Download Isostasy and Earth`s Global Topography Measure the density of 1

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GEOS 100 Lab 1 - Based on AGI manual 10 edition F-2014
Thinking like a Geologist: Observing and Measuring Earth Materials and Processes
This lab is worth ~2% of the course total. Use and hand in this lab handout and do not tear pages
from your lab manual to preserve it for later use.
Work in pairs (or in larger groups for some of the “experiments”) and hand in one
lab for each pair, by the beginning of the following lab period.
The written part of the lab is based on the lab manual.
In addition, familiarize yourself with F300, the maps and diagrams on the walls, and minerals and
rock specimens. These are the materials that you will be dealing with during the course (and the
rest of your life). You will become aware of the geology of western Canada and how the rocks and
processes around Victoria are related to larger scale processes over space and time.
Turn to Lab 1 of the lab manual and work your way through the readings and exercises.
Answer the questions from the manual in the corresponding spaces provided.
Activity 1.1 Geological Inquiry (Read and examine: pp 4, 9 & 25, Fig 1.1)
Part A
1.1A Aster Image 1,2 & 3: What are the dominant false colours shown and wavelengths do they
represent?______________________________________________________________________
____________________________________________________________________________(3)
Image Bands 4, 6 & 8: What are the dominant false colours shown and wavelengths do they
represent: ___________________________________________________________________ (3)
1.1B Ground View – Visible Light Photo. Note the trucks have 3 m tires and carry 13 Tons of ore.
What physical materials appear as Brown___________, Tan __________ & Green ________? (3)
1.1C Ore rich rocks blasted from the walls/benches of the open pit mine and their minerals. How
large are the ore rich rocks carried away by the trucks? __________________________ metres (1)
1.1 D Name 3 copper bearing ore minerals mined at La Escondida Mine ____________________,
______________________________________, and _________________________________. (3)
What is the richest copper ore of the 3 minerals? ____________________________________ (1)
1.1 E What is the density of native (metallic) Copper ______________________________ g/cm3
and how much does a penny weigh? ____________________________________________ g (2)
1.1 F Approximately how much copper is needed per square cm of circuit board? ________g (2)
1.1 G Approximately how big (diameter) is a single copper atom in metallic Cu? ________nm (1)
Part C
1.1A Compare the remote sensing images and note the location and size of the active and older
inactive mine pits. The false colours come from pixels that are several meters across and certainly
cannot detect either single copper atoms nor directly detect the minerals which contain the copper.
Heat in the infrared bands actually measures differences in soil and rock and vegetated surfaces
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related to: moisture content, albedo, heat capacity and chemical reactions like the oxidation of
pyrite (fool’s gold, FeS2) which is actually more common than the ore minerals we are interested
in mining. Explain in a sentence or so how geologists might use these Aster Infrared satellite
images to discover new ore deposits in this same region? ______________________________
____________________________________________________________________________
__________________________________________________________________________ (2)
1.1B Closely examine the ground view photo (B) and explain how geologists can locate enriched
zones of Cu ore minerals at this scale and use that information to profitably run the mine? ____
____________________________________________________________________________
__________________________________________________________________________ (2)
1.1C Copper iron disulphide (CuFeS2) is the most common primary copper bearing ore mineral
and the Cu-Carbonates (azurite and malachite form in shallow weathered zones from the
introduction or rain and groundwater. What must be done to these ore bearing rocks and minerals
to provide pure copper metal? ____________________________________________________
___________________________________________________________________________ (2)
Part D
1.0 Presuming Escondida Mine wishes to extend its fiscal lifetime by finding new deposits, how
you as a keen exploration geologist use the satellite imagery to decide between, and purchase the
rights for just one site from: A, B, and C which are offered for tenure. Consider what the mine
sites look like on these images and the possible significance of the false colours. Which site do
you recommend and why? _______________________________________________________
___________________________________________________________________________ (2)
2.0 Having chosen one of the 3 sites, what activities and tests should your exploration plan include
to test whether there is copper present and if so whether it is in profitable enough concentrations to
call it a new ore body? __________________________________________________________
____________________________________________________________________________
___________________________________________________________________________ (2)
Skip Activity 1.2
Activity 1.3 Basketball Model of Earth
Label in the correct relative position the spheres of the Earth on the following page using
the scale provided, wherein the position of the Inner Core at 1196 km is represented by a circle at
22.3 mm radius. The ratio (scale factor) of km in the real Earth per mm in your diagram is given
by 6371 km per 119 mm.
1. Write the numerical value of this ratio here after converting both numbers to meters:____ m/m.
_____________________________________________________________________ (2 points)
2. What is the fractional value of each radius in the table, if the basketball’s radius is 1.00 for the
top of the Crust? If you do this correctly, the top of the crust should be the surface of the
basketball and the ocean and atmosphere sit above that.
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Hint: the thickness of each layer is the difference between its top and its base. The fractional
radius needs to count the total thickness of all layers below that level. We want the top of the crust
to be the total radius, the oceans and atmosphere sit above that so their fraction is >1.000.
Complete the numerical values in the table below for 11 points.
(11)
Sphere
Atmosphere
Hydrosphere
Crust
UM Lithosphere
UM Asthenosphere
Lower Mantle
Outer Core
Inner Core
Distance to top/base (km)
Thickness of layer Fraction of Earth Radius
97.2
0
3.79
35
35
1.000
100
650
2890
5150
6378
1228
0.193
CARTOON EARTH NOT TO SCALE
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Activity 1.4 (Skip A through E)
Measurement and derivation of liquid density ρH2O (deionized water) in g/mL:
F-1. Explain how you can derive the density of deionized water using a graduated cylinder and a
balance. _____________________________________________________________________
___________________________________________________________________________ (2)
F-2. Obtain a thermometer and note the temperature of the water in the lab today then look up its
ideal density for this temperature using the chart on the board at the front of the lab. Note the
temperature and published density for pure water. ____________________________________
___________________________________________________________________________ (2)
F-3. Perform this measurement for > 50 ml of deionized water and perform the calculation to turn
your mass and volume measurements into the derived quantity density. Do not use an empty
graduated cylinder but start with a noted amount (eg. 5.00 mL) to get an accurate initial reading
as the scale is always better relatively than the exact zero position. Show your math and calculate
the answer to 2 decimal places. If you are not within 5% of the correct value repeat the exercise to
eliminate your sources of error. Discuss your sources of error. _________________________ (4)
Measuring the density of an irregular solid (plasticine modelling clay), ρCLAY in units of g/mL.
G. Explain the procedure for a lump of clay, a graduated cylinder and water (for displacement).
Think about Archimedes in the bathtub! Perform the calculation. ______________________ (4)
H-1. Explain why the lump of modelling clay sinks in water? _________________________
__________________________________________________________________________ (1)
H-2. Describe what you can do to make the same clay float and draw what you did to make this
happen. ___________________________________________________________________ (2)
I. Look at the table you filled out and the cartoon on Page 3 of this handout and explain the reason
for the order and arrangement of the spherical shells within and above the Earth. ____________
_____________________________________________________________________________
_________________________________________________________________________ (2)
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J. Calculating rates and gradients:
Grand Canyon of Colorado, flat on top of plateau. Flat lying strata uplifted. Incised Horseshoe
Bend meander from a former lower gradient river prior to uplift and incision.
J-1-a. Most terrain on earth is relatively flat (low relief). Erosion cuts down because of gravity and
slopes to the water table (energy minimum and cohesion). Even uplifted plateaux were former
basin floors including the Colorado Plateau above the Grand Canyon of the Colorado River
(Arizona, New Mexico, Colorado, Utah). Geologists have been puzzling over why flat lying
ancient rocks of the Colorado Plateau (Late Paleozoic) should have become uplifted at a much
younger time (Later Tertiary). Judging from the oldest sediments from the Colorado River filling
the downstream regions of the Colorado River (5-6 Ma) and canyon depth 1.60 km, depth (=
height uplifted) divided by time span (oldest materials) to provide an uplift and incision rate for
cutting the canyon and forming the high standing plateau. Geologists have believed the time span
to be on the order of 6.0 Ma (mega-annum, million years). Calculate the uplift rate in __________
km/Ma and in ________________________ cm/a (cm per annum, year). _________________ (4)
J-1-b. Recent work (Polyak et al., 2008, Science V.319, p.1377-1380) from the western plateaucanyon has found vadose zone (above the water table) stalactites in 9 cave sites near the bottom of
the canyon with 7 to 17 Ma dates from disequilibrium U/Pb (Radium) dating of the calcite. The
argument is that canyon cutting dropped the water table enough to form cave systems and adorn
them with speleothems, and that the formation of those calcite deposits and their elevation marks
the river depth at that time. The depth in the west canyon realm is about 1615 m. Assume this
downcutting (= uplift) occurred over 17 Ma. What is the rate in _____________________ km/Ma
and _______________________________________ cm/yr? __________________________ (4)
Other researchers emphasize pieces of Cretaceous and Eocene strata and argue parts of the Grand
Canyon are reused older river systems from 70 Ma (Cretaceous, Dinosaur era)! In geoscience, we
measure or observe facts. How we view or interpret those facts is more of an art and a skill than a
concrete science. Getting the truth out of the incomplete geological record requires precisely
measuring certain facts, cleverly relating them to fundamental constraints from regional studies
and just as cleverly learning to recognize to ignore bad data and shaky assumptions. For further
discussion of this continental scale, time spanning, uplift history problem see Rebecca Flower’s
article in Geology http://geology.gsapubs.org/content/38/7/671.full . The geologically recent uplift
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history and topographic invertion (basins became uplands) extends along the western Cordillera of
North America from Mexico to the Chilcotin Plateau north of Kamloops, B.C. The Colorado
plateau is just a big puzzle piece in the middle of this problem.
J-2. The geothermal gradient sets a limit on how deep underground mining can be conducted. The
deepest mine, Anglo Gold Ashanti’s Tau Tona Mine in Carletonville South Africa had rock face
temperatures of 60° C at 3.9 km depth in 2008. Most of the heat in the rock is internally generated
by the radioactive decay of U, K and Th in the crustal rocks of the South African Shield. The
mean annual surface temperature there is 14.75°C at an elevation of 1541 metres above sea level.
Air temperatures in the mine without air conditioning reach 55°C and need to be lowered to 28°C
to carry on with the mining. Even so up to 14 miners died in one year. Show your work
and calculate the geothermal gradient in this region within the upper lithosphere.
___________________________________________________________________________ (4)
Skip activity 1.4-K
Activity 1.5 Density, Gravity and Isostasy
Omit C and D.
A-1. Measure the dimensions to 2 decimal places and calculate the volume of a wooden block.
List the dimensions in cm (H, W, L) and calculate the volume as their product. __________ (4)
A-2. Weigh your wooden block while it is dry and calculate its density in ρwood in g/cm3 showing
all of your work. ____________________________________________________________ (3)
B-1. Measure the height of your wooden block and record this as Htotal here _________ cm. (1)
B-2. Gently place your wooden block in a water basin at the end of the lab bench on its widest
side. Quickly remove it and mark the wet/dry position with a pencil or pen. If you block is uneven,
you might wish to do this on 2 or 4 edges and average them. Record Hbelow _________ cm. (1)
B-3. Draw your wooden block showing the Htotal, Hbelow and record the Habove ________ cm. (4)
Labelled Drawing showing “plimsoll line” = water line:
C-1. Write the Isostasy Equation for Hbelow in terms of Htotal and the densities ρwood in g/cm3 and a
ρwater in g/mL. Recall that an equation is a general mathematical formula which allows us to
measure or observe something and calculate something else. It is more useful and applicable than
just performing a calculation for a particular set of numbers. It is a model relating all such values.
Hbelow Equation:
(5)
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C-2a. Test your Hbelow equation by substituting your Htotal, and the densities ρwood in g/cm3 and a
ρwater in g/mL for your block and our deionized water in the lab today. If your measurements are
precise and your math is correct you should predict a value for Hbelow that is very close to the real
wetted depth you measured on your block. This is a test of your work and of the validity of your
equation (predictive model). Calcualte Hbelow here ___________________________________ (3)
C2-b. Calculate your % error in your model or calculated value using the difference between your
measured value on the block and your predicted value. Your value should be within 5% otherwise
explain the reason for the discrepancy here. Use the following equation:
%Error = 100 x (Hbelow measured – Hbelow calculated) / Hbelow measured
(4)
D-1. Isostasy is the geological concept that lighter things like wooden blocks in water, icebergs in
the polar seas or mountains and crust in denser peridotite mantle float, and float only to one
particular level or elevation. Higher floating things tend to be lighter or thicker or both and the
converse is true as well. While it is easy for us to pluck a wooden block out of the tub and measure
the wet part, it is not so easy to do this for an iceberg (Ask Captain Smith!) or a mountain. It
would be much more useful as we can easily see the Habove of these things to rewrite your isostasy
equation in terms of Habove . As a hint, recall that we may substitute equal things for one another
and still keep an equation valid. I this case, you need to replace your Hbelow values with their
equivalent in terms of Htotal and Habove, then rearrange and solve the equation for Habove . Do this
substitution and derivation here: ______________________________________________ (5)
D-2a. Test your Habove equation to see if your measurements and math are correct like we did for
step C above. Calculate your Habove and write it here. ___________________________ (3)
D-2b. Calculate your % error in your model or calculated value using the difference between your
measured value on the block and your predicted value. Your value should be within 5% otherwise
explain the reason for the discrepancy here. Use the following equation:
%Error = 100 x (Habove measured – Habove calculated) / Habove measured
(4)
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E-1a. Unlike our rectangular wooden block, most geological objects we’d like to know about are
irregular. Sea ice has bubbles and cracks and an average density of about 0.917 g/cm3 . Unlike our
deionized water or fresh Victoria tap water, the seas have lots of dissolved salts and are colder as
well. Examine figure 1.10 on p 21 with the iceberg and the grid. Use the Hbelow isostasy equation
and the total height (thickness) of the iceberg to calculate how much of it should be below the
waterline. Calculate and show your work to predict what Hbelow should be here:
(4)
E-1b. Now calculate the %error for Hbelow as you did in step C-2b. Show your calculation, your
%error and discuss why the error is greater here that it was for the wooden block.
(5)
E-2a. Use the isostasy equation for Habove and predict what Habove should be for your iceberg show
your work and write the answer here.
(4)
E-2b. Now calculate the %error for Habove as you did in step C-2b. Show your calculation, your
%error and discuss why the error is very much greater here that it was for the wooden block or
even for your Habove in the previous step.
(5)
E-3a Real world objects like icebergs, mountains, continents, ocean basins etc., are rather irregular
and using a single (1 dimensional) thickness as an analog of the volume or mass is poor. Due to
this irregular shape, the cross sectional area is probably a better estimate of mass and buoyancy
than height alone. This time instead of height, count all of the squares and fractional squares and
sum them to obtain the total cross sectional area and the dry area and wetted area above and below
the plimsoll line. This takes about 5 minutes if you split the work between 2 students to count
whole and partial squares. List your Areas here: Areabelow = ________ , Areaabove = ________ and
Areatotal = ___________ .
(3)
E-3b. Use your Hbelow equation substituting your total Areatotal and densities for sea ice and sea
water to predict your Areabelow . Show your work and put your calculated area below here. Now
use this to calculate the %error in your area as before. This time you should be much closer
(within 2%). Discuss your error and give reasons for the improvement.
(6)
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E-3c. Use your Habove equation substituting your total Areatotal and densities for sea ice and sea
water to predict your Areaabove . Show your work and put your calculated area above here. (4)
E-3d. Use your Habove equation substituting your total Areatotal and densities for sea ice and sea
water to predict your Areaabove . Show your work and put your calculated area below here. Now
use this to calculate the %error in your area as before. This time you should be much closer
(within 5%). Discuss your error and give reasons for the improvement.
(6)
E-4. Examine Figure 1.10 of the iceberg again and note the tilted ledge that marks the old
waterline. Using what you know about isostasy and floatation, what will happen to the position of
the current water line if the iceberg loses mass by either melting from above or having a chunk
break off below. Discuss this and suggest a general rule concerning how much of an iceberg
shows to aid future Captains!
(2)
F-1. Clarence Dutton was the first to propose the “Isostasy Hypothesis” to explain how ancient
shorelines, beaches, wave cut cliffs, surge channels and other coastal features came to be elevated
up to several hundred metres above sea level. Explain how blocks of rocky crust might behave like
icebergs over geological spans of time.
(2)
F-2. Suppose you could find something that could be dated on one of these uplifted shorelines,
extinct fossils, carbon in plant or shells etc. How could you use this new information to calculate
an uplift rate such as post glacial rebound or tectonic strain?
(2)
Activity 1.6: Isostasy and Earth’s Global Topography Measure the density of 1 real rock
sample for each type of crust (Continental and Oceanic) and use this and the mantle density
to predict and account for high standing continents and continental mountain ranges versus
and low lying oceanic basins.
A. As you did for the lump of clay, obtain and weigh piece of basalt and use a plastic graduated
cylinder to measure its volume by displacement and determine the density of a piece of basalt. My
basalt sample: mass _______ g , volume ______
 basalt = _________g/cm3
(3)
Average density of basalt (yours plus 9 in table A p.36) =___________ g/cm3
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(1)
If your basalt is out of range of the other 9, reject it and average only the other 9 for step C.
B. As you did for the basalt, obtain and weigh piece of granite and use a plastic graduated cylinder
to measure its displaced volume and determine the density of the granite. My granite sample: mass
_______ g , volume ______
 basalt = _________g/cm3
(3)
Average density of granite (yours plus 9 in table B p.36) =___________ g/cm3
(1)
If your granite is out of range of the other 9, reject it and average only the other 9 for step C.
C. From seismic wave velocities and peridotite samples taken from ophiolites and volcanic
inclusions we know the average density of peridotite and upper mantle it comprises to be 3.30
g/cm3 . Both high standing granitic continental crust and low lying basaltic ocean crust “float” on
this denser solid mantle peridotite, like wood does on water. When seen from space the Earth
presents 2 different crustal elevations (a bimodal distribution of heights) and not much in between.
The real object of today’s lab is to use your familiar isostasy model equations for Habove and Hbelow
to explain and account for global topography and bathymetry. The densities come from your lab
measurements while the crustal thicknesses (depths to the mantle) come from seismic soundings.
1. For 5 km thick seafloor basaltic crust in peridotite mantle calculate: H basalt above =
km to
obtain how high the basalt would “float”. Show your work using the 1 dimensional height or
thickness.
(3)
2. For 30 km thick continental granite in peridotite mantle calculate: H granite above =
km to
obtain how high the granite would “float”. Show your work using the 1 dimensional height or
thickness.
(3)
3. If there were such a block of basalt floating next to such a block of granite, calculate how much
higher the granite would float. For this net elevation difference = Continental Crust above mantle
minus Oceanic crust above mantle: (H granite above - H basalt above) =
km or _____m. (2)
4-1. The hypsographic curve in Figure 1.11 on p.23 comes from plotting a histogram of all land
elevations and seafloor depths. (The project that made this global map took 5 years and tens of
people to digitize and integrate into a single database at the national geophysical data centre in
Boulder Colorado.) Subtract the 2 modes on this curve to obtain the “true” average difference in
the height of land and depth of seabed measured relative to sealevel as a datum (reference
elevation). How close are your calculated isostasy H above difference results compared to the true
elevation differences? Write down the difference between the average continental land elevation
and average ocean basin depth in terms of distances ______________ (metres) and percent errors
________________ % using your 3 rock, 1 dimensional isostasy model. Assume the topographic
averages to be the true value for this error calculation.
(3)
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4-2. Reflect on the errors from 4-1 when you compared your isostatic prediction to the actual
difference between the 2 main predominant elevations. If your error is less than or equal to ~5%
you should find this amazingly good. If it is more where did you go wrong in your calculations or
assumptions. Finally comment on how powerful (or not) and accurate (or not) it is to use this
isostatic model and a 3 rock mantle and crust. This is the true power of science in that it can make
simplifications and generalizations that explain most of the variation we observe. Explain in your
own words what conclusions you can draw and what reservations or qualifications you might have
after this exercise.
(5)
F. Pratt was perplexed at a survey near Hyderabad in northern British India of the day because
surveying a closed triangle around 3 cities and back failed to close by an amazing 70 km. He was
forced to conclude the surveyor’s plumb bob was off from the vertical and deflected by the mass
of the Himalayas. He interpreted this to be due primarily to rocks of different density beneath
adjacent regions traversed by the survey with substantially lower density but somewhat thicker
crust beneath the mountains compared to the plains before them. George Airy used astronomical
zenith and transit data from La Condamine’s Peruvian survey to conclude similar mass problems
in the Andes Mountains. He interpreted this to be due to substantially thicker roots beneath
mountain ranges, but rocks of essentially the same density. Both of these hypotheses predate the
science of seismology and any real knowledge of crustal thicknesses or mantle depths. Use the
data provided in the manual p21-38 and your calculations, to make an inference concerning the
Pratt (variable density) versus Airy (variable thickness) hypotheses for crustal elevation and
isostasy’s driving forces. Which model best explains continents and continental mountain ranges
or between those and ocean basins? Which model best explains the elevation differences between
mid ocean ridges and ocean basins? Is one model more correct than the other or does the real Earth
require that we understand and use a combination of both models to account for different features?
Feel free to make and label your own sketches here.
(4)
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