first. Chapter 2 explains the theory of plate tectonics and Chapter 3 focuses
on an important consequence of the dynamic Earth: earthquakes. The first three chapters combine
to form the basis of this course. You will have completed the course only when you have finished
these chapters and one of the optional chapters (Chapter 4, 5 or 6). The other optional chapters
can be used as additional course material or as project material during other courses.
An interdisciplinary course
So how does this course relate to your other classes? Studying the Earth is an interdisciplinary
science: all the natural sciences are required to understand processes within and at the surface of
the Earth. This course will build on theory from your Mathematics, Physics and Chemistry classes.
The table below shows where elements of each subject are studied during the course. The red
thread, plate tectonics theory, has probably already been covered in your Geography class.
However, if you did not take Geography, or geology has not yet been studied within your
Geography class, you can still follow this course. The glossary in the back of the reader will help
you with any unfamiliar terminology.
Four kinds of exercises
The reader comprises four types of exercises:
1*: An exercise with one asterisk tests the knowledge that you have acquired in other courses. The
exercises assume some familiarity with the subject.
2**: An exercise with two asterisks is directly related to the text preceding it.
3***: An exercise with three asterisks requires that you to apply the theory that has just been
explained to other, similar cases. You will have to use what you have learned in your other courses
as well as what you have just learned from this course. You should be able to apply your new
knowledge to these cases.
4****: Four asterisks denote optional exercises which are more challenging.
Every chapter ends with a final exercise. Here you will revisit the main questions of the chapter
and, in answering them, test what you have learned. Also, you will write down any new questions
that have come up while studying the chapter. The final exercises can be used in the examination
as well.
You can use atlases, the Internet and Google Earth to help you with the exercises. Where needed,
they are denoted by A (atlas), I (Internet) or G (Google Earth).
Glossary
Earth scientists use many technical terms and concepts. These are underlined in the text and
explained in the glossary.
8
Introduction
This course
The Dynamic Earth
Basic theory
Plate tectonics
Earthquakes
Volcanoes
Mountain
building
Structure of
the Earth
Math,
Geography
Physics,
Geography
Physics,
Geography
Chemistry,
Geography
Math, Geography
Physics
Previous
subject matter
Classes
Waves and
vibrations
Earthquakes
Magnetism
General
structure
Paleomagnetism
Geomagnetic
field
Plate motion
reconstruction
Radioactive
decay
Dating
techniques
Forces
Heat source
Isostasy, plate
motion
Heat and phase
changes
Driving
motion
Math and
geometry
Calculating plate
motion
Chemistry
Chemical
equilibrium
9
Average
composition
plate
Earthquakes
Heat source in
certain layers
Isostasy,
formation of
faults
Magma
generation
Liquid and
viscous layers
Calculations
faults
Melt diagrams
Phase diagrams
Types of
magma, types of
rock
on
Composition of
the different
layers
The Dynamic Earth
Chapter 1.
Basic Theory
Basic Theory
The main question of this chapter is:
How do we work with the basic tools of earth scientists: maps, rocks and
dating methods?
This question is addressed by answering the following section questions:



How do we use maps and the atlas? (1.2)
What types of rocks are recognized? (1.3)
How do we date these rocks? (1.4)
Objective: To obtain the skills necessary for this course.
10
Basic Theory
The Dynamic Earth
1.1 Introduction
This course discusses movements within the Earth. Some simple tools that earth scientists use
when studying these movements are:
Maps and atlases (1.2): To maintain an overview of the Earth, and to see where specific
processes take place, we make use of maps, atlases and the Internet. Section 1.2 explains how to
use these tools.
Rocks (1.3): Rocks contain a lot of information about the Earth. Section 1.3 discusses the three
main types of rocks.
Dating of rocks (1.4): Plate movements are slow. In the earth sciences we do not consider
timescales of 30, 100 or even a 1000 years, but timescales of millions or billions of years. How we
date rocks using such timescales is explained in section 1.4.
1.2 How to use maps and the atlas
In order for you to study the moving Earth, figures and maps are included in this textbook. We
make frequent use of the Dutch Grote Bosatlas (see e.g. http://en.wikipedia.org/wiki/Bosatlas).
For example, the notation GB 174A refers to map 174A of the 53rd edition of the Grote Bosatlas.
Google Earth is a useful tool for most exercises too. The capital letters A, I and G indicate which
tool to use for each exercise: the Atlas, the Internet, Google Earth or a combination of these.
Exercise 1-1*: Where do earthquakes and volcanic eruptions occur?
A, I
Keep track of the occurrence of earthquakes and volcanic eruptions, while working on this module.
Draw their locations in on a map. Some of the other chapters will have exercises where you can reuse this map, for example Exercise 3-3 and exercise 4-1.
a. Print out the blank map of the world and mark the places where you know earthquakes and
eruptions occur.
b. Check for new earthquakes and eruptions in newspapers and at www.earthweek.com and other
similar websites. On your map, mark the location, magnitude, number of casualties and, when
available, the actions and precautions taken to limit the damage done by these earthquakes
and eruptions. The general term for such actions and precautions is hazard management.
Exercise 1-2*: Finding the locations of earthquakes, volcanoes and mountain chains with
Google Earth
G
a.
b.
Look up the locations of the earthquakes and volcanic eruptions found in exercise 1-1 using
Google Earth.
Use GoogleEarth for any exercise when you are adding data to your map, such as exercise 3-3.
1.3 Types of rock
Much of what we know about processes within the Earth and on its surface comes from studying
rocks. There are three main types of rocks: igneous, sedimentary and metamorphic.
1.3.1
Igneous rocks
Igneous rocks are formed when liquid magma or lava solidifies. When this occurs close to or at the
Earth’s surface, the rock formed is called volcanic or extrusive. When this process takes place
much deeper within the Earth, intrusive rock is formed.
Unlike the deeper intrusive igneous rock, volcanic rock forms at the Earth’s surface when liquid
magma cools quickly. This fast cooling means there is little time for crystal growth, resulting in
fine-grained rocks with small crystals. A crystal is a homogeneous solid with smooth flat surfaces
called faces. This regular morphology is the result of the regular arrangement of the atoms making
up the crystal.
11
The Dynamic Earth
Basic Theory
An example of a rock that has cooled
quickly is basalt. It is a black rock that
has very few visible crystals. Basalt
often forms at the bottom of the ocean,
where the heat dissipates quickly in the
cold seawater. When molten material
cools slowly there is time for a greater
number of crystals to form. If there is
enough space, these crystals will be
larger too. An example of a rock that has
cooled slowly is granite, an intrusive
rock that solidifies deep beneath the
Earth’s surface. Granite cools slowly,
enabling it to form large crystals, but
often there is not enough space for
crystals to grow into perfect crystal
shapes. Several different crystals can
easily be recognized within granite:
quartz (transparent), feldspar (pink) and
biotite (black). Biotite crystallizes first,
followed by feldspar and then quartz.
Quartz grows into the space left over by
the other crystals. It does not obtain Figure 1.1: The Rock cycle, (igneous rocks), sedimentarythe crystal shape it could grow into if and metamorphic rocks.
Source: commons.wikimedia.org.
more space were available.
The characteristics of igneous rocks depend on the circumstances under which they formed. The
composition of the source material of the magma is also important. You will learn more about this
in Sections 4.1 and 4.2. Possible characteristics of igneous rocks are




A low density, like pumice, or a high density, like basalt
Large crystals, especially in intrusive rocks
Can contain metal ores
A smooth and glassy morphology, like volcanic glass; it solidified so quickly there was no
time for crystals to form.
Basalt, granite, andesite, pumice and tuff are all examples of igneous rocks.
1.3.2
Sedimentary rocks
Sedimentary rock forms after the transport and deposit (sedimentation) of loose material, the
result of weathering and erosion. This loose material, or sediment, can be transported and
deposited by wind (Aeolian sedimentation), oceans (marine sedimentation), rivers (fluvial
sedimentation) or ice (glacial sedimentation). The sediment, for example, sand, is slowly buried
under new layers of loose material. The pressure of the build-up of layers compresses the material
creating rock. In our example sandstone is formed. Horizontal layering and fossils are often present
in sedimentary rocks. Sediment deposited on the ocean floor is usually composed of calcium
carbonate particles from marine organisms and some clay; this will become limestone. Shallower
waters and rivers carry more sand; therefore this is where sandstone is formed. General
characteristics of sedimentary rocks are






Individual grains can be distinguished, such as sandstone
A coarse surface, like sandpaper
Can contain fossils
A dull, matte exterior
Can contain layering
Rocks can contain calcium carbonate that can be detected using hydrochloric acid (HCl): if
you put some drops of HCl on limestone, the rock will react and start to fizz.
Examples of sedimentary rocks are sandstone, limestone, shale and lignite.
1.3.3
Metamorphic rocks
Metamorphic rock is formed when igneous and sedimentary rocks are exposed to high pressure
and temperature conditions. As a result of this metamorphism, the rock is very compact and
12
Basic Theory
The Dynamic Earth
additional layering can form. This layering will be perpendicular to the direction of the applied
pressure. This is comparable to flattening a balloon with your hands: the balloon is elongated in the
vertical direction (parallel to your hands) and shortened in the horizontal direction. New minerals
form during metamorphism because of the high pressure and temperature. These give the rock a
shiny appearance.
Metamorphism takes place deep within the Earth’s crust where both the temperature and pressure
are high. However high temperatures alone can also cause metamorphism. Rocks exposed to high
temperatures from hot magma intruding into the Earth’s crust become metamorphic. This is
known as contact metamorphism.
General characteristics of metamorphic rocks are



Typical shimmer or shine
Characteristic layering
Separate grains cannot be distinguished any more.
Examples of metamorphic rocks are marble (formed from limestone), slate (formed from clay),
quartzite (formed from sandstone) and granite gneiss (formed from granite).
Exercise 1-3***: Classifying rocks: what goes where?
Your teacher will supply you with a set of rock samples. Number each of them and write down as
many characteristics as you can think of, e.g. colour, density, layering, smoothness or coarseness
and the presence of fossils. Separate the samples into igneous, sedimentary and metamorphic
rocks and try to name each sample. You should at least be able to recognize a basalt, a granite and
a sandstone sample.
13
The Dynamic Earth
Basic Theory
Box: Carbon
Carbon is an abundant element in the Earth. Lignite and coal are good examples of rocks
containing carbon. Both form under high pressure and temperature from organic matter, the
remains of plants. As a mineral, carbon is found in the form of diamond and graphite (and it can
have the shape of ‘Bucky ball’, C60, but this is not considered here because they are artificial, not
natural).
The crystal structures of graphite and diamond are very different (see Figure 1.2). Diamond is
formed under extreme pressure in the order of 109 Pascal (1 Giga Pascal or 1 GPa). This is four
orders of magnitude greater than normal air pressure of 105 Pa (1 bar or 1 atmosphere). Within
the three-dimensional crystal structure of diamond, each carbon atom is connected to four other
atoms. This way, diamond forms one large molecule with a continuous and stable lattice that is
equally strong in every direction and contains no weak points. Atoms are connected through strong
covalent bonds. The melting point of diamond is therefore very high, 3600oC. Diamond is insoluble
and very strong. All the electrons are used in forming bonds between atoms, which makes diamond
an excellent insulator.
In graphite, atoms form hexagonal rings. These rings are connected in the horizontal plane,
forming one large molecule. The bonds between different planes are weak; they are known as
vanderWaals bonds. The distance between layers is more than twice as big as the distance
between atoms in the same plane. When you use a pencil or put on mascara, carbon layers slide
off leaving a mark or deposit because the weak bonds between the layers have been broken.
Unlike diamond, graphite has many free electrons, which makes it a good conductor. Its density is
only two thirds that of diamond. At a pressure of 10,000 atmospheres, graphite can be compressed
into diamond.
Diamond is formed under high pressure, while graphite forms under lower pressure. This implies
that at the low pressure of the Earth’s surface graphite is stable, while diamond is not! At the
Earth’s surface diamond is described as ‘metastable’. This is comparable to super-cooled water:
When liquid water is cooled carefully, it can reach a temperature of e.g. –5oC without solidifying
and turning into ice. With super-cooled water, only a small amount of movement is needed to
initiate solidification, but for diamond, the energy needed for this phase change is much larger, the
reason why it is hard to change its metastable state.
Other minerals can also be stable or metastable. At the Earth’s surface – at a standard
temperature of 20oC and pressure of 1 atmosphere - sand and clay minerals such as illite and
kaolinite are stable, while ruby and emerald are metastable.
Figure 1.2: Carbon bonds of a) diamond and b) graphite.
14
Basic Theory
The Dynamic Earth
1.4 Dating of rock
We live in the Holocene, the youngest episode, or epoch, of Earth’s history. The Holocene is part of
the Cenozoic, the youngest era (see Figure 1.3). The Precambrian spans the period starting 4.6
billion years ago with the formation of the Earth, and ending 542 million years ago. Little is known
of this period, which is again divided into three parts (see Figure 1-3): the Hadean, the Archean
and the Proterozoic. Only a few rocks dating back to these early times have been found and little
remains of the primitive life that existed at this time.
After the Precambrian, the Phanerozoic began: the eon of life. The Phanerozoic is also divided into
three parts: the Paleozoic, the Mesozoic and the Cenozoic (see Figure 1.3). The Paleozoic started
542 million years ago and comprises the Cambrian, Ordovician, Silurian, Devonian, Carboniferous
and Permian periods. During the Carboniferous period, coal deposits formed in many countries; salt
deposits formed during the Permian period. The Mesozoic, starting 251 million years ago, consists
of the Triassic, Jurassic and Cretaceous. This was the time of ammonites and dinosaurs. Mammals
evolved during the Cenozoic, which started 65 million years ago.
The Cenozoic is made up of the Tertiary and Quaternary periods, of which the Quaternary period is
divided into the Pleistocene and the Holocene mentioned above. Alternating glacials (cold periods)
and interglacials (warm periods) characterize the Quaternary. The Holocene corresponds to the
current interglacial. Modern humans evolved approximately 200,000 years ago, during the
Pleistocene. If we compare the lifetime of the Earth to a 12-hour clock where 00:00:00.00 is the
time the Earth came into being, man’s arrival corresponds to 11:59:58.20 a.m., or 1.8 seconds
before noon (see the 12-hour clock of Figure 1.3).
Hadean
(time
2.05h)
Archean
(time
3.24
h)
Proterozoic
(time
5.06h)
Paleozoic (time 46 min)
Mesozoic (time 29 min)
Cenozoic (time 10 min)
Figure 1.3: The geological history of the earth shown in a 12 hour clock (source:
www.vob-ond.be). The Precambrian is sub divided in the Hadean, the Archean and
the Proterozoic.
How did earth scientists come to such a timescale? The age of the Earth is determined with the
help of two types of dating techniques: relative dating and absolute dating. Both are discussed
below.
1.4.1
Relative dating
Relative dating is based on the order of geological events. Relative dating uses e.g.:



15
The principle of superposition: the rock layer at the bottom of a sequence is the youngest
Fossils, the remains of plants and animals in rocks: fossils often characterize a certain
period of time
Paleomagnetic reversals: you will learn more about reversals in Chapter 2
The Dynamic Earth

Basic Theory
The astronomical timescale: this type of dating uses small changes in the orbit of the Earth
around the Sun. Mathematician Milanković calculated these changes, which can be traced
back in sequential layers of rock.
Exercise 1-4**: How much time is needed to deposit 300 meters of clay?
Small clay sediments are usually deposited at a rate of about 1 centimetre per 1000 years. The
Dutch subsurface contains a thick layer of clay – part of the Rupel Formation – that is in parts over
300 meters thick.
a. Disregarding soil settling and drainage, how long would it take for 300m of clay to be deposited?
b. If you take soil settling and drainage into consideration, would this deposition take more or less
time? Hint: both settling and drainage result in denser material.
1.4.2
Absolute dating
The real (numerical) age of a rock can be determined using absolute dating techniques. These
techniques are based on the process of radioactive decay. Certain elements have isotopes that are
unstable and start to decay after a given time. As they decay, these isotopes are converted into
isotopes of another element and emit radiation.
With the help of experiments, the time it takes for half of the original amount of isotope to decay
have been established for every radioactive isotope. This period of time is called the half-life of an
isotope. The half-life does not depend on the original amount of isotopes: a tonne of radioactive
material decays to half a tonne in the same amount of time as a milligram of the same material to
half a milligram. The half-life is not effected by temperature, pressure, chemical reactions or other
processes. Every unstable isotope has a different half-life.
If the half-life of an isotope is known and the amount of new isotope formed can be measured, the
absolute age of a rock that contains both isotopes can be determined. For dating rocks older than
50,000 years, the potassium isotope 40K is often used. Rocks containing potassium are common;
the potassium fraction is made up of 7% 41K, 0.012% 40K and 93% 39K. The former and latter are
stable, but 40K is radioactive. On average, 11% of 40K decays to 40Ar (argon) by electron capture:
an electron from the K-orbit is pulled into the nucleus. Together with a proton, it an extra neutron
is formed. The half-life of the 40K isotope decaying to 40Ar is 1.31 · 109 years. So, after 1.31 billion
years, half of the 40K isotopes have decayed to 40Ar.
To use this decay reaction for dating, you must find rocks that did not contain 40Ar when they first
formed. Otherwise the original 40Ar influences the age calculation, resulting in an incorrect age
determination. Volcanic rock is a good candidate: argon gas is completely expelled from molten
lava. It is only when lava solidifies that 40Ar forms from the decay of 40K. This 40Ar is captured in
the crystal lattices of the minerals containing potassium. As the 40Ar/40K ratio can be measured,
the age of the volcanic rock can be determined.
Exercise 1-5***: K/Ar dating
a.
b.
c.
Why is the K/Ar dating method of little use when dating Pleistocene deposits?
What are the two main controls for the reliability of K/Ar dating?
Argon is a gas and can easily escape. What will be the resulting error in your dating due to
argon escape? Explain.
Other decay reactions used in absolute dating are rubidium/strontium (87Rb to 87Sr decay, half-life
of 4.9 · 1010 years) and uranium/lead (238Ur to 206Pb and 235Ur to 207Pb decay, half-life of 4.47 · 109
years and 7.04 · 108 years respectively).
Exercise 1-6**: Discrepancy between different dating techniques
A geologist discovers the fossils of a fish that is characteristic for the Devonian period. The fossils
are found in slightly metamorphosed rock. The age determined with Ru/Sr dating is only 70 million
years. How could you explain the discrepancy between relative and absolute dating?
14
C dating is used for geologically young rock, that is, rock no older than 70,000 years. This
method is based on the ratio of the amount of 14C (a radioactive isotope of carbon) compared to
the amount of 12C in material containing carbon. Plants and animals have a constant amount of
both isotopes due to their continuous carbon exchange with the atmosphere. 14C is formed as the
result of the interaction of cosmic neutrons and 14N in the atmosphere. The ratio 12C to 14C is about
1 to 1.2 · 10-12, although this is not constant through time and the ratio must be corrected for this
16
Basic Theory
The Dynamic Earth
variation. When plants and animals die, the exchange of gases with the atmosphere ceases and the
amount of 14C decreases due to radioactive decay. The half-life of 14C is 5730 ± 40 years. Since the
atmospheric isotope ratio 12C/14C is known, the age of organic material can be determined from the
ratio of carbon isotopes present in a sample. Because the half-life of 14C is relatively short, after a
certain amount of time there is too little 14C to detect, hence the maximum determinable age of
70,000 years. Carbon dating can only be used on rocks and deposits containing organic material
(e.g. wood, charcoal, seeds, nuts, bones and shells) and peat.
1.4.3
Radioactive decay and age calculations
Radioactive dating
Scientists use radioactive carbon (14C) to date biological remains because the amount of 14C in the
atmosphere has been more or less constant throughout history. As plants incorporate 14C and 12C
through photosynthesis and animals through eating plants, the amount of 14C within living material
is in equilibrium with the atmosphere. However, when a plant or animal dies, it no longer absorbs
14
C. As 14C decays and its concentration decreases, the 12C/14C ratio within the plant or animal
changes. Therefore the quantity of 14C found in biological remains depends on the length of time
they have been buried.
Simple
14
C-dating calculations
The factor by which the amount of 14C in organic material has decreased is used to determine the
time passed since decay set in. This factor is easily established when understanding decay through
time.
The half-life is symbolized by t½. Every period of time of t½ = 5730 years results in a decay factor
½. After 5730 years the original amount of 14C should thus be multiplied with ½, in which case only
half of the amount remains. As one half-life has passed, only half of the original 14C isotopes are
left.
So
After a period of 5730
After a period of 3 x 5730
years the decay is (½)
years the decay is (1½) x (½) x (½) = (½)3
In general, after a period of n x 5730 years, decay is (½)n.
This also applies to non-integer values of n. For example, if n = ¼, after a period of ¼ x 5730
years the decay should be (½)¼ because four of those periods will give a decay of ½.
The above can be summarized in the following equation:
N(t) = N(0)*( ½)n
Here N(t) is the amount of decaying isotope left at time t, while N(0) is the original amount of that
isotope. The fraction ½ indicates halving the original amount n times, and n corresponds to the n
from the previous example, the number of half-lives. If n = 3, three times 5730 years have
passed.
What percentage of the original amount of radioactive isotope remains after n = 3? Take N(0) = 1
and n = 3, this will give N(t) = 1*(½)3. Thus N(t) = 0.125, or 12.5%.
Example
In a peat sample, only 10% of the original amount of
14
C is left. How old is the sample?
Suppose the sample is n half-lives old. As 100% = 1, 10% = 0.1. N(0) is therefore 1 and can be
left out of the equation. What remains is:
(1 / 2) n  0.1
You can find n by taking the logarithm of both sides and then using logarithmic identities.
n  log(1 / 2)  log(0.1)
The age of the organic material is then n times the half-life of 5730 years, in this case 19,000
years.
17
The Dynamic Earth
Basic Theory
General equation for radioactive decay (here we will use exponential functions)
N(0) is the original amount of radioactive isotope; N(t) is the amount of isotope after time t; t½ is
the half-life of the isotope; and n is the number of passed half-lives, n =
t
t1 2
. If, for example,
three times 5730 years have passed and the half-life is 5730 years, then for this t = 17,190 years
and t½ = 5730 years, n = 3.
This gives:
 t 


1 2 
N (t )  N (0)  1 / 2  t
You know ½ = e-ln2; you can check this on your calculator. This allows you to express the formula
above as an exponential function. Usually not the half-life, but the decay constant λ is used in such
a formulation:

ln 2
t1/ 2
Therefore, the general equation for radioactive decay is written as:
N (t )  N (0)  e  t
Exercise 1-7***: Calculations on radioactive decay
a. Derive the last equation yourself. Differentiate it to obtain an equation for the rate of change of
amount of isotope, N’(t).
b. Show N’(t)/N(t) = -λ by using substitution.
c. Describe the meaning of λ: λ is the ratio between…. Hint: Look at the equation in b and the
meaning of the derivative of N(t).
In addition, you can now do the optional exercise 1-1 you can find at the end of this chapter.
1.4.4
The dating of rock and the geological timescale
All absolute and relative dating techniques have the same limitation: the older the tested material,
the less accurate the results. Therefore as many different techniques as possible are applied to the
same rock. Unfortunately only certain types of rocks are appropriate for a certain techniques:
fossils are only found in sedimentary rock, 40K dating can only be done on igneous rock and 14C
dating only on organic material.
Absolute and relative dating enables scientists to establish extensive and detailed geological
timescales. The most commonly used timescale is from the International Commission on
Stratigraphy (see www.stratigraphy.org). Simple representations of this timescale can be found in
Figure 1.4 and in the atlas, map GB 192E.
18
Basic Theory
The Dynamic Earth
Figure 1.4: Geological timescale. The top of the first column corresponds to the entire second column
and
the
top
of
the
second
column
corresponds
to
the
third
column.
Source:
http://www.geo.ucalgary.ca/~macrae/timescale/timescale.
Exercise 1-8*: Mass extinctions and the geological timescale
Several times during the geological past, many (sometimes over 70%) of the species present
became extinct within a short period of time. These events are called mass extinctions. The four
most important mass extinctions occurred 444 million years ago, 416 million years ago, 251 million
years ago and 65 million years ago.
a. In what periods of the timescale of Figure 1-4 did these events occur?
b. What is it about the timescale that makes these extinctions so obvious?
Final exercise Ch1. Answer the section questions and the main question
a.
b.
Answer the three section questions as well as the main question from the beginning of this
chapter.
If you find you have new questions after reading this chapter, write them down.
Optional exercise 1-9****: Determining the age of ice
(Based on a question in the Dutch final exam Physics, havo 1998-I. Question a, b and c lie outside
the scope of this course, but are essential to the question as a whole.)
“Greenland. A group of scientists are investigating the ice at the North Pole. They drill a hole in
the ice over 3 km deep, retrieving ice cores of 2.5 m in length and 84 cm2 in cross section. By
investigating the ice cores, knowledge of the past - for example of the average temperature on
Earth during the formation of the ice - is gained. Past temperatures are known from the
concentration of two particular oxygen isotopes.
The age of the ice can be obtained by dating ash layers within the ice with C-14 dating. The
concentration of C-14 in the ashes is compared to the normal concentration of C-14 in the
atmosphere.”
19
The Dynamic Earth
Basic Theory
After: Mens en Wetenschap, July 1994
The temperature of an ice core is -4°C.
a. Calculate the mass of the ice core. Hint: You can look up the density of ice, and calculate the
volume of the core.
Oxygen isotopes are mentioned in the article.
b. Name one difference and one similarity on a molecular level between the two different oxygen
isotopes.
C-14 dating is based on the decay of the radioactive isotope 14C.
c. Write down the decay reaction of 14C.
With time, the concentration of 14C in the ashes found in the ice cores decreases due to radioactive
decay. Measurements show that the present concentration of 14C in the ashes is 25% of the normal
concentration in the atmosphere.
d. Calculate the age of the ashes.
20
Plate Tectonics
Chapter 2.
The Dynamic Earth
Plate Tectonics
The main question of this chapter is:
Which theory lies behind the concept of plate tectonics, what drives plate
tectonics and to what extent do we notice plate motion in daily life?
This question is addressed by answering the following section questions:







Which observations advanced the theory of plate tectonics? (2.1)
Which three steps led to the theory of plate tectonics? (2.2)
What does the interior structure of the Earth look like? (2.3)
What causes plates to move? (2.4)
What types of motion occur along plate boundaries? (2.5)
Are movements only noted along plate boundaries? (2.6)
How do we describe plate motion? (2.7)
Objective: To describe the current distribution and motion of plates by making use of the
theoretical knowledge you gained from Mathematics and Physics classes.
21
The Dynamic Earth
Plate Tectonics
2.1 The observations that led to plate tectonics theory
Consider capturing the Earth on film from a satellite: in a day several things would clearly change.
For example: different places would experience day or night, cloud coverage or perhaps tornados.
But the spacing of the continents would not appear to change. However, if you were to continue
recording the Earth for, say, a century, you would see even the continents move about. Continents
do not move fast, they move at about the same speed as your fingernails grow.
Exercise 2-1*: When did The Netherlands lie at the equator?
Your fingernails grow at about 2 to 3 mm per month, knowing this
a. How long would it take for a part of a continent to move from the equator to the current
position of The Netherlands?
From Section 1.3.3 ‘Metamorphic rocks’, you know that extensive coal deposits occur in The
Netherlands. Since coal forms from tropical swamp vegetation, the deposits imply that The
Netherlands used to lie at the equator.
b. Assuming plates move with a speed of 2 to 3 mm per month, how old are the Dutch coal
deposits and during which geological period did they form?
c. Research shows that coal in The Netherlands formed during the Carboniferous period (named
after the coal, which is typical for sediments of this period). Is this dating consistent with
question b? If not, how do you explain the discrepancy?
How long have we known that parts of the Earth’s crust move? Before plate tectonics theory,
scientists assumed only vertical crustal movements could take place. Their assumptions were
based on the observation that the surface of the Earth is divided into oceans and continents. Both
are relatively flat, but they are significantly offset in elevation. The bottom of the ocean is about 3
km deep, while the continents are 1 to 2 km high. Weathering and erosion should have evened out
this difference in elevation by now. As the difference still exists, scientists thought that vertical
movements must have preserved it. They expected the lighter continental rock to rise higher and
higher with time, while the heavier oceanic rocks were supposed to sink.
However, some scientists suggested that horizontal movements occurred in addition to vertical
motion. Explorers in the 15th and 16th century, trying to map the Earth, noticed something peculiar
about the coastline of the Atlantic Ocean: the east coast of North and South America looked like a
reverse cut-out of the west coast of Africa and Europe. They surmised that America and Africa were
connected in the past. From 1900, more and more observations were made that supported this
connection:



The same fossil species occurred on both continents (Figure 2.1) These organisms could
not have crossed today’s vast oceans, so the continents must have been connected some
time in the past.
There were traces of large ice sheets covering several continents. Such vast glaciations
could only have occurred if all the ice-covered parts were situated at the pole at the same
time.
The same rock assemblages were found on both sides of the Atlantic. Most likely, they
formed in one place before the continents split up.
It was Alfred Wegener, a German meteorologist, who greatly improved our understanding of
plate motion. He wrote the book The Origin of the Continents and Oceans (1925), which
formed the basis of the modern view on plate motion. He suggested that all continents were
connected in the past, forming the supercontinent Pangaea, but then drifted apart during the
Tertiary period. Wegener called his idea the continental drift hypothesis.
22
Plate Tectonics
The Dynamic Earth
Figure 2.1: Because the same fossil species occurs on different
continents, it is evident that the continents were juxtaposed at some
time in the past. (Source: http://www.daaromevolutie.net/images)
Exercise 2-2**: Wegener’s arguments for continental drift.
A
The fact that the continents fit together almost perfectly, and other observations such as the
distribution of fossils and the large 250-million-year-old ice sheets, fuelled Wegener’s ideas about
plate motion.
a. Use the atlas to name the geological period during which the large ice sheets formed.
b. Figure 2.2 shows where Wegener found traces of ice covering the continents in the past. What
two conclusions can you draw based on Figure 2.2 about the previous connection between the
ice-covered continents and their location?
Figure 2.2: Distribution of traces of
glacial cover in 250-million-year-old
sediments. (Veenvliet, 1986)
Wegener’s hypothesis left several issues unexplained:


Which part of the crust actually moves? The continents themselves, the oceans or
something deeper?
What mechanism is strong enough to cause crustal movements?
It wasn’t until 1960 that science made it possible to resolve these issues.
Exercise 2-3**: Questioning Wegener’s continental drift hypothesis
a. Think of a mechanism that could explain continents drifting apart.
b. Write down some questions you would ask Wegener to decide whether or not you agree with
his theory.
23
The Dynamic Earth
Plate Tectonics
In Geography classes nowadays, you can learn that the continental and oceanic plates on the
Earth’s surface move with respect to each other and that the interior of the Earth moves as well.
These ideas form the paradigm of plate tectonics, which has been the leading paradigm in the
earth sciences since the late 1960s. A paradigm is a coherent set of models and theories providing
a certain mindset with which to analyse reality.
However, not everything about plate tectonics is known yet. Much uncertainty still exists about the
processes active within the interior of the Earth that drive plate tectonics.
The steps needed to get from Wegener’s continental drift hypothesis to the paradigm of plate
tectonics are explained in the next section.
Plate tectonics considers the movement of plates. Plates are composed of continental and/or
oceanic crust and the upper part of the mantle. You will learn more about the structure of plates in
Section 2.3.
2.2 Three steps to plate tectonics.
2.2.1
Determining the oceans’ bathymetry: Where does new material form?
The first studies that provided insight into what causes the Earth to move came from a record of
the bathymetry (relief) of the ocean floors. Mid-twentieth century equipment allowed for even the
deepest parts of the oceans to be mapped. These measurements showed that in the middle of
oceans there were shallower areas. These areas formed ridges over the whole length of the oceans
(see Figure 2.3). Further research demonstrated these Mid-Ocean Ridges (MORs) were made of
active underwater volcanoes. Researchers concluded that it is at MORs where new material rises up
from the depths.
Figure 2.3: Topography and bathymetry of the Earth.
24
Plate Tectonics
The Dynamic Earth
Exercise 2-4*: Topography of the ocean floors
A
Recife in Brazil and Mount Cameroon in Africa lie more or less on the same latitude at both sides of
the Atlantic Ocean.
a. Draw a depth profile starting from Recife to Mount Cameroon. Ascension’s highest volcano
reaches up to 859 m. Use the atlas.
b. What is the difference in elevation between the highest and lowest point of this profile?
2.2.2
Paleomagnetism: How do we prove plates move?
Scientists wondered if the formation of new material at MORs could have anything to do with the
plates drifting apart. If so, the crust on both sides of a MOR should increase in age the further it
gets from the ridge. Paleomagnetism, i.e. the rock record of the past magnetic fields of the Earth
(paleo is the Greek word for past), enables the dating of the crust.
2.2.3
The Earth’s magnetic field
“A wonder of such nature I experienced as a child of 4 or 5 years, when my father showed me a
compass. That this needle behaved in such a determined way did not at all fit into the nature of
events which could find a place in the unconscious world of concepts. I can still remember - or at
least believe I can remember - that this experience made a deep and lasting impression upon me.
Something deeply hidden had to be behind things ...”
Albert Einstein
The outer core of our planet
consists of liquid iron and nickel
(see Chapter 6), and acts as a
large magnet with north and
south magnetic poles. The Earth’s
magnetic field resembles that of a
bar magnet positioned within the
Earth (see Figure 2.4: The Earth
as a large bar magnet. (Source:
http://stargazers.gsfc.nasa.gov)).
Physics class taught you how to
work with magnetism. You will
now use that knowledge to
measure the magnetic field in the
place where you live (Exercise 25). To practise working with
magnetism,
you
can
also
Figure 2.4: The Earth as a large bar magnet. (Source:
complete Optional Exercise 2-1
http://stargazers.gsfc.nasa.gov)
(at the end of Chapter 2).
25
The Dynamic Earth
Plate Tectonics
Exercise 2-5**: Determining a magnetic field (including a practical)
You will need: coiled wire, a magnetic needle and a variable power source.
In this practical we will determine the magnitude and direction of the Earth's magnetic field
strength in your hometown. This is called the magnetic induction B, being a vector i.e. having a
magnitude and a direction.
1) Take a coil with loops that weave through a sheet of plastic and position it horizontally. The coil
needs to be about 25 cm long with 40 loops.
2) Place a magnetic needle within the coil. Make sure the magnet can spin freely in the horizontal
plane.
3) Align the middle line of the coil with the magnetic needle (see Figure 2.5) Connect the coil to
the power source in series with a variable resistor and an electric current meter. Varying the
strength of the current will show that at an electrical current strength of 90 mA the needle does not
maintain a fixed position, but will spin freely.
a. Calculate the magnetic induction B generated by the coil. Use
Bcoil   0 
NI
L
with B the
magnetic induction, μ0 the permeability of free space of 4π · 10-7, N the number of loops on the
coil, I the current strength and L the length of the coil.
b. Why does the needle not maintain a fixed position at 90 mA?
c. Copy Figure 2.6 and mark the direction of the current in the coil. The dark part of the compass
needle in Figure 2.6 denotes the north magnetic pole.
Take a magnetic needle that can spin freely in the vertical plane (Figure 2.7).
d. Measure the angle between the needle and the horizontal plane.
e. Use this angle to calculate the direction and magnitude of the magnetic induction of the Earth's
magnetic field (Btot). Hint: Use the cosine of the angle found and study Figure 2.7.
Figure 2.6
Heart line
Figure 2.7
Figure 2.5
26
Plate Tectonics
The Dynamic Earth
The magnetic poles of the Earth’s magnetic field lie close to the geographic poles. The geographic
poles, at 90° north and south of the equator, are the two locations where the Earth’s rotation axis
meets the surface. The location of the magnetic poles varies slightly on a yearly basis (figure 2.8),
but these variations are not big enough to influence, for example, the calculations you did to
discover the magnetic field for your hometown.
Figure 2.8: The movement of the magnetic north pole.
(Source: http://www.digischool.nl/ak/)
Besides small yearly variations, the magnetic poles also experience variation on a larger scale:
every ten to one hundred thousand years the poles reverse. During such a reversal the north
geographical pole changes from south magnetic pole to north magnetic pole or vice versa (Figure
2.9). Scientists do not know why magnetic reversal occurs; most likely it is related to processes
within the Earth’s core and mantle. Because we do not know why reversals occur, it is not possible
to predict the next reversal.
Figure 2.9: Reversals of the Earth’s magnetic field. In the present
situation (normal), the north geographic pole coincides with the south
magnetic pole.
Rocks contain a record of magnetic reversals: the magnetic minerals locked inside them are
aligned with the direction of the ambient geomagnetic field at the time the rock solidified or was
deposited. This is called paleomagnetism. Earth scientists can read these directions and are able to
determine whether the rocks were formed during a period of normal (as it is now) or reversed
(opposite to now) polarity.
Geomagnetic reversals, which occur either side of periods of normal or reversed polarity, can be
dated using techniques such as radioactive dating or by referring to fossils. With the age of
reversals known, a paleomagnetic timescale can be computed (see Figure 2.10).
27
The Dynamic Earth
Plate Tectonics
Figure 2.10: Paleomagnetic reversals
during
the
geological
past.
Black
represents a period of normal polarity,
white a period of reversed polarity.
(Source: kennislink)
28
Plate Tectonics
The Dynamic Earth
In 1950, ships were fitted with equipment especially designed for taking paleomagnetic
measurements of the ocean floor. Measurements taken with this equipment showed which areas of
oceanic plates had normal and which had reversed polarity; the recorded reversals showed a
symmetrical pattern perpendicular to the MORs (see Figure 2.11).
To summarize: first, active volcanoes were found at MORs. Secondly, a symmetric pattern was
discovered
in
the
paleomagnetic signal of the
ocean floor. By combining
these
observations,
scientists
reached
the
conclusion that new ocean
floor is formed at a MOR (the
ridge axis in Figure 2.11.
New ocean floor consists of
basaltic magma that rises up
through the volcanoes (more
information
on
basaltic
magma can be found in
Chapter 4). The moment
basaltic lava solidifies; it
records the magnetic polarity
of that particular time.
Reversal of polarities creates
a
symmetrical
pattern
around the MOR. New ocean
floor is added on both sides
of the MOR, while older parts
Figure 2.11: The black and white magnetic pattern surrounding the migrate away from the ridge.
Mid Atlantic Ridge, a Mid-Ocean Ridge (MOR), is symmetrical around This process is called seathe ridge. (Source: http://www.cliffshade.com)
floor spreading (see Figure
2.12)
Figure 2.12: The formation of new oceanic crust,
and sea-floor spreading; the sideways migration
of newly formed and older crust.
29
The Dynamic Earth
Plate Tectonics
Figure 2.13 is the result of paleomagnetic dating of the ocean floor.
B
B
AA
The age of the Ocean crust
Figure 2.13: The age of the oceanic crust. (from: Berendsen, Fysisch geografisch onderzoek)
2.2.4
Deep trenches: where oceanic crust disappears beneath continental crust
We now know that new crust is constantly being formed (step a) and that the Earth’s plates move
(step b). Does this mean that the total amount of crust keeps increasing? This would contradict the
law of conservation of mass. Obviously, somewhere crust is being destroyed.
Ocean bathymetry does not only show ridges in the middle of the oceans, but also very deep
trenches along some of the continents. These deep trenches are called subduction zones (Figure
2.14). They are areas where oceanic crust disappears into the Earth. Because of subduction, the
amount of crust remains constant and hardly any oceanic crust older than 200 million years has
been found (see Figure 2.13).
Combining steps a (bathymetry), b (paleomagnetism) and c (subduction zones or trenches), it can
be concluded that



New crust is formed at MORs (step a and Ib)
Plates move away from each other at MORs (step b)
Crust disappears in subduction zones (step c)
These processes are summarized in Figure 2.14.
The paradigm, or theory, of plate tectonics combines the continental drift hypothesis and sea-floor
spreading, the mechanism of formation and destruction of oceanic crust.
30
Plate Tectonics
II
The Dynamic Earth
III
I
II
I
Figure 2.14: A cross section of the Earth. You can see Mid-Ocean Ridges (I) where crust is being
formed, moving plates, and subduction zones (II) where crust disappears. Plate boundaries are
divergent (I), convergent (II) and transform (III) (see Section 2-5). (Source: www.usgs.com)
Exercise 2-6**: Plate movements
A
Study Figure 2.13, and use the atlas.
The part of oceanic crust formed, say, during the Early Tertiary is larger in the Pacific Ocean than
in the Atlantic Ocean.
a. Find a possible cause for this.
b. Where can you find the thickest sequence of oceanic sediments, at A or B of Figure 2.13?
Explain.
c. Explain why the oceanic crust is no older than the Jurassic period.
d. Knowing America and Africa started drifting apart during the Jurassic, calculate the average
plate motion velocity per year. Work out the velocity for each plate with respect to the ridge as
well as the velocity of the plates with respect to each other.
2.3 Structure of the Earth
So how do plates move? Do they float like rigid plates over a liquid interior? This used to be the
generally accepted view because liquid lava from the interior of the Earth was seen to extrude
during volcanic eruptions. However, the molten mass (called magma as long as it remains within
the Earth and lava upon reaching the surface) exists only at a few places within the Earth. For you
to understand plate movements, you need to understand the structure of the Earth first. It is
discussed in this section, and more thoroughly in Chapter 6. Chapter 6 also explains how we
deduced the structure of the Earth.
Research shows that the Earth is not a homogeneous sphere, but consists of several shells of
different material and characteristics. From centre to surface, the Earth is divided into an inner and
an outer core, a thick mantle consisting of a lower and upper mantle, and a relatively thin outer
layer, the crust (see Figure 2.15). Early plate tectonics theory stated that the solid crust moved
over the liquid mantle. However, it is the crust together with the upper cold part of the mantle that
forms the moving plate - the lithosphere. The lithosphere is about 80 to 100 km thick. Lithospheric
plates move on top of the asthenosphere, the viscous, but certainly not liquid, part of the mantle
that extends to a depth of 300 km.
31
The Dynamic Earth
Plate Tectonics
Nine large and about twenty
smaller tectonic plates make up
the lithosphere (Figure 2.15).
Some of the lithosphere forms
the ocean floor and is therefore
called oceanic plate. Other
lithosphere
forms
the
continents
and
is
called
continental
plate.
The
movement
of
Earth’s
lithospheric plates over the
asthenosphere is called plate
tectonics.
Figure 2.15: A cross section of the Earth.
(Source: mediatheek.thinkquest.nl/~ll125/nl/struct_nl.htm)
The composition and thickness
of oceanic and continental
plates are strikingly different.
The crust of oceanic plates is
made up of basalt, while
continental crust is mainly
composed
of
granite
and
sediments. More information on
the formation of basalt and
granite can be found in Chapter
4.
Figure 2.16: Configuration of the tectonic plates. By zooming in on, for example, the Mediterranean
Sea or Indonesia, even smaller plates can be seen. (Figure 4.3 of Marshak, Earth; Portrait of a
Planet, 2nd edition, W.W. Norton & Co, 2005)
32
Plate Tectonics
The Dynamic Earth
2.4 The engine driving plate motion
What processes initiate plate motion? Deep within the Earth
temperatures are much higher than at the surface. This
temperature difference causes the viscous material of the
mantle to flow very slowly. This type of flow is called
convective flow. Figure 2.17 shows an example of convection.
Mantle convection can be compared to water in a pot flowing
because it is heated from below. However, in the mantle,
viscous solid material flows instead of water, therefore mantle
convection is a much slower process.
Convective flow plays an important role in the formation of
new crust at a MOR, in moving tectonic plates, and during
subduction, as summarized in Figure 2.17. Convection and the
related processes at the surface of the Earth are investigated
further in Chapter 6.
Figure 2.17: Convective flow in a
pot
of
water.
The
flame
represents the heat coming from
the interior of the Earth, while the
water represents the viscous
mantle.
Figure 2.18: Schematic drawing of a cross section of the Earth
illustrating convective flow patterns. Convective flow can be related
to processes at the Earth’s surface. (Source: http://pubs.usgs.gov/)
2.5 Types of motion at plate boundaries
We know that plates move and what drives this plate motion, but what do we notice of plate
tectonics ourselves? The centre of a tectonic plate is relatively stable. Along plate boundaries, the
movement of a plate is obvious. Three types of movements are seen: plates moving apart from
each other, plates moving towards each other and plates sliding sideways past each other (see
Figure 2.14).
2.5.1
Divergent plate motion: two plates moving apart from each other
Examples of divergent plate motion can be found in the middle of several oceans, at the oceanic
spreading ridges (MORs). When two plates move apart at these undersea mountain ridges, the
newly formed empty space is filled with mantle magma rising from below. The magma cools at the
ridge and new lithosphere is created. The MOR in the Atlantic Ocean is an example; this is where
33
The Dynamic Earth
Plate Tectonics
Africa and America move apart. Iceland is situated on top of a MOR (and on top of a hotspot, see
Chapter 4); here, you can stand on the North American Plate with one foot, and on the Eurasian
Plate with the other. Volcanoes and small earthquakes (due to the motion of MOR segments) can
occur along divergent plate boundaries.
2.5.2
Convergent plate motion: two plates moving towards each other
Since new lithosphere is created at MORs and the overall amount of crust does not change, old
lithosphere must disappear as well: this happens when two plates move towards each other. This is
known as convergent motion. Based on the kind of the plates involved, three types of convergent
motion are recognized:
1. When a continental and an oceanic plate meet, the heavier oceanic plate, made up of mostly
basalt, will dive below the relatively light continental plate in a process called subduction. For
example, to the west of South America, the oceanic Nazca Plate subducts beneath the South
American Plate.
2. When two continental plates approach each other, a mountain chain (e.g. The Himalayas) is
formed.
3. When two oceanic plates move towards each other, the oldest, and therefore the coldest and
heaviest, will subduct. For example, this happens in the ocean near Japan.
On or near convergent plate boundaries, earthquakes, mountain chains and volcanoes can occur.
2.5.3
Transform plate motion: two plates sliding past each other
The San Andreas Fault in the state of California is a famous example of a transform fault on land.
However, most transform faults are located under water, linking spreading ridge segments (the
stepped geometry of MORs is used in Exercises 2-18 and 2-19). When two plates move past each
other, earthquakes often take place.
It is not hard to recognize plate boundaries from topography and bathymetry when you are familiar
with their morphology: Spreading ridges form long mountain chains on the ocean floor. Subduction
zones are characterized by a deep-ocean trench and a mountain chain on the upper continental
plate. The stepping of MORs indicates the presence of transform faults (see Figure 2.27).
Exercise 2-7**: Types of plate boundaries
A, G
Answer questions a-d for each of the following places: Jan Mayen; Valparaiso; Jakarta; Anchorage;
and the Galapagos Islands.
a. Which type of plate boundary do you expect to find here?
b. Upon what data from the atlas are your expectations based?
c. What geological phenomena, related to the type of plate boundary, do you expect to occur
here?
d. Use Google Earth to check if the phenomena you listed at c actually occur.
2.6 Intraplate motion
Plate tectonics theory states that tectonic plates move over the asthenosphere as rigid pieces, with
deformational processes such as earthquakes, volcanoes and mountain building concentrated on
the plate boundaries. However, when looking at the distribution of earthquakes on Earth (see atlas)
you can see that some earthquakes occur far from any plate boundary, in the interior of the mostly
continental plates. Examples of intraplate deformation areas are the earthquake area in Limburg,
The Netherlands (see exercise 3-1), and a large area in East Africa. Nowadays we can map the
behaviour of intraplate deformation zones precisely through satellite positioning (see Figure 2.19).
The new observations of intraplate deformation do not mean plate tectonics theory is no longer
valid; rather plate tectonics describes a large part of the behaviour of the outer layer of the Earth,
with the zones of intraplate deformation acting as exceptions to the rule.
34
Plate Tectonics
The Dynamic Earth
Figure 2.19: Intraplate deformation zones mapped with the help of satellites. The colours indicate
the
amount
of
stress:
blue
indicates
low
stress,
red
high
stress.
(Source:
http://gsrm.unavco.org/model/images/1.2/global_sec_invariant_wh.gif)
Exercise 2-8**: Deformation zones
A
Figure 2.19 shows a large zone of intraplate deformation in Africa.
a. Which African countries does this zone cover? Use the atlas.
Figure 2.19 also shows that the African zone of deformation changes into a plate boundary towards
the north.
b. Which type of plate boundary does the deformation zone change into and what kinds of
processes take place here?
c. What is a possible scenario for the geological future of East and West Africa? Explain.
d. Would such a scenario apply to The Netherlands and Germany as well? Use Figure 2.19 and GB
76.
2.7 Describing plate motions
Since the acceptance of the theory of plate
tectonics, scientists have often used it to
calculate, for example, in what direction and with
what velocity plates move with respect to each
other or for how long certain plates (e.g. Africa
and America) have been drifting apart. Besides
describing motions of the past, future plate
motions are calculated as well. Knowing plate
velocities allows scientists to better understand
the consequences of plate motion, such as
earthquakes.
D’
A
A’
This section explores the movement of the African
Plate with respect to the American Plate.
In Exercise 2-6d you calculated the average
B
velocity with which Africa and America diverge,
about 1.08 cm per year, assuming the plates
B’
move on a flat plane. However, to be able to
calculate the exact movement of Africa with Figure 2.20: a displaced square
respect to America, we must consider motion on a
35
D
C’
C
The Dynamic Earth
Plate Tectonics
sphere. Every displacement on a sphere can be seen as a rotation around an axis through the
centre of that sphere. This will be shown in the next section as well as how to find this axis of
rotation.
2.7.1
Rotation poles
Plate motion can be described using rotation poles. Below, you will study the geometric concept of
rotation poles. We will start off with a simple example of a square moving over a flat surface.
Exercise 2-9*: A rotated square
Figure 2.20 shows a square moved from position ABCD to position A’B’C’D’.
a. Cut out a square of the same size and place it on top of position ABCD.
b. Putting the tip of your compass or pencil on the square allows you to rotate it easily. Try it.
c. Rotating the square to position A’B’C’D’ requires putting the compass tip at exactly the right
spot. Try to find that spot and mark it P with a sharp pencil on the loose square as well as on
this page. By experimenting, you have shown that pivot point P exists. P is the rotation pole of
the square.
The next steps will help you find the rotation pole of a motion quickly and accurately.
Exercise 2-10**: How to find rotation pole P of a displaced square
Use Figure 2.20
a. If P is the rotation pole, why should the distance between P and A equal the distance between
P and A’?
b. Draw the perpendicular bisector of line segment AA’ on Figure 2.20. Why should the bisector go
through P? Hint: a perpendicular bisector cuts a line into two segments of equal length, at an
angle of 90˚ to the line.
c. Also draw in the perpendicular bisector of line segment BB’.
d. Now you should be able to determine the position of P exactly. Indicate its location on Figure 220.
e. Show that the perpendicular bisectors of lines CC’ and DD’ also go through P. Explain.
To summarize: moving the square from ABCD to A’B’C’D’ equals rotating the square about rotation
pole P.
f. What does this say about angles  APA',  BPB',  CPC' and  DPD'?
F
e
D
d
E
Figure 2.21:
Exercise 2-11**: Instantaneous rotation
Figure 2.21 shows a moving triangle. The direction and speed of points D and E of the triangle are
given by vectors d and e, respectively. Think of this motion as a displacement of the triangle to
D’E’F’, with the distance travelled to D’E’F’ invisibly small. This way the perpendicular bisector of
DD’ coincides with the line starting from point D, perpendicular to vector d. Also, the perpendicular
bisector of line EE’ coincides with the line perpendicular to e in point E.
a. Take the same steps as in Exercise 2-10 to determine the rotation pole Q. You will find Q at the
crossing point of two lines perpendicular to the vectors d and e.
b. Now you can construct the direction of vector f of point F because the line QF, is perpendicular
bisector of FF’, going through Q, is orthogonal to vector f. Draw in the direction in which point F
moves.
c. The lengths of the vectors d and e should have the same ratio as the lines DQ and EQ. Why?
d. Are the ratios d:e and DQ:EQ equal? Calculate the length of vector f, in relation to the length
of d or e, and draw in f with its correct length.
36
Plate Tectonics
The Dynamic Earth
Exercise 2-11 shows that a starting movement of which you only know the velocity can also be
seen as a rotation. When the triangle eventually starts moving, a rotation pole exists at each
moment in time. The pole will not remain in the same location however, except when the
movement is an ongoing rotation around that point. In general, the rotation pole only exists in a
certain location for an instant of time. Thus, we speak of an instantaneous rotation and an
instantaneous rotation pole. These notions are useful when describing plate motions on the Earth.
First, repeat the steps you took in exercise 2-11 and exercise 2-11 to determine a rotation pole
and any unknown vector.
Step 1: Vectors
Find the vectors that represent the movement of several points of the rotating object. The vectors
can either show the displacement of a point to get to its present position (exercise 2-11) or they
show the velocity (direction and magnitude) with which a point is moving (exercise 2-11 and
exercise 2-14a).
Step 2:
In the displacement-case, determine the perpendicular bisectors of the displacement; these are
lines perpendicular to the displacement vectors. In the velocity-case, draw lines perpendicular to
the velocity vectors, starting at the tail of the vectors.
Step 3: Rotation pole or pivot point
The point of intersection of the different perpendicular lines is the rotation pole.
Step 4: Unknown vector (optional)
In a case where the rotation pole is known and the travelled distance can be neglected, you can
construct any unknown vector (exercise 2-11b-d). The wanted vector is perpendicular to the line
running from the rotation pole to the point the vector acts on.
Exercise 2-12**: Can you always find a rotation pole?
a. Think of a composition of two equally sized squares ABCD and A’B’C’D’ (not in the same
position) that does not have a rotation pole.
b. Draw a triangle DEF with vectors d and e acting on points D and E that does not have a
instantaneous rotation pole.
Exercise 2-12 shows that movements on a plane sometimes do not have a rotation pole. In this
case, the perpendicular bisectors of AA’ and BB’ or the perpendiculars of the vectors are parallel
and do not cross each other; the movement is a parallel displacement.
2.7.2
Motion on a sphere
In the examples above we used geometric figures: squares and triangles. However, we did not use
any characteristics of squares and triangles to determine the rotation pole; using perpendicular
bisectors or perpendiculars to vectors of velocity works on any figure. Therefore, this method can
also be applied to moving lithospheric plates. Plates move on a spherical surface though, so will
they always have a rotation pole?
37
The Dynamic Earth
Plate Tectonics
Exercise 2-13***: Motion on a sphere
In Figure 2.22 a rigid body moves on a sphere. Point A moves to point A’, point B to B’.
a. Describe and sketch how to find the rotation pole of the body.
Finding the rotation pole is difficult
as you cannot use perpendicular
bisectors on a spherical surface.
Instead, use the intersection of the
plane perpendicularly bisecting AA’
with the sphere’s surface. This
intersection is a line along the
surface of the sphere; it is curved
like the lines in Figure 2.22.
b. Explain why the rotation pole
lies on the line of intersection.
A
D
A’
2.7.3
Great circles
The special perpendicular bisectors
used for motions on a sphere can
also be called cross sections. They
always cut through the centre of
the sphere because the distances
from the centre to the two points
on the surface are equal. The line
of intersection is a great circle. We
will discuss great circles later on.
Exercise 2-14***: Instantaneous displacements on a sphere
always have a rotation pole
E
B
B’
Figure 2.22
Comparable to the example with the triangle (exercise 2-11) in which you used lines perpendicular
to a velocity vector, on a sphere you can use great circles perpendicular to the direction of rotation.
There is one convenient difference with motion on a flat surface however: you can always find the
rotation pole!
a. Why can you always find a rotation pole for motion on a sphere, unlike for displacements on a
plane?
b. Sketch how to find the rotation pole of the plate segment containing points D and E Figure 2.22
Exercise 2-15***: Other particulars of rotation poles on a sphere
In fact, there are always two rotation poles; better: two intersections of a pair of great circles. The
second intersection can be found exactly opposite the first one. You can draw a line from one to
the other through the sphere’s centre. This line is the axis of rotation.
a. Mark the two rotation poles of the plate segment with points D and E in Figure 2.22. Hint: the
poles lie on a constructed great circle, directly across from one another.
b. Imagine the plate segment lies on a transparent spherical shell covering the sphere. The whole
shell then rotates about the instantaneous rotation axis. Draw in on the shell the great circle
that lies exactly in between the two rotation poles; this is the equator of the spherical shell.
38
Plate Tectonics
The Dynamic Earth
Exercise 2-16***: Angular velocity and
linear velocities
An instantaneous rotation has an angular
velocity (see Figure 2.23), which, when
describing plate tectonics, is measured in
degrees per million years. The angular velocity
is denoted by ω.
a. Imagine a point R on the equator of a
rotation moving with an angular velocity ω
of 10 degrees per million years. How many
centimetres per year does that point move?
b. Points lying off the imaginary equator have
a lower actual velocity (e.g. in cm/year)
than point R. Why?
c. A point bisecting the great circle segment
between the rotation pole and the imaginary
equator has an actual velocity of only
1
2 2
d.
of the velocity at the equator. Explain.
Figure 2.23
What point has an actual velocity half that of a point on the equator?
2.7.4
Resultant motion
So far we have only considered a body rotating with respect to a sphere. Plate tectonics, however,
considers the movements of plates along, over and under each other: these are the relative
motions of plates. Take for example plate A and plate B of which we know the motion with respect
to reference body plate C. We can use these motions to obtain the relative motion of A with respect
to B and vice versa.
Let us look at motion on a plane first: In Figure 2.24 a transparent red copy of the plane rotates
about point A, while a transparent green copy rotates about B. The rotations of plate A about
rotation pole A are indicated by the red arrows, while the green arrows indicate the rotation of
plate B about pole B. It is evident from the arrows, which indicate the actual local velocity, that the
rotation velocities of both plates differ.
Figure 2.24:
39
The Dynamic Earth
Plate Tectonics
The black arrows represent the resultant velocities in which we are interested. Somewhere along
the line between A and B lies a point where the magnitude and direction of a green arrow equals
those of a red one. As the rotation about B is larger than that about A, this point will be closer to B
than to A. The black arrows indicate a rotation about that point, the rotation pole of plate A with
respect to plate B. This pole and its angular velocity are characteristics of the relative motion of
lithospheric plates.
Exercise 2-17***: Determining the rotation pole of plate C and D
Figure 2.25 shows rotation poles C and D: the rotations have the same direction, but the angular
velocity of D is twice that of C. Find the point where the actual velocities of plate C and D are
equal. In other words, find the rotation pole of the relative motion of C and D. Hint: Consider
Figure 2.24 and the distance between the rotation pole and both A and B. Also, D rotates twice as
fast as C, but, at the rotation pole, velocities are equal. Using the formula velocity = distance/time
for the same amount of time will give you…?
For motions on a plane as well as motions on the surface of a sphere, the following is valid: the
relative motion of two rotating plates can be seen as a rotation of one plate with respect to the
other. This can be shown in the plane with simple trigonometry. The rotation pole and angular
velocity of a relative motion in the plane can be calculated easily as well. Because the same
concepts apply to motion on a sphere, it is also possible to calculate the rotation pole and angular
velocity of plate motions. However, such calculations are more difficult, we leave them to specially
designed computer programs.
Rotation calculations have proved to be useful not only in plate tectonics, but in determining the
higher-velocity relative motion of stars and planets as well!
Figure 2.25
2.7.5
Determining rotation poles
The motion of a plate over the surface of the Earth can be represented by a rotation about an
imaginary axis with a certain angular velocity. The two points where the axis of rotation cuts
through the surface are called rotation poles – they are not the same as the rotation poles of the
Earth itself (see left figure of Figure 2.26).
You can determine the location of a rotation pole by studying an oceanic spreading ridge: there is a
clear geometric relation between the orientation of the segments of a spreading ridge and the
corresponding transform faults and fracture zones, and the location of the rotation pole (see Figure
2.26). The next two exercises discuss this geometric relation.
Figure 2.26: The motion of plates on a sphere. The left globe shows the
difference between the Earth’s rotation axis and the axis of rotation of a
plate. The right figure shows a spreading zone including a spreading ridge
and transform faults.
40
Plate Tectonics
The Dynamic Earth
Exercise 2-18**: Relation between spreading ridge and rotation pole
a. Explain the sentence in bold from the last paragraph in your own words. Clarify with a drawing.
b. Use Figure 2.26 to describe the relation between the orientation of the transform faults
(perpendicular to the rifts) and the location of the rotation pole.
Figure 2.27 is a detailed map of the bathymetry of the central part of the Atlantic Ocean. Oceanic
lithosphere in this area formed through spreading at the Mid-Atlantic Ridge. The white lines are
added to indicate the spreading ridge segments, otherwise they are difficult to discern.
Transform faults are obvious from bathymetric maps, as is the way the faults link ridge segments.
Therefore, transform faults are used in determining the location of rotation poles.
Exercise 2-19****: Determining the rotation pole of the Atlantic Ocean
Using a computer program and a polarity timescale, we will describe the motion of two plates. This
exercise consists of two parts:
I. Where does the rotation pole of the motion of Africa with respect to South America lie?
Using the bathymetric map of the central part of the Atlantic Ocean (Figure 2.27), we will find the
rotation pole of the motion of Africa with respect to South America.
II. What is the rotation velocity? We will use the paleomagnetic timescale (Figure 2.28) to
calculate the rotation velocity.
Part I. Where does the rotation pole of the motion of Africa with respect to South
America lie?
First use Figure 2.27 to construct at least 10 great circles perpendicular to transform faults. The
point of intersection of the great circles determines the rotation pole. The last part of this exercise
requires the use of a computer program. Make sure to follow the next steps:
a. Find several obvious transform faults in Figure 2.27 Remember that at a transform fault plates
move past each other. Determine (1) the coordinates of the point where ridge and transform
fault cross, and (2) the azimuth of the transform fault. The azimuth is the orientation of the
fault; it is given by the angle between the fault and true north, measured in a clockwise
direction. Use your protractor to measure the angle.
Figure 2.27: Bathymetric map of the central part of the Atlantic Ocean. The white lines
indicate the spreading ridge segments. The transform faults are perpendicular to these
segments.
41
The Dynamic Earth
b.
Plate Tectonics
Convert the orientation of the transform faults into that of the perpendiculars of the faults by
subtracting 90˚. This step is needed because we are looking for great circles perpendicular to
the transform faults. Use the coordinates and orientations you find as inputs for the computer
program (www.geo.uu.nl/jcu - plate tectonics) to produce a map of great circles. The rotation
pole of the motion of Africa with respect to South America lies at the intersection of the great
circles. Read off the coordinates of the pole and estimate the uncertainty in the coordinates.
Part II. What is the rotation velocity?
In 1968, scientists Dickson, Pitman and Heirtzler published one of the first magnetic profiles that
ran perpendicular to the spreading ridge in the southern Atlantic Ocean. Their profile (Figure 2.28),
called V18, crossed the Mid-Atlantic Ridge at -30.5°N en -13.5°O. The black and white sequence
at the bottom of Figure 2.28 is important. It shows the interpretation of the magnetic curves.
d. Use Figure 2.28 together with the paleomagnetic timescale of Figure 2.29 to calculate the
average spreading velocity of the last 3.4 million years at the latitude of profile V18. Be
careful: the spreading has two directions. B (Brunhes) is the youngest and GIL (Gilbert) the
oldest magnetic period of Figure 2.28.
The velocity of rotation is expressed in degrees per million years. When calculating this velocity,
you assume that the angle between the rotation axis and the line from the centre of the Earth to
the point where the velocity is determined is exactly 90˚. This point thus lies on the equator of the
rotation.
Figure 2.28: The magnetic profile perpendicular to the spreading ridge. The zero on the upper axis
represents the spreading ridge, from there the distance to the ridge is given in kilometres. The
middle curve shows the observed magnetic signal. The upper curve represents this signal mirrored
with respect to the spreading ridge and the lower curve was calculated from a model,
approximating the observations well. The black and white sequence at the bottom shows the
interpretation of the magnetic curves. Black blocks indicate a normal polarization of the oceanic
crust, while white blocks represent a reversed polarity state. The letters below the sequence refer
to the names of the geomagnetic periods, for example, B = Brunhes Chron. See Figure 2.29 for the
names and ages of the other geomagnetic periods. (Figure 7 of Dickson, Pitman and Heirtzler,
Journal of Geophysical Research, 73, 2087-2100, 1968)
42
Plate Tectonics
The Dynamic Earth
Figure 2.29: Geomagnetic polarity timescale showing the ages of several geomagnetic periods.
Black blocks represent a normal polarity state, white blocks a reversed polarity state.
e.
f.
What is the velocity of rotation about the pole determined in Exercise 2-19c? Hint: Use velocity
[kilometres/million years] = rotation velocity [radians/million years] · radius turning-circle
[kilometres]. Take the radius of the Earth, about 6400 km, as the radius of the turning-circle.
Since rotation velocity is always expressed in degrees per million years, you will have to
convert the velocity from radials to degrees per million years with PI radials = 180 degrees.
Why is the assumption of a 90-degree angle so important in the previous question? By how
many degrees per million years would the rotation velocity differ for an angle smaller than
90˚?
Final exercise Ch2. Answer the section questions and the main question
g.
Answer the seven section questions as well as the main question from the beginning of this
chapter.
h. If you find you have new questions after reading this chapter, write them down.
43
The Dynamic Earth
Plate Tectonics
Optional exercise 2-1: The magnetic field of the Earth
(From a Dutch Physics final exam question, 1998-I, VWO)
To be able to complete this exercise on the Earth’s magnetic field, you are expected to be familiar
with oscillation, amplitude, equilibrium position, harmonic oscillation,
vmax 
2 A
,
T
magnetic
induction B expressed in tesla (T), magnetic flux (Φ) and the relation between (a change in) flux
and voltage.
A horizontally positioned compass needle points in the direction of the horizontal component Bh of
the geomagnetic field strength B. The needle is displaced from its equilibrium position; the tip of
the needle starts to oscillate harmonically with an amplitude of 3.0 mm and an oscillation period of
1.8 s.
a. Calculate the velocity of the tip of the compass needle upon passing the equilibrium position.
A coil is placed parallel to Bh and connected to a variable
regulated power source. The compass needle is positioned in the
middle of the coil (see Figure 2.30). An electric current runs
through the coil such that the direction of the coil’s magnetic field
is opposite to the direction of Bh. At an electrical current strength
of 2.2 mA in the coil, the magnetic field strength of the coil is
equal to Bh. Therefore, the resultant magnetic field strength
within the coil is zero. If the needle is set off from its equilibrium
position now, it will not oscillate, but spin. The coil has 1600 Figure 2.30
loops and is 25 cm long.
The magnitude of the magnetic field strength within the coil can be calculated with
Bcoil   0
NI
l
with  0 the permeability of free space of 4π · 10-7, N the number of loops on the coil, I the
strength of the current in the coil and l the coil’s length.
b. Calculate the magnitude of  h .
The power source and compass needle are now removed. The
ends P and Q of the coil are instead connected to a device that
records the voltage as a function of time. Starting from the
position drawn in Figure 2-31, the coil is then rotated several
times in the vertical plane with constant angular velocity. The
sense of rotation is also shown in Figure 2.31. The vertical
component
v
of the geomagnetic field is directed downwards.
Figure 2.31
c.
Use Figure 2.31 to explain which end of the coil (P or Q) has the highest potential the moment
the coil passes the position drawn in Figure 2-31.
The voltage produced by rotating the coil is plotted against time t in Figure 2.32 One of the
moments where the coil passes the position of Figure 2.31 is set as t = 0.
d.
e.
Use Figure 2.32 to show that the direction of the geomagnetic field strength  is at a 68degree angle with the horizontal plane.
Calculate the magnitude of the magnetic field strength B of the Earth’s magnetic field.
Ucoil
Figure 2.32
44
Earthquakes and tsunamis
Chapter 3.
The Dynamic Earth
Earthquakes and tsunamis
The main question of this chapter is:
How does plate motion cause earthquakes and tsunamis and how do we record
the effects of plate motion?
This question is addressed by answering the following section questions:






How can we use the waves generated during an earthquake to assess the location and
strength of the earthquake? (3.1)
How are plate tectonics and earthquakes related? (3.2)
What causes an earthquake? (3.3)
How do plates move during an earthquake? (3.4)
How do we quantify the strength, or magnitude, of an earthquake? (3.5)
How do earthquakes cause tsunamis? (3.6)
Objective: To describe earthquakes and tsunamis, to understand what causes them, how they
develop, and, if possible, predict future occurrences. For this, you can use the knowledge you have
gained from Mathematics and Physics classes.
45
The Dynamic Earth
Earthquakes and tsunamis
3.1 Earthquake waves
This section describes how the location of an earthquake can be determined by examining
recordings of the waves generated during the earthquake.
Figure
3.1:
The
hypocentre
and
epicentre of an earthquake. (Source:
www.knmi.nl)
From Chapter 1 and 2, we know that tectonic plates
move. Plate motion is a continuous process that
results in the build up of stress on the plate
boundaries and on faults within the plates. This stress
is released through sudden, jerky, displacements.
These sudden movements along the fault plane
generate vibrations. It is these vibrations that we call
an earthquake. The point within the Earth where an
earthquake originates is called the focus or
hypocentre; the location on the Earth’s surface,
directly above the hypocentre, is the epicentre (see
Figure 3.1) Figure 3.2 shows where earthquakes,
recorded during a period of only 3 weeks in 2009,
occur on Earth.
Solid rock vibrates during an earthquake. The vibrations, or waves, travel either through the Earth
(body waves) or along the surface of the Earth (surface waves). Both types of waves are recorded
by seismographs (see Figure 3.3).
Figure 3.3 shows the wave pattern recorded by a seismograph. Two waves can easily be
distinguished: the P-wave and the S-wave. Both waves are body waves, travelling in three
dimensions through the interior of the Earth. P-waves and S-waves contain a lot of information
about the earthquake that generated them.
(See http://www.geo.mtu.edu/UPSeis/waves.html for more information on and applets of the
motions caused by P- and S-waves.)
Figure 3.2: The location of the earthquakes registered by the US Geological Survey between June 6
and June 28, 2009. (Source: http://neic.usgs.gov/neis/qed/)
46
Earthquakes and tsunamis
The Dynamic Earth
Figure 3.3: A schematic representation of a seismograph recording, called a seismogram. This
seismogram is analogue: it is made by tracing a pen over a sheet of paper. On the website of the
Seismology group of Utrecht University (www.geo.uu.nl/Research/Seismology/) you can see the
digital seismic signal recorded in Utrecht.
The P-wave, the primary wave, arrives at a seismic station first; it is faster than all other waves
generated by an earthquake. P-waves are longitudinal waves, this means they vibrate in the same
direction as the direction in which they travel (see Figure 3.4). In other words, particles of the
material through which a P-wave passes move parallel to the direction in which the wave itself
moves. Sound waves move in the same way through air. Within the Earth’s crust, P-waves have a
velocity of 5-8 km/s, depending on the density of the rock through which they pass.
Figure 3.4: A longitudinal wave (P-wave).
The S-wave, the secondary wave, is a transverse wave. Transverse waves vibrate perpendicular to
their direction of motion (see Figure 3.5). S-wave velocity is almost half the velocity of P-waves.
Therefore, it takes longer for S-waves to arrive at a seismic station.
There are numerous seismograph stations around the world. The data they record is used to
determine the exact location of an earthquake, its focus, and to gain insight into the nature and
extent of an earthquake. This data helps us to better understand earthquakes and enables us, for
example, to predict future earthquake locations. Unfortunately, because the exact timing of
earthquakes is still impossible to predict, it is not possible to issue precise earthquake warnings.
To practise working with seismic waves, you can complete Optional Exercise 3-1 at the end of this
chapter.
We can use seismograms to determine the exact location of an earthquake. Because P- and Swaves have different velocities, they arrive at a seismic station at different times. The difference in
47
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Earthquakes and tsunamis
arrival times is a measure of the distance between the earthquake’s epicentre and the
seismograph.
Figure 3.5: A transverse wave (S-wave)
In Exercise 3-1, five seismograms of the same earthquake, recorded by seismographs at different
locations on Earth, are used to locate the earthquake’s epicentre.
Exercise 3-1**: Locating an earthquake in The Netherlands
On April 13, 1992, at about 3:20 a.m. local time, an earthquake occurred in The Netherlands.
Afterwards, interpretation of the seismic data afterwards showed that this earthquake was the
largest ever recorded in The Netherlands. In this exercise you will answer the following questions:
a. Where was the epicentre of the earthquake?
b. When exactly did the earthquake initiate?
To answer these questions, use the information below:
- 3:20 a.m. local time corresponds to 01:20 Universal Time (UT), or Greenwich Mean Time (GMT)
(24-hour clock notation).
- Figure 3.6 shows five seismograms of the April 13 earthquake. The seismograms were recorded
by seismographs in Germany, Belgium and The Netherlands. Figure 3.6 is only a selection of the
many recordings done worldwide. For example, the earthquake was recorded in California and
Australia as well. To accurately determine the earthquake’s epicentre, we use the recordings of the
seismic stations closest to the earthquake.
- The seismograms in Figure 3.6 starts at reference time 01:20:15 GMT. Note that this time is
arbitrary; it is not the actual origin time of the earthquake, because the actual moment it began is
still unknown.
- Figure 3.8 shows the locations of the seismographs that produced the five seismograms.
- Figure 3.9 shows a graph of P- and S-wave travel times for places within a 500 km radius from
the epicentre. This graph was made under the assumption that the earthquake took place at a
depth of about 18 km. You can see that the time difference between P- and S-wave arrivals
increases for seismometers farther from the epicentre. Thus, using the difference between the Pand S-wave arrival times, we can calculate the distance between seismograph and epicentre. This
is called the epicentral distance.
Answer questions a. and b. If needed, you can use the hints below.
Hints to answer question a. Where was the epicentre of the earthquake?
i
Mark the time of arrival of the P-wave in each of the seismograms and calculate the
difference between P- and S-wave arrival times. Identification of S-wave arrival times is
difficult so they have already been indicated.
ii
Use Figure 3.9 to determine the epicentral distance for each seismic station.
iii
Figure 3.8: Draw a circle around each station on the map with a radius equal to each
station’s epicentral distance.
iv
The epicentre of the earthquake lies where the different circles intersect.
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Earthquakes and tsunamis
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Hints to answer question b. What was the origin time of the earthquake?
i
Determine the arrival time of the P-wave at one of the seismometers.
ii
Calculate the travel time of the P-wave for that seismometer’s epicentral distance (Figure
3.9).
iii
Subtract the travel time from the time of arrival. This will give the exact origin time of the
earthquake.
Final questions
a. Why don’t the circles around the seismic stations intersect at one exact point?
b. Why don’t the lines in the travel time graph go through the origin?
Time from 01:20:15 GMT (s)
Time from 01:20:15 GMT (s)
Figure 3.6: The seismograms belonging to Exercise 3-1.
49
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Earthquakes and tsunamis
Figure 3.7: The locations of the seismographs of Exercise 3-1.
A larger version of Figures 3-6 to 3-9 is available as a PDF-file. Print these figures out and use
them to draw on.
Figure 3.8: The location of two large Sumatra earthquakes. The earthquake that
caused a tsunami in December 2004 is denoted by a yellow star and a second large
earthquake that occurred shortly after the first by a red star. The part of the fault
plane that was active during each earthquake, called the rupture zone, is also
indicated. (Source: US Geological Survey (USGS))
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Earthquakes and tsunamis
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Figure 3.9: The fault planes to the southwest of Sumatra that were active during
different earthquakes. For each fault plane, the date and the magnitude (in
seismic moment, see Section 3.5) is given. (Source: K. Sieh, Caltech, USA)
3.2 The relationship between plate tectonics and earthquakes.
Exercise 3-2*: Where do earthquakes occur?
Read the newspaper article fragment below:
A, I
Central America, October 9, 2005
The earthquake in El Salvador and Guatemala had a magnitude of at least 5.8 on the Richter scale.
The epicentre of the tremor lies at a depth of 28 kilometres in the Pacific Ocean, about 51
kilometres from the Salvadorian city Barra Salada.
At least 610 people were killed.
a.
b.
c.
d.
Mark the location of the El Salvador and Guatemala earthquake on the map you used in
Exercise 1-1. Mark the earthquakes studied in Exercise 3-1 and Optional Exercise 3-1 as well.
Mark the location of more recent earthquakes. Use, for example, the website
http://www.earthweek.com.
Take a look at GB 192B (GB 174B). Compare the distribution of earthquakes with the location
of the plate boundaries. Can you find a correlation between the two? Are there any exceptions?
If so, how do you explain these exceptions?
What mistake is made in the newspaper article fragment above?
Earthquakes are most common along convergent plate boundaries (two plates moving towards
each other) and transform plate boundaries (two plates sliding past each other). Little seismic
activity is found along the third type of plate boundary, the spreading ridge, where plates move
away from each other.
Exercise 3-3**: Plate motion near Japan
A
From a Dutch final exam question in Geography (2007-II)
Many more earthquakes have occurred along the north-western boundary of the Philippine Plate
than along the eastern boundary.
a. Use the data from map GB 157 (GB 140) and GB 192B (GB 174B) to explain the difference in
the numbers of earthquakes between the Philippine Plate boundaries.
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It is evident from maps GB 157A and D (GB 140A and D) that the depth of the hypocentre of an
earthquake in the vicinity of Japan and the distance of the earthquake from the Japan Trench are
related.
b. What is the connection between the hypocentre depth of an earthquake and the distance to the
Japan Trench? Do not consider earthquakes with a hypocentre depth less than 50 km.
Earthquakes along subduction zones are often very powerful, which makes them easier to study.
We will investigate subduction zone earthquakes further by zooming in on earthquakes near
Sumatra, Indonesia.
The large Sumatran earthquake of December 26, 2004, and the tsunami generated by it were the
result of the active subduction zone along which Sumatra lies. The magnitude of the earthquake
attracted a lot of attention from the scientific community; as did the enormous amount of data that
modern technology was able to capture. The data record of the Sumatra earthquake helps us to
learn more about earthquakes in general.
The Sumatran earthquake from December 2004 is one of the most powerful earthquakes that has
occurred since seismographic recording began in around 1900. Like all other earthquakes, it was
caused by the relative motion of parts of the Earth along a pre-existing fault plane. The Sumatran
earthquake fault plane has been active for a very long time (millions of years). However, during
the December 2004 earthquake over 1000 km of the plane was active.
The area where the Sumatran earthquake happened has a known pattern of
plate motion: The Australian-Indian Plate subducts underneath the Eurasian
Plate on which Indonesia lies. The Sumatra earthquake thus took place on a
convergent plate boundary setting, in a subduction zone
The subduction zone runs along the south-western shore of Sumatra and the southern shore of
Java (Figure 3.9 and Figure 3.10) south of the red line lies the deep-sea trench. At the latitude of
northwest Sumatra, the Australian-Indian Plate subducts in a north-northeast direction underneath
the Eurasian Plate with a velocity of 6 cm/year.
Eurasian Plate
Australian –Indian Plate
Figure 3.10: The motion of the Australian-Indian Plate with respect to the Eurasian
Plate. The orange arrows indicate the direction of motion of the tectonic plates, the
red arrows the direction of the December 2004 earthquake at Sumatra. (Source:
Tsunami Laboratory, Novosibirsk, Russia)
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Earthquakes and tsunamis
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After an earthquake, scientists try to characterize the motion that has taken place as quickly as
possible. They want to find out how the plates involved in the earthquake moved with respect to
each other. Motion along a fault is an expression of the relative motion between the two blocks
that meet at the fault plane. When the blocks are part of lithospheric plates, the direction of motion
along the fault plane, called earthquake slip vector, or simply slip, is an expression of the relative
plate motion. The slip can be determined within an hour after an earthquake. To do this, scientists
first analyse the seismograms of different seismic stations to produce a focal mechanism diagram.
This characterizes the orientation of the fault and the direction of the motion along the fault.
Additional later analysis can improve on the first estimation.
3.3 The development of an earthquake
The Sumatran earthquake of December 2004 measured magnitude 9. The data collected from it is
very useful when studying how earthquakes are generated (see Section 3.5 for more information
on the term magnitude). The magnitude of an earthquake depends on the extent of the fault plane
along which slip took place and on the amount of slip. During the Sumatran earthquake, 2 to 20
metres of slip occurred along approximately 1200 km of the fault plane (an extremely large
segment of the fault).
The earthquake started in the south-eastern part of the activated fault plane and extended in a
northwesterly direction. Displacement along the fault progressed for 12 minutes, i.e. the slip
propagated in a northwesterly direction along the fault plane over a distance of 1200 km in only 12
minutes (this amounts to 1.7 km/s). In some parts of the active fault plane the vertical
displacements were up to 15-20 m, while in other parts displacements reached only 2 m.
How can we explain the large 20 m displacements as well as the smaller displacements? Why is the
displacement not the same everywhere? On average, the velocity of relative plate motion is several
centimetres per year. So how can plates move 20 m in 12 minutes so suddenly? During the years
that precede an earthquake, stress builds up because the subducting plate sinks underneath the
upper plate several centimetres per year. This sinking, however, is hindered by friction. It is only
when the built up stress overcomes the friction that the fault slips in a sudden, fast movement.
Think of an earthquake as being like trying to move a large, heavy cabinet. First, you push very
hard and stress builds up, then, suddenly, the cabinet moves.
How do we explain the difference in displacements along the fault plane? In some parts of the fault
the relative plate motion has been blocked for longer periods than in other parts because of
Figure 3.11: The three phases of earthquake
generation. Stress builds up (upper and middle
figure) and is then released resulting in an
earthquake (lower figure). (Source: www.usgs.gov)
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variations in the material properties. This results in differences in the amount of friction.
Thus, in some parts more stress builds up than in other parts. Relaxation in an area where there
has been a small build up of stress results in a small displacement (2 m), while in areas where
there has been a large build up of stress, the result is large displacements (20 m). The generation
of an earthquake can be divided into several phases, which are depicted in Figure 3.11. Stress
builds up at depth along a fault during the first phase. The plates deform along their boundaries
(phase 2) until the stress is relaxed by means of an earthquake (phase three): in a sudden
movement, the plates move past each other along the fault. The results of this motion can be seen
at the surface of the continents or ocean floors Involved. The building up of stress and the
relaxation of that stress can be modelled with simple friction experiments using elastic strain.
Practical/demonstration: stick-slip behaviour
A simple experiment can show how a continuous motion (plate motion) can result in jerky, shock
like movements (earthquakes) along the plane of contact (the fault plane). The pictures Figure
3.12 show how a glider that is rough on the bottom moves over a rough surface. An elastic band is
used to build up stress on the glider. The friction between the glider and the rough surface initially
prevents the glider from moving. However, when the stress on the elastic band is increased
further, this resistance is overcome and the glider moves with sudden jerks, in a start/stop
manner. This process is called stick-slip behaviour. By placing weights on the glider, the pressure
on the plane of contact and, thus, the friction are increased. More friction reduces the number of
shocks, but increases the magnitude of the shocks at the same time.
The above experiment demonstrates how the properties of the fault and the amount of pressure on
the fault can influence the magnitude of an earthquake. A rough fault surface with many asperities
increases friction and therefore blocks slip longer. Increased pressure on the fault has the same
effect. The greater the friction, the stronger the earthquake is.
Figure 3.12: Three photographs of a stickslip behaviour demonstration.
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Earthquakes and tsunamis
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Exercise 3-4**: Stick-slip behaviour
When pulling a snow sledge, it is hard to begin pulling it. Once you get the sledge moving (with
constant velocity), pulling it is relatively easy. The biggest pull is needed to get the sledge started;
you have to accelerate, but, more importantly, you have to overcome the friction between the
sledge and the snow. Friction between solid surfaces even exists when the surfaces seem as
smooth as a mirror because, on a microscopic scale, even smooth surfaces have protrusions and
indentations. These are known as asperities.
You may be aware of several different types of friction: rolling friction, sliding friction and air
friction. Within these groups, however, we further distinguish static and kinetic friction.
Static friction exists between the surfaces of two solid objects that are in contact with each other
but are not moving with respect to each other (the objects are static). Imagine a book lying on a
table: Unless you exert a horizontal force on the book, it will remain still. When you exert a force
(pull or push) on the book and it still does not move, it is static friction that prevents the
movement. As long as the book does not move (its velocity being constant and zero), there is no
resultant force, the static friction is equal to your pull or push: Ftotal = 0. To move the book, the
force you apply must overcome the maximal static friction.
The direction of static friction is always opposite to the applied push or pull. The magnitude of the
friction can vary between zero and maximal static friction, according to the relation: Ff ≤ μs · Fn.
Static friction Ff is given in Newtons (N), μs is the dimensionless coefficient of static friction, and Fn
is the normal force, also in Newtons (N). The subscript f denotes friction, the s static friction and
the n the normal force. The ≤-sign implies that the static friction is either smaller or greater than
the coefficient times the normal force. The first is valid when an object is not yet moving, the latter
when an object is about to move. In other words, static friction increases in proportion to applied
force, until it reaches its maximum. At that point, the static friction switches to kinetic friction.
When the book in the example above moves over the table, kinetic friction has taken over.
Overcoming kinetic friction requires less force than static friction; moving an object is easier when
the object is already moving. The direction of kinetic friction is opposite to the direction of motion
because it works against that motion. The magnitude of friction is determined by the roughness of
the surface of the objects in contact and is proportional to the normal force (in the example, the
table exerts a normal force on the book). This proportionality relation is reliable, but it is not a law
in physics. The equation Ff = μk · Fn governs kinetic friction, with Ff the kinetic friction (in N), μk the
dimensionless coefficient of kinetic friction and Fn the normal force (in N). The subscript f denotes
friction, k stands for kinetic friction and n for the normal direction of the force. Ff is constant, so
here an = sign is used. The table below lists values of coefficients of friction for various materials.
It is evident that μk < μs. Note that the coefficient depends on the humidity of the material and
varies with lubrication of the surface.
a. The coefficient of static friction is always larger or equal to that of kinetic friction, it cannot be
smaller. Explain.
μk
Surfaces in contact
μs
Wood-wood
0.4
0.2
Ice-ice
0.1
0.03
0.15
0.07
Metal-metal, non-lubricated
0.7
0.6
Rubber-dry concrete
1.0
0.8
Rubber-wet concrete
0.7
0.5
Rubber-other surfaces
1-4
1
Ball-bearings
< 0.01
<0.01
Human joints
0.01
Metal-metal, lubricated
55
0.01
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Earthquakes and tsunamis
Figure 3.13:
b.
Study the sketch above. What should be expressed at the letters A through E?
3.4 The motion of plates during an earthquake
The direction of the motion of the Sumatran earthquake was not the same as the relative motion
between the tectonic plates, which was north-northeast. The displacement along the fault, the slip,
was directed towards the east, perpendicular to the trench along the southwest coast of Sumatra.
This difference in direction is possible through strain partitioning. Strain partitioning allows the
shortening in one direction to be decomposed into shortening in two perpendicular directions. Thus,
the relative plate motion is not only facilitated by the subduction contact (see Figure 3.14, left
side), but also by a second transform-type fault that cuts through the leading edge of the upper
plate (Figure 3.14, right side). Thus, there are two strain components: one component is
perpendicular to the plate contact (subduction) and one is parallel to the contact (transverse
motion along transform fault).
Near Sumatra, the two components of motion did not take place at the same time. The 2004
Sumatra earthquake was the expression of the first component, the subduction motion (red
rectangle on right-hand side of Figure 3.14). An earthquake on March 6, 2007, (see newspaper
article below) represented the second component (the yellow rectangle moves with respect to the
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Earthquakes and tsunamis
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area on the far right). The second component took place along a separate, vertical fault, called the
Great Sumatra Fault, which runs parallel to the southwest coast of Sumatra. This transverse fault
was not yet active during the 2004 earthquake.
In summary, the decomposition of motion into two components, along the subduction contact and
along the transform contact, is called strain partitioning.
Figure 3.14: A schematic view of (the development of) an earthquake. The left
figure shows the plate motion and the fault plane near Sumatra. The red
rectangle in the right figure shows the motion during the 2004 Sumatra
earthquake, while the yellow rectangle shows the motion of the Sumatra
earthquake of March 6, 2007.
Sumatra earthquakes cause tens of deaths (Source: www.nrc.nl, March 6, 2007)
Padang, March 6. This morning, two earthquakes on the Indonesian island Sumatra caused at least
69 deaths. The number of casualties is expected to rise, as hundreds of buildings have collapsed.
Also, casualties and damage have not yet been reported in the more remote areas.
The epicentre of the earthquake is located on land, near Solok, a city north of the West-Sumatran
capital Padang. The first earthquake, at 11:00 a.m. local time, had a magnitude of 6.3 on the
Richter scale, the second, at 1:00 p.m. local time, a magnitude of 6.0. Both fall in the category
‘strong earthquakes’ and were felt as far away as Malaysia and Singapore.
In areas with frequent earthquakes, subsequent earthquakes are often related. This can be in the
form of the strain partitioning as explained above, but strain partitioning can also occur for
earthquakes with slip in the same direction, but at different locations.
The latter type of relationship also took place on Sumatra. The December 26, 2004, earthquake
was followed by an earthquake of the same type (subduction – see red rectangle in Figure 3.14) of
magnitude 8.7 on March 28, 2005. This earthquake occurred to the southeast of the 2004 fault
plane. Could the second earthquake have been caused by the first, because the first earthquake
added more stress to an area already under stress? Generally speaking, stress is released during
an earthquake. In some cases, however, earthquakes add stress locally, usually near the end of
the active fault. The stress levels near the end of an active fault are often already close to the
critical value, i.e. the boundary between no motion and motion, no earthquake and earthquake. In
a situation such as this, adding stress can easily cause another earthquake; the 2004 earthquake
brought about the 2005 earthquake in this way.
In exercise 3-6 we will break down relative plate motion vectors. To do this, we will continue to
study the motion on a sphere as we did in Section 2.6.
Exercise 2-17: a discussion of the rotation pole of two plates moving with respect to each other.
Both in two dimensions and on a sphere, the following is valid:
57
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


Earthquakes and tsunamis
The relative motion of two rotating plates can be seen as a rotation of one plate with
respect to the other.
The rotation pole of the relative motion lies on a line (or great circle in case of motion on a
sphere) that connects both original rotation poles.
The ratio of the two rotation velocities determines where on the line (or great circle) this
rotation pole lies.
For a plane, the above concepts can be proven with trigonometry; you can easily calculate the
rotation pole and angular velocity of the relative motion. It is more difficult on a sphere but the
same concepts apply.
Additionally, on a sphere you can use the following:

You can use vector addition when you use vectors in the direction of the rotation axis with
a length proportional to the angular velocity to represent rotations,. After breaking down
the vectors into x- and y-components, sum up the components separately to find the
resultant vector.
It is better to leave calculations on a sphere to specially designed computer programs. You can find
such programs on www.geo.uu.nl/jcu under the heading Sumatra earthquake. Be aware that it is
usually not easy to see that the new rotation pole lies on the great circle through the two poles just
by looking at the coordinates calculated by the program.
Exercise 3-5**: Determining the rotation pole of Plate C and D, using the computer
program on www.geo.uu.nl/jcu
a.
b.
Investigate the results of the computer program in the case of Exercise 2-17, with C the point
(0°, 0°) and D the point (1°, -1°) on the Earth. With this example, you should be able to see
whether the result lies on the great circle through C and D.
Now use the same coordinates for C, together with D = (90°, 0°). Take the relative velocities
equal or opposite and check the four concepts of relative motion stated above.
Now you can complete Optional Exercise 3-2: Resultant rotations as resultant vectors, see the end
of this chapter.
The following also applies to motion on a sphere (see also Exercise 2-17, 2-18, 2-19 and 3-5):



A rotation is determined by three numbers: 1) the longitude of the rotation pole, 2) the
latitude of the rotation pole, and 3) the corresponding angular velocity in [°/My]. Together,
these numbers define the rotation vector with its head in the direction of the rotation axis
and its length equal to the angular velocity in [rad/My] (radians per million years).
Rotations can be combined. Think, for example, of the motion of Africa with respect to
Eurasia. The motions of Africa and of Eurasia with respect to North America are known, and
both are used to calculate the rotation pole of Africa with respect to Eurasia:
ωAfr(Eur) = ωAfr(NAm) + ωNAm(Eur) = ωAfr(NAm) + -1 · ωEur(NAm)
The last term of the equation above shows that changing the order of the plates (e.g.
ωNAm(Eur) to ωEur(NAm)) equals changing the sign of the angular velocity.
Exercise 3-6***: Breaking down relative plate motion
The goal of this exercise is to find the rotation pole of the convergent motion near Indonesia. In
Indonesia, the Australian-Indian Plate subducts underneath the Eurasian Plate. There, strain
partitioning in different directions occurs.
Figure 3.15 shows a map of Southeast Asia and the boundaries of the tectonic plates. The central
area, which contains most of Indonesia, can be seen as part of the Eurasian Plate.
Table 3-1 gives the coordinates of the rotation pole and the (angular) velocity according to the
global velocity model NUVEL-1A, of each of the more important tectonic plates. The velocity given
is a relative velocity: the poles describe the motion of the plates with respect to the Pacific Plate.
a. Calculate the rotation pole describing the subduction underneath Indonesia. Use the
information in Table 3-1 and the computer program at www.geo.uu.nl/jcu (called Sumatra
Earthquake). Note: the program requires velocities in degrees per millions of years.
58
Earthquakes and tsunamis
b.
c.
d.
The Dynamic Earth
Now use the program to determine the direction and magnitude of the velocity at the plate
boundary. Do this for (at least) three locations including the points on the plate boundary with
longitude 100°E, 105°E and 110°E. Draw in the velocity vectors on Figure 3.15 using the scale
1 cm = 10 mm/year. Are there any major differences in velocity between the three locations?
Why?
Determine the expected trench-parallel component for each of the three locations with the help
of the geometric construction on the map on Figure 3.15. Where on the boundary of the upper
plate do you expect trench-parallel transform faulting? In what direction will the small strip of
lithospheric plate between the subduction zone and the transform fault move?
At 100°E longitude, the subduction direction determined from earthquake focal mechanisms is
31° east of north. Determine the magnitude of the velocity of subduction and trench-parallel
transform faulting.
Plate
African Plate
Antarctic Plate
Arabian Plate
Australian Plate
Caribbean Plate
Cocos Plate
Eurasian Plate
Indian Plate
North American Plate
Nazca Plate
South American Plate
Degrees north
59.160
64.315
59.658
60.080
54.195
36.823
61.066
60.494
48.709
55.578
54.999
Degrees east
-73.174
-83.984
-33.193
1.742
-80.802
251.371
-85.819
-30.403
-78.167
-90.096
-85.752
Velocity [˚/My]
0.9270
0.8695
1.1107
1.0744
0.8160
1.9975
0.8591
1.1034
0.7486
1.3599
0.6365
Table 3-1 The rotation pole and velocity of several plates with respect to the Pacific Plate,
according to the NUVEL-1A velocity model. (De Mets et al, 1994)
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Figure 3.15: A map of Southeast Asia showing the boundaries of the different tectonic
plates.
3.5 The strength (magnitude) of an earthquake
There are several ways to measure the strength of an earthquake. Here, we will discuss the three
most common scales: the Mercalli scale, the Richter scale and the seismic moment. The Richter
scale is the most well known magnitude scale. Before Richter established it, the Mercalli scale was
used.
MERCALLI SCALE
This scale quantifies the effects of an earthquake by describing the intensity of earthquake
vibrations. Most of the immediate damage caused by an earthquake is due to vibration.
Italian Giuseppe Mercalli (1850-1914) designed this scale that gives a number to the different
levels of intensity of vibrations. The scale indicates the observed effects (damage) of an
earthquake on humans, objects, buildings and the landscape. The intensity varies with distance
from the epicentre and depends on the type of rock and soil in the subsurface. The greater the
epicentral distance, the less the ground will move as a result of an earthquake and the smaller the
damage. Thus the intensity should also be smaller. However, when the local subsurface intensifies
the seismic vibrations, intensity can increase far from the epicentre. This happened during the
powerful earthquake in Mexico in 1985.
The Mercalli scale is divided into 12 intensities, each denoted with Roman numerals starting from I
(no tremors felt, earthquake only recorded by seismic instruments) to XII (cataclysmic). Scientists
often use the Mercalli scale to estimate the strength of earthquakes that occurred prior to 1900
before seismographs were invented. Written reports on the earthquakes provide the observations
needed to apply the Mercalli scale.
More
information
on
the
Mercalli
scale
http://earthquake.usgs.gov/learn/topics/mercalli.php.
can
be
found
on
the
website
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Earthquakes and tsunamis
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In 1935 the American seismologist Charles Richter proposed a scale based on the strength of
earthquake vibrations as measured by a seismograph.
RICHTER SCALE
The magnitude of an earthquake (its strength expressed in Richter scale units) is calculated using
the amplitude of the deflections on seismograph recordings. Seismologists must first correct the
amplitudes to account for the distance between epicentre and seismic station. This is because with
distance, seismic waves lose amplitude through geometric spreading and absorption.
In other words, with greater distance from the epicentre, vibrations become weaker for two
reasons. Firstly, the waves and their energy are spread out over a larger area, so, on average, a
wave has less energy. This process is called geometric spreading. Secondly, the ground the waves
travel through absorbs the energy of the waves due to friction of the ground particles.
To visualize geometric spreading and absorption, think of what happens when you drop a rock in a
pool of water. The ripples spread out in circles. Where the rock hits the water, the ripples are
higher than those further away. The spreading of the waves and the friction of the water particles
causes the wave height to decrease.
The Richter scale is logarithmic: a ten-fold increase in deflection on the seismogram corresponds to
an increase of one unit of magnitude. Thus an earthquake of magnitude 8 on the Richter scale has
amplitudes that are ten times greater than those of an earthquake of magnitude 7.
Large earthquakes occur less often than smaller ones:
Magnitude on the Richter scale
>8
7-8
6-7
5-6
4-5
3-4
2-3
Occurrence
once a year
18 times a year
108 times a year
800 times a year
6200 times a year
49000 times a year
300000 times a year
There is an obvious difference between the intensity (Mercalli scale) and the magnitude (Richter
scale) of an earthquake. The intensity depends on the place of measurement, whereas the
magnitude is independent of the location of the measurement and, therefore, characteristic of the
strength of an earthquake itself.
Exercise 3-7**: The Richter scale
The equation 10logE = 5.24 + 1.44M shows the relationship between the energy of an earthquake
and its Richter scale magnitude as established by experiments. E stands for the energy of an
earthquake in Joules and M for the corresponding Richter scale magnitude.
a. How much energy is released during an earthquake of magnitude 5 on the Richter scale? Hint:
If 10log(E) = a, then E = 10a. This follows from standard logarithmic identities.
Every day, the Sun provides the Earth with 1022 J of energy.
b. What magnitude does an earthquake have that releases as much energy as the Earth receives
in sunlight each day?
It is sometimes stated that small earthquakes act much like safety valves, releasing a little bit of
energy at a time and preventing the build up of stress to catastrophic levels. Assuming we indeed
need to release a fixed amount of energy,
c. How many magnitude 5 earthquakes are needed to prevent a magnitude 8 earthquake?
Compare the amounts of energy released in Joules.
Scientists often use the seismic moment to quantify the strength of an earthquake. This is because
this expression provides a physical measure of the earthquake itself.
SEISMIC MOMENT AND MOMENT MAGNITUDE
More recently, a third measure of the strength of an earthquake was developed: the seismic
moment. From this, the moment magnitude followed.
61
The Dynamic Earth
Earthquakes and tsunamis
The seismic moment (M0) is calculated by multiplying the shear modulus G of the rock bordering
the fault plane with the average displacement, or slip, along the fault dav and the total fault area A:
M0 = G x dav x A. M0 is given in Newton meters [N·m].
The most recent magnitude scale (1977) makes use of the seismic moment and is called the
moment magnitude. It is calculated as follows: Mw = log M0 /1.5 – 6.1. The moment magnitude of
a certain earthquake is similar to the Richter magnitude of that earthquake.
The seismic moment depends on the shear modulus and the slip along fault plane with its size. It
thus depends only on characteristics of the source area of the earthquake, not on effects observed
away from the fault. Therefore, the seismic moment is drastically different from the Mercalli and
Richter scale.
The seismic moment can either be determined from seismograms or from field observations at the
fault.
The moment magnitude is especially important for very strong (> 7.5) earthquakes, because the
Richter scale underestimates the strength of such earthquakes. The moment magnitude of the
Sumatra earthquake is 9.3, which means that it would not be the fifth strongest earthquake ever
(based on the Richter scale), but the second strongest. However, the strength of the 1960 Chilli
earthquake and the 1964 Alaska earthquake will have to be recalculated before we can say so for
certain. Unfortunately, recalculations are not easy since instruments in the sixties were not as
sensitive as nowadays.
3.6 The relation between earthquakes and tsunamis
Tsunamis are potentially devastating waves of water, caused by sub-marine earthquakes in which
fault slip leads to vertical displacement of the seafloor. Sumatra’s 2004 tsunami is probably the
best known example of a tsunami.
The uplift of the ocean floor due to fault slip is accompanied by an uplift of the entire column of
ocean water above it. This causes the tsunami (Figure 3.11). The uplift increases the potential
energy of the water mass and generates waves that travel in all directions (see Figure 3.16). The
waves have very long wavelengths that dissipate slowly. The first motion of a tsunami can be
either upwards or downwards. In the latter case, a drawdown of coastal waters occurs exposing the
ocean floor beneath.
Figure 3.16: The travel times (in hours) of the Sumatra tsunami. The
tsunami was generated by a submarine earthquake, and it soon hit the
coasts of Sri Lanka, India, Malaysia, Thailand and Indonesia and later
those of the Middle East, Madagascar and Africa. (Source: Kenji Satake,
National Institute of Science & Technology, Japan.
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Earthquakes and tsunamis
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Away from the coast the velocity of a tsunami is a simple function of the depth of the ocean:
v  g h
with v the velocity of the wave, g the gravity acceleration (9.81 m/s2) and h the depth of the ocean
floor. The average velocity of the 2004 Sumatra tsunami was 750 km/h.
It is obvious from the velocity equation that when water depth decreases (when the ocean
becomes shallower) the tsunami wave slows down. In the open ocean, the amplitude (height) of
the Sumatran tsunami was approximately half a meter; the damage that would be caused by such
a wave would be relatively minor. However, upon approaching the coast, the amplitude of the
wave increased significantly due to the decreasing water depth. The resulting wave was several
meters high and had catastrophic effects.
Research (Margaritondo, G., 2005) shows that, in general, wave height A is inversely proportional
1/ 4
to water depth H to the power ¼, or A  cH
. From this equation you can see that when water
depth H decreases upon arrival at a coastline, wave height A increases.
The Japanese word ‘tsunami’ translates into ‘harbour wave’. In the past a tsunami could not be
seen in the open ocean because of its minor amplitude and large wavelength. It was only noticed
when it reached a harbour and had obtained an amplitude of several meters. Today tsunami wave
heights can be measured in the open ocean using satellites.
Exercise 3-8a****: Tsunami propagation calculations
In this exercise you will calculate the propagation of the Sumatran tsunami through time by
answering questions such as `Where was the tsunami wave after 6 hours?’ and `How long did it
take for the wave to reach the coastline of Madagascar?’ For this exercise use the simple tsunami
velocity equation given above.
Figure 3.18 is a bathymetric map (a topographic map of the ocean floor) of the Indian Ocean and
part of the Atlantic Ocean. Its shows three paths A, B and C, along which different parts of the
expanding wave front of the 2004 tsunami travelled. The tsunami paths start at the earthquake’s
epicentre and are simplified for this exercise. Along each path in Figure 3-16, the white dots denote
distances of 1000 km.
Figure 3.17 shows the bathymetric profile along path A, as measured every 100 km. The horizontal
axis represents the distance from the epicentre.
a. Divide the first 5000 km of the bathymetric profile along path A into 3 to 5 segments and
determine the average water depth of each segment. Hint 1: Take a relatively linear part of the
ocean floor to determine the average water depth. Hint 2: Neglect the large fluctuations in
depth in the first 1500 km and take this part as one segment.
b. Now calculate the average tsunami velocity for each segment. Hint: Use the equation from the
previous page.
c. Calculate the time it takes for the tsunami to bridge each segment. Plot the distance travelled
by the tsunami along path A against time. Hint: Use x = v · t, or, in words, distance is velocity
multiplied with time.
d. Repeat steps a through c for the rest of path A.
e. The bathymetry along path B is similar to that of path A for the first 5000 km (figure 3-20).
Why do you think the bathymetry differs after 5000 km? What effect does the different
bathymetry have on the propagation of the tsunami wave? Repeat steps a through c for path
B, starting from 5000 km.
f. Now use the profile along path C (Figure 3.20) to determine the time between the earthquake
and the arrival of the tsunami wave at the coast of Madagascar.
63
The Dynamic Earth
Earthquakes and tsunamis
Figure 3.18: A bathymetric map of the Indian Ocean and part of the Atlantic Ocean.
Three paths A, B and C are indicated along which different segments of the
December 26, 2004, Sumatra tsunami travelled.
Figure 3.17: The bathymetric profile along path A.
64
Earthquakes and tsunamis
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Exercise 3-8b****: Tsunami propagation calculations with Excel
The tsunami propagation through time can also be determined precisely by using the bathymetry
data with 100 km step size and EXCEL. Directions for the calculations with the original bathymetry
data can be found below.
A. The data files
For each of the three tsunami paths there is a data file with bathymetry measurements:
profileA.dat, profileB.dat and profileC.dat. The first few lines of profileA.dat are:
95.85
3.32
0
-756.407
95.2708
2.63133
100
-1781.25
The first column gives the longitude in degrees east, the second column the latitude in degrees
north, the third column the distance from the epicentre in kilometres and the fourth column the
water depth D as a negative number in meters.
B: Reading data into EXCEL (for EXCEL 2003)
You can read in the data per column as follows:
i
Open a new EXCEL file. Put your cursor on cell A4; this way you leave some lines open above
the data.
ii Choose Data >> Import external Data >> Import Data. Browse for the right data file and
choose All Files for the option File Types. Click Open.
iii Every time you click Next, new options will appear. The Data Format screen is especially
important. Select (with Shift-Click) all columns, choose Advanced and switch the decimal
separator to . (point) and the thousands separator to ‘ (quotation mark).
iv Click Finish and check to see that the starting cell is A4. [This is, of course, not obligatory, but
the example below assumes your data starts at A4.]
C: The bathymetric profile
You can image the bathymetric profile right away: Click on the depth D column and choose Insert
>> Chart >> Line. You do not need the graph for any calculations, but you might want to use
graphs for step E.
D: The calculations
Methods in short:
Determine the velocity in each 100-km segment; determine the time needed for the tsunami to
cross each segment; sum the segment travel times. You can give these calculations in the first
data line and then copy them up to the last line of data. EXCEL will then automatically do the other
calculations for you. (Be careful to start calculations with an = sign.)
Methods in detail:
– Use cell F4 for the tsunami velocity ( v
 g  h ).
Type: = SQRT(9.81 · - D4) [the reference to
cell D4 can be given by clicking on D4].
– Use cell G4 for the travel time per segment. Each segment is 100 km long and the velocity in F4
is in meter per second. Compose a proper equation for the travel time in seconds with a reference
to cell F4.
– Sum up travel times in column H. In the cells of column H, you sum up the value of the
neighbouring G-cell and the H-cell above. So, for the first data line, you sum up G4 and H3. H3 is
empty, but EXCEL will attribute it value 0, or you can assign it value 0 yourself.
- Now you have your first complete line of calculations. Copy these calculations by selecting cells
F4-G4-H4, putting your cursor on the right lower corner of the selection and dragging it to the last
line of data. Column H will now tell you when the wave passed each distance in column C.
– Column H gives the time in seconds; make an extra column that gives the time in hours.
E: Improvements and further investigations
a. Do you think your calculations would be more accurate if you were to use the average of the
velocities at the beginning and end of each segment as segment velocity? You can try this
method with EXCEL or predict its effects yourself.
b. Plot the bathymetry of each path on the spreadsheet and compare the three profiles.
65
The Dynamic Earth
c.
Earthquakes and tsunamis
You can also construct other graphs. For example, a plot of distance versus time. Do this by
copying column C to the right of your last column, selecting both columns and making a Chart
of the scatter-type.
Figure 3.20: The bathymetric profile along
path B.
Figure 3.20: The bathymetric profile along path C.
66
Earthquakes and tsunamis
The Dynamic Earth
Final exercise Ch3. Answer the section questions and the main question
a. Answer the six section questions and the main question from the beginning of this chapter.
b. If you find you have new questions after reading this chapter, write them down.
Optional exercise 3-1: Earthquakes and seismic waves
(From a final exam in Physics, Havo 1999-I, question 6)
During an earthquake, longitudinal and transverse waves (the P- and S-waves of Section 3.1)
travel through the Earth.
a. What is the difference between longitudinal and transverse waves?
In a certain type of rock, transverse waves have a velocity of 3.4 km/s and a frequency of 1.2 Hz.
b. Calculate the wavelength of the transverse waves in this rock.
Seismographs register earthquake vibrations. Figure 3.21 shows a simple type of seismograph: A
heavy block hangs suspended on a spring and can move freely, but only in the vertical plane
(because of hinge A). During an earthquake, the spring-block system is not allowed to resonate
with the earthquake vibrations. To prevent resonance, the frequency of the spring and block is
small (only 0.37 Hz) compared to the frequency of the earthquake’s vibrations. The mass of the
block is 4.2 kg.
Spring
Hinge
Figure 3.21: A seismographs.
c.
Calculate the spring constant.
Figure 3.22: Registration of an earthquake in Greece.
The velocity of longitudinal waves differs from that of transverse waves. Due to this difference, the
waves do not arrive at a seismic station at the same time. Figure 3.22 shows a recording of the
seismograph of an earthquake in Greece, measured by the KNMI in De Bilt, The Netherlands. The L
denotes the arrival of the longitudinal waves, the T that of the transverse waves. You can see that
the longitudinal waves arrived first. It is assumed that both types of waves followed the same path.
The earthquake took place 2300 km away from the seismograph. Take the average velocity of
transverse waves as 3.4 km/s.
d. Determine the average velocity of the longitudinal waves in two significant digits.
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Earthquakes and tsunamis
Optional exercise 3-2: Resultant rotations as resultant vectors
In this chapter we have investigated the resultant motion of two plates, the motion of one plate
with respect to the other. Focus on the equators especially on the equators belonging to those
motions, to prove the fourth point stated just above Exercise 3-5: when you use vectors in the
direction of the rotation axis with a length proportional to the angular velocity to represent
rotations, you can use vector addition.
Study Figure 3.23. Rotation poles A and B
are indicated together with their angular
velocities ωA and ωB. (In this case, ωA : ωB
= 2 : 1, but the following deductions are
valid for every velocity ratio.) Equators cA
and cB belong to poles A and B,
respectively, and cross in point P. The
actual velocity of P as a point on the Ashell is vA and that of P as part of the Bshell is vB.
a. Explain why |vA| : |vB| = ωA : ωB. Hint:
Use v = ω·R, with R the radius of the
Earth (see BINAS).
b. Explain why the angle between the axis
of rotation of A and that of B is equal
to the angle between vA and vB.
Figure 3.23
Using the above definitions, we can draw two vectors, starting in the centre M, along the rotation
axes of A and B with their length ratio equal to the ratio ωA : ωB. Call the vectors mA and mB; mA is
already drawn in.
c. Also draw in mB.
Vector couples vA-vB and mA-mB are similar (they have equal angles and proportional lengths).
The resultant velocity vC, the difference between the two velocity vectors vA and vB, also works on
point P. We know the resultant motion has a rotation pole C as well. C should lie on the great circle
through A and B, because in C the motion around A should equal the motion around B.
d. We are going to try to draw C and the arc CP. CP is perpendicular to vC. Why?
e. Draw the equator of C and then construct arc CP and rotation pole C.
The angular velocity ωC is determined by the magnitude of vC. The following relationship holds,
which is also valid if you replace B by A: |vC| : |vB| = ωC : ωB.
f. Explain why the above relationship holds.
Starting at M you can draw resultant vector mC.
g. Why does mC lie along the rotation axis of C?
Using mC, you can determine C and angular velocity ωC directly, without using P.
h. Draw in vectors mA and mB along the axes of A and B with the same magnitude ratio as ωA and
ωB .
i. Determine resultant vector mC.
The direction of vector mC gives the position of C and its magnitude gives ωC.
To summarize: The arrows in the direction of the axes of the rotation poles and with
magnitudes proportional to the angular velocities act like vectors in case of resultant
motions. You can determine the resultant vector through vector addition.
68
Volcanoes
Chapter 4.
The Dynamic Earth
Volcanoes
The main questions for this optional chapter are:
What types of volcanoes exist, what do they emit during an eruption, and what
do volcanic products look like at the Earth's surface?
These issues will be addressed by answering the following section questions:







What types of volcanoes exist, and where on Earth do we find them? (4.1)
How are different kinds of igneous rocks formed? (4.2)
How is magma formed? (4.3)
How do volcanoes affect Iceland? (4.4)
How much gas was emitted during the Laki eruption of 1783? (4.5)
How did this eruption lead to an increase of acidic components in the atmosphere? (4.6)
What are possible effects of volcanic acid rain? (4.7)
Objective:
In this chapter you will learn about the processes that occur in and around volcanoes. You will use
theoretical knowledge you have acquired during your chemistry lessons.
69
The Dynamic Earth
Volcanoes
4.1 Volcano types and occurrences
Exercise 4-1*: Volcanoes and plate tectonics
A, I
Eruption: Indonesian volcano Karangetan, October 29th, 2007
“Karangetan volcano on the Indonesian island Siao erupted this morning. Hours before, hundreds
of villagers were evacuated from the slopes of the 1.700 m high volcano. Villages, farms and trees
were thickly covered in ash, but no substantial damage or casualties have been reported.
Karangetan is one of the most active volcanoes on the Indonesian archipelago.” (From
www.trouw.nl)
a.
b.
c.
Mark the volcano on your empty world map.
Mark on your map any recent volcanic eruptions. Use www.earthweek.com for more
information.
Now take a look at GB 192B (GB 174B). When you consider plate boundaries, does anything
strike you when looking at the locations of volcanoes that you have found? Are there any
exceptions? If yes, can you explain these?
The epicentres of earthquakes are concentrated around plate boundaries. The majority of
volcanoes can also be found in these zones (see Figure 4.1 and GB 192B and D (174B and D). In
this chapter we will study the relationship between plate tectonics and volcanism. First we will look
at the different types and occurrences of volcanoes.
Figure 4.1: Active volcanoes in the world: The Smithsonian Global Volcanism Program. Source:
http://volcano.si.edu/world/find_regions.cfm
4.1.1
Volcano types
There are many types of volcanoes but the two main types are shield volcanoes and composite or
stratovolcanoes. They differ in their form: a shield volcano is flat and wide – hence its name; it
looks like a shield that is lying flat. A stratovolcano, however, has a cone shape. Whether a shield
or a stratovolcano will form is mainly determined by the composition of the material that is emitted
during an eruption.
Shield volcanoes (Figure 4.2): shield volcanoes are formed where eruptions produce mainly lava
flows with a basalt composition. Basalt magmas crystallize at a relatively high temperature,
contain much iron and magnesium but little sodium and potassium, have a relatively high density,
and are relatively fluid (not viscous). This latter characteristic is especially important in determining
70
Volcanoes
The Dynamic Earth
Crater
Eruption
Room
Figure 4.2: A shield volcano. Source: Grotzinger et al,
Understanding Earth (2005)
the shape of the volcano. A low viscosity means that basaltic lava flows easily, and will therefore
spread over a wide area. This results in a volcano with a relatively flat and wide shape. Basaltic
magma is formed when the upper mantle partially melts. This happens especially at divergent plate
boundaries and at so-called ‘hotspots’ (more about hotspots in the next section). Examples of
basaltic volcanism are found in Iceland (a divergent plate boundary and a hotspot) and Hawaii (a
hotspot).
Crater
Ash layers
Passages
Figure 4.3: A stratovolcano. Source: Grotzinger et al,
Understanding Earth (2005)
Stratovolcanoes (Figure 4.3): This type of
volcano is formed where the magma is
composed primarily of andesite. Andesitic
magmas contain more silicon, sodium and
potassium and less iron and magnesium.
They are more viscous, resulting in steeper
slopes on the volcano, and have a lower
density than basaltic magmas. Another
difference is that a stratovolcano is formed
from alternating layers of ash and lava (this
is why they are also called ‘composite
volcanoes’). Because of the high viscosity
and the resulting low flowing velocity,
andesitic lavas do not travel far but stay
relatively close to their source.
Stratovolcanoes are known for their
explosive
eruptions.
Different
factors
explain this explosivity. Low viscosity causes rising magma to slow down or stagnate, so that
outflow can be blocked for extended periods of time. Pressure builds up until it is finally released in
an eruption. The magma also contains a lot of gas that cannot easily escape due to its high
viscosity. If the gas remains trapped, extra high pressure develops. When it finally erupts, it can be
extremely explosive. Some stratovolcanoes are characterised by a caldera. Here the explosive
eruption was so voluminous and fast that the whole roof of the underlying magma chamber
collapsed, leaving a cauldron-shaped feature in the landscape.
Stratovolcanoes are found mainly in subduction zones (places where an oceanic plate is pushed
beneath a continental or another oceanic plate), for example in a string of locations around the
Pacific. Here, the magma is also formed in the upper part mantle, but its composition changes from
basaltic to (usually) andesitic as the magma travels to the surface. This is a process called
magmatic differentiation, and will be explained later. The differences in magmatic composition are
elaborated in section 4.2.
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Volcanoes
Exercise 4-2**: The Pinatubo eruption
A
Pinatubo erupts (source: www.nieuwsdossier.nl)
June 15, 1991 – The eruption of Pinatubo volcano in the Philippines was one of the most violent
eruptions of the 20th century. The first shocks were felt on March 15th. Seismologists placed
instruments around the volcano and were able to warn the population. The first magma erupted on
June 7th. A few days later another eruption followed, whereby ash was spewed up to great heights
(24 kilometres). Eruptions kept coming until the biggest one in June, which lasted for three hours.
The ash covered most of the Philippines and Central-Luzon island was completely obscured. The
ash travelled as far as Vietnam and Cambodia. 300 people died as a result of the eruption, and
afterward the summit of the mountain was 260 m lower than before. Because of the particles in
the stratosphere, the average global temperature decreased by 0.4 degrees Centigrade.
a.
b.
c.
d.
Is Pinatubo a shield volcano or a stratovolcano?
Was the Pinatubo eruption explosive? Illustrate your answer using data from the above source.
Why was the pressure in the magma chamber so large?
Can we expect further eruptions from Pinatubo? Explain your answer.
Hotspots: In exercise 4-1 you learned that the presence of some volcanoes is not related to plate
boundaries but to hotspots instead. These are isolated areas where slowly rising material from the
mantle (a mantle plume) reaches the Earth’s crust. Enormous amounts of basalt can be extruded
when magma from such a mantle plume pierces the crust.
A whole island can be constructed from erupted basalt, which could essentially be the upper part of
a giant shield volcano if a hotspot in the ocean has remained active for a long time. If the plate on
which the island lies moves, and because the hotspot beneath it usually stays at a fixed position, a
chain of volcanic islands will often be formed. A well-known example is the Hawaiian island chain.
When sited under land, a hotspot can push up a whole region. If the pressure caused by the
hotspot continues for a long time, a whole landmass can start breaking apart. Fault-lines will form,
and basaltic mantle-derived magma will reach the surface. Silicic magmas can also be extruded if
deeper parts of the continental crust are melting as well. Examples of such continental hotspots are
Yellowstone in the United States and Mount Cameroon in Cameroon (Africa).
Exercise 4-3**: Volcanoes and plate motion reconstructions
A, G
Look up the Midway Islands in your atlas (if you are using Google Earth or Google Maps, search for
Sand Island) and the island of Hawaii.
a. What types of volcanoes are located on these islands, and how were they formed?
The Midway Islands were formed 27.2 million years ago, and Hawaii 0 to 0.4 million years ago.
b. Use this information and your atlas to calculate the average velocity of the Pacific Plate (in
whole centimetres per year), and the direction of movement of the Pacific plate during the last
27.2 million years. Show your calculation. (You may assume the Earth to be flat for this
calculation, as it involves only a small part of the Earth’s surface).
4.2 Formation of different types of igneous rocks
The previous section described how a shield volcano consists mainly of basalt and a stratovolcano
mainly of andesite. In reality, many more types of igneous rocks can be distinguished (as you saw
in chapter 1). We will now address these differences in more detail by looking at the composition of
magma. This composition gives us important information about the relationship between volcanism
and plate tectonics.
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Volcanoes
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Igneous rocks are formed
when
liquid
magma
solidifies (see Chapter 1).
These rocks are marked by
differences in texture. For
instance, basalt is much
finer grained than granite. If
it is not possible to identify
any crystals at all, the rock
consists of volcanic glass.
The texture of the rock tells
us how fast the magma
cooled. Liquid magma needs
time to form crystals. When
the liquid starts cooling,
small crystals of one or
more minerals will form and
will grow gradually as ions
are
attached
to
the
surfaces. The longer the
cooling takes, the more of
these crystals will grow. If
magma cools very quickly,
no crystals (volcanic glass)
or only very small crystals
(e.g. in basalt) will form.
Figure 4.4: Different types of igneous rocks. Source: Grotzinger et al, Magma cools quickly when
Understanding Earth (2007)
it
reaches
the
Earth’s
surface; the result is an
extrusive rock (like basalt). Slower cooling rates result in larger crystals; this happens when the
magma stays deep in the Earth’s crust where it remains warm over a much longer period of time.
Such rocks are called ‘intrusive rocks’ (like granite).
You can obtain more information by looking at the chemical composition and mineral content of a
rock. Igneous rocks can also be classified according to their chemical composition and the type of
silicates they contain. Examples of such minerals are quartz, feldspar, muscovite, biotite,
amphibole, pyroxene, and olivine. Two types of igneous rocks can be distinguished, based on their
mineral content: mafic rocks and felsic rocks (see Figure 4.4). Basaltic magmas (section 4.1) form
mafic rocks like basalt (extrusive rock) or gabbro (intrusive rock). Examples of felsic rocks are
rhyolite (extrusive rock) and granite (intrusive rock).
Mafic rocks (ma = magnesium (Mg), f = iron (Fe)) have a relatively low silicon content but contain
relatively large amounts of magnesium and iron. These are important building blocks for pyroxenes
and olivines. These minerals have a dark colour, which is why mafic rocks are usually dark. Basalt
is the best known and most abundant mafic rock. The entire ocean floor consists of basalt. On
some continents, thick layers of basalt can be found. For example, the Deccan Traps in India and
the Siberian Traps in Russia.
Felsic rocks (fel = feldspar, si = silica) have a high silicon content and contain little iron and
magnesium. These rocks are much lighter in colour because they contain light-coloured minerals
like feldspar and quartz. Granite is a felsic rock. It is one of the most common igneous rocks found
on Earth.
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Volcanoes
Looking at texture, chemistry and mineral content, it is possible to make the following rough
classification (compare to Figure 4.4):
Mafic
Felsic
Fine-grained – extrusive
Basalt
Rhyolite
Coarse grained – intrusive
Gabbro
Granite
Andesite, the extrusive rock found in many stratovolcanoes, is not mentioned in the table. Its
composition lies somewhere between basalt and rhyolite.
There are also rocks that we call ultramafic. These contain relatively little silicon but a lot of
magnesium and iron. The most common ultramafic rock is peridotite. This coarse grained, dark
green rock is the dominant rock in the mantle, and is the source of basaltic magmas (see chapter
6). It consists mainly of olivine and pyroxene.
4.2.1
Do felsic and mafic magmas have different properties?
You may wonder why a distinction between felsic and mafic rocks is useful. There is a relationship
between the composition of a rock and its melting temperature. Mafic rocks melt at higher
temperatures, felsic rocks at lower temperatures. Mafic magmas are usually hotter and start
crystallising at higher temperatures than felsic magmas. The more silicon is added, or the lower
the temperature gets, the higher the viscosity of the magma will become. Viscosity is a measure
for how difficult it is for a liquid to flow. So, the more felsic or colder a magma is, the more
inhibited is its capacity to flow, especially when it carries abundant crystals. In contrast, a hot
mafic magma, which is low in silicon, has a low viscosity and will flow easily.
4.3 Magma formation
We know how magma is formed, but much remains still to be discovered. The processes take place
so deep inside the Earth that direct observation is impossible. Instead, they must be simulated in
lab experiments. These experiments show that the melting point of a rock not only depends on its
composition, but also on the pressure applied to it.
Rocks consist of various minerals, each with its own chemical composition, and do not usually melt
completely when heated. The minerals contribute to the melt in certain proportions that may
change when melting proceeds; thus, magma that is created by partial melting of a rock will have
a chemical composition other than the rock itself. This is the reason why basaltic magma (mafic)
can be formed from a mantle rock that was originally a peridotite (ultramafic). Depending on the
amount of melting, magmas will have different compositions, even if the source rock from which
they are formed is the same. (Of course, magma compositions can also differ simply because their
sources are different; for example, if not the mantle but the lower crust is melting).
Theoretically, there are three ways to melt a rock in the mantle:
1.
2.
3.
By increasing the temperature. Surprisingly, this is not an important cause of magma
formation and volcanism.
By lowering the pressure. This is the cause of volcanism at mid-oceanic ridges and at hotspots.
In both cases hot mantle rock rises very slowly; in the case of mid-oceanic ridges because of
the upward motion in mantle convection, and in the case of hotspots because of the rise of an
isolated mantle plume. The rock remains hot (thermal conductivity in rocks is very low), while
the pressure decreases, causing the rock to melt.
By lowering the melting temperature. This happens when water comes into contact with the
mantle rocks (just like when salt is sprinkled on roads during winter to lower the melting point
of water so that it will not freeze). It is the main explanation for the origin of subduction-zone
volcanism (discussed below).
4.3.1
The composition of first-formed magma and final igneous rock
Magmas of different composition are formed, depending on source rock and melting conditions. The
next question is: will the same magma always yield the same igneous rock? The answer is no. Lab
research shows us that different factors play a role:
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- Firstly, the crystallisation history, which will determine the texture of the rock, in particular the
sizes of the visible grains. Rising magma can accumulate in a magma chamber, for example
somewhere within the crust. Because this environment is usually colder than where the magma
came from, it will start cooling and crystals will form. Ultimately, it could crystallise completely
inside the chamber and form a coarse-grained intrusive rock such as granite or gabbro. But (part
of) the magma could also find its way further up during this process; it could rise to the surface
and solidify there after a volcanic eruption. It would then form a fine grained or even glassy
extrusive rock (for example basalt or rhyolite) that will often carry larger grains of minerals that
crystallised previously at depth.
- Secondly, magma could change chemically in the course of its ascent to the surface. This is
known as magmatic differentiation. While it resides in a magma chamber, different minerals will
crystallise if the temperature drops. If these crystals do not stay floating in the liquid but sink to
the bottom, the remaining magma will change in composition. It is “differentiated” because these
removed minerals are different in composition than the original melt in which they crystallised.
Therefore, a rock resulting from such a differentiated magma has not the same chemical
composition as the first magma that formed during melting of the deep source.
In a basaltic magma, olivine will start to crystallise first, followed by pyroxene and other minerals.
The composition of the remaining magma changes, depending upon the type of minerals formed
(provided that these do indeed sink to the bottom). Bowen’s reaction series (Figure 4.5: The
varying composition of igneous rocks is explained by fractional crystallisation. Source: Grotzinger
et al, Understanding Earth (2007)) describes the order in which minerals crystallise. It usually
holds quite well but it is no more than a general guideline. Several factors (such as the depth of
crystallisation) can affect the order of crystallisation.
Figure 4.5: The varying composition of igneous rocks is explained by fractional crystallisation.
Source: Grotzinger et al, Understanding Earth (2007)
Basalt and granite are the two most common igneous rocks. Is there a relationship between the
formation of these two rock types? We have seen that their compositions differ greatly: basalt is
mafic and granite is felsic. Long ago it was thought that all granite originates from basalt by
magmatic differentiation. As a basaltic magma crystallises, olivine and pyroxene (dark minerals,
rich in magnesium and iron) are removed from it. What remains is a magma that is rich in silicon
and poor in magnesium and iron, yielding a light coloured rock (like granite or rhyolite). The
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problem is that you would need an enormous amount of basaltic magma to account for all the
granitic rocks on Earth.
The melting of entirely different source rocks could explain the difference between basalt and
granite: when upper-mantle rocks melts partially, a basaltic magma will form. Granite can be
formed through differentiation of basaltic magma, but also directly when the lower part of the
continental crust melts. This part of the crust can consist of all kinds of sedimentary, igneous and
metamorphic rocks, and has thus a composition that is very different from an ultramafic mantle
rock.
4.3.2
Magma formation and plate tectonics
So how does magma formation fit into the framework of plate tectonics? In section 4.1 we saw
that magma is formed at two types of plate boundaries: MORs and subduction zones
At MORs (Mid-Oceanic Ridges), the source material is the upper mantle, which is mostly peridotite.
The pressure is reduced as the hot rock rises slowly, causing it to melt partially. The difference in
density between the newly formed basaltic melt and the surrounding rocks will cause the melt to
escape and rise even faster independently, until it accumulates in a magma chamber in the crust.
There, it will partially crystallise as a gabbro, but some of it will reach the ocean floor and form socalled pillow lavas. These pillow-shaped blobs of basalt with a glassy crust are created as
outpouring lava cools quickly in the seawater. Gabbros and pillow lavas are present in MORs below
all oceans. If a basaltic magma is extruded above sea level it may form a shield volcano.
At subduction zones, oceanic (basaltic) crust is subducted beneath a continental or another oceanic
plate. Not only the basaltic part of oceanic crust is subducted, but a thin layer of deep-sea
sediments on top of it may go down as well. All the subducting material is gradually brought to
depths where the temperature and pressure become higher and higher. The rocks will be
metamorphosed because minerals of which they consist are transformed into other minerals that
are better “adapted” to the conditions at greater depths. During these reactions, minerals that
carry fluids in their crystal structure break down so that the fluids (mostly water) are released. The
water is driven out of the subducting slab, moves upward and enters the mantle of the overlying
plate. The addition of water lowers the melting point of the mantle material so much that it will
melt, which usually occurs at a depth of about 100-150 km. Again, the source rock is upper-mantle
peridotite so that the initial magma has a basaltic composition also here. This usually changes
when it rises and concentrates in magma chambers, as we discussed before. The concentration of
silicon in the magma increases, so that andesitic or even felsic magmas are formed. Compositions
can also become felsic if portions of the continental crust melt because of the heat of basaltic
magma that came up from the mantle. Granite forms if such a felsic magma crystallises at depth.
If it reaches the surface, violent eruptions may occur. The increased silica content makes the
magma very viscous and gases remain trapped inside. Enormous pressures can build up, which are
released in violent eruptions.
Figure 4.6 shows a schematic overview of the relationship between plate tectonics and the different
types of volcanism. Note that hot-spot volcanism is not related to any plate boundary.
Figure 4.6: Relation between plate tectonics
Grotzinger, et al, Understanding Earth, 2007.
and
volcanism.
Source:
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Exercise 4-4**: Igneous rocks
a. Imagine you could drill a hole through the Earth’s crust at a MOR; describe the rocks that you
would find:
i
What rock would you find at the sea floor? Is it an intrusive or an extrusive rock?
ii
What rock would you find in the lower crust? Is it intrusive or extrusive?
iii
What rock would you find in the upper mantle?
Most of the oceanic crust and almost the entire upper mantle consists of mafic and ultramafic
rocks, respectively.
b. How do you explain that much felsic rock is found in the Earth’s continents?
c. Where are the building blocks of felsic rocks?
A significant amount of water is stored in seafloor sediments and in the oceanic crust near
subduction zones.
d. Explain how the role of water influences the melting process in subduction zones.
4.4 Volcanoes on Iceland
We will now take a closer look at Iceland. This special piece of land is one of the few volcanic areas
on a MOR that lie above sea level. This situation is exceptional because both a divergent plate
boundary and a hotspot are present. Icelandic volcanism also has a great influence over a wide
area. A large eruption in 1783 had a big impact in Western Europe.
Figure 4.7: Geological map of Iceland. Source: Landmaelingar Islands.
In geological terms, Iceland is very young. The oldest exposed rocks are ‘only’ about 16 million
years old. These are found at the extreme east and west sides of the island (see Figure 4.7.)
Many different types of volcanoes occur on Iceland, both shield and stratovolcanoes. The shield
volcanoes have mild slopes, as we would expect. The biggest shield volcanoes, Skjaldbreidur and
Ok, lie in the western part of the country. An example of a stratovolcano (typical for its steep
slopes) is Hvannadalshnúkur, the highest point of the island (2100 m) on the south side of the
Vatnajökull glacier. A third type of volcanic feature is the fissure or linear volcano. This is a linear
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fracture in the landscape where lava erupts along the entire length or from several vents, usually
without much explosive activity. The fissures are generally no more than several meters wide but
can be kilometres long. The black lines in Figure 4.8 show the location and orientation of some of
them.
Exercise 4-5*: Volcanoes on Iceland
a. Explain why the oldest rocks are found in the extreme south-east and the extreme north-west
of the country.
Figure 4.8: Iceland with some of its most important volcanoes. The Skjaldbreidur and
Ok volcanoes lie northwest of Geysir. Hvannadalshnúkur lies mostly hidden beneath the
ice east of the Laki (or Lakigigar) volcano (see Öræfajökull in Figure 4.7)
b.
Think of an explanation why there are fissures, and explain their orientation.
Iceland lies on a mid-oceanic ridge, the Mid Atlantic Ridge. This ridge of the seafloor stretches from
north to south in the central part of the Atlantic Ocean where the Eurasian and American plates
diverge. Here, new oceanic crust is gradually formed from the basaltic magmas that rise from the
mantle below the ridge. Iceland is a part of the ridge that lies above sea level. It grows from its
centre outward to the east and west.
Why does Iceland lie above sea level? Because a hotspot immediately below the island generates
more volcanic activity than elsewhere along the Mid Atlantic Ridge. This explains the extreme rate
of magma production on the island.
Usually, a mantle plume beneath a moving oceanic plate will create a row of islands (like in the
case of Hawaii, see exercise 4.3). However, the magma producing hotspot below Iceland lies
exactly beneath the location where the plates diverge, so that the island grows in both directions.
The location of the hotspot itself is stable. It fuels the magma chambers of many volcanic systems
on Iceland.
Exercise 4-6*: Islands on a MOR
A, I
Iceland is not the only island on a MOR above sea level.
a. Look in your atlas for five more islands that lie on a MOR.
b. What is the difference between these islands and Iceland? Can you explain this difference?
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Now that we know more about Icelandic volcanism we will take a look at one specific eruption that
had a devastating effect.
In 1783 and 1784 the Laki volcano (see Figure 4.8) erupted for eight consecutive months. This
volcano produced one of the largest lava flows in human history. At least 15 km3 of magma
erupted from a fissure in the crust. When the magma travelled to the surface, gases that were
initially dissolved in it were able to escape, because their solubility in molten rock decreases with
decreasing pressure. These gases contained highly toxic components, causing severe health
problems in the population, poisoning trees and vegetation, and killing more than 60% of the cattle
on Iceland. A widespread famine that lasted many years killed about 20% of the population.
The effects were felt not only on Iceland. A dry fog hung over the north and west of Europe for
months. The summer of 1783 was very hot, while the following winter was extremely cold in
Europe and North America. Winters continued to be unusually cold in the following years and many
harvests failed. Famine was widespread, and more people died than under normal conditions.
A large amount of volatile components were brought into the atmosphere during the eruption.
Among these, sulphur dioxide (SO2) and hydrogen chloride (HCl) are potentially harmful. If their
concentrations in the air are high, rainwater will become acid. We will discuss this further in the
next sections. First, we will introduce a simplified model of the eruption and estimate the amounts
of SO2 and HCl that were released. In §4.6 we will explain how and why volcanic acid rain is
formed, and calculate the pH of rainwater affected by such an eruption. Furthermore, we will
discuss examples of possible effects of acid rain.
4.5 The quantity of gas emitted during the Laki eruption
In order to assess the effects of the Laki eruption, we need to know how much of each gas
component was emitted. We will focus on SO2 and HCl, as these components were most harmful.
Because the quantities of released volatile compounds were not directly measured when the
eruption took place, we will have to reconstruct the data by analyzing the erupted materials that
are still there. For this Thordarson and co-workers (1996) used a simplified model, which we will
follow here. (see Figure 4.9)
Figure 4.9 shows a hypothetical magma chamber of a certain volume. The magma inside contains
the volatile elements sulphur and chlorine (from here called ‘volatiles’ in short) in certain
concentrations (vi). Here, the volatiles are completely dissolved in the liquid. When magma reaches
the surface, it cools and solidifies in two different forms: a pile of tephra (ash and rock fragments)
and a lava flow. Part of each volatile remains inside these solidified products, but most is expelled
into the atmosphere. Some of this released portion stays in the vicinity of the volcano as a local
fog. The rest is spewed high into the atmosphere, and is especially relevant in our calculations
because this gas is transported away and has a damaging impact at great distances from the
volcano.
Schematically, we assume that the sequence of events was as follows:





79
Magma rises from the magma chamber with all the dissolved volatiles present.
The beginning of the eruption is quite explosive; during this time the tephra is emplaced. It
represents part of the original amount of magma. Much gas is released in the eruption plume.
Therefore, the concentrations of volatiles in the rest of the magma that remains underground
decrease.
This ‘degassed’ magma then rises to the surface as well, but, as it contains less gas, it flows
out as a lava in a relatively calm way.
As the lava flows out, it will lose more of these still present volatiles.
Low concentrations of volatiles stay behind as a residue, both in the solidified tephra and in the
lava, because ost of the gas escaped to the atmosphere.
The Dynamic Earth
Volcanoes
Eruption column
and distant fog
mv = mtot(r) (vi - vt)
Local fog
ml+mc = mtot(l) (vt –vc)
vt
lava
crust
mr = mtot(r) vi
vi
magma
chamber
Figure 4.9: Schematic view of the emission of a volatile gas
during the Laki eruption. After Thordarson et al. (1996).
Concentrations of a volatile (S or Cl, in ppm):
vi = in melt inclusions (representing original magma in the magma chamber)
vt = in tephra
vl = in lava (during its outflow)
vc = in the solidified lava (after its emplacement)
vs = total concentration in the solidified products
Mass of a volatile, magma, lava or tephra:
mr = original mass of a volatile in the magma chamber
mv =mass of a volatile released into the atmosphere at the crater
ml = mass of a volatile released into the atmosphere during the lava outflow
mc = mass of a volatile released into the atmosphere after the lava emplacement
ms = mass of a volatile in solid eruption products
mtot(r) = total mass of magma degassed at the crater
mtot(l) = total mass of the lava
mtot(t) = total mass of the tephra
All information on the amount of gas release during the eruption can only come from the solid
eruption products that are still there: the lava and the tephra. The residual concentrations of
volatiles in these rocks can be determined in the lab, by analysing samples taken at the site of the
eruption. If we then also know the initial concentrations of volatiles in the magma chamber it is
easy to calculate how much gas was emitted in total.
‘Melt inclusions’ are small quantities of the original magma that are locked inside a crystal as a
solidified microscopic ‘droplet’. This sometimes happens when crystals grow in a magma chamber.
Because the droplets are shut off from the surrounding magma, their composition (including the
concentrations of volatile elements) will not change anymore. The crystals reach the surface with
the erupting magma, and will be present in the solid eruption products. Geologists use melt
inclusions to determine the concentrations of volatiles present in a magma before it is (completely)
degassed. Despite the small size of the ‘droplets’ (sometimes no more than a few micrometres)
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advanced analytical techniques are capable to measure the concentrations of sulphur, chlorine and
other volatiles.
Exercise 4-7*: Melt inclusions
Basaltic magma consists of many different chemical components. When a basaltic liquid of say
1300 °C cools, it will start crystallising at some point (as in section 4.2). Crystals of different
minerals will form at different temperatures. Olivine, (Mg, Fe)2SiO4, is usually the first mineral to
crystallise in a basaltic melt.
Melt inclusions representing original basaltic magma are locked into early formed crystals (like
olivine). Explain why this will not be the case for minerals that crystallise at a lower temperature
(like quartz).
You can find out more about melt inclusions in table 4.1 and 4.2.
We can calculate the amount of volatiles that entered the atmosphere from the difference between
their concentrations in the magma chamber and their concentrations in the erupted products, and
by taking the total amount of erupted magma into account. In the following exercises we will do
this for sulphur (S) and chlorine (Cl), because these two volcanic volatiles had a bad impact on the
atmosphere.
Exercise 4-8**: How would you theoretically calculate how much of a volatile element
went into the air during an eruption in the past?
Formulate an equation for the total mass of a volatile that was emitted during an eruption in the
past (mb). Only use variables that we are able to determine now, after the eruption took place. Use
Figure 4.9 as a guide.
Hint: quantity before (inside the magma chamber) – quantity after eruption (left in the products) =
quantity escaped to the atmosphere.
Exercise 4-9***: How much were the losses of volatile concentrations in the magma
during the Laki eruption?
In the above section we described how degassing proceeded as a stepwise process. Here, we will
determine the concentration losses of sulphur and chlorine for each different step.
Use the measured concentrations of these volatiles as given in table 4-1.
Complete table 4-2 by filling in the decrease in concentration of both volatiles.
Melt inclusions, vi
Tephra, vt
Lava during transport, vl
Solidified lava after emplacement, vc
All solid eruption products (lava + tephra averaged), vs
S
1675
490
350
195
205
Cl
310
225
185
150
150
Table 4-1: Average concentrations (mass ppm = mg/kg) of sulphur and chlorine in eruption
products and melt inclusions.
ΔS
Decrease
Decrease
Decrease
Decrease
ΔCl
due to total degassing (vi – vs)
due to degassing at crater (vi - vt)
in the lava during transport (vt – vl)
in the lava after transport (vl – vc)
Table 4-2: Decrease in the concentrations of sulphur and chlorine (in mass ppm) during each
different phase of the eruption.
Exercise 4-10***: How much SO2 and HCl gas was emitted?
In tables 1 and 2 the concentrations of the volatiles were given in terms of the ‘pure’ elements
sulphur and chlorine, as measured by advanced methods for chemical analysis. However, they do
not enter the atmosphere as pure elements, but usually as molecules such as SO2 and HCl. We will
now calculate the amounts of SO2 and HCl gas emitted during each phase of the eruption.
Use your answers, the data in table 4-1, table 4-2 and Figure 4.9 and the example below to
calculate the variables in table 4-3 (use Excel for this exercise).
You can calculate the mass of each gas component that was emitted only at the crater as follows:
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mv  mtot ( r ) vi  vt   Vr  v x , i  vx , t r
with Vr = total volume of erupted magma = 15.1 km3
ρ = density of the magma = 2750 kg/m3
vx,i = mass fraction of element “x” in the melt inclusion (thus in the original magma)
vx,t = mass fraction of element “x” in the tephra
r = a constant to convert the mass of the pure element into the mass of the gas molecule:
molecule mass / element mass
SO2 (kg)
HCl (kg)
Original total mass inside the magma chamber
Total mass escaped during the eruption
Mass of the remaining portion in the solid eruption products (lava + tephra)
Mass emitted during the eruption
Table 4-3: Mass of SO2 and HCl (in kg).
You can find the molar masses of the elements in BINAS (book with tables) or on the Internet
(Wikipedia).
Exercise 4-11**: Difference between the percentages of S and Cl that escaped
What are the percentages of S and Cl that escaped during the eruption? Use the data given in the
previous exercise. Try to think of a reason why there is a difference.
140
SO2
120
HCl
9
Megaton (= 10 kg)
100
80
60
40
20
0
Through
Door deLaki
Lakiactivity
activiteit
(8 jun 1783 - 7 feb 1784)
Through
all vulcano’s
Door alle vulkanen
per DoorThrough
de mens humans
wereldwijdworldwide
per year jaar
per jaarper year
Figure 4.10: Gas emissions into the atmosphere: the Laki emissions
compared to the annual emissions of all volcanoes put together and
emissions caused by human activity (in the year 2000).
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Exercise 4-12**: The Laki eruption in perspective
In Figure 4.10 the Laki eruption is compared, in terms of emitted gases, to all volcanoes on Earth
and to human activities. It is estimated that volcanoes produce about 18 x 109 kg HCl and 6 x 109
kg SO2 annually. Human activity clearly contributes more: 68 x 109 kg SO2 and 13 x 109 kg HCl.
The burning of coal, oil and other industrial sources are the main sources of SO2, and the burning
of biomass and fossil fuels for HCl.
a. Use your answers for exercise 4-10 to calculate how much bigger or smaller the SO2 and HCl
emissions from the Laki eruption were than the average total annual volcano emissions.
b. Do the same, but now compare your answers to the total emissions due to human activity.
4.6 Acid rain in Western Europe.
The eruption plume of the Laki eruption reached a height of 9-13 km. The gases that escaped from
the crater could have reached the tropopause, the boundary between the stratosphere and the
troposphere. This is where a permanent strong wind blows: the polar jet stream. This ‘jet stream’
transported much of the gas eastward.
Examine the weather maps above (Figure 4.12 and Figure 4.11 to see how the particles travelled
towards Western Europe. As they travelled in the atmosphere, the gas molecules could have
reacted with water. However, the two gas molecules behave quite differently. HCl reacts with water
immediately so that it usually rains out quickly. SO2 is converted much more slowly to H2SO4 and
can therefore travel over much greater distances. This is why it could have reached Western
Europe. From now on we will consider only SO2.
Within 50 hours of the eruption the jet stream had transported the SO2 molecules all the way to the
Netherlands. However, it would take another 1-3 weeks to see the effects: a dense, dry fog lying
over the country and a red sun. This delay can be explained by the slow transformation of SO2 into
H2SO4. The tiny droplets that were formed are called ‘aerosols’. To understand the process by
which they are formed we will examine acid rain chemistry.
Figure 4.12: Meteorological map of
Europe on 23 June 1783, including
the atmospheric pressure (thin lines)
and the jet stream directions (bold
lines). Source: Thordarson & Self,
2003
Figure 4.11: Cross section of point A to point B in figure
1-11. This figure shows the eruption column of the Laki
volcano and the resulting transportation of the column to
the European mainland. Source: Thordarson & Self, 2003
Rain is part of the water cycle. Sunlight heats the oceans and causes the water to evaporate. Wind
blows this vapour around, and water is precipitated as rain or snow. In a ‘clean’ atmosphere, fresh
water would fill lakes and rivers, and supply whole ecosystems. You would expect this water to
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have a pH of about 7. However, the pH is lower than 7 because CO2 is present in the atmosphere.
Water reacts with CO2 in the following way:
H2O + CO2

H2CO3
(pKCO2 (25°C) = 1.47)
H2CO3 + H2O

H3O+ + HCO3- (aq)
(pKz1
(25°C)
= 6.35)
+
Even though H2CO3 is a weak acid, enough H3O is formed to lower the pH of fresh water to 5,66.
Exercise 4-13***: A pH of 5,66
The concentration of CO2 in the atmosphere is denoted with the partial pressure PCO2. We will take
PCO2 = 10-3.5 atm.
Use this information to show how the pH of fresh water drops to 5.66:
a. Give the reaction equations for all equilibria and use PCO2 = [H2O][CO2].
b. Then use substitution to solve the equation. Note that pH = -log[H3O+]
Since the beginning of the Industrial Revolution (about 1850), man-made emissions of compounds
such as SOx and NOx have caused a strong increase in the acidification of rain. Rainwater that
mixes with these compounds will be lowered in pH of so that it will become acid.
But even without the Industrial Revolution, volcanoes are already a natural source of acidification,
because volcanic SO2 could create acid rain. How does this happen?
We have already seen that SO2 is emitted from magma as a gas. This SO2 reacts with various
oxidants (like ozone, O3), forming SO3. This compound then dissolves in water, producing H2SO4
(sulphuric acid):
SO2(g) + O3(g)

O2(g) + SO3(g)
SO3(g) + H2O(l)

SO3(aq)
SO3(aq) + H2O

H2SO4
Sulphuric acid can then react with water to form H3O+:
H2SO4 + H2O

H3O+ + HSO4-
HSO4- + H2O

H3O+ + SO42-
SO2 can also react directly with water droplets, forming sulphurous acid:
SO2(g) + H2O(l)

SO2(aq)
SO2(aq) + H2O

H2SO3
Exercise 4-14*: Dissociation of H2SO4
H2SO4 will dissociate in water. Write down the chemical equations describing the dissociation of
H2SO4.
Hint: in every reaction, the molecule loses a proton: H+.
i
H2SO4 + H2O  ...
In the next sections we will focus on H2SO4. Being the strongest acid involved, it has the strongest
influence on the pH. Assume that the Laki volcano emitted 122 megatonnes of SO2. Also assume
that only 5,0% of the total emission reached the Netherlands, and that this was contained by 32.6
x 1015 kg of air.
Exercise 4-15**: The concentration of SO2 in air.
What would have been the final concentration of SO2 in the air, using these data? Express your
answer in mass ppm (mass ppm = mg/kg)
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Exercise 4-16**: Does the SO2 solubility in water limit the pH of rain?
SO2 dissolves in water, but there is a limitation to its solubility, which is controlled by the
temperature. Will this limitation determine the ultimate acidity of the raindrops in which the SO2
dissolves? Figure 4.13 to answer this question.
Solubility
Oplosbaarheid SO2
25
20
Figure 4.13:
Solubility of SO2 and
water at different
temperature
oplosbaarheid[g/100m l]
S
O
L 15
U
B
I
L
10
I
T
Y
5
0
0
20
40
60
80
100
120
T T[graden
(centigrades
°)
C]
Exercise 4-17***: The pH of rainwater affected by the eruption
Assume that all the SO2 will dissolve in the water that is present in the air (9 gram H2O per kg air).
a. Calculate the concentration of SO2 in mole/L. Use the molecular mass (64 mole/g) and the SO2
concentration you found in question 14.
b. Calculate the H3O+ concentration and thus the pH of the rain water.
Use the molar mass of SO2 and the density of water (look these up on Wikipedia). Hint: use the
chemical equation of the reaction of SO2 to SO42- (aq) and assume that this reaction proceeds
completely.
4.7 The consequences of acid rain
Acid rain has many negative effects:
1.
2.
3.
4.
A lower pH of surface water is harmful to fish populations and other water animals. At a pH
< 5 fish eggs will not hatch and fish die. Biodiversity will decrease.
Trees weaken, which makes them more vulnerable to diseases and storms. Entire forests
might die in this way.
Acid rain depletes the soil in important components. H3O+ ions cause soil minerals to
dissolve in water, releasing cations (e.g. Ca2+, Al3+) that are transported away. Important
nutrients become depleted, or plants could be poisoned by overdoses of cations.
Buildings and monuments are damaged by the acid.
We will now take a closer look at how the damage to buildings and monuments happens.
Limestone and marble are examples of rocks that have been used as construction materials since
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ages. Both rocks mainly consist of the minerals calcium carbonate (CaCO3) or magnesium
carbonate (MgCO3).
Limestone is a sedimentary rock, which transforms into the metamorphic rock “marble” when put
under high pressure and temperature. The crystalline structure of these rocks is therefore different.
Limestone consists of smaller crystals and is more porous, making it lighter and easier to work
with. It is used as a standard building material. Marble, on the other hand, has larger crystals and
a low porosity, and can be polished to a great lustre. It is often preferred for monuments and
statues for obvious reasons.
Both rocks are considered to be strong and durable. Yet, in recent times they can be strongly
affected by acid rain. What happens?
Exercise 4-18*: Dissolution of (Ca,Mg)CO3
Limestone is affected by acid rain. This is due to the reaction between calcium (or magnesium)
carbonate and a solution of sulphuric acid. Describe the reactions.
Exercise 4-19*: Climate effects of acid rain?
Figure 4.15: This photo of a statue
decorating Lincoln cathedral in the
United Kingdom, was taken in 1910
Source: Humphreys, 2003
Figure 4.15: In 1984, only 74 years
later, acid rain affected the statue so
severely that it is now barely
recognisable. Source: Humphreys,
2003
“Volcanic acid rain contributes to climate change”
What do you think about this statement? Explain.
The exterior of buildings and monuments are primarily affected by acid rain. Acid rain can easily
destroy the details on a relief (see Figure 4.15 for example). The structural cohesion of buildings is
usually not influenced.
The extent of the damage is determined not only by the pH of the acid rain, but also by the amount
of water that reaches a certain surface. Areas that are protected by roofing will not be damaged
nearly as much as decorations that are out in the open. But protected areas can still be affected in
other ways. When the water evaporates, it leaves all the ions behind that were dissolved in it.
Residues containing calcium and sulphate ions will cause the formation of gypsum, CaSO4▪2H2O(s).
This mineral contains water molecules in its crystal structure. Gypsum is very soft (hardness 2 on
the Mohs scale) and forms sheet-like or needle-like crystals. It has an open structure so that it
forms porous layers. Because the mineral is soluble in water, it will wash away in places where a
lot of rain falls. In sheltered locations, however, it will accumulate. This attracts dust, carbon
particles, dry ash and other pollutants, promoted by its open crystal structure (see Figure 4.18).
Surfaces on which gypsum accumulates will turn black.
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A serious problem arises when water containing dissolved sulphate ions enters deep into the
limestone pores. All combined, these pores have a surface area that is many times that of the
outer surface area of a rock, so that any reactions will be speeded up. When the acid water enters
the pores, gypsum crystals will form inside. Because the crystals have a slightly larger volume than
the pores, they put the rock under pressure, which may crack and break. If the gypsum is later
dissolved and washed away in fresh water, a very unstable rock remains. Porosity is therefore an
Figure
4.18:
Black
tarnish on a Chicago
building
made
of
limestone
Source:
USGS, 1997
Figure 4.18: Gypsum
crust on a balustrade
in
Washington
D.C.
Source: USGS, 1997
Figure 4.18: Electron
microscopy
photograph of gypsum
crystals with visible
dirt particles ‘trapped’
in the open structure.
Source: USGS, 1997
important factor affecting the durability and strength of a building material.
Exercise 4-20**: Negative effects of acid rain on buildings
Consider the scenario that a large volcanic eruption produces acid rain that falls on the Dam
Monument in Amsterdam and on the Dom tower in Utrecht (both in The Netherlands). Which of the
two will be affected most by such an event?
Hint: use the following websites(in Dutch):
http://www.nitg.tno.nl/ned/products/stenen%20rond%20de%20dom%208%20pag.pdf
http://www.monumentenonderhoud.nl/projecten/dam2.html
Exercise 4-21*: How does the pH change during the reaction?
You have seen that calcium carbonate reacts with H2SO4. What happens to the pH, and why?
Exercise 4-22***: How much CO2 is emitted?
Assume that the pH of the acid rain formed during the eruption is 3.19 and that all of the H2SO4 is
consumed during a reaction with calcium carbonate.
Use -log[H3O+] = pH, and use the chemical equation.
a. How much CaCO3 is dissolved per litre of rainwater?
Assume that the molar mass of CaCO3 is 100.09 g/mol.
We have seen that CO2 is released during the reaction between acid rain and limestone.
b. How much CO2 is released during the reaction (per litre of rain water)? Assume the molar mass
of CO2= 44.01 g/mole
Exercise 4-23***: Dissolving the Dam Monument
The Dam Monument in Amsterdam is 22m high. Imagine the simplified form of a cylinder with a
diameter of 4.5m. Now calculate how much acid rain would be needed to completely dissolve the
Dam Monument:
a. What is the total mass of the monument? Take the density or the rock as 2.93 g/cm3 is. Hint:
What is the volume of the cylinder?
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b.
Volcanoes
What is the volume of the rain water that would be needed to completely dissolve the
monument? Use your answer from exercise 21a.
Final assignment CH4. Main and section questions
a. Answer each of the seven section questions as well as the main questions asked at the
beginning of this chapter.
b. Did this chapter inspire you to thing about new questions? Write these down.
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Attachment 4-1
The Dynamic Earth
Melt inclusions
Many people believe that the solid crust of the Earth floats on a ‘sea’ of burning magma. This is
incorrect. Magma is formed only in specific locations; the rest of the mantle is solid rock. Rock
starts melting when conditions change, for example when temperature increases or pressure
decreases. Generally this happens in the upper part of the mantle.
The molten rock rises because its density is lower than the surrounding solid rock. Usually the melt
will accumulate in a magma chamber before it rises further to the surface during an eruption. If the
magma starts cooling in a magma chamber, crystals of one or more mineral types will grow. In the
1920s, Norman L. Bowen discovered that these minerals crystallise in a certain order. In a basaltic
magma, olivine will usually crystallise first (see section 4.2).
If a crystal grows fast enough, tiny droplets of the melt can be locked inside. A small volume like
this is called a ‘melt inclusion’ (see Figure 4.19). The moment the inclusions are ‘trapped’, they are
protected from contact with the surrounding magma that usually will change its composition. In
Figure 4.19: Photo B: Different elongate melt inclusions, most without gas bubbles. The photo is
about 700µm wide. Photo C: crystallised melt inclusion in quartz. Photo E: three glassy melt
inclusions of various sizes, each without bubbles. Source: Lowenstern, 2003.
this way, a melt inclusion records the original composition of a magma.
Melt inclusions are incredibly small, with a diameter of only 1-300 µm (µ = 10-6), and therefore
difficult to study. Advanced methods to analyze them have been developed (such as the electron
microprobe or ion microprobe). Using these, much information can be gathered from the melt
inclusions. For instance:
The original composition of the magma can be determined because the inclusions are locked in
during the growth of crystals in the magma chamber. For example, it will tell us in what
concentrations volatile elements were present in the magma before it arrived at the surface. This is
important information. As you have seen, geologists use these data to calculate the amounts of gas
that were emitted during historic eruptions.
Melt inclusions also provide information about the pressure and temperature conditions under
which magmas crystallise. They tell us more about the history of a magma.
If the inclusions themselves are cooled slowly, they may crystallise as well. Figure 4.20 shows what
happens, depending on the cooling rate.
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Figure 4.20: schematic illustration of four melt inclusions that
cooled at different rates. A: At high cooling rates, no crystals
and no gas bubbles will form and the inclusions solidifies to a
glass. B: gas bubbles may form when the cooling rate is slightly
lower. C: when the inclusion cools slowly, gas bubbles can
grow through diffusion and crystals can start forming. D: the
inclusion may crystallise completely if it is allowed to cool very
slowly. Source: Lowenstern (2003)
A melt inclusion consisting of glass with a gas bubble gives us information about the depth at which
the crystal started forming, while crystallised melt inclusions tell us more about the speed of
eruption and/or about the cooling rate.
Sources:
Lowenstern, J.B. USGS Melt Inclusion Page. August 2003. 1 December 2006.
http://volcanoes.usgs.gov/staff/jlowenstern/Melt%20Inc%20Page/melt_inclusion_page.html
Marshak, S. Earth: Portrait of a Planet. New York: W.W. Norton & Company, 2001. pp. 137-147.
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Attachment 4-2
The Dynamic Earth
The Earth’s atmosphere
The Earth is covered with a layer of air
which we call the atmosphere. It stretches
up to 700 km above the Earth’s surface. In
the past it was mainly studied for relating
it to the weather and weather patterns.
Today,
the
use
of
modern
space
instruments enables us to gain a much
more profound understanding of how the
atmosphere functions.
The atmosphere is of vital importance to
life on Earth. It contains oxygen, necessary
for organisms to breathe. It protects us
against the Sun’s ultraviolet radiation and
against (small) meteorites. It maintains
the Earth’s surface temperature, keeping it
warm enough for life. A constant water
cycle (water to vapour to rain, and back to
surface water) is kept in place by the
displacement of air in the troposphere. This
hydrological cycle is a crucial component to
sustain life.
The atmosphere can be divided into
various layers (see Figure 4.21). They are
identified according to their thermal
properties (differences in temperature),
chemical composition and density (see
BINAS or other book with tables).
Troposphere
Figure
4.21:
Schematic
picture
of
the
subdivision of the atmosphere into various
layers. The red line depicts the temperature
distribution.
The troposphere is the layer closest to the
surface and the one in which we live. It is
between 8 and 17 km thick. It has the
highest density and contains 75% of the gases present in the atmosphere. It is warmest near the
ground and cools quickly towards the tropopause, its upper boundary. The temperature drops from
17 oC at the Earth’s surface to about -60 oC at an altitude of 15 km. This causes great instability
inside the layer. Hot air is relatively light and will rise, whereas cold air is dense and will sink.
Consequently, our weather is mostly created within the troposphere.
Stratosphere
The stratosphere is bounded by the tropopause beneath it and the stratopause, which lies at 50 km
above the Earth’s surface, above it. Travelling upward through the stratosphere, the temperature
increases from -60 to about 10 oC near the stratopause.
The stratosphere contains 19% of all the atmosphere’s gases and very little water vapour.
Movements within the stratosphere are very calm compared to those in the troposphere, and
mostly occur in a horizontal direction. This explains the layered structure of high stratus clouds.
The Ozone Layer is also situated in the stratosphere. Ozone blocks UV radiation by absorbing it.
Mesosphere
Next is the mesosphere, 50 to 80 km above the Earth’s surface. The air here is too thin to absorb
any solar radiation, so the temperature drops here to -120 oC, the lowest value in the atmosphere.
Nevertheless, it is thick enough to slow or even burn meteorites that enter the atmosphere. A
glowing meteorite is the “falling star” that we see in the sky at night.
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Thermosphere
The temperature starts to rise again in the next layer, called the thermosphere. Heat transport
through conduction is important here. The air is even thinner than in the mesosphere, but it still
absorbs UV radiation from the sun. Temperatures in the upper part of this layer (700 km) can be
as high as 2000 oC.
Ionosphere:
The Ionosphere is part of the thermosphere but is also distinct layer in itself. It consists of ionised
gas particles produced by the UV light. This layer is important because it reflects radio signals that
are emitted from the Earth back to the surface. This is why radio signals can be received in all
parts of the world.
Exosphere:
This is the outermost layer of the atmosphere and lies between 700 and 800 km above the Earth’s
surface. The air is so thin that it gradually disappears into space as you go upward. Most of this
part of the atmosphere is made up of hydrogen and helium (but concentrations are extremely low).
The atmosphere’s composition
The atmosphere consists mainly of nitrogen (N2, 78%), oxygen (O2, 21%), and argon (Ar, 1%).
Other important constituents are water (H2O, 0-7%), ozone (O3, 0-0.01%), and carbon dioxide
(CO2, 0.01-0.1%).
Sources:
ThinkQuest. SpaceShip Earth. , http://mediatheek.thinkquest.nl/~ll125/nl/home_nl.htm>
NASA. Liftoff to Space Exploration. http://liftoff.msfc.nasa.gov/
Encyclopædia Britannica 2005 Ultimate Reference Suite DVD. Atmosphere. Copyright © 1994-2003.
Encyclopædia Britannica, Inc. November 26, 2006.
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Attachment 4-3
The Dynamic Earth
Aerosols
Aerosols are tiny particles floating in the air. Some have a natural origin, coming from volcanic
eruptions, dust storms (e.g. the Sahara sand that sometimes reaches Northern Europe), forest
fires, vegetation or sea salt. Human activity, such as the burning of fossil fuels and changing
natural landscapes, is another important source (Figure 4.22).
Aerosols can be divided into five categories according to their particle size and composition: dust,
soot, sulphate, sea salt (also called marine aerosol) and organic aerosol. Dust and sea salt are
generally larger than 1 µm; soot, sulphate and organic aerosols are usually smaller than 1 µm.
Ten percent of the total amount of aerosols in the atmosphere is produced by human activity. Most
of this is concentrated on the Northern Hemisphere, especially near industrial zones, in areas
where farm land is created by forest burning, and in overgrazed pasture land.
We do not know exactly how aerosols influence the climate, nor do we have a good estimate of the
Figure 4.22: Aerosols larger
than
1
micrometer
are
produced by sea salt and dust
which are transported by the
wind. Smaller aerosols are
formed
by
processes
of
condensation like the reaction
of SO2 to sulphate particles, and
also when soot and smoke are
formed in a fire. After they are
formed, aerosols are mixed and
transported
through
the
atmosphere.
The
most
important process that removes
aerosols is precipitation: rain,
snow or hail. Source: NASA
relative contributions of natural and human aerosols. Specifically, little is understood about the
general effect of aerosols: do they actually cool or heat the planet up?
So why are we concerned about aerosols?
Measuring their concentrations is important for two reasons. Firstly, aerosols cause smog (= smoke
and fog) that can lead to respiration problems (see Figure 4.22). This is evident in big cities where
the large use of fossil fuels produces many aerosols.
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Figure 4.23:
KNMI
Volcanoes
Smog above Mexico City. Source:
Secondly, aerosols play a role in the Greenhouse effect. Depending in the type, they can have a
cooling or a warming effect on the thermal balance of the Earth. Just like greenhouse gases, they
can absorb the infrared radiation that the Earth produces.
Cooling can be a direct or an indirect effect.
Directly: aerosols reflect solar radiation and consequently decrease the amount of sunlight that
Figure 4.25a: Clouds with a low aerosol
concentration and few droplets reflect the
light only poorly: most of the sunlight will
reach the Earth’s surface. Source: NASA
Figure 4.25b: In the case of a high aerosol
concentration, there are many nucleation sites
for rain drops. Up to 90% of the visible
spectrum can be reflected. Source: NASA
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reaches the Earth’s surface (see Figure 4.25 Figure 4.25b). The magnitude of this effect depends
on the size and reflectivity of the aerosols.
Indirectly: aerosols change the properties of clouds. Without aerosols, we would not have any
clouds at all. It is extremely difficult to form clouds without small aerosols that act as nuclei for the
formation of droplets. More aerosols mean more clouds. Because the total amount of condensed
water inside a cloud does not change very much, the droplets will be smaller on average. This has
two effects: clouds with smaller droplets reflect more sunlight (see Figure 4.25b) and these clouds
remain longer in the atmosphere because it takes more time for the droplets to grow large enough
to fall as rain. Both effects increase the reflection of sunlight back into space.
Under normal circumstances, the majority of aerosols form a thin fog in the low atmosphere. They
will rain out within a week. But aerosols are also found in the stratosphere (see Figure 4.26). For
example, a volcano can spew large amounts of aerosols into the atmosphere. Because it does not
rain in the stratosphere, aerosols can remain there for years. The effects are not only beautiful
sunsets, but also cooler temperatures, especially in the summer.
Figure 4.26: A volcano spewing aerosols. Source: NASA.
In the past thirty years much has been discovered about aerosols. Scientists can distinguish
different types, and can estimate the amounts that are present for each season and locality. But
much remains to be explored. Essential details about quantities and properties are missing, so that
it is not possible yet to accurately determine the effect of aerosols on temperature at the Earth’s
surface on a global scale.
Based on:
NASA Earth Observatory. Aerosols and Climate Change.
<http://earthobservatory.nasa.gov/Library/Aerosols/>
KNMI. Aërosolen. <http://www.knmi.nl/globe/informatie/aerosol.html>
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Chapter 5.
Mountain building
Mountain building
The main question for this optional chapter is:
How are mountains formed and how do rocks behave in this process?
We will answer this main question by addressing the following section questions:






What
What
What
What
What
What
is the relation between the process of mountain building and plate tectonics? (5.1)
do rocks tell us about the way mountains are formed? (5.2)
is the relation between force, stress and deformation? (5.3)
happens when deformation takes place quickly (brittle behaviour)? (5.4)
happens when deformation takes place slowly? (ductile behaviour) (5.5)
does this tell us about the way mountains are formed and about plate tectonics? (5.6)
Objective: To be able to understand and describe the (small scale) processes that are important for
the formation of mountains, and to discover how these processes work. For this you need some
knowledge from mathematics, physics and chemistry.
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5.1
The Dynamic Earth
The relation between mountain formation and plate tectonics
Mountains are found only in certain places. Well-known examples of mountain ranges are the Alps,
the Himalayas and the Rockies. But mountains play an important role for the geography
everywhere in the world. Soils all over the world originate as rocks and particles eroded from
mountain slopes, and without this erosion and transport, many areas in the world would lie below
sea level. To complete the cycle, current basins could form the source material for future mountain
ranges which are yet to form. To determine how this exactly works, we will first take a look at how
mountains are formed and how this relates to plate tectonics.
In this section, we will discuss the relation between mountains and plate tectonics. Next, we will
see what kind of information we can obtain from rocks and what they tell us about the processes
that are important for mountain formation.
Exercise 5-1*: Mountains and plate tectonics
A, I
When plates of the same type collide, a contact is formed between two plates of the same weight.
The clearest example is India, which was once connected to the South Pole. After migrating to the
north, it connected to Asia. Everything that once lay between the two continents is now heavily
deformed and folded, and currently makes up the Himalayas, the highest mountain range in the
world. Proof for this theory is, amongst others, the presence of fossil sea shells that are found in
the rocks.
a. Why will you find no news in the papers about the event described in the above text?
b. Draw the mountain range which is described in the text on your empty world map. Also draw
the Alps, the Ardennes, the Andes, the Rocky Mountains and the Ethiopian Highlands, and any
other mountain range you might have been to.
c. Surf to www.earthweek.com to see whether any earthquakes or volcano eruptions have
occurred anywhere near these mountain ranges.
d. What do you conclude? Is there a relationship between mountain ranges, volcanoes and
earthquakes?
e. Now take a look at GB 192B. What do you notice about the locations of the Himalayas and the
Andes compared to the type of plate boundaries that are indicated on the map?
To form a mountain range some source material must be present. Delta areas such as The
Netherlands or the Po basin could be the start of a new mountain range, because a lot of sediment
is present (and is still being deposited) in these regions. This deposition or accumulation of large
amounts of sediments generally takes place in coastal areas where rivers carry a lot of new
material to the sea. The basin (in the ideal case one which subsides slowly) supplies the rivers with
space for deposition. As you can see, basically two things are necessary: firstly, the supply of a lot
of sediment and secondly, room for the sediment to be deposited: usually some basin. This is step
one in the process of building a mountain range.
Earth Scientists call the process of mountain building orogenesis. It takes place at convergent plate
boundaries, and a distinction between two types of orogenesis can be made:
(1) Orogenesis as a result of convergence of an oceanic and a continental plate: in this
case, orogenesis takes place inside the continental plate - the oceanic plate only subducts. An
example of such an orogenic belt is the Andes. Sedimentary, volcanic and other (magmatic) rocks
are pressed together as a result of the compressional force of the subducting plate pushing against
the continental plate. This results in the formation of faults and folds, and part of the rock is
pushed up. In this case, the processes of accumulation and orogenesis take place simultaneously:
the material is pushed together and up because of the compressional forces which are caused by
the orogenesis.
(2) Orogenesis as a result of convergence of two continental plates: in this case, the rocks
of both plates are deformed. Both plates have the same weight and neither subducts, so that there
is no way out but up. An example of such an orogenic belt is the Himalayas, formed when the
continent India collided against the Eurasian plate. In fact, this process is still happening today.
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Mountain building
Oceanic plate
Continental Plate
Crust
lithosphere
asthenosphere
Figure 5-1: Mountain building by convergence of the Oceanic and continental
plate. On the continental plate, both vulcanism and mountain building can be
noticed.http://plaattektoniek.htmlplanet.com/plaattektoniek/botsingzones.h
tm
(Convergence of two oceanic plates will always result in subduction: it never happens that both
plates have exactly the same weight. This is because one of the plates is always older and
therefore heavier than the other. The older an oceanic plate gets, the more it cools and the higher
its density becomes. The older plate of the two will therefore always subduct beneath the younger
one.
Orogenic belts are formed through uplift. However, as soon as relief is formed, the process of
erosion begins. In the case of strong uplift (like in the Himalayas), the mountains will become
higher and higher because the uplift outweighs the erosion. As soon as the erosion starts
compensating for the uplift, the mountains stop growing.
So mountains are formed when plates converge. However, if the convergent motion stops, this
doesn’t mean that vertical motion stops as well. This vertical motion continues until isostasy is
reached: the gravitational equilibrium between the Earth’s hard crust and the underlying mantle
material which deforms much more easily.
You can visualise isostasy by thinking of the crust ‘floating’ on the mantle (see chapter 6 for a
more elaborate discussion). When the crust becomes heavier, as is the case when mountains are
built, it must sink in order to compensate for this extra weight. Think of a boat lying deeper in the
water when it is filled with cargo.
This is how it works: equilibrium is achieved when the mass of the crust lying on the mantle is
equal to the mass of the mantle material which is displaced. In other words, if an amount of crust
material of mass A is added to the crust, an amount of mantle material of the same mass A must
be displaced.
Think of the following simplified situation:
A 2 cm thick piece of wood floats in a bucket of water. About 1 cm of the wood is submerged in the
water. Think of the water as the mantle material and of the wood as the crust. Now suppose you
take a piece of the same type of wood, but this one is 4 cm thick. As you may have guessed, it
sinks deeper in the water, so that 2 cm will be beneath the surface: half of its height just like for
the other piece of wood.
Exactly the same is happening inside the Earth, only on a bigger scale.
The crust will move vertically until it is in isostatic equilibrium with the mantle. If the crust
becomes heavier, it will sink deeper into the mantle to achieve equilibrium. As a result, mountain
ranges have a so-called mountain belt root (see Figure 5.1).
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The Dynamic Earth
Figure 5.1: Scheme of a mountain root. Source: Earth Science, Tarbuck
and Lutgens, p. 158.
As long as the plate motion is quick enough, as is the case in the Himalayas, no isostatic
equilibrium will be reached. This is because the mantle may be plastic, but only on a very long
timescale. It cannot move rapidly to compensate for the new extra mass, so the Himalayas are so
high only because of the rapid convergence of the Indian plate towards the Eurasian plate. As long
as India keeps pushing, no isostatic equilibrium will be reached. When the orogenesis stops,
however, the system is bound to reach equilibrium at some point.
But even when the root has sunk deep enough to compensate for the overload, vertical motion
won’t stop. Erosion at the Earth’s surface causes the overload to decrease, so that the isostatic
equilibrium is disrupted and the root will move up again. New relief is formed in this way, causing
erosion, and more upward motion. In this way, rocks that originally lay kilometres beneath the
Earth’s crust can reach the surface. Mantle material will flow back to where the root lay before.
Vertical motion will continue to take place until all of the mountain range has been eroded.
Exercise 5-2**: Motion around the Netherlands
A
a. Look up in your atlas where the Ardennes are located and when they have been formed.
b. What convergent plate motion caused the Ardennes to form?
During the Permian geological period, all continents were connected and formed one
supercontinent called Pangaea (see GB 193). In the past, various cycles have taken place in which
continents were formed and drifted apart consecutively. At least two other supercontinents have
been discovered dating from before Pangaea. Such a cycle is called a Wilson Cycle.
c. Since the Archaean (2500 million years ago), at least four Wilson Cycles have been
distinguished. You can calculate the average duration of such a cycle. Given this information,
when would the next supercontinent be formed?
d. Take a look at GB 76. Explain how you think Western Europe will be positioned in the future
relative to Eastern Europe. Do you think mountains will be formed in this process?
5.2 Information about orogenesis: hidden in rocks
To understand how orogenesis takes place we can’t just wait until it happens somewhere: it takes
place over timescales which are far too long for human life. We have to retrieve as much
information as possible from rocks that we find in mountains which are already there. These tell us
about how they were formed and how the mechanisms work that take – or took – place at great
depths. Deep inside the Earth, where temperature and pressure are much higher than at the
surface, materials behave in a completely different way. Rocks can be deformed in many different
ways: fast or slow, under high pressure and temperature or not so much, in the presence of water
or not. All these factors influence the rocks, and many different structures can arise because of
them. This is why geologists go into the field to study the rocks and take samples. In places where
rocks surface that once lay deep beneath the Earth’s surface, much can be learned about their
behaviour deep inside the Earth’s crust. This way we can learn about how mountains are formed
and deformed.
Apart from just studying rocks from and in the field, experiments are carried out to investigate how
a material behaves under different circumstances. This knowledge not only helps us to understand
the processes resulting in the deformed rocks we see in the field, but also has important industrial
and social applications where materials play a role.
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Opdracht 5-3*: Looking at rocks
We will start looking at rocks. Look at the photos on the next few pages and try to answer the
following questions for each of them. Fill in the form you find after Figure 5.5.
a. What kind of structure do you see?
b. What kind of process caused this structure?
Answer the following questions for all the photos together:
c. Can you group the different examples of structures and processes? Explain your classification.
d. When you have divided them in groups, you can see that there are (roughly) two types of
deformational behaviour. What types of behaviour?
Figure 5.2: Rocks
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Figure 5.3: In the field left: Playa Marsella, Nicaragua, right; Lubrín, South Spain.
Picture’s: Geerke Floor
Figure 5.4: In the city. Left: Facade of a building at the Oude Gracht in Utrecht, the Netherlands.
Right: Iglesia de San Jeronimo, a church in Masaya, Nicaragua
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Figure 5.5: Upper picture: Cilindric samples of marble in an experiment: the two samples on the
right are pressed in vertical position within a laboratory. Picture from ‘Structural Geology’,
Twiss & Moores, 1992
Lower picture: Imitation of mountain building by Henry Moubry Cadell, 1887
http://earth.leeds.ac.uk/assyntgeology/cadell/mountains-gallery/image00.htm
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Observation sheet opdracht 5-3.
Visible structures
What process could have caused this
structure to form?
Figure 5.2 Stones
Top photo:
Bottom photo:
Figure 5.3. In the field
left photo:
right photo:
Figure 5.4 In the city
Left photo:
Right photo:
Figure 5.5 In an experiment
Top photo:
Bottom photo:
In sections 5.4 and 5.5 we will take a closer look at the processes causing the most important
types of deformational behaviour (the answer to opdracht 5-3). First we will take a closer look at
how deformation is influenced by force and stress.
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The relation between force, stress and deformation.
Force and stress are important quantities to describe deformation. Force is a quantity that is used
for many problems in physics. It describes how an object is pushed or pulled – its unit is the
Newton (N). Apart from that, we have pressure and stress. In the Earth Sciences, the term
pressure is only used in the case of all-sided pressure: a pressure which has the same magnitude
in all directions. Think of swimming under water: you feel the same pressure from all sides. This
pressure can be calculated with pw = ρgh. Here, pw is the pressure in the water (called hydrostatic
pressure), h is the height of the water column above you, ρ is the density of the water and g is the
gravity acceleration. (see Figure 5.6).
pw =
Figure 5.6: The pressure on a subject in the water
Stress is a term used in the Earth and Material Sciences to denote the force per unit surface (N/m2
or Pa, pascal) – just like pressure, however, there may be differences in stress in, e.g., the
horizontal and vertical directions. Two examples can illustrate the significance of stress:
1.
2.
You can imagine that a person on high heels has a higher risk of damaging the parquet
floor on which she’s walking than the same person on sneakers. This is because the stress
on the floor is higher in the first case: the force of her weight is concentrated on a smaller
surface.
See Figure 5.7
An object (in our case: a piece of rock) on which different stresses are exerted in the different
directions will tend to deform. Stresses inside the Earth are much greater than 1 Pa, so we usually
use Megapascal (MPa: 1*106 Pa) or even Gigapascal (GPa: 1*109 Pa). As a reference: even the air
pressure at the Earth’s surface is already 1*105 Pa, or 0.1 MPa.
Figure 5.7: The power is the same, only the force (force vs surface) is different.
A: a dinosaur can balance on a pilar with a cross cut of surface A1.
B: The same dinosaur falls down if it stands on the pilar, where the foot has a smaller
surface. A2.
Source: ‘Structural geology’, Twiss & Moores, 1992
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5.3.1
Stress and Mohr diagrams
We have seen that stress is defined as
the force on a surface. For a given force,
it depends on the orientation of the plane
what the exact stress on the surface is.
So if you take a small block of rock you
can imagine that the force which is
exerted on it causes a different stress on
each of its sides. When rotating the
block, you will find that there is always
one direction in which the stress is
highest – this is called the maximum
(area of ∆ a1a2a3)
principal stress, denoted with 1. The
direction in which the stress is lowest is
called the minimum principal stress, or
3. These directions can be proven to be
perpendicular to each other (try the
mathematical proof yourself if you like!).
As the world is three-dimensional, you
can imagine there to be a third direction:
the intermediate principal stress. This
stress, denoted with
to both
2, is perpendicular
1 and 3 (see Figure 5.8). We
always define 3  2  1. In Figure 5.8
the principal stresses are given on the
axes of the coordinate system.
5.3.2
Figure 5.8: Three components of
stress on a surface
Stress on any plane
If you know the three principal stresses and their directions, you can calculate the stress on any
other plane you want. Triangle a1a2a3. with area A, is marked gray in Figure 5.8. The orientation of
the triangle is denoted by its normal vector: a vector perpendicular to the surface starting in the
origin O. The normal touches the surface of the triangle in point h and makes an angle
3 with
the
surface of σ1 and σ2. The angles 1 and 2 are defined in the same manner – they have been
omitted in the figure for clarity. We don’t need to know the magnitude of all three angles: only two
2
2
2
are necessary to calculate the third because it is known that (sin 1) + (sin 2) + (sin 3) = 1.
(You can prove this by expressing the distance between h and the surface of σ1 and σ2 in Oh and
sin3. If you do that for all three directions and if you think of Pythagoras’ theorem in three
dimensions, you’re almost there.)
We want to determine the stress on triangle a1a2a3. The stress on a plane can be expressed as a
vector with components in the three principal directions. The value of each component can be
determined in the following way: we need to know what the ‘effect’ of triangle a1a2a3 is in that
direction. If you look at the triangle from the direction of σ3, for example, the triangle you see has
the size of triangle Oa1a2. Look at the figure and try to visualise this.
Exercise 5-4**: Stress on triangle a1a2a3
a.
b.
Angle 3 is also present at point a3. Draw this in the figure.
Hint: draw the large triangle O e3 a3 and draw the small one (Oe3h) in it.
Now show that Oe3 = sin 3  a3e3 and therefore that surface(a1a2O) = sin
3  A.
Now that we know how to calculate the component of the stress on the surface in the direction of
σ3, we can fill in the whole stress vector. Stress is defined as force per unit area, so the component
in the stress vector is 3 sin 3 (to see this: you just found that the area in the direction of 3
was A sin 3 so you multiply this by the stress in this direction - 3 – and divide it by the area of
the whole triangle – A). You can calculate the components in the other two directions in the same
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way. The whole stress vector, written in standard vector notation (x component, y component, z
component), in the direction of triangle a1a2a3 becomes:
(
1 sin 1, 2 sin 2, 3 sin 3)
5.3.3
Normal stress and shear stress
The stress on a plane depends on the principal stresses (1, 2, 3) and on the orientation of the
surface (given by its normal). It is seldom the case that the stress is exactly perpendicular to the
plane. For each stress vector, we can however determine to what extent it is perpendicular to the
plane, and to what extent it is parallel. For a given plane, we can decompose the stress vector in
exactly those components: the normal stress perpendicular to the plane and the shear stress
parallel to it (see Figure 5.9).
Figure 5.9: Deformation as a result of different types of stress.
Exercise 5-5**: Shear stress
Prove the following: If triangle a1a2a3 is parallel to one of the principal stresses, it follows that the
shear stress on a1a2a3 is zero.
Using some heavier mathematical techniques (a branch of mathematics called Linear Algebra) we
can express the stress components in terms of σ and θ. This is rather cumbersome, so we will just
discuss the two-dimensional case, where only σ1 and σ2 are involved. In reality, such a
simplification proves to be very useful.
(Lenght of a1a2)
Figure 5.10: Two-dimensional view of Figure 5.8
5.3.4
The 2D case
Consider the following two-dimensional figure (Figure 5.10).
In Figure 5.10 line A is the 2D section of a 3D surface like we used in Figure 5.10: Two-dimensional
view of . Because this is a 2D case, we only need one angle θ. Here, it is the angle between the
normal vector on line A and the direction of σ1. The stress on A is indicated by the vector σA,
decomposed into τ and σn.
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Exercise 5-6**: Stress vectors
a.
Show for the 2D case that
A
=(
1 cos  , 2 sin ).
Use vector notation: (x component, y
1 cos ,
decompose A in an
component). In other words, prove that the x component is equal to
and the y
x and a y
component equal to 2 sin  This means that you have to
component. Hint: remember that stress vector = force vector / area. And the force vector is
force: length. After that you can substitute using the trigonometric functions: cos
 = ...
How can you be sure that the 1 component of vector σA is smaller than the σ2 component?
(the quantities of both components are not given numerically, but you can see that θ in the
b.
figure is clearly smaller than 45
In the optional exercise 5.1 (see end of this chapter) you can derive yourself how τ and σn are
derived from σ1, σ2 and θ. This derivation results in the following equations:
 1   2   1 -  2 

 cos(2)
 2   2 
n  
  2 
  1
 sin(2)
 2 
where Θ is the angle between the normal stress (perpendicular to the plane) and the direction of
σ1.
5.3.5
Mohr’s circle
These equations look very complicated and difficult to work with. That is why the German civil
engineer Christian Otto Mohr devised a method to visualise stress situations in a material.
To see how this works, think of a circle of radius r. You may know that the coordinates in every
point on a circle are defined by x = r cos (α) and y = r sin (α). (Check this!)
If we move the whole circle in the positive x direction by a distance p, the y value for every point in
the circle stays the same, but every x coordinate changes by an amount p, resulting in:
x = p + r cos (α) and y = r sin (α), see Figure 5.11 (right hand).
y
y
(r cos α, r sin α )
r
X
p
r
x
α
Figure 5.11: Coordinates in a circle.
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Now compare the equations for a circle to the equations we have for the normal and shear stress:
circle
stresses
X coordinate
p + r cos (α)
Y coordinate
r sin (α)
If p is equal to
1   2
2
, r to
1   2
2
and α = 2θ then the equations are actually the same! This
means that we have to take σn for the x coordinate and τ for the y coordinate, and if we fill
everything in, we end up with the following Figure 5.12: The Mohr circle cirkel.) – we call this
Mohr’s Circle:
If you know the principal stresses σ1 and σ2 in a situation, you can draw the Mohr diagram by
r
p
2
θ
Figure
5.12:
The
Mohr
putting them on the σn-axis and drawing a circle through both of them, with its centre exactly in
between the maximum and minimum principal stress. Using this diagram, you can very easily
determine the normal and shear stress for any plane. You just need to known the angle between
the plane and the principal stresses. So the only thing you have to do is determine the angle and
just read the stress values from the circle.
You have to be aware of a few pitfalls here: the angle that you measure in the diagram is twice as
large as θ, so be certain to always fill in 2θ! Also remember that this diagram is only valid for the
two-dimensional case!
The meaning of σ1 , σ2 and σ3.
In most of the exercises we will just consider the maximum and minimum principal stresses in two
dimensions. In exercise 5.13, however, we will consider a three dimensional situation using σ1, σ2,
and σ3: the maximum, intermediate and minimum principal stress. Think of a very small
block/cube which is oriented in exactly such a way that no shear stress is exerted on any of its
sides. (see Figure 5.13).
In the Earth, nearly always one of the principal stresses is vertical. The vertical principal stress on
a piece of rock can be determined easily from the weight of the ‘pile’ of rocks lying on top of it. As
the block cannot just ‘escape’ to the sides, the stress in the horizontal won’t differ a lot to the
vertical principal stress. This is called the “confining pressure”, which you can compare to the
pressure you feel from all sides when swimming under water. In the case that σ1 = σ2 = σ3, a rock
will only change in volume, not in shape.
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In many cases however, the principal stresses are not completely the same. The Earth’s crust is
subjected to all kinds of forces (related to plate tectonics) and as a result, the principal stresses will
always differ slightly in magnitude. The difference in magnitude between the maximum and
minimum principal stresses, σ1 – σ3 , determines whether a rock will deform or not.
Figure 5.13: Pressure on a cube of rocks (source: The Earth – An Introduction to Physical
Geology, E.J. Tarbuck & F.K. Lutgens, Macmillan Publishing)
The vertical principal stress (in this case σ1) can be calculated using σ1 = ρ g h (see section 5.3)
where
ρ = density of the overlying rock
h = depth of the rock
g = gravity acceleration
You are now ready to do Optional Exercise 5-2 (CO2 storage and earthquakes) at the end
of this chapter.
In this section you have learned about stress and how to work with it. We’ve discussed the
principal stresses, normal and shear stress, the Mohr diagram and stress in the Earth. To conclude
this section we give you a step-by-step guide how to draw a Mohr diagram:
4.
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Make a graph with two axes: σn as the horizontal and  as the vertical axis.
1. Find the principal stresses σ1 and σ2. Indicate both on the horizontal axis.
2. Determine the centre of the circle – this is exactly halfway between the maximum and
minimum principal stress. The radius of the circle is the distance from the centre to either
of the principal stresses. You can now draw the circle.
3. To determine the stresses on a certain plane, find θ – the angle between the plane and σ1.
Remember to use 2θ in your Mohr diagram! Measure the angle from σ1, anticlockwise, the
way you see in Figure 5.11 and Figure 5.12
4. Now you can simply read the normal and shear stress from the horizontal and vertical
axes, respectively.
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5.4
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Fast deformation (brittle behaviour)
The Mohr diagram is a useful means to find out more about brittle behaviour of rocks. So what
does ‘brittle behaviour’ mean exactly and what kind of processes
are involved?
σ1 = 50 Mpa
Exercise 5-7***: Practicing with the Mohr diagram
25º
In Figure 5.14 you see a rock with the two principal stresses
indicated. The rock broke along the indicated line: this is the
fracture plane. We want to know what the normal and shear
stresses on the surface were at the moment the rock broke – this
can tell us more about the strength of the material.
σ2 = 20 Mpa
a. Draw Mohr’s circle on the graph paper below, using the
provided information and the step-by-step guide provided at
the end of the previous section.
b. Now determine what the normal and shear stresses on the
indicated plane were the moment the rock broke.
c. Now consider another rock under the same circumstances.
Figure 5.14: Principal stresses
For this rock we happen to know that it broke at = 15 MPa
on a rock
and σn = 35 MPa. Calculate the orientation of the fracture
plane.
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5.4.1
Experiments
In a laboratory, we can simulate situations to study how processes work. Experiments are
conducted to see how rocks behave when a force is applied to them. We want to do that in a way
which is as close as possible to the ‘natural’ conditions under which rocks in the Earth deform. For
example, experiments can be conducted at high temperature (~200 up to 1200°C). But the speed
of deformation can be varied as well to see how this influences the processes taking place.
Special instruments (like the one you see in Figure 5.15) are used to achieve the enormous forces
necessary for deformation of rocks.
Figure 5.15: Deformation device in the High Pressure and Temperature (HPT) rock deformation
laboratory of Utrecht University. The right picture shows a close-up. The rock sample (the white
cylinder) is contained in between two massive iron cylinders that can move towards each other
in a vertical direction. The speed and the force needed can be controlled and measured. A small
oven that is placed around the sample makes it possible to reach high temperatures. In this
small device, the oven consists of two parts that can be unfolded (right picture).
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Exercise 5-8***: Experiment with sandstone
An experiment has been conducted with a cylinder of sandstone (see
Figure 5.16). In table 5-1 you see the normal stresses (σn) and shear
stresses (), both in MPa, that were measured at the moment the rock
fractured. In some experiments, the angle of the normal to the
direction of σ1 was measured as well.
Table 5-1:
Normal and shear stress on the
fracture plane at the moment of
fracturing.
σn

angle
1
10.0
7.5
58º
2
20.0
12.5
58º
3
30.0
17.5
4
40.0
22.5
5
50.0
27.5
6
60.0
32.0
7
70.0
36.0
8
80.0
39.0
9
90.0
41.0
10
100.0
42.5
58º
Figure 5.16: Left: a shear fracture in deformed sand stone, Right: Rock fractures out of an
marble sample. http://www.emeraldinsight.com/fig/0830120103002.png,
a.
Make a graph of the shear stress (vertical) plotted against the normal stress (horizontal). Use
the information from Table 1. You can use the graph paper provided below. Make sure to use
the same scale on the horizontal and vertical axes! Take σn as x coordinate and τ as the y
coordinate. Try to draw a smooth line through all the points.
b.
Now draw Mohr’s circle for experiments 2 and 4 in the graph. Use a compass to draw the
circles and make use of the data in the table (don’t forget the third column!). Also determine
the values for the principal stresses σ1 and σ2 in these experiments (remember the convention:
σ1 > σ2 ). Hint: make use of the step-by-step guide in section 5.3 and take a look at exercise 57.
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The line you drew through the σn- points (question a and b) defines the so-called yield criterion.
As soon as a point on Mohr’s circle for a certain stress regime touches this line, the rock will ‘yield’:
it will fracture. This happens in the plane which corresponds to the place where the line and the
circle touch – in other words, where the normal and shear stress are equal to the stresses denoted
by the line.
We can now determine for every combination of σ1 and σ2 whether a rock will break or not, what
the orientation of the fracture plane will be and what the stresses in that plane will be. (to
determine all these things, you just need to draw the Mohr diagram for that particular situation).
c. What happens to this rock when σ1 = 40 MPa and σ2 = 20 MPa? And when σ1 = 50 MPa and σ2
= 17 MPa? Hint; draw the corresponding Mohr diagram. And remember, if they intersect...
The slope of the line determines another material property called the ‘coefficient of internal
friction’.
d. Now predict what the orientation of the fracture plane in experiment 9 will be (σn = 90,  =
41). Sketch the broken sample. Use Figure 5.16 as an example.
We’ve now only discussed ‘dry’ rocks. It turns out that the presence of water makes a big
difference. Many rocks have small pores in between the grains which are usually interconnected.
When these pores are filled with water, an internal pressure (Pf) starts working against σ1 and σ2.
The stress which is ‘felt’ by the rock is then reduced to the ‘effective stress’. The effective stress is
smaller by Pf) in all directions compared to the ‘dry’ rock.
e. Will the effect of Pf differ for the directions σ1 and σ2? (In other words, is Pf different in different
directions?)
f. What happens to the Mohr diagram when a rock has an internal fluid pressure Pf (and all
stresses become smaller by an amount Pf)?
g. Determine the fluid pressure Pf necessary inside the rock to make it break at σ1 = 90 MPa and
σ2 = 50 MPa.
h. What kind of place is more likely to develop earthquakes? A dry spot or a place where the
Earth’s crust is ‘wet’? Explain.
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5.6 Slow deformation (ductile behaviour)
In the previous section we discussed fast deformation, or brittle behaviour. Here we will study
ductile deformation: what happens when rocks are deformed at a very slow rate. We shall see that
rocks do not fracture in this case.
Exercise 5-9*: Introduction to ductile behavious
What factors do you think would influence ductile behaviour in rocks?
Here you will see how you can recognise slow deformation in rocks. Apart from that, we will also
discuss the underlying mechanisms that cause this kind of behaviour.
Exercise 5-10***: Maizena – liquid or solid? (including practical)
What you need (see Figure 5.17) : 200 grams of Maizena – about 150 mL water – a round bowl – a
spatula and/or a fork. Preparation: Pour the maizena in the bowl. Add the water little by little and
stir continuously but slowly! Stop when the mixture feels as a thick syrup and can move slowly.
Tip: add some lemonade or pigment to the mixture!
In this exercise we will discuss the term viscosity. This is a measure for the resistance of a fluid to
flow (to deformation), also called ‘thickness’ for true liquids like water or honey. The official
definition for viscosity is the ratio of shear stress τ and the speed of deformation.
Play with the Maizena and see what happens when you vary the speed at which you stir it. You will
see that when you stir at a higher speed (with more force), the viscosity of the mixture increases
(it feels more like a solid). If you stir more slowly (with a smaller force) you will see that the
viscosity of the mixture decreases (it feels more like a liquid). Note: a maizena solution is a socalled ‘non-Newtonian fluid’ – a fluid whose viscosity varies. This is unlike the behaviour of normal
fluids.
Figure 5.17: Demonstration
with Maizena
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Back to rocks:
a. What do you think will happen to the viscosity of rocks when the temperature is raised? Why?
b. Would rocks need to be melted before they can flow, or can they flow as a solid as well?
Figure 5.18: Church windows in Utrecht (Dom and Jans Church Picture: Geerke Floor.
Exercise 5-11***: Flowing glass?
Glass in old cathedrals (like in Figure 5.18 from the 12th century) is often wider in section at the
bottom than at the top. Many people think this is due to plastic deformation (deformation without
fracture), where the glass ‘flows’ down due to gravity.
a. Do you think this is a plausible explanation? Motivate your answer.
We can easily test this hypothesis by doing some calculations. The ‘characteristic time’ t necessary
for deformation is given by:
t

where η = the viscosity (dependent upon temperature); G =
G
the shear modulus (for glass with a value of 30 GPa). The shear modulus is a property describing
the elasticity of a material. It indicates how easily (and fast) a material can deform as a result of a
stress. The important thing for elastic deformation is that it’s not permanent: the material will
move back to its original shape as soon as the applied stress is lifted.
Viscosity is dependent upon temperature, for which the following law holds:    0 exp
 A
 T 
with η0 = a constant property of a material (you could call it ‘initial viscosity’. For glass this is η0 =
9 x 10-6 Pa s); A = another material property (not relevant here), with a value of A=3.2 x 104 K; T
= the temperature in K. Note: exp [A/T] means: e to the power [A/T] or e[A/T].
b. Calculate t. Take the average temperature to be 20 degrees Centigrade
c. What does this answer tell you about the probability of the explanation for the glass thickness
as discussed in the introduction?
So how does plastic deformation work? To understand this, we must zoom in on a process that
takes place on a very small scale: intracrystalline slip. Atoms in a crystalline material are arranged
in an extremely regular way. One of the mechanisms of plastic deformation is that part of the
atoms move to a new position. This must be an equilibrium position: a position in which the overall
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system has a low energy. This
happens through translational slip:
part of the crystal slips along a plane.
In Figure 5.19 the top row of atoms
(spacing b) slips over the bottom row
due to a stress which is applied to it.
You can calculate the shear stress
necessary to displace a row of atoms
in a perfect crystal using the following
formula:
 
Figure 5.19: Translational slip
G
2
where G is the shear modulus
of the material.
A material which is important in
geology and is easy to deform is rock salt. For this material, the shear modulus G is ~10 GPa,
which would result in a necessary shear stress of about 1.6 GPa. However, lab experiments have
shown that a shear stress of only 10 MPa (0.001 GPa) is necessary to deform rock salt (at 200 C)!
This clearly shows that the model of intracrystalline slip – where whole rows of atoms move
together to a new position – is not valid. There must be another mechanism explaining the
deformation of rock salt. More research has shown that instead, deformations happens in a
stepwise manner, using so-called ‘dislocations’. A dislocation is a defect in the crystal lattice (see
Figure 5.20 and Figure 5.21). A much smaller stress is necessary to deform the crystal as a result
of these defects.
Figure 5.20: Dislocations in the crystal lattice. The row with the black colored atoms stops
halfway the lattice; so, there the lattice has a defect along the line.
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Figure 5.21: Steps at the transport of a dislocation. In the first vertical row, the
connection between two atoms breaks. A new connection is made: connection with an
atom of next row. This process repeats, so eventually the upper half of the crystal
lattice has slipped over one atomic distance. If the process continues, the crystal will
eventually change shape visibly.
Exercise 5-12**: The influence of temperature
a. What do you think the influence of temperature is on ductile behaviour? Hint: how would
vibrations in the atoms influence deformation? And what is the effect of temperature on
vibrations?
b. Would temperature influence brittle behaviour in the same way?
The homologous temperature is used to compare materials. This temperature is defined as the
ratio ‘temperature of the material (in Kelvin) / melting point of the material (in Kelvin)’. See Table
5-).
Material
Melting point in °C
Basalt (rock)
1000-1200
Granite (rock)
650-800
Olivine (mineral
mantle)
in
the
Earth’s
1867
Quartz (mineral in the Earth’s crust)
1650
Aluminium
660
Iron
1538
Ice
0
Table 5-2: The melting point for various substances.
What deforms easier? Granite at 300°C or ice in a glacier? Why? It turns out that the material
deforms easier when the ratio mentioned above has a higher value. In general, a material will only
deform in a ductile manner if the homologous temperature (the ratio T/Tmelt) is larger than 0.4.
Note: always take T in Kelvin! If you do the calculations you will see that ice flows more easily than
granite at 300°C.
The speed of deformation is a measure for how fast deformation takes place. ´Deformation´ is
defined as a change in size and/or shape. The speed of deformation is the parameter describing
the speed at which this happens and it has unit s-1. To see why, consider a bar of 100 mm (L0). It
is deformed so that after 1 second, its length is only 99 mm (L1).
The deformation is defined as:
117
e = ( L0 - L1 ) / Lo
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The speed of deformation is then e per unit time. In this example the deformation e is 1 mm / 100
mm = 1% = 0.01. The speed of deformation then becomes 0.01 s-1.
Inside the Earth, deformation takes place at a very low rate. Geological processes usually take
place at about 0.000 000 000 000 01 s-1, or ~1 x 10-14 s-1.
Exercise 5-13***: Experiments with salt
Rock salt is a material which deforms relatively easily. In a lab experiment, rock salt has been
deformed at different temperatures and at different rates. The results are indicated in tabel 5-.
temperature (ºC)
σ1 - σ3 (MPa)
Speed of
deformation (s-1)
1
100
13.6
5.3 x 10-7
2
100
17.9
2.8 x 10-6
3
100
22.1
7.5 x 10-6
4
100
32.1
3.3 x 10-5
5
150
7.2
5.3 x 10-7
6
150
13.3
4.5 x 10-6
7
150
20.0
3.6 x 10-5
8
200
5.0
5.0 x 10-7
9
200
7.5
2.4 x 10-6
10
200
13.0
2.4 x 10-5
Tabel 5-3: Deformation of rock salt at various pressures and
temperatures.
a.
Make a graph of the speed of deformation (horizontal axis) and the stress (vertical axis). The
stress is the differential stress σ1-σ3. As you can see, the results vary up to about a factor 100,
so it’s best to use a logarithmic scale. Do this for both of your axes.
b. Can you see any trends in your graph? Describe them.
The standard law for intracrystalline slip is a so-called ‘flow law’ (there are other flow laws):
  Q 

 
  A n e   RT 
With  the speed of deformation (in s-1), σ the differential stress σ1-σ3 (in MPa), T the temperature
(in K) and
Q the energy that is necessary to initiate the process (the activation energy). R is the
gas constant (8.314 J/mol K) and A and n are constants in flow laws.
c.
Rewrite this flow law in such a way that you get a straight line for every temperature on a
graph with two logarithmic axes. Hint: the kind of formula that gives a straight line is
d.
What is the big difference between a lab experiment and the geological reality?(see Figure
5.22)? Think of a way to avoid this problem.
Y  a  bX
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Figure 5.22: Deformation of salt rocks (Cardona, Spain)
5.5
What different types of deformation tell us about orogenesis.
So how does this all relate to the way mountains are built? You have learned a lot about the way
materials can deform, and now you will see how Earth Scientists use this knowledge to better
understand the processes of orogenesis.
An example: we can tell what the stress state in a rock was from the directions of the faults we
see. Using this information, we can reconstruct how tectonic plates moved in the past. If we see
evidence of ductile deformation, we know that the rocks we see must have been subject to high
temperatures. Using deformation structures, we can even calculate the time it took to form a
certain structure, and under which circumstances this took place. We are also able to say more
about the height of mountain range and the depth of its root. If you forgot what this was all about,
reread section 1 from this chapter. We will now do some calculations about the root of mountains
(Exercise 5-14).
Exercise 5-14***: Mountains and their roots
You’ve seen in Chapter 2 that the Earth is made of roughly three concentric shells: the Core on the
inside, the Mantle, and the Crust on the outside. The mantle is not liquid, but we know that the
outer, upper parts are more or less fluid, ductile. Therefore you could say that the rigid crust
‘floats’ on this ductile mantle. The crust consists of plates.
If for some reason or another a continent becomes heavier, it just sinks a little deeper into the
mantle. In the North Sea, sediments like clay and sand are deposited, adding mass to the crust.
Here the crust becomes heavier and sinks. On the other hand, the continent becomes lighter when
erosion breaks down mountains. It will start to rise. This is what happens with the Alps.
Generally, the Earth ‘tries’ to obtain a state of equilibrium. Plates rise and sink with respect to the
mantle until equilibrium has been reached. Compare this to the growth and melt of glaciers. And,
again just like glaciers, you can only see the tip of the iceberg. Mountains have deep roots.
You also know that a fluid will have the same level everywhere in the reservoir (or in a set of
connected reservoirs). Same level, same pressure. In this exercise you will calculate the depth of a
continental root.
a. What would be the best depth to calculate the pressure for? In other words, what is the best
reference point?
b. The pressure at that depth must be the same beneath a continental plate and beneath an
oceanic plate. Make an equation that compares the pressure beneath both types of plate.
Calculate the depth of the root using this equation. Use figure 5.23 and figure 5.24.
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+ 8000
m
mountain
0m
continent
~~~~~~~~~~~~~~~~ water ~~~~~~~
1030 kg/m3
- 2500 m
2700 kg/m 3
oceanic crust
2900 kg/m3
- 9500 m
~
~
~
root
?m
~
~
~
~
mantle rock
3300 kg/m 3
~
~
Figure 5.23: The depth of the mountain root can be calculated using these data.
w
h   crust
 mantle   crust
H = height of mountain
W = depth of the root
ρcrust = 2.7 g/cm3
ρmantle = 3.3 g/cm3
Figure 5.24: Data and formulas to calculate the depth of a mountain root
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Mountain building
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Geologists go on field work (Figure 5.25) to study rocks in the field. They also take home samples to
study using advanced instruments such as light and electron microscopes. They try to make a
reconstruction of the way the mountains have formed using these observations. As you see,
observations on many different scales are used: from defects on the scale of the crystal lattice
(micrometre and smaller!), up to faults and folds in a mountain side (kms). The larger the number
of observations, the more accurately you can reconstruct the process of orogenesis. However, you
must make a very careful distinction between small scale movements and the overall motions of
tectonic plates.
Experimental lab work on the behaviour of materials complements field and rock sample data.
Experimental work can give Earth Scientists a better understanding of the way rocks deform. It
gives insight into the processes underlying deformation and into the circumstances necessary for
deformation to take place.
Figure 5.25: Fieldwork in the Alps, Utrecht University, summer 2007. Photograph by Hans de Bresser
Final exercise chapter 5. Main questions in this chapter.
a.
b.
121
Answer each of the section questions separately.
Did you form new questions after studying this chapter? Write them down.
The Dynamic Earth
Mountain building
Optional Exercise 5-1: Derivation of the equations for shear stress and normal stress in
the 2D case. The Mohr diagram.
n , , the principal stresses 1 and 2 and A are indicated.
We know the vector components of A: A = (1 cos  , 2 sin )
To find the relationship between n , and the principal stresses 1, 2 and the angle , we use a
new figure in which only the principal axes, the normal stress and the angle  are given. All vectors
Look at Figure 5.26.
are drawn with their tail in the origin. All vectors point in the opposite direction with respect to
figure 5.24, but this doesn’t matter for their relationship
a.
The tips of n, A,  and the point O make a rectangle in the figure. Why? Draw the rectangle
in your figure (but not too visibly).
b.
The angle between
correct letter.
 and the axis of 2 is also Why is that? Indicate this angle with the
(Lenght of a1a2)
Figure 5.26: Twodimensional representation of
Figure 5.8
Figure 5.27: Same situation as in figure 5.26, but in a different coordinate
system.
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Mountain building
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The essence of the derivation is the fact that you end up with two different expressions for
A. One
is A = ( 1 cos  , 2 sin ) , the other is A = n +  Note: this latter notation is a vector
addition! The thin lines in the figure help you to see the different components of each of the
vectors. The σ1-components of
n and must add up to the σ1-component of A; they must
1 cos  . A similar argumentation holds for the σ2-components.
Next we will use the letters n and for the lengths of the vectors. Using the figure you can see
therefore be equal to
that the following holds:

sin 
– cos 


n cos 
n sin 


1 cos 
2 sin 
c.
Check this by marking the six parts of the above formulas in the figure
d.
Using these two equations, we can obtain the formulas for n and τ. We do this by first
‘extracting’ Mohr’s circle from the equations you found. We write both equations as formulas
for a line, but instead of using x and y, we use
n and. Show that the result is the following
1
 = – -----------    n –  1 
tan 
 = tan     n –  2 
We will now draw these lines in a graph with
the values of (n ,
n and on the axes. The intersection of the graphs is
that we are looking for.
e.
The second equation seems the easiest one. What is the slope of this graph? And therefore,
f.
what is the angle it makes to the n axis? Where does this line intersect with the n axis?
The lines are perpendicular to each other! Why is that? Hint: multiply the slopes of both
graphs.
g.
The line corresponding to the first equation intersects with the
Figure 5.28 shows another graph with
n axis at 1. Why?
n and on the horizontal and vertical axes; the points 1
and 2 are indicated.
h. Also draw the line corresponding to the second equation.
i. Indicate the intersection of both lines with P and show they are perpendicular.
21 as its centre. What geometric rule says
j.
The point P is on the circle with the middle of line
so?
k.
Express the coordinates of the centre of the circle M and of the radius of the circle in
1 and 2.
l. The line MP makes an angle of 2the n. axis! Use geometry to prove this.
m. Show how the formulas between exercises 5.9 and 5.10 can be read directly from this figure.
Figure 5.28: Coordinate system with n and. The line corresponding
to the equation indicated is drawn.
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Mountain building
Optional Exercise 5-2: CO2 storage and earthquakes
It is generally accepted that carbon dioxide (CO2) is a greenhouse gas which contributes to global
warming. Many countries actively try to decrease their CO2 emissions. One way to achieve this is to
store CO2 in the subsurface, and a lot of research is carried out to investigate the feasibility and the
best way of doing this.
One option is to store the CO2 in old,
depleted gas reservoirs (see Figure
5.29. These are often sandstones
with a lot of pore space, which could
potentially hold a lot of carbon
dioxide.
Such
reservoirs
must
however be examined carefully in
order to check whether the gas can’t
escape in some way and to see
whether or not earthquakes would
take place as a result of the storage.
Figure 5.29: Map of the Netherlands with oil and gas
reservoirs Empty reservoirs may be suitable for CO2 storage.
Source: TNO.
You work for a consultancy agency
and your current project is to offer
advice concerning CO2 storage in an
exhausted reservoir rock in the north
of the Netherlands. You will examine
the risk of earthquakes as a result of
the storage. A too large risk would
make the reservoir unsuitable for
storage.
You have the following information:
the reservoir lies at 1850 m below
the surface and the temperature at
depth is 60 °C. The experiments in
exercise 5.8 were conducted to
obtain information about the material
properties of the reservoir rock. The
density of the rock is 2280 kg/m3.
Apart from these material properties
you know the following:
σ1 is the pressure as a result of the
overlying rocks.
σ3 = 23.3 MPa
Pf = 0
Use the yield criterion (graph) for sandstone which you constructed in exercise 5.8.
a.
b.
c.
d.
Is the reservoir stable, or is there a chance the rock may fracture under its load? Hint;
pressure as a result of the overlying rock: σ1 = ρ g h, and σ3 are given. Use a Mohr diagram
like the ones you used in exercise 5.8.
CO2 is injected into the reservoir until it reaches an internal gas pressure of 30 MPa. How
stable is the reservoir now? How would you explain this?
Now imagine that the internal friction of the reservoir rock was measured incorrectly. In reality
its value turns out to be 1,5 times as high as the experiments seemed to show. How does this
influence the stability of the reservoir (with and without CO2)?
And what would happen if the temperature in the reservoir turned out to be 90 °C instead of
60 °C?
124
Convection: the Earth as an heat engine
Chapter 6.
The Dynamic Earth
Convection: the Earth as an heat engine
Within the interior of the Earth, heat is produced by the decay of radioactive isotopes. This heat
must be transported to the surface of the Earth, because only there heat can be lost to space. The
transport of heat results in material flow (convection) within the Earth, which forms the basis of all
plate tectonic processes.
The main question of this optional chapter is:
How can we use the Earth’s heat transport mechanisms to explain plate
tectonics and other large-scale processes?
This question is addressed by answering the following section questions:
125

What is the interior structure of the Earth? What sources provide us with information about
the Earth’s chemical and mineralogical composition and internal temperature?

How can internal heat production (by radioactive decay) and heat transport (by conduction
and convection) explain the internal temperature of the Earth and the heat flow through its
surface?

What role does convective flow play in the mantle of the Earth and how is convection
related to plate tectonics?
The Dynamic Earth
Convection: the Earth as an heat engine
6.1 Introduction
Plate tectonics (Chapter 2) and geological phenomena like mountain building (Chapter 5) suggest
that large-scale processes are at play within the Earth. Scientists in the Geodynamics field of study
try to explain these processes with the help of physical principles. Internal heat production, heat
transport (conduction and convection) and the resulting temperature distribution, all directly linked
to the Earth’s thermal state, are key to explaining geodynamical processes, which shape the
Dynamic Earth on a geological timescale.
This chapter discusses the internal dynamics of the Earth. We construct several physical models to
explain plate tectonics and consequent mountain building and volcanism and test them against
observations (mostly from seismology).
To construct a model of the Earth, it is crucial to be familiar with the Earth’s interior structure.
Therefore, Section 6.2 considers what we can learn about the structure and chemical composition
of the Earth from Astronomy, Seismology, Mineralogy and other fields of study.
Section 6.3 assumes that the natural decay of radioactive isotopes acts as an internal heat source
of the Earth. Based on this assumption, two models of the Earth’s thermal state are tested. The
first model only considers radioactive decay and heat conduction. Calculations for this model show
that the only (radioactive) heat source of this model can provide about two thirds of the observed
heat flow through the Earth’s surface. The model also predicts that the rock making up the interior
of the Earth is molten. This contradicts seismological and petrological observations that state the
Earth mantle is solid.
In addition to conduction, the second model incorporates convective flow in the mantle. Model
predictions show a lower internal temperature than for the first model; the Earth's mantle remains
solid because convection can transport heat upwards efficiently enough to prevent the temperature
from rising above the melting point. However, is flow possible in a solid mantle? Yes, it is:
seismological observations and lab experiments with mantle rock demonstrate that rock at the
pressure and temperature of the mantle moves very slowly (this is called creep behaviour). You
can compare this movement with the flow of ice in a glacier.
With the help of seismology and laboratory data, we determine the temperature at different depths
within the Earth in Section 6.4. The results of the second model fit in well with these temperatures.
Additionally, in Section 6.5, the convection model is tested against geophysical observations. To do
so, we study images of the mantle’s three-dimensional structure obtained through seismic
tomography. We also check if the heat flow through the Earth surface corresponds to the largescale convective flow in the mantle. Finally, the temperature distribution of the convection models
and the ‘dynamo theory’ that states the Earth magnetic field is generated in the liquid iron outer
core are compared.
6.2
The interior structure and chemical composition of the Earth
6.2.1
The large-scale structure of the Earth
Throughout the last century, the large-scale structure of the Earth (crust, mantle and core) has
been defined and subsequently refined more precisely. Most of what is known about the Earth’s
structure comes from seismological research. Figure 6.1 shows the structure of the Earth
schematically. The curved lines represent the paths along which wave energy travels from
earthquake focus to seismic station. The lines are called seismic rays; they are comparable to light
rays that also refract or reflect at the interface between two different media. At sharp transitions
(for example, from air to glass), refraction shows as an angle in the path of the light ray. The angle
of refraction results from the difference in the velocity of light between both media and, thus, from
the difference in refractive index. Seismic waves in the Earth experience both sharp and more
gradual transitions. At a gradual transition, a ray path is curved instead of broken at an angle,
because the wave’s velocity changes only slowly.
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Convection: the Earth as an heat engine
The Dynamic Earth
Exercise 6:1**: The refractive index and wave velocities
a.
b.
c.
d.
What is the refractive index of a material in the case of light travelling through it? How can you
calculate the refractive index from Snell’s law?
How are the refractive index and the velocity of light related?
Indicate at which depth within the Earth sharp transitions occur in the refractive index
according to Figure 6.1. Why would such transitions occur at those depths?
Where can you find more gradual transitions? What could cause this type of transition there?
Figure 3.13 shows that seismic rays refract at a greater angle to the normal (a line perpendicular
to the media’s interface) deeper within the mantle. This means that wave velocity increases with
depth. However, at the boundary between mantle and core, waves refract at a lesser angle: the
velocity in the core is lower than in the mantle. Within the core itself, rays again refract away from
the normal with increasing depth, because velocity increases.
Figure 6.1: The structure of the Earth (starting from the centre): the inner core, the
outer core, the mantle and the crust. The seismic rays of an earthquake at the North
Pole are shown together with the seismograms recorded for this earthquake at
different seismic stations.
Between 104o and 140o (starting from the epicentre, which, in this case, is the North Pole, in a
clockwise direction along the surface), no seismic waves reach the Earth’s surface (Figure 6.1).
This core shadow is caused by the refraction of waves entering and leaving the core.
With the starting time of an earthquake known, the travel time of a seismic wave can be
determined from a seismogram (see Chapter 3). Figure 6.2 shows a seismogram recorded in
Utrecht, The Netherlands. You can find seismograms of more recent earthquakes at the website of
the Seismology group of Utrecht University: www.geo.uu.nl/Research/Seismology.
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Convection: the Earth as an heat engine
Figure 6.2: A seismogram showing P- and S-signal phases corresponding to
longitudinal and transverse body waves, respectively. Body waves travel
through the Earth. The later, larger amplitude signal phases arise from surface
waves travelling along the surface between earthquake and seismic station.
From the travel times of a wave recorded at different seismic stations, the change of velocity of
that wave with depth can be determined. Knowing the velocity helps study the earthquake that
caused the wave, but also provides information about the deep Earth. Seismic studies have shown
that the Earth has a core with a 3480-kilometer radius. The core can be divided into a solid inner
core with a radius of 1221 km and a liquid outer core. Transverse waves cannot travel through a
fluid, so, because they do not cross the outer core, we know the outer core is liquid. The liquid
outer core also explains the Earth tide, the motion of the Earth in response to the gravitation of the
Moon and Sun. The Earth is not a perfect sphere, but an ellipsoid (a flattened sphere) that, through
the Earth tide, changes shape (several tens of centimetres) periodically. The amplitude of this
motion can only be explained by a (partially) liquid core.
Figure 6.3: Left panel: The Preliminary Reference Earth Model (PREM) with density ρ, primary
and secondary seismic wave velocities vp and vs, gravity acceleration g and pressure P (Anderson
& Dziewonski 1981). Right panel: The simplified mineral structure of the Earth (see Section 6.4).
The transitions at a depth of 410 and 660 km correspond to sudden changes in the curves of
material properties ρ, vp and vs (Yuen et al. 2007).
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Convection: the Earth as an heat engine
The Dynamic Earth
The structure of the Earth is described in the standard Preliminary Reference Earth Model (PREM)
(see Figure 6.3). The PREM model is mostly based on seismological observations. It shows the
distribution of important physical quantities, such as density ρ, pressure P and seismic wave
velocities vp and vs, with depth within the Earth. In Figure 6.3 the core-mantle boundary (CMB) is
clearly visible at 2900 km, because here both wave velocities change, with the secondary wave
velocity vs even becoming zero.
Exercise 6-2: Increasing seismic wave velocities
Figure 6.3 shows that seismic wave velocities vp and vs increase more or less gradually towards the
centre of the Earth, but suddenly decrease at the mantle-to-core transition.
a. Explain why the curvature of the wave rays in Figure 6.1 corresponds to a velocity increase with
depth according to Snell’s law.
b. At a depth of 2900 km, vs becomes zero. Why?
P- and S-waves and elastic deformation
Waves deform the medium they travel through. The elastic parameters of a medium describe its
resistance to this deformation. Together with the density of the medium, the elastic properties also
determine the velocities of longitudinal and transverse seismic waves, vp and vs. Two elastic
parameters are important: shear modulus G and incompressibility K. The shear modulus gives the
resistance of a medium to changing shape, while the incompressibility describes the resistance to a
change in volume. When we consider a change in shape, we imply that the volume of the medium
remains the same; for example, changing the shape of a cube results in a parallelepiped with the
same volume as the original cube. Consequently, considering a change in volume means that the
cube remains a cube, but does become bigger or smaller. A change in shape is caused by shear
strain, a change in volume by (hydrostatic) pressure.
Because both longitudinal and transverse waves deform the shape of a medium, elastic parameter
G occurs in the velocity expression of both types of wave. However, only longitudinal waves result
in a change in volume of the medium, because they also stretch and compress rocks. Remember,
particles of the medium a longitudinal wave travels through vibrate in the direction of the wave,
while for transverse waves particle motion is perpendicular to the direction of the wave. Such
vibrations cannot cause a change in volume, so the equation for transverse wave velocity does not
contain incompressibility K. So, the velocity expressions are:
vs 
G

Because a liquid cannot resist a change in shape, its stiffness is zero. The shear modulus G in a
liquid is therefore zero. Since vs depends directly on G, transverse waves have no velocity in a
liquid and cannot travel through a fluid medium.
Wave
type Longitudinal
Transverse
Property
Arrival
Primary
Change in shape?
Yes,
cube
becomes
rectangular box
Change in volume?
Yes, through compression
Propagation
medium?
through
a
solid Yes
Secondary
a Yes,
cube
parallelepiped
No
Yes
Propagation through a liquid Yes
medium?
No
Velocity in water
1500 m/s
0
Velocity in granite
5500 m/s
3000 m/s
Table 6-1: Several properties of longitudinal (P-) and transverse (S-) waves.
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becomes
a
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Convection: the Earth as an heat engine
Figure 6.4: A chondrite from Mexico. The
spherical chondrules are clearly visible.
Early in the 20th century, analyses of seismic wave travel times already showed that wave
velocities increase with depth within the Earth. In Fig. 6.1 this is evident from the wave rays: the
rays refract with increasing angle to the normal with depth. Could the velocity increase depend on
density ρ? The density of rocks increases with depth, so if incompressibility K and shear modulus G
are constant, velocity should decrease with depth according to the two expressions above (check
this). However, because velocity increases with depth, K and G should increase with depth even
more than the rocks’ density does. They do so because pressure also increases with depth: and the
resistance to deformation becomes larger.
Exercise 6-3**: The velocity of longitudinal and transverse waves
a.
What is the vp/vs ratio at a depth of about 2000 km? Use the PREM model (Figure 6.3) to
answer this question.
b.
Explain why vp and vs decrease for increasing density ρ when the elastic parameters are held
constant.
c.
Deeper within the Earth, density is higher. How can the wave velocities increase as well?
d.
Write down two observations that suggest a liquid outer core.
Years of seismic observations have enabled scientists to establish a detailed depth profile of the
seismic velocities. The profile shows large increases in velocity and density, especially in the 400700 km depth range. This zone is called the transition zone and can be seen in the PREM model.
The right panel in Figure 6.3 shows the transition zones; terms like ‘ringwoodite’ indicate
differences in the chemical and mineralogical composition of the mantle material.
The chemical composition of the Earth
How can we gain insight in the chemical composition of the deep Earth? Not through drilling: the
deepest drilling so far only reached 12 km, which does not even cross the continental crust
(continental crust has an average thickness of 35 km). Surface rock does not give any direct
information about the composition of the mantle either, because it was brought up from the crust
or shallow mantle. Volcanic rock is also derived from crustal or shallow mantle material. Moreover,
the magma composition changes upon rising slowly through the crust. Minerals in the magma with
a high melting point solidify at a certain depth in the crust or shallow mantle and, thus, do not
reach the surface together with the remaining liquid magma. Only a few volcanic deposits and
several locations of past continent-continent collision show rocks from several hundreds of
kilometres of depth.
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Convection: the Earth as an heat engine
The Dynamic Earth
Thus, we are left to indirect data to determine the composition of the deep Earth: the composition
of meteorites.
There are two major classes of meteorites: iron meteorites and stony meteorites. Iron meteorites
are composed of at least 95% iron and nickel. Stony meteorites have a more variable composition
and consist of over 90% of O, Fe, Si and Mg (oxygen, iron, silicon and magnesium). Some
meteorites contain small spherical particles called chondrules; these meteorites are therefore called
chondrites (see Figure 6.4).
Chondrites are seen as the oldest material in our solar system. The chondrules are thought to
represent frozen droplets from the cooling dust and gas cloud the solar system was formed from.
Scientists assume that the terrestrial planets (Mercury, Venus, Earth and Mars) are mainly
composed of chondritic material.
Spectral analyses of the sunlight show that the atomic composition of the non-volatile particles of
the photosphere, the outer layer of the Sun, strongly resembles that of chondritic meteorites (see
left panel of Figure 6.5). Also, the average composition of the Earth’s crust and mantle rock is
clearly similar to the chondritic composition. This chondritic composition consists for over 90% of
only a few elements (Fe, O, Si and Mg) as shown in the diagrams of Figure 6.5 (right panel).
Figure 6.5:
Left panel: The atomic com-position of
the non-volatile elements of the Sun’s
photosphere
(‘solarphoto-sphere
abundance’) compared to the average
composition of chondritic meteo-rites
(‘meteorite abundance’). Composit-ions
are normalized to 106 for silicon.
131
Right panel: The composition of the Earth
according to the chondritic hypothesis
(Brown & Musset 1993).
(a) percentage of mass
(b) percentage of atoms
The Dynamic Earth
Convection: the Earth as an heat engine
Exercise 6-4*: Comparing the composition of the solar photosphere and meteorites

How does Figure 6.5, left panel, show that iron is more abundant in the photosphere than
magnesium?

Which non-volatile element is most abundant (atomically) in meteorites?

What percentage of the atoms of a meteorite is oxygen?

Explain why oxygen is not included in the left panel of Figure 6.5. If you would include it,
where would you expect it?
Scientists think that during the formation of the solar system the Earth formed through accretion of
chondritic material. This theory is supported by the age determination of chondrites and terrestrial
rocks: radioactive dating shows that chondrites are about 4.5 billion years (4.5 Gy) old, and the
oldest dated rocks from Earth are 4.4 Gy old zircon grains.
Crust and mantle rocks have a lower concentration of iron than chondritic meteorites; this deficit is
called iron depletion. During the accretion of chondritic material, the impact energy of meteorites
was transformed into heat, leading to an increase in temperature. Most of the iron and nickel in the
chondritic material melted and, due to a high density and low viscosity, sank to the centre of the
forming Earth in a process of core-mantle differentiation.
The ‘sinking’ of liquid metal was a self-sustaining process: sinking released more potential energy
and, thus, increased temperatures in the mantle and led to more melting of metals. This process
most likely resulted in a complete melting of the Earth’s mantle and the formation of a magma
ocean (which, obviously, solidified again later). The settling of iron from this ocean into the core
explains the iron depletion of crust and mantle rock.
Exercise 6-5*: Similarities between the composition of meteorites and the Earth
Compare the composition of the different layers of the Earth with the composition of the two
meteorite classes (iron and stony meteorites). Which type of meteorite corresponds to which layer?
Explain.
The mineralogical composition of the Earth
Meteorite studies and lab experiments with silicon rocks at high pressures and temperatures (HPT
experiments) demonstrate that the upper mantle (to a depth of 660 km) consists of peridotite. The
term peridotite includes all mantle rocks made up of a certain mixture of minerals, mainly olivine
(Mg;Fe)2SiO4, pyroxene (Mg;Fe)SiO3 and garnet (Mg;Fe)3Al2Si3O12. The iron content of peridotite is
about 10%, but this as well as the concentration of other elements can vary.
The material of the Earth’s mantle consists of about 95% of magnesium, iron, silicon and oxygen.
This average composition is well explained by the chondritic hypothesis that the Earth formed
through the accretion of chondrites.
Oxide
Weight percentage
The chemical composition of a rock is often expressed in the
[wt%]
different oxides from which the rock can be synthesized. The
SiO2
46.1
average composition of mantle rock peridotite is given in
Table 6-2.
MgO
37.6
Synthesis of rock from the oxide mixture is accomplished by
FeO
8.2
heating the oxide mixture above the melting points of the
individual oxides at a pressure of 1 bar. From the melt, we
Al2O3
4.3
can
crystallize
the
minerals
olivine
(Mg;Fe)2SiO4,
CaO
3.1
orthopyroxene (Mg;Fe)SiO3, clinopyroxene (Ca;Mg;Fe)2Si2O6
and garnet (Mg;Fe)3Al2Si3O12. Iron, aluminium and calcium
Na2O
0.4
are present in these minerals as a solid solution. For olivine,
TiO2
0.2
Fe / (Mg+Fe) ~ 0.1. This means that one out of ten
magnesium atoms in the crystal lattice of olivine is replaced
K2 O
0.03
by an iron atom. The weight percentages of olivine, pyroxene
Table 6-2: The composition of
and garnet in representative mantle material are about 60, 30
the theoretical mantle material
and 10 percent, respectively.
peridotite
according
Ringwood (1975).
to
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Convection: the Earth as an heat engine
The Dynamic Earth
So, olivine is a silicate with in total two atoms Mg and/or Fe per SiO44- ion. Pyroxene is a silicate
with in total two atoms Mg and/or Fe per Si2O64- ion. Because the Mg and Fe content of olivine and
pyroxene vary, we refer to them as solid solutions series rather than pure materials. The crystal
shape of both minerals changes with increasing pressure (thus, with increasing depth). Because
this variation occurs in a step-like manner, the Earth is built up of shells with a different
mineralogical composition (see PREM model, Figure 6.3b). This we know from experimental HPT
research and seismological data.
With each phase change, the density of olivine increases. At 1 bar, α-olivine forms. α-olivine
changes into β-olivine (wadsleyite) at about 15 GPa (1 GPa = 109 Pa) at a depth of 410 km. At 17
GPa (or a depth of 520 km), γ-olivine (ringwoodite) forms. Ringwoodite dissociates into the
minerals periclase (MgO) and perovskite (MgSiO3) at 24 GPa or about 660 km.
Exercise 6-6*: Seismological determination of the layered mantle structure
How do you think the contrasts in seismic wave velocities between the layers of different mineral
phases (Figure 6.3, right panel) are expressed in seismic recordings?
6.3 A model for the Earth’s thermal state
To find out `how the Earth works’, we have to study the thermal state of our planet. In the 19th
century, the English physicist Kelvin proposed a mathematical model for the thermal evolution of
the Earth. Kelvin assumed that the Earth had cooled gradually since the time it solidified from the
magma ocean. His calculations resulted in an age of the Earth of maximally 40 million years (My)
(since solidification). This age was much smaller than that estimated from geological data. For
example, the thickness of sediment sequences combined with observed erosion and sedimentation
rates suggested an age of several hundreds of millions of years. Even calculations using the
burning of fossil fuels as an internal heat source (even though this was thought to be an
improbable process) did not result in a longer lifespan for the Earth.
Internal heat production
A solution to this problem was found when at
the beginning of the 20th century natural
radioactivity was discovered. Radioactivity is a
source of internal heat production for the Earth
much greater than external heat sources such
as sunlight, meteorite impacts, tidal flows in
seas and oceans or the tidal deformation of the
solid Earth. Internal heat production through
radioactivity greatly slowed down the cooling of
the Earth, so, as expected, cooling lasted much
longer than predicted by the Kelvin model.
Nowadays we presume the Earth formed 4.6
billion years ago (4.6 Gy) from chondritic
material and, since then, cooled very slowly.
In Chapter 1 you used radioactivity and halflives to determine the age of rocks. Here we will
use information about the radioactivity within
the Earth’s interior to estimate the internal heat
production. Radioactive isotopes naturally decay
to stable isotopes in several steps.
Figure 6.6: Evolution of the heat production of a
radioactive fuel mix of chondritic composition
with time. Time starts at t = 0 with the formation
of the Earth and runs till the present day 4.5 Gy
later. The upper black curve shows the heat
production of the combined isotopes.
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The Dynamic Earth
Convection: the Earth as an heat engine
This exponential decay releases a substantial amount of heat in the mantle (and crust). From
Chapter 1 you know:
t
 1  t1/ 2
N t   N 0   
2
with N(t) the number of radioactive particles at time t, N(0) the number of particles at t = 0, t the
time passed and t½ the half-life. The half-life is the time it takes for half of the radioactive isotopes
to decay to a daughter isotope.
Radioactivity always releases energy; within the Earth, this energy is almost completely
transformed into heat. Therefore, the heat production density H (in W/kg), the power produced by
decay (in watt) per mass (in kg), is proportional to the number of particles that decay per unit of
time: H ~ dN/dt. So:
t
 1  t1/ 2
H t   H  0   
2
The half-life t½ differs for every isotope (see Table 25 of BINAS). Because one element decays
faster than the other, the composition of the mix of radioactive elements changes continuously.
From the chondritic hypothesis for the Earth’s composition, we can learn much about the
radioactive isotopes in the mantle. When the Earth was young, about 4.6 to 3 Gy ago, decay of
isotopes with a relatively short half-life dominated the radioactive heat production. Long half-life
isotopes only became more important later on, when the short-lived isotopes had mostly decayed.
This is illustrated in Figure 6.6, where the heat production of the different isotopes in a chondritic
composition is plotted against the Earth’s lifespan. You can see that the relatively short-lived
uranium and potassium isotopes 235U and 40K were the dominant heat source in the early Earth. In
the present Earth, however, the thorium isotope 232Th is the principal heat source, and 238U is the
second most important.
Exercise 6-7**: The nuclear activity of the Earth
Study Figure 6.6 and BINAS.
a. Estimate (without using your calculator) how long it will take for the current nuclear fuel of the
Earth to fall below a heat production density of 1 . 10-12 W/kg. Only consider the isotope that
is most important now and in the future and take the current heat production density at 5 . 1012 W/kg.
b. Now use your calculator to calculate this period accurately.
c. Calculate the current heat production of the whole Earth, assuming a chondritic composition
with H = 5 . 10-12 W/kg. The mass of the Earth is 6 . 1024 kg.
Models for the internal heating of the Earth usually assume an average isotope composition with an
average half-life. These models suggest a current heat production density of about 5 . 10-12 W/kg
and a half-life of 2.4 Gy.
d. ***Calculate the amount of energy produced through radioactive decay by material of this
average composition in the 4.5 Gy that have passed since the formation of the Earth. First
consider 1 kg of material, then the total mass of the Earth.
A first step to modelling the Earth’s heat regulation: a conductive model
The processes that shape the Earth take place on very long geological and cosmological time scales
of millions and billions of years. It is practically impossible to reach the interior of the Earth for
direct observations of the composition, temperature or heat production at depth. Thus, we rely on
indirect observations through seismology and geological field studies. More so, we use numerical
modelling to investigate the Earth’s interior.
Model studies are used to explore possible scenarios for the evolution of the Earth on geological
time scales as well as for the current situation of the Earth’s interior. The results (model
predictions) are tested against geological and geophysical observations.
We will start with a simple model of the Earth’s thermal state before considering a more complex
one. The production and transport of heat result in high temperatures deep in the Earth and low
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Convection: the Earth as an heat engine
The Dynamic Earth
temperatures at the surface. Vice versa temperature differences lead to the transport of heat from
high temperature regions to low temperature zones. This heat transport within the Earth drives
plate tectonics, mountain building, volcanism and the generation of the Earth magnetic field.
There are three ways of transporting heat: conduction (vibrations are passed on by atoms in the
crystal lattice), thermal radiation (through electromagnetic wave energy) and convection (flow).
When material convects, energy is transported by material transport. In stagnant solids, heat
transport takes place through a combination of radiation and conduction, however. The combined
process can be described effectively as conduction.
The first, simple type of model of the Earth’s thermal state, that was especially considered in the
first half of the last century, assumes a homogeneous, spherically symmetric Earth that
experiences only conductive heat transport. A homogeneous Earth has the same composition
throughout, so it is not divided into a core, mantle and crust. Spherical symmetry implies that at a
given radius, temperature is the same everywhere. In the special case of such a model that we
investigate here, the temperature at each point within the Earth is also constant through time; it is
a stationary situation, called steady-state conduction. At each moment in time, the internal heat
production is in equilibrium with the heat loss to oceans and air at the Earth’s surface.
The conduction model is based on Fourier’s heat conduction law that describes the diffusion of
heat. Diffusion considers heat flux density J (in W/m2), the energy per unit time (in watts) that
flows through an area of 1 m2. The heat flux is generated by temperature differences between
different regions:
J = - k dT/dr
T is the (absolute) temperature at a certain depth and r is the
distance from the centre of the Earth (the radius). J is
proportional to the temperature gradient dT/dr, the derivative
of temperature T to distance r from the centre. Thermal
conductivity k [Wm-1K-1] is a material property: it has a
characteristic value for every different medium (see BINAS,
Tables 9 and 10).
The model assumes a uniform distribution of the heat
production density H [W/kg] throughout the sphere that
corresponds to the chondritic hypothesis for the Earth’s
composition. Within the whole sphere of radius R, we first
consider the heat produced within a smaller sphere with radius
r (see Figure 6.7). The heat production per unit of time in the
Figure 6.7: A uniformly heated spheresphere of radius r is called Q . In the case of thermal
in
with radius R and a smaller sphere
equilibrium, it should be equal to the total heat flux Qout
with radius r within.
through the surface of the sphere with radius r.
Exercise 6-8*: Thermal equilibrium
What happens to the temperature if the heat production in the radius-r sphere does not equal the
total heat flux through the sphere’s surface?
Heat production Qin can be calculated with:
Qin = H . m = H .  . 4/3  r3
Here, H is the heat production density, m the mass
of a sphere with radius r and density :
m =  . V =  . 4/3  r3
The heat loss through the surface, Qout, is:
Qout = J . 4  r2 = - k dT/dr . 4  r2
With Fourier’s law of heat conduction:
J = - k dT/dr
In a steady-state model:
Qin = Qout
Or:
H .  . 4/3  r3 = - k dT/dr . 4  r2
Thus:
dT / dr = - H r / 3k
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The Dynamic Earth
Convection: the Earth as an heat engine
Exercise 6-9***: Temperature distribution and heat production
According to the equation deduced above, the Earth’s internal temperature decreases from centre
to surface.
a. How can you see from this equation that the absolute temperature gradient increases when
going from centre to surface?
b. What should you measure in chondrites to determine the magnitude of the gradient at the
Earth’s surface when assuming a chondritic composition for the Earth?
An equation that contains the derivative of a function (here the function is T(r) and dT/dr is the
derivative) is called a differential equation. In our case, the derivative of temperature T with
respect to radius r is a linear function of r. We want to find the radial temperature distribution T(r),
or geotherm, to be able to calculate the temperature at any given distance from the centre.
Because of the spherical symmetry of our model, the geotherm is constant along a concentric
spherical surface. Therefore, temperature is the same for all points with the same given radius.
How can we determine T(r) from differential equation dT/dr = - H r / (3k)?
We need a function T(r) with a derivative dT/dr that is a linear function of r. T(r) is the primitive
function of dT/dr. Because the derivative of r2 is 2r, the geotherm T(r) must be proportional to ½
r2. An at first arbitrary constant must be added. This integration constant is determined when the
temperature in one point is specified. For this purpose we will use the temperature at the surface
of the Earth of 10oC: T(R) = TR = 283 K.
Exercise 6-10***: Solving for the geotherm
The solution of the differential equation for the geotherm is T(r) = T(R) + ρH(R2 - r2) / 6k.
Check the solution (the primitive of dT/dr) by solving the integral
dT '
H
'
'
r dr ' dr  T ( R)  T (r )  ( 3k )r r dr
R
R
with boundaries R, the distance from the centre to the Earth’s surface, and r, the distance from the
centre to some point r within the Earth.
Exercise 6-11***: The temperature distribution in the conductive spherical model
Use the following data for this exercise: the radius of the Earth is 6378 km, the temperature at the
Earth’s surface is 283 K, k is 4 WK-1m-1, the average density of the Earth is 5500 kgm-3 and H is
5 . 10-12 Wkg-1. Also use the equation for the geotherm given in Exercise 6-10.
a. Sketch the temperature with distance from the centre of the Earth if the geotherm were to be
correct.
b. Determine the temperature at the Earth’s centre.
c. Determine the temperature at the point midway between the centre and the surface. This point
approximates the depth of the core-mantle boundary.
Exercise 6-11 gives temperatures far above the melting points of rocks and metals. On the one
hand, this shows that assuming heat production through radioactive decay can explain high
temperatures within the Earth for long periods of time, which is an important improvement of the
Kelvin model. On the other hand, the high temperatures found are not realistic, because they
require a significant part of the Earth’s interior to be liquid or even to be in the gas phase. This
contradicts seismological observations that show that the outer core is liquid and the mantle solid.
In conclusion: the conductive equilibrium model is a good step forward in modelling the Earth’s
thermal state, but does not yet suffice. The uniform heat production density results in a
temperature contrast between centre and surface that is unrealistically high. This high contrast is
the result of the required heat flux through the surface and the low thermal conductivity (high
thermal resistance) of mantle rock on which conductive heat transport depends.
Exercise 6-12**: Heat production within the Earth
Measurements show that thermal power that 'leaks' through the surface of the Earth is
approximately 44 · 1012 W. This observation can be related to the conductive model under
consideration. Use the parameters given in Exercise 6-11 to complete this exercise.
a. Calculate from this the heat flux through the Earth’s surface predicted by the model
b. Calculate the total amount of heat produced in the model Earth by radioactive decay.
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Convection: the Earth as an heat engine
The Dynamic Earth
c. Compare the result of b. with the total actual amount of heat lost through the Earth’s surface
determined by the measurements. Did you expect this?
d. Assume the difference of c. is related related to the cooling of the Earth. Show that the current
cooling rate of the Earth is about 72 K per billion years.
An extended conductive model?
We could modify the conductive model by assuming that the heat producing radioactive isotopes
are not uniformly distributed, but concentrated in a spherical shell with R - d < r < R. Results of
such a model show lower interior temperatures, because heat is mainly produced at shallow
depths. But, why would radioactive elements be concentrated in the outer layers of the Earth?
Scientists have tried to explain this layering with the solidification of mantle rock in the young
Earth. From Petrology Studies it is known that radioactive elements in a magma concentrate in the
remaining melt upon crystallization of the magma. When the melt is less dense than the solidified
material, the decreasing remainder of the melt that becomes enriched in radioactive isotopes over
time, will collect in the shallow mantle during the solidification of an early magma ocean.
A model with layered internal heating requires that the layering remains intact. However, plate
tectonics, subduction and mountain building represent vertical motions in the Earth that destroy
such layering. Therefore, the layered conductive model is not plausible.
Modelling the Earth’s thermal state: a convection model
Conduction alone cannot explain the Earth’s thermal state; therefore, we will now discuss a model
that also includes convective flow. We assume the Earth model is divided into a core and a mantle.
Convection takes places in the mantle. Could this model lead to a geotherm lower than the melting
temperatures of mantle rock, like seismological observations suggest?
Geological (mountain building, Chapter 5) and geophysical (plate tectonics, Chapter 2) phenomena
show that the Earth’s mantle is not static. Take, for example, the process of postglacial rebound.
During the last glacial period, Northern Europe and North America were covered with a thick layer
of ice. Melting of the ice layer disturbed the equilibrium situation. Since then, Scandinavia (among
others) is slowly pushed upwards to re-establish this equilibrium. Another example of mantle flow
is the slow, large-scale cycle of lithosphere production (at MORs) and destruction (in subduction
zones). The flow of mantle material takes place even though the mantle is solid; this is possible
because solids like ice and rocks creep. For example, consider the flow of ice in a glacier, or the
deformation of rocks (Chapter 5).
Obviously, flow of a solid is much slower than flow of a liquid, under conditions prevailing in the
Earth's mantle, namely only several centimetres per year. Solid materials that display creep
behaviour are very viscous. Viscosity is denoted by the Greek letter η. Already in 1935, the
geologist Haskel estimated the viscosity of the mantle (from postglacial rebound data from
Scandinavia) to be in the order of 1021 Pa s. This is much larger than the viscosity of water, which
is in the order of 10-3 Pa s.
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6.4 The start of convection in a
viscous medium
Imagine a viscous medium, like syrup, that
is heated from below. Heating of the
bottom results in a local temperature
increase. The medium expands in the
heated
region,
so,
locally,
density
decreases. The density difference with the
surroundings results in an upward force
(Archimedes’ law) that, when big enough,
causes upward flow. The rising hot material
is cooled at the surface. Therefore, it will
sink again: a convection cell is formed.
The bottom of the Earth’s mantle is formed
by the hot boundary with the outer core,
while the boundary with the crust
represents the mantle’s cold top.
Figure 6.8 shows a possible convection cell
in the mantle: flow is driven by the
temperature difference between the lower
mantle and the Earth’s surface.
Figure 6.8: A schematic drawing of the large-scale
convective flow in the Earth’s mantle. Convection is
driven by the temperature difference between the cold
lithosphere and the warmer core-mantle boundary.
Oceanic crust is formed at a mid-ocean ridge and is
recycled at the trench of a subduction zone.
It is not hard to imagine a convection cell
in a liquid or in the air (for example, in a
thundercloud on a warm day), but in the
solid mantle? Scientists have shown that
flow in rocks is possible using a specific equation. To give you an idea where that equation came
from and what it represents, we will take another look at the viscous syrup layer mentioned above.
In a laboratory experiment, we heat the bottom of the layer just a little. The small temperature
contrast between top and bottom of the layer is not enough to cause the fluid to flow: convection
only starts when the temperature contrast is larger than a critical value. Rayleigh and Benard have
studied this phenomenon extensively.
Before the critical value for the temperature difference is reached, the viscous layer only conducts
heat. In case the critical value is exceeded, however, the liquid starts to move: hot liquid flows up,
while cool liquid sinks. Convection increases the upward heat flux. If the temperature difference
increases further, convective heat transport will dominate over conduction.
Exercise 6-13: Heat transport within a viscous fluid
Consider a viscous fluid heated from below. The liquid is at rest.
a. Which type of heat transport dominates in the current state of the liquid?
b. How can you cause the fluid to start moving?
c. Which type of heat transport then dominates?
Rayleigh showed that the convective behaviour of a viscous fluid heated from below can be
described with only one dimensionless number: the Rayleigh number. This number depends on the
type of material (with its characteristic density ρ, thermal expansion coefficient α, diffusion
coefficient κ [kappa] and viscosity η [èta]), the gravity acceleration g, the applied temperature
difference ΔT and the thickness h of the fluid layer:
Ra 
 g  Th 3

Below the critical value of Ra ~ 1000, no material flow occurs. So, there will be no heat transfer
through convection, but only through conduction. Above the critical value, the heat transport
capacity of the viscous material increases greatly because of the convective flow.
Within the mantle, the Rayleigh number must exceed its critical value for convection to occur.
Using the mantle viscosity known from postglacial rebound and the estimated temperature contrast
between the top and bottom of the mantle, you find that the Rayleigh number is indeed large
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Convection: the Earth as an heat engine
The Dynamic Earth
enough (Ra = 106-107). Thus, convection cells can form in the Earth’s mantle. We can now use the
Rayleigh number to describe the cells in detail.
Computer calculations of a Rayleigh-Benard convection cell
Figure 6.9 shows the results of computer simulations of a Rayleigh-Benard cell at three different
values of the Rayleigh number: 104, 105 and 106. The bottom of the model domain is kept warm,
the top cool: the bottom temperature is set to 1, the top temperature to 0 (in arbitrary units).
Depth is 0 at the top and 1 at the bottom.
Figure 6.9a gives the temperature distribution in the cell. For each Rayleigh number, a hot plume is
seen to rise up from the warm lower boundary (left red region). On the right side of the cell, you
can also see a cold downwelling (blue region). The warm plumes are often thought to represent hot
spots in the mantle, such as those underneath Hawaii and Iceland. The cold downwellings
represent the subduction of an oceanic plate. With increasing Rayleigh number, the hot and cold
structures become thinner, and the well-mixed interior of the cell becomes larger (white region).
The interior has a temperature close to the average temperature of top and bottom.
Temperature
Rayleigh number
Figure 6.9: From left to right: Figure a, b and c. a) The temperature distribution in a RayleighBenard convection cell. Red represents high temperatures, blue low ones. b) The horizontally
averaged temperature at different depths within the cell. c) The ratio of the heat flux Q and the
conductive part of the heat flux Qconduct.
Figure 6.9b shows the horizontally averaged temperature with depth for the corresponding
convection cells. The graphs resemble the geotherm that gives the (horizontally) averaged
temperature distribution within the Earth. They show that the temperature in the upper and lower
boundary layer changes strongly with depth. In the thick layer in between the boundary layers,
where convection occurs, the average temperature hardly changes though (it remains close to
0.5). Thus, the largest temperature variation occurs in the boundary layers. The boundary layers
become thinner for increasing Rayleigh numbers. Within these layers, vertical heat transport can
only occur through conduction, because there is no vertical flow.
The decreasing thickness of the boundary layers with increasing Rayleigh number results in a
higher heat flux (with the interior temperature constant at about 0.5). This can be explained with
Fourier’s law: The temperature increase over the boundary layers remains the same, but the layers
become thinner. Because heat flux is proportional to ~1/Δl, with Δl the thickness of the boundary
layer, the flux increases for higher Rayleigh numbers.
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Convection: the Earth as an heat engine
Figure 6.9c gives the ratio between the total heat flux Q and the heat flux Qcond that represents the
heat flux through the layer if only conduction takes place. The graph shows that convection is a
critical phenomenon. When the Rayleigh number is below the critical value of approximately 780, Q
/ Qcond = 1 because only conduction takes place. Above the critical value, the heat flux quickly
increases with the Rayleigh number due to the contribution of convection. For example, for Ra =
106, the heat flux through the cell is about 23 times larger than in a cell without convection.
The Rayleigh-Benard convection simulations and the estimates of the mantle’s Rayleigh number
(Ra > 106) indicate that convective heat transport is much more effective than heat conduction
alone. Therefore, this process could play an important part in controlling the thermal state of the
Earth. In the next section, we will investigate whether Rayleigh-Benard convection calculations can
predict realistic values for the Earth’s interior temperature. Can this model explain why the outer
core is liquid and the inner core is solid? And what about the layering of seismic velocities and
density found in the PREM model?
6.5 The internal temperature of the Earth
6.5.1
Composition and temperature of the Earth’s interior
Information about the deep Earth is obtained from seismology, gravimetry (the study of the Earth’s
gravitational field) and laboratory experiments. When the composition of a part of the mantle is
known, HPT experiments can be used to assess the influence of high temperatures and pressures
on the phase of the material. Phase transitions within the Earth (solid-solid and solid-liquid) can be
recognized from sharp changes in the material parameters density and seismic wave velocity in the
PREM model. At a solid-solid phase transition, one crystal shape changes into another with the
same chemical composition. For example, olivine, the most important mantle mineral (see Section
6.2.4), experiences several solid-solid phase transitions with
increasing depth, such as the spinel-post-spinel transition
(see Figure 6.10).
Phase boundary
When HPT experiments have demonstrated how the pressure
at which a solid-solid phase transition occurs depends on
temperature, a line can be constructed that represents the
phase boundary in a pressure-temperature phase diagram
for a given material (see Figure 6.10 for an example).
We found sharp transitions in mantle material properties
with increasing depth in the mantle (see PREM model, Figure
6.10). We can connect these transitions to experimentally
determined phase changes in olivine. The temperature of the
phase change can then be established as follows:
1) Determine the location/depth of the phase transition
(from seismological data and the PREM model).
2) Use the PREM model to determine the pressure at this
depth.
Temperature T
Figure 6.10: Schematic pressuretemperature phase diagram for
the phase change at about 660
km
depth
that
forms
the
boundary between upper and
lower mantle.
3) Apply the pressure found in 2) to look up the temperature in the, experimental phase diagram
as indicated by the arrows in Figure 6.10.
We will use this method to determine several fixed points for the temperature distribution within
the Earth, the geotherm. This way we can use phase transitions as a thermometer for mantle
temperatures.
6.5.2
Clues to the Earth’s temperature distribution
Assuming a chondritic composition for the mantle and core, the mantle mainly consists of peridotite
(with minerals such as olivine and garnet, see Section 6.2.4) and the core of iron and nickel (see
Section 6.2.3). We can use HPT experiments to study the phase changes of these materials. Many
rocks have been investigated at the temperatures and pressures of the mantle and core. For most
rocks, the pressure at which a phase transition occurs can be approximated as a linear function of
temperature (see Figure 6.10, for example).
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Determining the temperature at the boundary between upper and lower mantle
We will use the method described above to determine the temperature at the transition from upper
to lower mantle at a depth of about 660 km. Seismological data shows that primary and secondary
wave velocities as well as density suddenly increase at this depth; indicating that olivine undergoes
a phase transition here. HPT experiments show that the high pressure phase of olivine, called
ringwoodite ((Mg;Fe)2SiO4 with spinel structure), changes into post-spinel, which consists of the
minerals perovskite (Mg;Fe)SiO3 and magnesiowüstite (Mg;Fe)O.
The spinel-post-spinel phase transition takes place at a pressure of about 24 · 109 Pa (you can read
off the pressure from the PREM-model, left panel of Figure 6.3, the right panel gives the
corresponding mineralogical interpretation of the phase change). From the phase diagram for the
spinel-post-spinel phase change, we find the phase change temperature: at P660 = 23.9 GPa, T660 =
1900 ± 100 K.
Determining the temperature at the inner and outer core boundary
In a similar way, the temperature of the solid-liquid phase transition at the solid inner core and
liquid outer core boundary is determined with HPT experiments and the PREM model. The PREM
model shows a pressure at the inner-outer core boundary of 330 GPa. From the experimentally
determined melting temperature of the core material (mainly Fe, Ni and S) and the pressure value
of 330 GPa pressure, it is estimated that the temperature at the boundary is about 4850 K.
Figure 6.11 shows the three fixed points of the geotherm:
1. The temperature at the Earth’s surface, about 283 K.
2. The temperature of the phase transition at a depth of 660 km (upper-lower mantle boundary),
about 1900 K (the left dot).
3. The temperature of the phase transition at a depth of 5150 km (inner-outer core boundary),
about 4850 K (the right dot).
The estimated temperature curve is interpolated between the three fixed points. Melting
temperatures of the mantle and core material are also indicated (dashed lines, denoted by
‘melting’). These lines show that temperatures in the mantle are below melting temperatures, while
Figure 6.11: a: A graph of the averaged
temperature with depth, called the geotherm
(solid line). The pressure is also indicated at
important boundaries. The dashed lines give
the melting temperature with depth. UM =
upper mantle, LM = lower mantle, OC = outer
core and IC = inner core.
b: The temperature, denoted by core adiabat
in the liquid outer core against pressure P.
The boundary between the outer and inner
core is determined from the intersection of
the melting temperature (Fe-O-S melting- and
the geotherm. CMB = core-mantle boundary
and ICB = inner core boundary. (R. Boehler
1996)
temperatures in the outer core are higher than the melting curve.
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Exercise 6-14**: The inner-outer core boundary
a. The caption of
Figure 6.11b says: “The boundary between the outer and inner core is determined from the
intersection of the melting temperature (‘Fe-O-S melting’) and the geotherm.” Explain. Hint: How
do the inner and outer core differ?
b. Explain why the solid inner core has grown through time at the expense of the outer core.
Determining the temperature at the core-mantle boundary
We can also determine the temperature jump at the core-mantle boundary at a depth of 2900 km
(see
Figure 6.11b). This jump controls the heat flux out of the Earth’s core; therefore, we first have to
discuss the core-mantle boundary and the type of heat transport at this boundary. From now on,
we assume that heat transport in both the mantle and core only takes places through convection,
so we ignore conductive heat transport. We will follow the heat flux from the core to the Earth’s
surface and pay special attention to what happens to the heat flux at the core-mantle boundary. At
this boundary, no vertical convective flow can take place.
Convective heat transport is very efficient in the outer core because of the strong upwellings of
liquid core material (the viscosity of liquid iron is low, so there is little resistance to flow). When a
convective material flow arrives at the bottom of the core-mantle boundary layer, it collides with
the solid mantle material that is only half as dense. Therefore, the flow is deflected horizontally: no
upward convective flow is possible here. The solid mantle material above the boundary has a very
high viscosity. Here, convection is still possible (as creep), but at a speed of only several
centimetres per year.
In the core-mantle boundary layer, heat flow is only possible through conduction. The layer around
the core acts as an insulator, because conductive heat flow is much less efficient than convective
flow. At both the bottom and the top of the boundary layer, there is a large change in temperature.
At the core side of the layer, temperatures are about 4000 K, while at the mantle side they are
about 2500 K. This means that the temperature decreases about 1500 K in only 200 km (7.5
K/km)! For comparison, in the outer core (over 2000 km thick), temperature decreases only 500 K
(0.25 K/km). That is 30 times less! Because convective heat flow is 30 times faster than conductive
heat flow, the assumption that we can neglect conduction in case of convection is allowed.
Temperatures also decrease strongly in the lithosphere, from the upper boundary of the mantle to
the surface of the crust. Within the mantle and core, however, temperatures increase only slowly
with depth; this corresponds to the convection cells of Figure 6.9.
Exercise 6-15**: Explaining Figure 6.11
Use the questions below to find out if you understand
Figure 6.11 better now you have read the text above.
a. What do the black dots on the solid line represent?
b. How are the fixed temperatures interpolated and what assumptions have been made in doing
so?
c. Which types of heat transport were neglected?
d. At what depth does the core-mantle boundary lie? What happens to the geotherm at this
boundary?
e. What causes the geotherm behaviour at the CMB?
Exercise 6-16**: The temperature in mines
Miners know from experience that temperature increases with depth. In the shallow marl mines in
southern Limburg, The Netherlands, temperature is constant at 14oC. But in the old coal mines
hundreds of metres deep, temperatures are much higher.
a. Calculate the temperature increase per kilometre of depth with the help of Fourier’s law.
Assume that temperature increases linearly with depth. Use typical crust and shallow mantle
properties: J = 70 · 10-3 W m-2 and k = 3.0 W m-1 K-1.
b. What is the temperature in a mine shaft at 1.5 km depth?
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Exercise 6-17**: The temperature distribution in the outer core
Use the data in Figure 6.11 to estimate the temperature increase per kilometre in the outer core.
6.5.3
Heat flux and the Earth’s magnetic field
The liquid outer core mainly consists of the ferromagnetic metals iron and nickel that enable the
generation of the Earth’s magnetic field, an important property of the outer core. Does the
convective model for the Earth's thermal state that we have developed so far allow for this
‘magneto-hydrodynamic' process, or geodynamo?
The geodynamo is generated by convective flows in the liquid iron-nickel outer core that are
accompanied by electric currents in the electrically conducting material. These electric currents
generate a magnetic field. Subsequently, interaction of the fluid flows and the magnetic field
generates an electrical potential field and corresponding electric current through electro-magnetic
induction. To maintain this geodynamo process, the heat flux out of the core cannot become too
high or too low.
Because of the insulating effect of the core-mantle boundary layer, the core loses heat slowly. This
way, the outer core can remain liquid and convection is sustained. But, heat loss cannot be too low
either. Research shows that the core should lose at least 1012 W to the mantle in order to keep the
dynamo process working. This heat must then be brought up to the crust by convective flow in the
mantle to be lost to space. According to the convection model, most heat is brought up where
there is a convective flow upwards. From plate tectonics, we know where to find such a flow:
underneath a mid-ocean ridge. Figure 6.12 gives the heat flux distribution at the Earth’s surface.
You can see that most heat is indeed lost at mid-ocean ridges, where material rises from depth.
Figure 6.12: The heat flux at the Earth surface. The white lines show the continent contours, the
dashed black lines the mid-ocean ridges. The colouring represents the magnitude of the heat flux q0 in
MW.m-2 given to the earth surface. The total heat flux can be calculated by: Q = 44.1012 W. There can
be seen that the mid-ocean ridges function as a heat flux for the convectering mantel system; there,
the heat flux is the largest and within the deep sea trough the smallest.
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Exercise 6-18**: The convection model and the Earth’s magnetic field
The convection model states that there is an insulating boundary layer between the core and the
mantle. Temperature decreases strongly through this layer (7.5 K/km).
a. Use Fourier’s law to calculate whether enough heat (at least 1012 W) passes the core-mantle
boundary layer to sustain the geodynamo. Use a thermal conductivity of 3 WK-1m-1 to calculate
the heat flux density J [Wm-2]. The core has a radius of 3300 km.
b. Why is upwelling of mantle material at mid-ocean ridges needed to maintain the Earth’s
magnetic field?
c. Does the convection model contradict the generation of the Earth’s magnetic field?
The removal of heat from the core through the core-mantle boundary and from the mantle above is
essential to the survival of the geodynamo. Mars, a neighbouring planet, lost its magnetic field
about 4 Ga. However, there are reasons to believe that Mars still has a liquid iron core. A plausible
explanation for the disappearance of the dynamo on Mars lies in the decreased heat transport
when early plate tectonics ceased and Mars became a one-plate planet.
Computer models of the geodynamo are nowadays able to reproduce the important characteristics
of the geomagnetic field, such as its dipole nature and varying strength and the irregular reversals
of the field with an average period of several hundred thousands years (for example, see
http://www.es.ucsc.edu/~glatz/geodynamo.html).
6.6 Liquid magma within solid mantle rock
According to seismological data, the mantle and crust are predominantly made up of solid rock.
Still there are regions where rock is molten, mainly underneath spreading ridges. This is known
from volcanoes from, for example, Iceland.
At mid-ocean ridges, the molten rock forms new basaltic oceanic crust. How can solid rock that
cools while it rises become liquid? Chapter 5 has touched upon this subject already, but you will
understand the process better with the knowledge you have gained from this chapter.
We can explain the melting of rising mantle rock with the help of a (melting) phase diagram of
mantle material (peridotite). When the pressure on a sample of peridotite decreases because the
rock reaches shallower depths, its melting temperature decreases as well. Figure 6.13 shows the
formation of melt underneath an oceanic spreading ridge schematically. On the left side, you see a
symmetric upward flow of mantle rock underneath the ridge. The vertical dashed line indicates the
model’s symmetry axis. The right figure, with a corresponding depth/pressure axis, shows the
melting phase diagram of peridotite. The thick solid line shows that the melting temperature
increases with pressure, so, also with depth. The geotherm indicates the temperature of the rising
mantle rock. This line and the thick phase line intersect at a depth of about 70 km. Starting from
this depth, the rock will gradually melt while it rises farther. The heat needed for melting is
extracted from the rock itself. Therefore, melting rock, rising to the surface, cools a little faster
than before the onset of melting, hence the bend in the geotherm at 70 km depth. Melting rock has
a porosity of about 1 volume percent; therefore, melt rises faster than solid rock. The formed
magma concentrates in magma chambers underneath the spreading ridge. The outflow of basaltic
lava from the chambers feeds the formation of new oceanic crust.
Exercise 6-19*: Is the interior of the Earth liquid?
Many people argue that because molten rock flows out of volcanoes, the interior of the Earth is
molten as well. Would you argue differently? Explain.
6.7 Recent developments
6.7.1
Observing subduction in the mantle
The convective flows depicted in Figure 6.8 correspond to a mantle circulation pattern of upward
flow underneath MORs and downward flow at subduction zones, where lithosphere sinks into the
deep mantle. We can actually see that cool oceanic lithosphere can sink deep into the mantle from
images of the mantle obtained with seismic travel time tomography. Such an image is shown in
Figure 6.14. Two subduction zones are visible in this cross section running from the Aegean Sea to
Japan. You can recognize subducting lithospheric slabs as thin blue structures. The blue colour
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Spreading Mid Ocean Ridges
Temperature
Depth first melting
Upwards mantle stream
Figure 6.13: Left panel: Schematic representation of the formation of basaltic
oceanic crust through partial melting of rising mantle rock underneath a
spreading ridge. Right panel: The schematic phase diagram of peridotite mantle
rock. The intersection of the geotherm with the phase line determines the depth
above which melting occurs.
indicates a higher seismic wave velocity, which corresponds to lower temperatures. The slabs enter
the mantle at an angle and are visible up to great depths.
Figure 6-1: A tomografic division of seismic speed deviation in a mantle cross cut of the Aegean
Sea towards the Japanese islands. The dotted lines of approximately 400 to 660 km depth point
out the location of two solid phase transitions of the olivin mantle material. The 660 km phase
transition line marks the boundary between the upper and lower mantle. Subduction zones come
to an expression as sharply bordered areas with high wave speed. The white symbols near Japan
point out earthquake locations in the subduction zone.
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6.7.2
An additional fixed point for the temperature distribution in the mantle
In Section 6.4.2 we learned that the temperature difference ΔT over the core-mantle boundary
layer is about 1500 K. The discovery of another phase transition in the mantle provides an
additional fixed point for the mantle’s temperature distribution. This phase transition is indicated in
Figure 6.3 with ‘new phase’. During this phase transition, the mineral perovskite changes into the
denser mineral post-perovskite. Experiments have demonstrated that this phase transition takes
place at 120 GPa and about 2500 K, and seismological observations have confirmed it's presence in
the deep mantle.
With more detailed information about the temperature structure directly above the CMB, it is
possible to determine the heat flux out of the core. This is important for our understanding of the
magneto-hydrodynamic convection process in the liquid outer core that maintains the Earth’s
magnetic field. Rough first estimates (see Exercise 6-18 as well) point to a global CMB heat flux of
1013 W. This estimate is still quite uncertain, because the thermal conductivity close to the core is
not very well constrained.
6.8 What have we learnt?
In this chapter we have tried to find the engine driving the motion within the Earth and at its
surface. We turned to the Earth’s thermal state to uncover how the internal heat produced by
natural radioactive decay can be lost at the Earth’s surface without the interior temperature rising
above the melting temperature of mantle rock. Slow convective flow in the mantle solves the
Earth’s heat problem and the resulting mantle circulation explains the observed motion of oceanic
and continental plates and, thus, plate tectonics. We have also seen that the mantle convection
model coincides with the measured distribution of the heat flux through the surface of the Earth
and that the thermal boundary at the CMB, predicted by the model, is confirmed by data from
seismology and mineral physics.
So, did we find all the answers? No, as in most natural sciences, in geodynamics answering one
question brings up another. For example, these questions remain unanswered (for now):
Has large-scale plate tectonics always been active on Earth? Or did plate tectonics only start when
the Earth had cooled sufficiently? If so, was a smaller scale chaotic type of mantle circulation
responsible for the heat loss of the young Earth?
Why do the other terrestrial planets Mercury, Venus and Mars and the Moon no longer show any
signs of plate tectonics? This is one of the main questions of comparative planetology, a branch of
science that has expanded over the last few years due to the enormous amount of data available
from planetary research missions. Comparative planetology has recently been extended to planets
outside our solar system i(see http://www.exoplanet.eu and http://kepler.nasa.gov).
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Glossary
Accumulation of sediment: the build up of loose deposits.
Anomaly: a deviation from the average or reference value (for example for gravity).
Asthenosphere: the viscous part of the mantle that lies directly underneath the lithosphere, found
between a depth of approximately 80 and 300 km . The tectonic plates move over the asthenosphere.
Azimuth: the horizontal angle measured clockwise from the north of the fault orientation at the surface.
Basalt: dark extrusive rock formed during volcanic eruptions. Basalt is rock that has cooled fast, so few
or no visible crystals are formed. During cooling, basalt usually fractures into polygonal columns. In The
Netherlands, these columns are used to reinforce dikes.
Bathymetry: depth measurements of the ocean floor, or a map showing ocean depths.
Caldera: a circular depression of the landscape formed by an explosive volcanic eruption. A caldera is
formed when the roof of a volcano’s large, shallow magma reservoir collapses due to the extrusion of
large amounts of magma over a short period of time.
Chondrites: the largest group of meteorites. They contain chondrules, small spherical particles, after
which they are named. The chemical composition of the Earth resembles that of the chondrites.
Conduction: the transport of heat through a substance; the passing on of vibrations by atoms in a
lattice.
Convection: The transfer of heat by flow of material caused by hotter, less dense material rising and
colder, denser material sinking under the influence of gravity.
Convergent plate boundary: the margin between two tectonic plates where the plates move toward
each other, one of which subducts underneath the other.
Core: the central part of the Earth, starting at a depth of 3450 km. The core is divided into a liquid outer
core and a solid inner core.
Crust: the outer layer of the Earth. The crust is relatively thin: oceanic crust is about 7 km thick and
continental crust 30 to 50 km thick.
Crustal root: the thickened crust underneath a mountain chain that allows the mountains to maintain
isostatic equilibrium.
Crystal: a homogeneous solid with well-developed surfaces which express the regular internal
arrangement of the crystal’s atoms. The more time and space available for the cooling of a melt, the
larger a crystal will grow.
Deformation: the change in the shape, volume, position or orientation of a rock.
Divergent plate boundary: the margin between two plates that move away from each other.
Dome: a swell resulting from the slow extrusion of viscous lava from a volcano the build-up of viscous
lava in the crater of a volcano. Sometimes this build-up hampers the extrusion of magma, causing it to
slow down.
Epicentre: the location on the Earth’s surface directly above the hypocentre of an earthquake. The
effect of an earthquake is felt most strongly at its epicentre.
Erosion: the removal of rock through physical processes such as water flowing, ice or wind.
Focus of an earthquake (= hypocentre): the point of origin of the earthquake within the Earth .
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Glossary
Force: this describes the push or pull exerted on an object. The unit of force is Newton [N].
Fracture zone: a region of cracks in the ocean floor continuing from a transform fault between two midocean ridge segments.
Granite: coarse, crystalline igneous rock. Granite cooled slowly beneath the Earth’s surface and had
enough time to grow large crystals.
Great circle: a special circle on the surface of a sphere. It is the largest circle on a sphere and dividing
it into two equal halves. A great circle therefore has the same centre as its sphere.
Half-life: the time it takes for a certain amount of radioactive isotope to decay to half its original value.
Every radioactive isotope has a unique half-life.
Hazard management: the measures taken to control or reduce the effects of natural hazards - such as
risk assessments, taking precautions and writing disaster scenarios.
Hotspot: a stationary plume in the mantle made up of hot mantle rock rising from large depths of the
Earth. Volcanism occurs in the region above the plume, where material starts to melt at shallower
levels. Hawaii, for example, was formed in this way.
HPT experiments: High Pressure and Temperature experiments to model processes taking place in the
interior of the Earth.
Hypocentre: the location within the Earth’s crust where earthquake vibrations originate.
Insolation: solar radiation that reaches the surface of the Earth.
Isotopes: atoms of the same element that have a different atomic mass. Isotopes have the same
number of protons in their nucleus, but a different number of neutrons.
Isostasy: the concept that where the crust is in gravitational equilibrium with the mantle. Because the
Earth’s crust has a lower density than the mantle, it ‘floats’ on top of the mantle (like wood floating on
water).
Lava: liquid rock that extrudes from a volcano, flows over the Earth’s surface and eventually solidifies.
Limestone: sedimentary rock mainly consisting of calcite (CaCO3).
Lithosphere: the crust and the upper part of the mantle that form the tectonic plate. Beneath the ocean
the lithosphere is about 70 km thick, whereas a continental lithosphere can be well over 125 km thick.
Longitudinal wave (primary wave, P-wave): a seismic wave that oscillates in the same direction as
its propagation direction. The P-wave is the first wave to arrive at a seismic station.
Magma: liquid rock below the Earth’s surface. When magma extrudes slowly, not explosively, and flows
over the Earth’s surface, it is called lava.
Magma chamber: part of the crust where magma is contained in a closed reservoir. This chamber is the
source of volcanism.
Mantle: the 2900-kilometre thick layer between the Earth’s crust and core. The solid mantle is divided
into an upper mantle and a lower mantle.
Marble: metamorphic limestone consisting of carbonate crystals (mostly calcite, CaCO3). Marble comes
in several different colours and is often used for tiles and statues.
Metamorphic rock: the rock formed due to transition of the mineral content of the original rock (for
example, sedimentary or igneous rock) as a result of high pressures and/or temperatures.
Mid-Atlantic Ridge and Mid-Oceanic Ridge (MOR, spreading ridge): the plate boundary
underneath an ocean where two plates diverge and new oceanic crust is formed.
Milankovitch: The Serbian mathematician who described the variation in the Earth’s orbit around the
Sun with the help of mathematical equations. The Earth’s orbit varies in three ways: its eccentricity
varies with a period of 100,000 years, its obliquity has a period of 40,000 years and its precession a
period of 20,000 years. These kinds of orbital variations change the insolation of the Earth, which in turn
affects the Earth’s climate. Thus Milankovitch linked the Earth’s orbital variations to the ice ages.
Orogenesis: mountain building.
Paleomagnetic timescale: the timescale based on paleomagnetic datings that use the Earth’s
magnetic field and its reversals to determine the age of rocks.
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Phase change: the transition of a material from the liquid phase to a solid or gas phase or vice versa.
Solid material can also exist in different phases. For example, carbon can be found in a diamond form
and a graphite form.
Plates: the Earth’s surface is divided into several tectonic plates. These plates are made up of the
lithosphere, which consists of oceanic and/or continental crust, and the underlying upper part of the
mantle.
Plate tectonics: the theory that states that the Earth’s surface is divided into several large, rigid plates
that move slowly with respect to each other. Along the plate boundaries, geological phenomena such as
volcanism, earthquakes and mountain building take place.
Polar jet stream: the strong, concentrated winds in the troposphere that drive weather systems.
Pressure: force per unit area exerted on an object. Pressure is stress equal in all directions.
Sedimentary rock: rock formed through the transport and deposition (sedimentation) of loose material.
Seismograph (seismometer): a device that records seismic waves.
Shield volcano: a shield-shaped volcano made of mostly basaltic lava flows. Shield volcanoes are
characterized by slow extrusions that result in gently sloping flanks and are commonly found at MORs
and hotspots.
Shear modulus: the material property of elasticity with respect to shear deformation.
Slip: the size and direction of the relative motion along a fault plane.
Stress: the force exerted per unit area, in Pascal (1 Pa = 1 N/m2).
Igneous rock (extrusive or intrusive rock): the rock formed through the crystallization of magma.
Strain partitioning: plate motion is not accommodated perpendicular to the plate contact, but the
relative motion is partitioned into two components, one perpendicular and one parallel to the contact.
Stratovolcano: a conical volcano built up of alternating layers of lava and tephra (ashes, pyroclastic
flow deposits and more). The volcano forms through explosive eruptions and is most commonly found
along subduction zones.
Subduction: the process by which the ocean floor dives underneath a continent or island arc.
Tephra (pyroclastic deposit): the collective term for deposits of fragmented volcanic material that are
produced in an explosive volcanic eruption, such as ash, volcanic bombs and blocks and mud flows.
Tectonics: motion and deformation of (parts of) the Earth’s crust or lithosphere.
Thermal boundary layer: the lower mantle layer above the core-mantle boundary that is characterized
by a large contrast in temperature.
Tomographic map: map or image based on the spatial variation of seismic wave speeds in the mantle.
Transform fault: a fault formed when two tectonic plates slide past each other.
Transverse wave (secondary wave, S-wave): a wave that oscillates in the direction perpendicular to
its propagation direction. Transverse waves arrive at seismic stations after the longitudinal body waves.
Tsunami: extremely long waves of water generated by vertical movement of the ocean floor.
Volatile: the constituent part of magma that can easily escape when it is in its gas phase (when the
magma rises or cools). For example, water (H2O), CO2, SO2, HCl and H2S.
Weathering: the disintegration of rock due to vegetation and the weather.
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