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Thermal Convection
and Viscosity of a Fluid
L.W. Braile
[email protected]
November, 2000
Objectives: Experiment with thermal convection. Illustrate how thermal energy (heat)
can generate motion (flow) in a fluid. The thermal convection in this model is similar to
the convection that is inferred for the Earth's mantle. Convection can produce horizontal
flow that can cause (or is related to) plate motions. Investigate the viscosity of a fluid
and illustrate that the Earth's mantle can be thought of as a solid for short duration
processes (such as the propagation of seismic waves), and as a very viscous fluid for long
duration processes (such as mantle convection and plate tectonic movements).
Materials:
1 Glass bread loaf dish (1.5 liter; a 2 liter, 20x20 cm or 8x8 inch glass dish can be
substituted if two Sterno cans or 3 small candles are used because of the
extra width of the container)
2 Ceramic coffee cups
1 small can Sterno or 2 small candles
vegetable oil (about 800-1000 ml)
10 ml (~ 2 teaspoons) thyme
spoon
matches
metric ruler
stopwatch
funnel (to pour oil back into container)
3 pieces of thin (about 2mm, or 1/16" thick) balsa wood, each 4x10 cm
For viscosity experiment:
Karo light corn syrup (about 60 ml)
Cookie sheet
Aluminum foil
3 small containers, such as 1/8 cup measuring cups
Silly Putty

Copyright 2000. L. Braile. Permission granted for reproduction for non-commercial uses.
1 Teflon coated pan or cookie sheet
Thermal Convection Experiments: Mix the vegetable oil and the thyme (spice)
in the loaf dish. Stir thoroughly to distribute the flakes of thyme. Arrange loaf dish and
other materials as shown in Figure 1. (Because of the viscosity of the oil and the density
of the flakes of thyme, the pieces of thyme are approximately neutrally buoyant. If left
unstirred for a long period of time, the thyme will not be evenly distributed in the volume
of oil – some of the thyme will tend to float and some tend to sink. However, the thyme
stays distributed for a sufficient length of time to perform the experiment. If the thyme
becomes significantly separated, just stir to mix thoroughly, let the mixture stand without
heat until the flakes of thyme are not moving, and begin the experiment again by adding
heat.)
1. Observe the oil and spice mixture. With no heat (energy) being added to the
system, these should be little or no movement of the liquid. The flakes of thyme
will flow with the liquid, showing the direction and velocity of any fluid flow.
2. Light the Sterno can and let the liquid heat up for a couple of minutes. (If you do
not wish to use the Sterno as a source of heat, you can use two small candles
(Figure 2) or a coffee cup with a one-cup electric element heater to heat water in
the cup and provide heat to the bottom of the loaf dish.) As the oil heats and
begins to flow, observe the pattern of fluid flow (circulation) by noting the
location of individual flakes of thyme over time (Figure 3). Be sure to view the
model several times during the experiment, both from above the dish and
from the side of the dish. Draw a sketch of the circulation (copies of Figure 4
can be used as a base diagram for sketching the flow using arrows). Is the pattern
approximately symmetric on the two sides of the heated area? Where do you
observe upward flow? Where do you see downward flow? Where do you
observe horizontal flow?
Note that the flow defines a convection cell (actually two cells) in which upward
flow above the flame (caused by heating of the fluid which causes expansion and
a reduction in density) causes horizontal flow near the surface of the liquid.
Cooling of the liquid near the ends of the container increases the density of the
liquid and produces sinking and a return horizontal flow toward the center of the
container, thus completing a "cycle" of fluid flow in the convection cell. Note
that the heat added to the bottom of the container is carried to the surface and
distributed primarily by movement of the heated liquid (convection current) rather
than by conduction. This type of energy movement is called thermal convection
because added heat causes the fluid flow (circulation by convection) by lowering
the density of the liquid. The difference in temperature between the near surface
region of the oil measured above the heat source and near the ends of the loaf dish
(far from the heat) will be about 2-3C and can be observed using a sensitive
thermometer. (It is not necessary to heat the oil for a long time, or to a high
temperature, to cause convection. The convection will begin shortly after the heat
is applied to the bottom of the loaf dish. The heating time will be somewhat
longer using the candles.)
3. Measure the horizontal velocity of the convective flow near the surface of the
liquid by placing a metric ruler on the top of the container (oriented along the
long direction of the loaf dish). By looking down on the convecting fluid and
observing an individual flake of thyme, measure the distance that one flake moves
in a period of time such as 10 or 20 seconds or more. (One can also perform this
measurement by viewing from the side of the dish.) Divide the distance (in cm)
by the time to determine the velocity in cm/s (usually slower than about 1 cm/s).
Measure the velocity and direction of movement at several locations for the nearsurface flow of the liquid. Are all of the measurements approximately the same?
Where are the velocities the largest? Where are they the smallest? What could
explain these variations in velocity? Are the directions of flow "away from" the
heated central area of the container? What effects or characteristics of the model
might cause variability in the velocities?
4. Place the thin pieces of balsa wood on the surface of the liquid as shown in Figure
5. Observe the motion of the pieces of wood (representing the relatively rigid
parts of plates such as most continental regions) over time. You should see plate
separation or divergence (analogous to continental rifting and subsequent sea
floor spreading of the oceanic lithosphere along mid-ocean ridges) at the center of
the container where significant upward fluid flow is caused by the heating.
(Because of surface tension, the two pieces of wood at the center of the loaf dish
may tend to "stick together". In this case, use a pencil or other tool to slightly
separate the wood. Once the surface tension is reduced, the plates will move with
the underlying fluid flow.) Additionally, as time progresses, two of the plates
should collide analogous to the continental collision that often accompanies
subduction where two plates are moving towards each other (converging). Using
a metric ruler as in step 3, measure the velocity of one of the pieces of wood.
How does this velocity compare to the fluid flow velocities that were obtained
previously?
Convection in the Earth: Thermal convection is inferred to exist on a large scale in
at least two regions in the Earth. The liquid outer core and the upper mantle that behaves
as a solid for seismic wave propagation and as a very viscous fluid for long duration
geologic processes including convection. The heat that causes convection within the
Earth comes from two sources – original heat from accretion and heat released during
radioactive decay of unstable isotopes. Although the Earth is about 4.5 billion years old,
some heat remains from the accretionary process during its formation because fragments
of Earth materials were heated to very high temperatures by impact during formation of
the planet, and Earth materials have relatively low thermal conductivity so that
significant heat has been retained from the early stages of Earth history. A more
important source of heat, however, is the natural, spontaneous, radioactive decay of
unstable isotopes of elements that are distributed throughout the Earth, particularly in the
crust and mantle. These radioactive elements include Uranium, Thorium and Rubidium.
These sources of heat cause the Earth's temperature to increase with depth to a
temperature of about 5000C in the inner core.
The Earth's outer core is inferred to be mostly liquid iron. Convective flow within
the outer core not only brings heat to the core-mantle boundary where some of it is
transferred into the mantle, but also causes the Earth's magnetic field by motions of the
electrically conductive inner core material. Temperatures are hot enough in the upper
mantle  1200C to cause thermal convection of the highly viscous upper mantle rocks,
although the flow velocity is apparently very low - on the order of cm/yr. Mantle
convection in either the upper mantle or the whole mantle has been suggested (Figure 6).
The mantle flow is a likely cause of plate tectonic motions. There is still considerable
debate about the details of convection in the mantle and the relationship of convection to
plate tectonics. For example, there is evidence from the identification of subducted slabs
in the Earth's upper mantle, that lithospheric slabs (subducted plates) sometimes extend
(penetrate) to depths greater than the upper mantle (below the mantle transition zone,
including the 670 km discontinuity, where seismic wave velocity increases rapidly with
depth indicating changes in composition or crystalline structure or "packing" of mantle
minerals). Therefore, mantle convection may not be as simple as the upper mantle
convection or whole mantle convection models that are illustrated in Figure 6. Similarly,
the exact relationship of mantle convection to plate motions is not presently known.
Mantle convection could be the primary cause of plate tectonics. Alternatively, mantle
convection could be a more passive response to plate motions. In either case, it appears
clear that heat within the Earth is the ultimate driving force for plate tectonics and mantle
convection. For more information on plate tectonics and mantle convection, see almost
any recent, introductory, college-level textbook on geology, such as Press and Siever
(1994), Lutgens and Tarbuck (1999), or Skinner and Porter (1999).
Viscosity Experiments:
Newtonian viscosity is a law of friction for fluids.
Viscosity is defined as the shearing stress divided by the rate of shear for the fluids.
Shearing stress is the force per unit area (at a point) directed parallel to the direction of
shear or flow. Viscosity can be thought of as resistance of a fluid to flow. For example,
if a fluid (such as water) flows easily, it has low viscosity; if it does not flow easily (such
as molasses, honey, or heavy oil), it has higher viscosity. Viscosity is measured in units
of Pascal-seconds (Pa-s) which are equivalent to Newton-seconds/m2.
1. To illustrate the meaning of shearing stress and viscosity and show the
differing viscosities of two fluids, try the following experiment. Place a piece
of the balsa wood on the surface of the oil in the loaf dish. Press down very
lightly on the wood with your finger (to create friction between your finger
and the wood) and then push horizontally (parallel to the surface of the fluid)
on the wood. Note that it takes very little force to move the piece of wood.
The viscosity of the fluid is low, equivalent to a small shearing stress (in the
definition of Newtonian viscosity given above) and a large rate of shear or
flow. Note also that the movement of the wood along the surface has virtually
no effect on the rest of the fluid. The oil, and the thyme in the oil, do not flow
(except for the oil immediately below the wood or adjacent to the sides of the
wood which is affected by surface tension of the oil). In addition to
illustrating the low viscosity of this fluid, this experiment demonstrates that
fluids are not capable of sustaining or propagating shear stresses (the
movement of the wood and associated movement of the fluid adjacent to the
wood do not cause flow in the remaining volume of the oil), and thus do not
propagate seismic shear waves, which, in solids, involve shearing motion and
shear stresses.
2. Next, make a cube out of a piece of silly putty. The silly putty can be thought
of as an elastic solid for short-duration stresses (if you roll it into a ball, it will
bounce off the floor, similar to a rubber ball, if dropped), and a viscous fluid
for longer time processes (note also the viscosity comparison illustration
described below). Place the cube of silly putty on a table and place a piece of
balsa wood on top of the cube. Using the same procedure as in the previous
experiment, push down lightly on the wood (just above the silly putty cube)
and push horizontally. Continue to apply a force in the horizontal direction.
After some time (many seconds), the flow in the silly putty will be visible and
the cube will be distorted by shearing. In this experiment, the shearing stress
is larger (you have to push harder on the silly putty in a horizontal direction to
get the silly putty to flow) and the rate of shear is much slower. Therefore,
according to the definition of Newtonian viscosity (shear stress/rate of shear),
the viscosity of the silly putty is much higher than the oil.
3. To investigate the viscosity of some fluids and to demonstrate that viscosity of
a fluid is also influenced by additional effects, such as temperature of the
fluid, try the following experiment. Line a large cookie sheet with aluminum
foil and make an inclined plane by placing one side of the cookie sheet on the
ceramic cups, thus raising that side by about 10 cm. Draw a short horizontal
line on the foil near the top of the inclined plane and an additional line about
10 cm "downslope" from the first line. In sequence, pour the following fluids
(about 20 ml each) onto the foil just above the first line: water, Karo syrup
heated to 40C, Karo syrup at room temperature (~ 20C), refrigerated Karo
syrup (~5C). (Use the 3 measuring cups for the syrup; heat the syrup in one
container; refrigerate the syrup in one container; and use the third container
for the room temperature water and room temperature syrup.) Using the
stopwatch, time how long it takes for the liquid to flow the 10 cm from the
upper line to the lower line (one experiment resulted in the following times:
water: 0.5s; heated syrup: 2s; room-temperature syrup: 6s; refrigerated
syrup: 24s). Prepare a data table showing the fluid, temperature and flow
time to allow easy comparisons and analysis of the results. The viscosity of
these fluids is roughly proportional to the length of time of flow (or inversely
proportional to the flow velocity). The water has the lowest viscosity and the
refrigerated Karo syrup has the highest viscosity of these fluids. Note also
that the viscosity of the Karo syrup was greatly affected by temperature with
the higher temperature corresponding to lower viscosity. In general, viscosity
of a fluid is controlled not only by the composition of the fluid, but also by the
pressure and temperature of the fluid, and sometimes by the size and duration
of the stress that causes fluid flow.
Examples of viscosities for some common fluids and some Earth materials are
shown in Table 1. Note that there is a very large range of viscosities. Also;
note that the viscosity of the Earth's mantle is very large. Mantle rocks, even
at high pressure and temperature, behave approximately as solids except over
long time periods or when the rock is molten (melted to convert the solid to a
liquid) such as in magma chambers. Magma chambers have been identified in
the hot mantle beneath mid-ocean ridges and in the crust beneath volcanoes.
Mantle flow (thermal convection of the mantle) occurs with very low rates
(velocity of flow of a few cm/year). (Challenge question: How much faster is
the flow velocity of the vegetable oil in the thermal convection model
experiment as compared to mantle flow velocities?) Finally, place a ball of
silly putty on a Teflon coated pan or cookie sheet. Tilt the pan or cookie sheet
to form a steep (at least 45 degree slope) inclined plane. Place a strip of tape
(about 10 cm long) beside the silly putty and put a mark on the tape to mark
the position of the "leading edge" of the silly putty. Let sit for several days.
Check the position of the lower edge of the silly putty every day or two and
mark the position. The silly putty will slowly flow down the inclined plane.
Flow will occur faster if the silly putty is located in a relatively warm place.
Note that the silly putty is far more viscous than the water or syrup used in the
earlier experiment.
Investigation of Density – GEMS; Plate Puzzle; Plate
Tectonics Flip Book; Earth's Interior Structure; Investigating Plate Tectonics Using
Foam Models; View the video "Inside Hawaiian Volcanoes" (Smithsonian) to see
convection currents in a lava lake and lava lake analogies to plate tectonics (plate
separation and divergence, transform faulting, and plate collision and subduction).
Related Activities:
References:
Atwater, T., Continental Drift and Plate Tectonics, videotape, 20 minutes, 1988, (to
order: send check for $15 payable to the "Regents of the University of
California" requesting the 1988 Continental Drift and Plate Tectonics videotape
to: Rick Johnson, Instructional Consultation, UC-Santa Barbara, Santa Barbara,
CA 93106).
Lutgens, F.K., and E.J. Tarbuck, Foundations of Earth Science, Prentice Hall, Upper
Saddle River, New Jersey, 454 pp., 1999, (Chapter 5 on Plate Tectonics).
Press, R., and R. Siever, Understanding Earth, (3rd edition), W.H. Freeman, New York,
682 pp., 1994, (Chapter 20 on Plate Tectonics).
Simkin, T., J.D. Unger, R.I. Tilling, P.R. Vogt, and H. Spall, This Dynamic Planet – A
World Map of Volcanoes, Earthquakes, Impact Craters, and Plate Tectonics,
Smithsonian Institution and U.S. Geological Survey, Map – 1:30,000,000 scale,
1994, (1-888-ASK-USGS; http://pubs.usgs.gov/pdf/planet.html).
Skinner, B., S. Porter, and D. Botkin, The Blue Planet: An Introduction to Earth System
Science, (2nd edition), J. Wiley, New York, 1999.
Smithsonian Institution, Inside Hawaiian Volcanoes, videotape, 25 minutes, 1989,
(http://nmnhwww.si.edu/gvp/products/inv.htm).
Table 1: Viscosity of Selected Fluids and Materials
Fluid/Material
Temperature (C)
Viscosity (Pa-s;
Pascal-seconds =
Newton-seconds/m2)*
Air
Water
Honey
Flowing hot lava
(Hawaiian volcano)
Glass
Ice
Rock Salt
Shallow mantle
Asthenosphere
Deep mantle
20
20
20
~ 1150
1.8  10-5
1.0  10-3
1.6
~ 80
~ 20
0
20
~ 1000
~ 1300
~ 1012
~ 1012
~ 1014
~ 1023-1024
~ 1019-1020
~ 1021-1022
> 1500
*Viscosity is often given in units of Poise; 10 Poise = 1 Pa-s.
Figure 1. Arrangement of coffee cups, Sterno can and loaf dish on a table top (side view) for the
thermal convection experiment. Short lines represent flakes of thyme in the oil. Arrows show
expected directions of fluid flow defining convection cells after heating of the fluid.
Figure 2. Alternate setup using two candles instead of the sterno for heat.
Figure 3. Close-up photo (side view) of the oil and thyme in the loaf dish. Heat from the candles
causes the oil and thyme to rise in the middle of the dish (above the candle flames), flow
horizontally (away from the center) near the surface of the oil, sink near the cooler edges of the
loaf dish and flow horizontally toward the center along the bottom of the dish, thus completing
the convection cells.
Figure 4. Sketch of fluid flow experiment apparatus. Copies of this figure can be used to record
observed directions of fluid flow (using arrows drawn on the diagram) in the oil after convection
begins when heat is added.
Figure 5. Arrangement of 3 pieces of balsa wood on the surface of the oil (view from above the
dish) to illustrate "plate motions".
Figure 6. Hypothetical cross-sections through the Earth showing possible patterns of convection.
Upper diagram: Schematic diagram illustrating convection in the Earth's upper mantle. Lower
diagram: Schematic diagram illustrating convection in the Earth's mantle in which the
convection cell and related flow operate throughout the mantle.
Relationship between convection currents
and plate motions?
Reading: Chapt. 11 of text. A nice overview.
Two basic models:
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coupled: currents in the mantle raft the overlying plates around. Traction
stresses at the base of the plates would be critical.
decoupled: plates move due to internal body forces, and influence the
shallow convection current pattern in the mantle.
locally exclusive, but not globally.
Possible driving forces for plate tectonics:
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bottom tractions by convection currents.
trench pull.
ridge push (sliding off a high)
trench suck.
see Fig. 11.10 for various forces involved.
global expanding or contracting forces
membrane forces on spinning ellipsoid (e.g. variants of polar fleeing
forces)
Basics of mantle convection: flowage in response to
bouyancy forces.
Conduction vs. convection vs. advection. Advection is often assumed to be
absent in the mantle, but is it? We won't have time to really address that here.
Bouyancy driven by gravity acting on density contrasts caused by thermal
differences and phase changes. Both are important.
Importance of Clapeyron slope: For most mineral transformations the
transformation pressure increases with increasing T (i.e. a positive Clapeyron
slope). This means that in a colder mantle region the transformation can occur
at a shallower level and in a hotter region it occurs at a deeper level. We
already considered this in the context of the olivine to spinel transition in the
slab and the mechanism of trench pull. We can also consider thermal plumes. If
there is a density increase in a colder region of convective downwelling, the
phase transition will occur at a elevated level producing a negative bouyancy
and enhancement of downwelling would be expected. By the same line of
reasoning a hot spot a positive bouynacy force would exit. In this case a plume
may be self perpetuating once it forms. Which is consistent with the long
history of some mantle plumes (see below). In fact you could ask why would a
mantle plume ever die?
Mantle viscosity:
viscosity

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

resistance to flow.
technically it is ratio of deviatoric stress (measure of size of shear stress)
over shear strain. There are different types of viscosity defined in
slightly different ways (see Davies for an explanation). There is also
different viscous behavior - linear (Newtonian) and power law.
higher the number the more viscous
units are Pascals per second.
for kinematic viscosity units are meters squared per second.
Mantle material is of varying viscosity: lithosphere vs. asthenosphere, and
upper vs. lower mantle. Is there a viscosity contrast across the 370 km phase
change boundary?
estimations of mantle viscosity from glacio-isostatic rebound:

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rebound history takes an exponential form.
deformation due to ice load will penetrate to depth comparable to its
radius (Davies).
some larger loadings reach into lower mantle.
lower mantle viscosity of 6*E+21Pa-s, upper mantle viscosity of
3*E+20 Pa-s. For comparison
Significance of the Rayleigh number in convection:


balance between bouyancy and viscous forces in a simple layer of
thickness D. Dimensionless number.
input parameters:
o coefficient of thermal expansion.
o temperature gradient in excess of that associated with increasing
pressure (superadiabatic component).
gravitational acceleration.
thermal diffusivity
o thickness of convecting fluid = d.
o kinemtic viscosity
Ra = gravitational acceleration * density * volume coefficient of thermal
expansion * temperature of interior fluid * depth of layer cubed all
divided by the thermal diffusivity * viscosity (Davies)
note that as viscosity increases Ra decreases and convection less likely.
As thermal diffusivity increases Ra decreases and convection less likely.
for a given geometry there is a number that needs to be exceeded for
convection to occur. For the spherical mantle your text indicates this
value is 2380 (Keary & Vine). As R increases there are different
styles/geometries of convection.
estimates for even the lower mantle yield a Ra value of circa 3*E6. In
other words bouyancy forces far overpower viscous retarding forces and
convection should be vigorous. See Turcotte or Davies for a fuller
explanation.
o
o
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Geometries of convection:

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parallel elongate cylindrical cells (sheet upwell and downwelling).
hexagonal patterns
spokes, plumes.
bimodal patter of perpendicular cells.
stable vs. unstable (turbulent) patterns.
pattern a funciton of the Rayleigh number.
very wall or very wide circulation cells are not stable (excepting
plumes). Often a width to depth ratio of 2 for cells.
Hot spots:


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

can persist for over 100 Ma.
have a different trace element chemistry than ridge basalts, one less
evolved.
depth of origin?
birth in an LIP.
minority view as a propagating crack.
Stratified vs. whole mantle convection:

670 km phase change: major viscosity barrier, depth of deepest
earthquakes, major velocity changes.

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trace element geochemistry suggest must have incomplete mixing as can
see different reservoirs.
mantle reservoirs for melts:
o lithospheric mantle.
o upper mantle.
o lower mantle via hot spots.
megaliths (subduction residue), and periodic penetration of the 670 km
boundary.
Cretaceous LIPs, and a model of mantle overturning.
Model simulations of mantle convection:

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
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physical models vs. computer models
dragging mylar over the system.
internal heat production vs. heat from below.
convection movies from Caltech.
Los Alamos convection movies.
Viewing present patterns of convection:

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seismic tomography where thermal differences change seismic velocity.
Cold areas are faster than hot.
by seismic anistropy caused by preferred orientation of manlte crystals
due to solid state flowage.
by broader gravity anomalies reflecting deeper density variation.. New
advances with satellite data.
anomalies in Pacific in Hawiaan area are parallel to the direction of plate
motion relative to the hotspot reference frame, and about 500 km width.
The latter suggest these are d=w rolls within the upper mantle.
by hot spot and LIP manifestations.
Parting thoughts on the mechanisms:



Fact that hot spot is a relatively fixed reference frame suggests that there
is a deep convection pattern characterized by plumes that is independent
of plate motion.
By necessity there must be shallow plumes under ridges. This in
connection with hotspots and the scale of subduction zones suggests
multiple scales and circuits of convection.
To a first order approximation world stress maps show a pattern that is
consistent with ridge push and trench pull.


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The initiation of continental rifting is difficult to explain with simple
ridge push and trench pull (consider EAR).
Fact that changes can occur relatively sudden (think of kink in Hawaian
hot spot track needs to be explained.
May be on the verge of a broad paradigm shift explaining interior
convection and its surface manifestations.
Some References:
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Anderson, D. & Dziewonski, A.M., 1984, Seismic tomography; Sci. Am., Oct.
issue.
Davies, P.A. & Runcorn, S.K., 1980, Mechanisms of Continental Drift and Plate
Tectonics; Academic Press, N.Y., 362p., Collection of articles - 3 of which have
greater pertinence
o Jacoby, Plate sliding and sinking in mantle convection and the driving
mechanism
o Turcotte - Some major questions concerning mantle convection
o Runcorn - Some comments on the mechanism of continental drift
Davies, G. F., 1999, Dynamic Earth Plates, Plumes and Mantle Convection;
Cambridge University Press, 458 p.
Holmes, A., 1965, Principles of Physical geology, Nelson-London, Chapt.
XXVIII Heat floor, volcanic activity, and convection.
Garfunkel, Z., editor, 1985, Mantle flow and plate theory; New York: Van
Nostrand Reinhold, 304p.
McKenzie, D.P. & Richter, 1976, Convection currents in the earth's mantle, Sci.
Am., p. 72-89.
McKenzie, D.O., Watts, A., Parsons, B., Roufosse, M., 1980, Platform of mantle
convection beneath the Pacific ocean; Nature, v. 228, p. 442-446.
McKenzie, D.P., 1983, The Earth's Mantle, Sci. Am., v. 249, #3, 14p.
Turcotte, D.L., 1975, The driving mechanisms of plate tectonics; Reviews of
Geophysics and Space Physics, v. 13, #3, p. 333-334.
Peltier, W.R., eidtor, 1988, Mantle convection; unknown publisher.
Harmon D. Maher Jr. reserves copyrights to the materials in this site. Material may be used for non-profit educational purposes as long as
proper attribution is given. For permission for any other use please contact author. Thank you.
Plate
Driving
Forces and
Tectonic
Stress
Structure Seminar
Arlo Brandon Weil
University of Michigan, Ann Arbor, MI
click here for spinning globe
Table of Contents
Introduction
Active Plate Driving Forces
Tectonic Stress
Quantification of Plate Driving Forces
Net Torque
Discussion and Conclusion
References
INTRODUCTION
"In science a phenomenon or a hypothesis can become so familiar and its utility in
providing as explanation, or consistent description of a greater number of diverse facts
so evident, that the underlying mechanism may often be left unstudied"
(Runcorn, 1980)
WHAT Drives Plate Tectonics ???? This question has been the subject of intense
debate ever since the plate tectonic theory was first eccepted by the geologic community
in the late 1960's. The major concern is whether mantle convection and the activity of
mantle plumes dominate the driving forces of plate motion, or whether surface boundary
and plate forces, such as slab pull and ridge push provide the most important forces. The
argument is basically whether the plates are passively riding along on the top of a mantle
convection cell, or whether the plates themselves the active drivers, dragging along with
them the mantle below.
To begin understanding and evaluating the different forces involved in the plate tectonic
process, we must first isolate these forces and define their physical and mechanical
properties. Once we have done that, we must make sure that any hypothesis or model that
we devise to produce these forces is compatible with the observations and characteristics
that we know and understand about the Earth. Mainly, is the model (1) compatible with
the rigid behavior of lithospheric plates, (2) compatible with the wide variety of plate
sizes, geometry, type, and motion; does it (3) satisfy the existence of complex plate
boundary conditions, (4) provide enough energy to account for all the motion; is it able to
(5) produce the observed tectonic stresses observed in the upper lithosphere; and does it
(6) satisfy the long-lived steady state relative plate motions (on the order of tens of
millions of years), as well as sudden dramatic changes in motion we observe from
modeled plate reconstructions (i.e., the Pacific plate circa 43 Ma).
With this basic set of plate driving force parameters and conditions developed, we can try
to relate our predicted forces back to the causal effects of tectonics at the Earth's surface.
To date, our best tool for observing the effects of plate driving forces (PDF's) is the
existence of large-scale tectonic stresses. Tectonic stresses result from plate driving
forces. Therefore, using measured data for the Earth's lithosphere, we can begin to think
quantitatively about the different magnitudes of the involved forces.
There are several methods one can use to quantify PDF's, namely: (1) finite element
deformation modeling, using the inter-plate stress fields to constrain the driving forces,
(2) empirical mathematical relationships between plate boundaries, plate age, type, and
velocity, and (3) active Net Torque analysis. Compared to the others, the last method
does a better job at accounting for all the large number of active forces as well as the
complex boundary conditions and plate characteristics that our PDF model must satisfy.
Using a combination of the known tectonic stresses along with a quantified force
relationship, we should be able to devise an accurate account of all the active forces
involved in today's plate motion. In addition, we should better understand the magnitude
scale for the different categories of mantle and plate forces.
The Active Forces Involved in the Driving of Lithospheric Plates
As stated earlier, in order to fully understand what drives the lithospheric plates of the
Earth, we must first identify and understand the forces involved. A number of forces have
been postulated since the dawn of the tectonic theory, including ridge push, slab pull,
trench suction, collisional resistance, and basal drag (Forsyth et al., 1975; Richardson,
1992). In the past ten years, many scientists have begun to assume that the boundary and
body forces of the plates, rather than the frictional drag produced by mantle convection,
are the most dominant group of forces driving plate motions. In the following section, the
basic physical properties of each of the main forces believed to be involved in the total
net motion of plates will be described and defined (fig.1).
Figure 1: Basic schematic of different Plate Driving Forces.
Ridge Push (fig. 2) has been considered in two different manners, as a body force and as
a boundary force. As a body force, ridge push has been attributed to the cooling and
thickening of the oceanic lithosphere with age (McKenzie, 1968; McKenzie, 1969;
Richards, 1992; Vigny et al., 1992). This type of force can be thought of as created by the
horizontal pressure gradient attributable to the cooling and thickening of the oceanic
lithosphere, and calculated as this force integrated over the area of the oceanic portion of
a given plate (Lister, 1975). In this respect, Ridge Push can be considered a body force,
rather than a boundary force acting over the oceanic part of a plate (Wilson, 1993). When
making such a calculation however, one must take into account that oceanic lithosphere
older than 90 Ma is no longer cooling significantly, and therefore not contributing to the
effective ridge push force (Ziegler, 1993). The alternative, Ridge Push as a boundary
force, is caused by the "gravity wedging" effect ( Bott, 1993). This effect results from
warm, buoyant mantle upwelling beneath the ridge crest which causes a topographyinduced horizontal pressure gradient. Here the force would be acting as a boundary force
at the edge of the lithospheric plate, proportional to the length of the ridge, and not as a
body force over the entire oceanic portion of the plate. In both of the above cases Ridge
Push would be amplified, by as much as a factor of two when hot spot activity is centered
on a spreading ridge axis (Ziegler, 1993). This is important when considering the effects
of ridge push as a cumulative force acting on all the plates, and must be taken into
account in any net force calculations.
Figure 2: Schematic of Ridge Push forces.
The Slab Pull (fig. 3) forces are derived from the negative buoyancy of the cold
subducting lithosphere and are dependent on the angle, temperature, age and volume of
the subducting slab, as well as the length of the respective trench (Chapple and Tullis,
1977). Slab Pull is considered a boundary force, and from most estimates is responsible
for some of the largest forces, or torques in the driving system (Wilson, 1993). Several
empirical studies have shown a strong correlation between plate velocities and age of
subducting oceanic lithosphere for plates with long subduction boundaries (Forsyth and
Uyeda, 1975; Chapple and Tullis 1977). This might suggest that slab pull is the dominant
acting force. However, there are several plates that have little or no portion of their
boundaries subducting and it is therefore important to look for other contributing forces.
Figure 3 : Schematic of Slab Pull and Collisional Resistance forces.
Related very closely to Slab Pull is Collisional Resistance (fig. 3). For every subducting
slab there is an associated resistive force provided by the relatively high viscosity of the
warmer, more ductile upper mantle. Together, the negative buoyancy of the sinking slab
and the resistive nature of the slab entering the mantle is called the Net Slab Force. The
sum of these two forces is exerted at the colliding margin (Ziegler, 1992) and contributes
to the intra-plate stress field of the surface plates (Wilson, 1993). Alternatively, recent
work has shown that the slab forces may be largely balanced within the slab itself and
contribute relatively little to the deformation of the surface plates (Richards, 1992).
Trench Suction (fig. 4) forces are observed in the overriding plate at subduction zones as
a net trenchward pull, often times resulting in back arc extension (Forsyth and Uyeda,
1975; Chase, 1978). Trench Suction is thought to result from small-scale convection in
the mantle wedge, driven by the subducting lithosphere. This force is difficult to isolate
from other forces because of how little we know about mantle convection in the shallow
subsurface (Ziegler, 1993). Related to Trench Suction is Slab Roll-Back. This is caused
by the small-scale convection current on the back-side of subducting slabs. We see this
phenomena today in the Hellenic Arc of Greece, and possibly in the western Pacific. This
current produces a pull away from the trench, consequently rolling back the hinge of the
subducting slab. Both trench suction forces can be thought of as a conservation of matter
argument requiring an asthenospheric counter-current in the wedge-shaped region
between the down-going slab and the upper plate. It is this counter-current that will result
in the trenchward pull of the overriding plate (Chapple and Tullis, 1977).
Figure 4: Schematic of Trench Suction forces.
Plate Tectonic Resistive forces (fig.5) are exerted on the overriding plate in a subduction
zone at the contact with the descending slab. This force is thought to result in a shear
stress that is distributed over the subduction thrust interface, that dips in the direction of
the plate's interior (Wilson, 1993). However, tectonic resistive forces are considered
equal and opposite in sign to the force exerted on the subducting plate, and therefore do
not contribute greatly to the net driving force for plate motion (Meijer and Wortel, 1992).
The last major force, Basal Shear Traction or Basal Drag (fig. 5) is important because
of its relevance to the fundamental question of whether plate motions are active or
passive. Basal Shear Traction is the resistance or dragging force associated with the
interface between the upper mantle and the lithosphere. Today this force is thought to be
small, but until we know more about the coupling between the lithosphere and the mantle
is better constrained, we cannot be certain how important it is. It is thought to have a
small magnitude per unit area, but when spread over the entire under-surface of big plates
can result in a large cumulative resistance.
Figure 5 : Schematic of Plate Tectonic ans Basal Shear Traction Resistive forces.
The lack of good correlation between plate velocity and surface area has traditionally
been used to argue against Basal Shear Traction (BST) as an important driving force. In
recent models researchers have considered BST a passive force, either driving or resisting
plate motion, but not dominating plate motion (Richardson, 1992). The contribution of
BST on the motion of plates depends on whether the flow pattern at the lithospheremantle interface is radial or unidirectional and parallel or anti-parallel with respect to the
overlying plate motions (Forsyth and Uyeda, 1975; Doglioni, 1990). However, the
mechanical nature of this interface and its flow pattern are unknown. Other researchers
are advocates of drag forces playing an important role in driving plate motion, while the
plates remain passive (Vlaar et al., 1976; Jacoby et al., 1980). In this case the lateral
motion of the plates would be caused by the mantle's exertion of a drag force on the
overriding lithosphere, above warm upwellings, which would subsequently create a
deviatoric stress regime. Here, the Shear Traction is estimated to be small per unit area
and would be proportional to the horizontal, or toroidal, component of the upper-mantle's
flow velocity relative to the overlying plate velocity (Ziegler, 1993). But it is important to
point out that the mechanics of upper-mantle flow are poorly constrained at this time.
Tectonic Stresses and Their Relationship to Plate Driving Forces
We must now seek out information on the subsequent effects, or in geologic terms, the
associated stress related to these forces. In order to do this it is very important that we
understand the regional patterns of the present-day tectonic stress field. Tectonic stresses
are those stresses produced by the forces that drive plate tectonics (Middleton et al.,
1996). Because of their integral relationship to the present motion of plates, the
magnitude and direction of tectonic stress is very difficult to predict unless we can
measure recent tectonic movement or seismic activity. In order to distinguish a measured
tectonic stress from those stress fields that are locally derived, we must look at the spatial
uniformity of the in situ stress field. For tectonic stresses the stress fields are typically
uniform over distances many times (2 to more than 100 times) the thickness of the elastic
part of the lithosphere, while local stresses are only a fraction of that same thickness
(Zoback et al., 1989). It is also found that for tectonic fields the three principal stresses lie
in approximately horizontal and vertical planes, with the horizontal stress component
almost always larger than the vertical component. As a consequence the orientation of the
principal stress axes of the measured stress tensor can be constrained by specifying the
direction of just one of the horizontal principle stresses (Zoback, 1989). This is
convenient for recording and measuring crustal stresses.
Once measured, tectonic stresses can give valuable information about the forces acting on
the plates and therefore the dynamics of plate tectonics. A group of some 30 scientists
from all over the world, headed by Mary Lou Zoback, have created a working database of
in situ stress measurements for most of the Earth's lithospheric plates. They collected
over 7300 in situ stress measurements, of which 4400 are considered tectonic stresses.
These measurements were taken from bore-hole breakouts, hydraulic fractures, style of
active faulting, volcanic alignment, seismic focal mechanisms, and transform fault
azimuths. The entire database then underwent a scrutinous quality rating to asses the
reliability of the individual data, with any unsatisfactory data discarded (Zoback, 1989;
Zoback, 1992).
The World Stress Map Project (WSMP), because of its huge database, has provided
significant advancement in our efforts to determine he relative importance of different
plate driving forces (fig. 6). The project has also provided constraints on the magnitude of
both broad scale and local stresses acting on the lithosphere. Subsequent analysis has
shown that a majority of the data can be adequately explained by the geometry of plate
boundaries and the conventional ridge push, slab pull, and subduction forces, and do not
necessarily require a significant contribution from sublithospheric mantle flow inferred
from seismic tomography (Zoback and Magee, 1991; Wilson, 1993). It appears that
regionally uniform horizontal intra-plate stress orientations are consistent with either
relative or absolute plate motions indicating that plate-boundary and body forces must be
the dominant contributors to the stress distribution within plates (Zoback, 1989; Zoback,
1992).
Figure 6 : World Stress Map Project's averaged maximum stress data (red
arrows). Color contour representative of elevation. After
Zoback et. al.
(1992) .
Numerous observations suggest that drag forces and resisting forces do not strongly
control the stress field of the uppermost brittle part of the lithosphere. The general state of
compression in the old oceanic lithosphere (older than ~80 Ma) indicates that the
integrated ridge push force dominates over the associated mantle drag forces (Richards et
al., 1992). Also, the predicted stresses related to whole mantle flow inferred from seismic
tomography do not match well with the broadest scale tectonic stress data, especially
when compared to the correlation of the boundary and body forces with tectonic
directions (Zoback, 1992).
Correlations between the World Stress Map's tectonic stress measurements and PDF's
were immediately obvious after the measurements were plotted on a map of the Earth's
plate boundaries. Normal faults that showed maximum tension perpendicular to ridge
crests were seen for most of the world's spreading ridges. Old oceanic crust (>35 Ma)
experiences mainly thrust or strike-slip faulting. This tectonic style is consistent with an
intra-plate stress field dominated by compression associated with the net slab and/or ridge
forces. Orientations of compressional stresses which dominate the interiors of most
continental cratons, most importantly North America and Western Europe, are similar to
those predicted for ridge push and slab forces (Zoback, 1992; Richards,
1992). Furthermore, stress measurements show, on a broad scale, stress fields changing
in style (i.e. compressional to tensional) over individual plates with a tendency for the
maximum horizontal stress direction (Sh Max) to be parallel to the absolute plate motion.
This last fact is an important observation which directly relates to the relationship
between plate boundary and body forces and the motion of plates. Using the evidence
provided by the WSMP that plate boundary and body forces appear to dominate the
driving mechanism of plate motion, the next step is to quantify the different magnitudes
of the individual PDF's.
The Techniques of Quantifying PDF'S
Before we begin to tackle the problem of quantifying PDF's, we must understand the
inherent difficulty in making inferences about plate driving motions from kinematics. The
difficulty lies in the physical equation that states that the motion of a rigid plate is the
integrated effect of all summed individual torques acting on that plate. The magnitudes of
these individual torques, however, are non-unique and unconstrained. The simple
example below shows how different combinations of coefficients, or in this case scalar
magnitudes of torque, can lead to the same outcome.
Example:
xTA + yTB + zTC + wTD = 0
1 + 3 + -2 + -2 = 0
2 + 2 + 2 + -6 = 0
1 + -1 + 1 + -1 = 0
Another difficulty with using analytical or numerical methods to account for the large
group of PDF's is the complexity of the multiple plate boundary conditions and relations.
Nevertheless, it has been shown that against an absolute reference frame we can come up
with a relatively accurate solution (Forsyth and Uyeda, 1975; Carlson et al., 1983). By
solving an inverse problem with a known absolute motion reference frame, we can
estimate relative magnitudes for individual plate driving forces.
There are essentially three different techniques geologists and geophysists use in order to
quantify the different plate driving forces. Deformational modeling studies using intraplate stress fields were popular in the late 1970's and early 1980's. Some of the earlier
attempts included Solomon et al. (1975), Richards et al. (1975), and Bott (1991). These
studies used finite element models in an attempt to predict both global and single plate
motions based on the forces driving and resisting the individual plates. The results of
these models worked well for individual boundaries and even for some of the individual
plates, but integrated over the entire globe, the model broke down and did not adequately
account for all of the appropriate complex boundary conditions. A second approach was
based on empirical relationships between plate size, age, type, geometry, motion, and
velocity (Forsyth and Uyeda, 1975; Carlson et al., 1983). From these relationships strong
correlations between plate velocities and the age of oceanic lithosphere were derived.
However, this method did not allow for other types of forces other than those associated
with the subducting slab, such as basal drag, tectonic resistance, etc.
The third approach, and the method I feel to be the most important and informative, is the
Net Torque Method. This technique studies the driving mechanism of plate motion by
balancing the net torque acting on each plate (Forsyth and Uyeda, 1975; Chapple and
Tullis, 1977). The advantage of this method is the incorporation of all Plate Driving
Forces into the equation, both driving and resistive. Inherent is the important concept that
the net torque acting on a plate is ultimately responsible for a plate's motion.
The Net Torque Method
The laws of rigid body rotation state that if there is no
acceleration and/or inertia acting on that body, then all applied
forces, or torques, must sum to zero. It follows that the net
torque acting on that body must also be zero, by definition.
This is Newton's second law of motion which states that the
acceleration of any object is directly proportional to the net
force acting on it, and inversely proportional to its mass. This
property is central in determining the relative magnitudes of
the torques acting on an individual plate (fig. 7).
Figure 7 : Schematic diagram showing the different
mathematical components of a torque acting on a
lithospheric plate. (R) is the radial distance from the axis of
rotation, or lever arm distance, (Beta) is the co-latitude position of the plate
boundary, and (alpha) is the angle between the strike of the boundary and the
azimuth to the pole of the torque axis. Figure taken from Forsyth and Uyeda (1975).
There are several basic assumptions that must be made in order for the Net Torque Model
to work. It is assumed that the inertia and acceleration of the individual plates are
nonexistent or negligible, and thus the plates are in dynamic equilibrium. The boundary
and body forces, for this problem, are considered the main driving forces as opposed to
active-mantle flow. And lastly, because the plates are confined to move on the surface of
the globe, their respective motions are, by definition, described as a rotation about an axis
passing through the center of the Earth. If, as assumed, there is no acceleration, the sum
of the net torques will add to zero.
Equation 1: Basic equation showing that the product of the lever arm distance, or
radial distance from center of rotation, and the applied force equals zero when
summed over a plate of area (P) .
With these assumptions we can then determine the relative magnitudes of the forces that
minimize the net torque acting on each plate. The inverse problem that determines the
relative strengths of each of the different PDF's is solved with respect to an inferred
absolute reference frame. Today the world's hot spots are our best source for an absolute
plate motion reference frame. In this case we are assuming the mantle is fixed with
respect to the Earth's axis of rotation. To solve the inverse problem a matrix must be
created with the known number of forces and plates and the unknown scalars for the
different forces. The basic equation is then solved for each plate in three dimensions as
follows:
Equation 2 :
Variables are listed below.
where n is the number of forces acting on the plate, xij is the coefficient of magnitude
(scalar) of the jth force, and aij holds all the physical and geometrical constants of the
plate. If there is a real solution, the determinant must equal zero. Once the possibility of a
real solution is found, the next step is to solve for the unknowns (xij ) by a least squares
method. Since we know the solution to the scaled matrix is zero, a least squares method
can be used to retrieve n eigenvectors for which several eigenvalues can be found. Here is
where a problem arises. As a consequence to the existence of several solutions, or
eigenvalues for each scalar (xij) , the coefficients become non-unique. However, the
degree to which the solution is non-unique can be estimated and minimized.
The non-unique solution may at first glance be perceived as a huge drawback, but the
relative magnitude of the forces involved are found with accuracy. In two of the most
referenced torque studies, Forsyth and Uyeda (1975) and Tullis and Chapple (1973), the
pulling of the slab and the collisional resistance from the mantle provide the dominant
role in controlling plate motion. The remaining forces for these two models have the
same relative magnitude, and thus can not be uniquely determined. A more detailed
analysis of the least squared no net torque method can be found in Forsyth and Uyeda
(1975) and Tullis and Chapple (1973).
Richards (1992) did a detailed Net Torque analysis combined with data from the World
Stress Map Project to better understand and resolve the remaining force magnitudes (fig.
8). He found that the ridge push force exhibits a strong correlation with the azimuth of
the absolute velocity of the plates. This correlation suggests an alternative explanation for
the alignment of intra-plate stresses and absolute plate motion. The relationship between
ridge push forces on intra-plate stresses is also consistent with slab forces being an
important component of the plate driving mechanism. Because of the equal and opposite
nature of the slab pull and collisional resistant forces, the sum net slab force contributes
relatively little to the deformation, or stress field, of the surface plates. Therefore other
forces must account for our observations, namely ridge push.
Figure 8: Diagram from Richards, (1992) showing Ridge Boundaries and Force
Directions in the top diagram, and Ridge Torque (black arrows) vs. Absolute
Velocity (green arrows) in the lower diagram. Notice the nice correlation between
the two vector directions.
Discussion and Conclusion
To the question, "What drives plate tectonics?" we have presented two options: (1)
mantle convection, and (2) lithospheric plate boundary and body forces. It is in the
opinion of this author that it is the plates themselves that are the dominant source of force
involved in the absolute movement of the lithospheric plates over the surface of the
Earth. The strong correlations between observed tectonic stress and absolute plate
motions shown by the World Stress Map Project point directly to the present lithospheric
stress fields being dominated by the individual plate boundary and body forces (Zoback
et al., 1989, Zoback, 1992). These observations, along with the Net Torque Model, allow
us to begin to put a coherent story together in terms of the relative magnitudes of
different PDF's. Although the slab forces (slab pull and collisional resistance) dominate
the other PDF's, their equal and opposite nature allows ridge push to be the most
important observable plate driving force.
This solution for Plate Driving Forces works for today, but what about the past? Did slab
and ridge forces always dominate, and did they always dominate in that order? These
questions are important when considering the driving forces behind plate motion over
time. Plates must rearrange themselves throughout supercontinent cycles, continuously
changing the constructive and destructive nature of their boundaries. It is logical to
assume then that these changes in the interactions and movements of plates must also
change the relative importance of different PDF's in time and space. It follows then that
the forces that drive plates are depenent on the nature of boundary conditions and plate
arrangement through time.
There are still many unanswered questions related to PDF's. Can plate driving forces be
responsible for the breakup of supercontinents? Are plate boundary and/or plate body
forces responsible for the initiation of subduction zones and spreading ridges? Most
researchers believe in these special cases, mantle forces related to large convection cells
must dominate the driving forces (Jacoby, 1980; Carlson et al, 1983;Wilson, 1991;
Zeigler, 1991). So, in a sense, it is because of the present condition that we have today's
magnitudes and effective forces, and through time the dominant forces will change from
plate to mantle and back. After all, is it not the mantle itself that inevitably supplies the
energy and heat that runs the system?
"Plates could not move, or even exist, if not for the Earth's heat which must be removed
from its interior to the surface through mantle convection. In this sense the mantle drives
the plates, for it is the interior of the Earth that is the ultimate source of energy of all
motion."
(Runcorn, 1980)
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Bott, M.H.P, 1991. Ridge Push and Associated Plate Interior Stress in Normal and Hot
Spot Regions, Tectonophyics, 200: p 17-32.
Bott, M.H.P., 1991. Sublithospheric Loading and Plate-Boundary Forces. In: Whitmarsh,
R.B., Bott, M.H.P., Fairhead, J.B. & Kusznir, N.J. (eds) Tectonic Stress in the
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of the Lithosphere at Trenches, Geophysical Research Letter, 10: p 297-300.
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Academic Press : p 159-172.
Jurdy, D.M., and Stefanick, M., 1991. The Forces Driving the Plates: Constraints from
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Kusznir, N.J. (eds) Tectonic Stress in the Lithosphere. Philosophical Transactions of the
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Plate tectonic driving forces: Earth’s heat generation and loss.
Peter van Keken
Geological Sciences
University of Michigan
Introduction
Earthquakes and volcanoes provide the most direct evidence for the dynamic nature of
the solid Earth. The frame work of plate tectonics has provided a good way to explain
where they occur and how they are linked to continental drift and the overall geological
evolution of the Earth. In order to make an earthquake or volcano the Earth needs to find
a source of heat. In the case of earthquakes this heat is converted to mechanical work
(that fractures the rock and causes the shockwaves to emanate from the hypocenter of the
earthquake). In the case of volcanoes the heat is used to melt solid rock to form magma
that then rises to the surface. In all cases the internal energy of the Earth is partly
converted into mechanical work. Examples from our daily life include car engines where
the energy from fossil fuels is converted into the work that is needed to drive the car.
A process that converts heat to mechanical work is typically called a heat engine. Plate
tectonics itself is caused by such a heat engine and in this module we will explore how
this works by exploring:




the surface expressions of the Earth’s heat loss and their relationships with
earthquakes, volcanoes and topography
the sources of the Earth’s internal heat
how this heat is used to make plate tectonics happen
how this has varied in the past and what it holds for the future of the Earth as a
dynamic planet.
This module provides a number of exercises for exploring data and making model
predications that can be performed on a standard PC using the provided public domain
software and Microsoft Excel. The lab exercises can be seen as addition to, but not a
replacement of, standard Earth Science introductory texts. The students are expected to
have a working knowledge of the plate tectonic cycle as provided for example by
Tarbuck and Lutgens, “Earth”, 6th edition, Chapter 19, or Press and Siever,
“Understanding Earth”, 2nd edition, Chapter 20.
Exploring Earth’s heat loss.
When exploring places like Hawaii or Yellowstone it is immediately apparent that the
Earth releases a lot of heat. The temperature inside the Earth increases dramatically with
depth, as was discovered in early mining efforts. In most areas on the continents the
temperature increases by about 20 to 40 degrees Celsius for every kilometer of depth.
The surface of the Earth is cool and heat is therefore conducted out of the earth. This is
similar to the cooling of a cup of hot tea by conduction through the cup and surrounding
air. The larger the temperature contrast, the faster heat will move from hot to cold. This
relationship between temperature contrast (or temperature gradient) and heat loss is an
important tool to understand the evolution of the Earth.
[Quantitative: according to Fourier’s law, the conductive heat flow between hot and cold
areas is proportional to the temperature gradient and the conductivity of the material that
is between the hot and cold parts. Higher conductivity means more efficient heat loss.
Mantle rocks have a typical conductivity of about 3 W/mK. With a temperature gradient
of 20 K/km this provides us with a quantitative estimate of the continental heat loss of
about 3*0.02 (W/mK)(K/m)=0.06 W/m2 or 60 milliwatts per square meter. If every
location on Earth had similar heat flow we can estimate how much the Earth loses
overall. Q: provide the amount of heat lost by multiplying the heat loss per square meter
by the surface area of the Earth.]
By measuring how quickly temperature increases with depth in the Earth, we can make
quantitative estimates of the amount of Earth heat loss. In addition to measurements in
mines we can measure the temperature in drill holes, such as those made for the oil and
gas exploration or scientific drill holes. A global compilation of heat flow data that have
been obtained this way is available at http:link_to_global_heatflow_database. We cannot
measure the heat flow in every single location of the Earth, but by using realistic
interpolation we can make an estimate for the overall heat flow. The most recent heat
flow map that was made this way is shown below. Note that this is a very smooth
representation of heat flow and only shows the large-scale features.
[QTVR of Henry Pollack’s heat flow, topography, volcanoes and earthquakes].
Q: Identify areas with high heat flow. Note that these areas are not randomly distributed
around the globe, but that they correspond with a specific type of plate boundary. Explain
why they would correspond to this type only, and not to the other types of plate
boundaries.
Q: Name and order the three dominant areas of Earth’s heat loss.
Q: Compare the zones of high heat flow with Earth’s topography. Are there any rules of
thumbs about the relationship between topography and heat flow you can derive?
_______________________________________________________________________
[Interactive map of heat flow and topography]
Project: In order to study the relationship between heat loss and topography better we
provide you with an interactive tool to query image maps. We have provided map
representations of heat flow and topography where you can use the pointer to find the
value of the each pixel in the map. Find the area with the highest heat loss and measure
the topography along a cross section that is perpendicular to the ridge. Do the same with
heat flow. You can import these into an Excel spreadsheet (or graph them by hand). Plot
both curves as a function of distance from the ridge in the same graph. Is there a strong
correlation between topography and heat flow? Explain why it makes sense that high
topography corresponds to high heat flow (if in doubt, think about what happens to a
metal rod if you put it into a hot fire, or the mercury in an old fashioned thermometer
when it warms up).
_______________________________________________________________________
Plate tectonics and mantle convection
[Cartoon showing cross section through lithosphere/asthenosphere from mid oceanic
ridge to subduction zone]
The observations of heat flow and topography now provide a first prediction what the
driving forces of plate tectonics are. Compare your observations with the cartoon
showing the standard plate tectonic cycle. Hot mantle asthenosphere comes up
underneath a mid-oceanic ridge. As it cools it forms the stronger lithosphere that spreads
away from the ridge. The older the lithosphere, the longer time it has had to lose heat to
the surface. This makes the older lithosphere both cooler and denser. After a few tens of
millions of years the lithosphere is sufficiently cold and dense that it can sink back into
the mantle at a subduction zone.
This cycle of hot material that moves up to the surface and cold material that sinks down
again is surprisingly similar to what you see in a pot of soup that is warming on the stove,
or in lava lamp. This type of motion of material is called convection, and therefore plate
tectonics is associated with the larger scale process of mantle convection.
_______________________________________________________________________
Project: The lava lamp
[QT of lava lamp ]
Q: how does a lava lamp work? As lava lamps have become fashionable again you may
be able to experiment with one yourself. Otherwise use the images and movie provided
here. There are two types of material in the lamp (transparent oil and opaque wax that
collects at the base of the lamp when it’s cool). At the base of the lamp is a light that can
be switched on to provide heat to the overlying wax/oil mixture. Where does the wax
expand and where does it contract again? Where is the lamp losing most of its heat? Is
this an example of a heat engine? What is the source of the heat?
[series of snap shots of a lava lamp that is cooling down]
Now explore what happens if you switch off the light. Does the motion of wax stop
immediately? Is this still an example of a heat engine? If so, what is now the source of
the heat? Imagine that you have a small and large lava lamp that you switch off at the
same time. Which one will stop first?
_______________________________________________________________________
Our experiments with the lava lamp provides us with the idea there are multiple heat
sources: the direct heat provided by the hot lamp and the somewhat more indirect
provided by the cooling of the hot liquids in the lamp. By analogy, it is therefore
possible that the Earth is slowly cooling down from a hot state after its formation 4.5
billion years ago and that plate tectonics is caused by the mechanical work provided from
the cooling Earth.
In order to investigate this further we need to better understand what type of heat sources
are available in the Earth and how they influence plate tectonics. As we will see, the
cooling of Earth is an important heat source, but there are other, more direct sources as
well.
Earth’s heat sources
When investigating how heat is generated and lost in the solid Earth it is essential to
make a heat budget in which we identify the different processes. For example, in the case
of a cooling cup of tea, we can measure the total amount of heat lost until the tea reaches
room temperature. Recall the first law of thermodynamics: heat cannot be created or
destroyed, but it can be converted from one form to another. Consequently, the amount of
heat is equal to how much heat was originally in the cup of tea (or better: it is the
difference in heat content between the tea when it was hot and is current room
temperature). A simple way to keep the tea hot is to put it on a hot pad (or to insert an
electrical heating element). In that case, the tea still loses heat, but it is continuously
replenished by the heat from the heating element, which is fueled by electrical energy.
In case of the Earth, we have a good estimate of the total amount of energy that is lost
from the solid Earth. The BIG question is: what is the source of all this heat?
Q: Take a minute or two to think or discuss with others what the sources may be for heat
in the Earth. Compare for example heat sources you know in every day life. Which ones
can you exclude?
Let’s now investigate what the heat sources may be. You may have thought about the
energy coming from the Sun. This is a dominant source of energy at the surface of the
Earth. It makes life possible and causes convection in the Earth’s atmosphere and oceans.
However, it is quite unimportant for the Earth’s solid interior. The main reason is that the
heat of the sun is not conducted very deeply into the Earth. Think for example about a
basement or cellar in a house that remains at pretty much constant temperature
throughout the year. This is even more dominant as you go deeper in the Earth. The soil
and rocks that make up the surface of the Earth are very good insulators.
In the previous section, we have already identified that an important source of heat is the
cooling of the Earth. This logically implies that the Earth was hotter in the past.
Q: what is the main reason that we think the Earth was much hotter in the past? Think in
particular about how the Earth formed 4.5 billion years ago. Was there a source of heat
then?
In addition to the early heat sources, there is continuous generation of heat in the earth by
the decay of radioactive elements. In silicate rocks the radioactive decay of isotopes of U,
Th and K are particularly important.
Q: Review the physics behind the decay of radioactive elements. Why does this generate
heat?
We can actually quantify the amount of heat that is generated by radioactive decay if we
have a good idea of the composition of the Earth. Based on this we know that radioactive
isotopes in the present day mantle contribute about 40% of the total present day heat loss.
Q: what is your prediction for the amount of radiogenic heating in the future? Will it
increase, stay the same or decrease? Argue why.
Q: Similarly, was the more, less or the same amount of heat generated by radioactive
isotopes in the past?
_______________________________________________________________________
Project: Radiogenic heating.
We can quantify the amount of radiogenic heating in the future and past by extrapolation
from the present day state. Recall that the decay of a certain amount of radioactive
material is a predictable process.
[Figure showing radiogenic decay]
If after a certain amount of time T only half of the original amount is left, we know that
after a time interval that is twice as long only a quarter will be left. The length of time T
is called the half-life of the material. This behavior actually allows us to find the age of
certain materials, such as is common with the C-14 method used in archeology and
paleoclimate, or U-Pb or Ar-Ar dating techniques for geological material. The most
important isotopes that fuel the Earth’s interior have very long half-lives as is shown in
the table below
[Table showing decay times of U, Th, K]
The spreadsheet linked here provides a way to calculate how the present day
concentration of radioactive elements in the mantle will decay as a function of time.
For convenience, we do not use the proper physical units associated with these quantities,
but instead provided the amount of heat (as a ratio of the present day heat loss). Note that
at present day U-235 and Th-232 are the most important radiogenic elements and that the
sum of the heat production is about 40% of the present day heat loss.
Use the spreadsheet to make a plot of how the amount of heat production changes in
time. Show the individual contributions and the sum. You can either graph it by hand or
edit the spreadsheet program.
How long does it take for the total heat production to be half of that of the present day?
Now use this same technique to predict the amount of radiogenic heating in the past.
Graph again the individual contributions and the total. When was the radiogenic heating
twice as high as present day? When was it equal to the present day heat loss? How high
was it right after formation of the Earth?
_______________________________________________________________________
Plate tectonics: past, present and future.
Now that we have quantified our predictions for the radiogenic heating in the past and
future, it is time to think about the big picture again. Answer the following questions to
make qualitative predictions about the past and future of plate tectonics.
Q: What does the higher radiogenic heat production imply for the past heat loss?
Q: How will this affect the speed of plate tectonics?
Q: What will happen with plate tectonics if we wait long enough?
We can quantify your predictions by doing some modeling in a simplified Earth. Before
getting to the project we will first look at how convection velocity and heat loss are
related to the amount of heat inside the mantle and how this can help us to model the
evolution of the mantle.
Thermal convection.
To help quantify the relationships between internal heat, temperature and the speed of
plate tectonics it is useful to think of the analog of the lava lamp again. Although it may
seem odd to compare the solid silicate Earth to the liquids in the lava lamp, it is not
unreasonable. Most of the Earth’s silicate interior (mantle and crust) is near its melting
point and at the very long geological timescales it behaves like a fluid, although one that
exhibits a lot of resistance to motion (it is very ‘sticky’) and consequently allows only
low convection velocities (few inches per year).
Let’s say we are interested in investigating how we can speed up or slow down the speed
of the convection.
Q: What would you suggest to do to the way the lava lamp is set up to make the flow go
faster? (Note: there is more than one answer possible!) Think in particular of what drives
the flow and what resists it.
A: The question above phrases our approach in terms of driving and resistive forces. The
convection happens (is driven) because 1) heat is supplied to the wax; 2) the resulting
higher temperature of the wax causes it to expand; 3) the expansion reduces the density
and the wax becomes lighter than the overlying oil; 4) the wax is allowed to rise because
the oil is liquid. This leads us to the following suggestions for making the convection go
faster: 1) if we can supply more heat, the temperature of the wax will be hotter and the
resulting expansion is bigger. For example, we can put a brighter (higher wattage) bulb in
the lava lamp to make the convection go faster. 2) Materials respond differently to
temperature. Some expand quickly, whereas for others it takes a large temperature
difference to notice an effect. It follows that by replacing the wax with a substance that
expands more strongly with temperature, we would increase the driving force and the
convection would go faster. The relative amount by which a material expands for a given
temperature contrast is a material property called the thermal expansivity ; 3) We can also
think about the role of the overlying oil. The speed with which something can move
through a liquid depends on how much resistance the fluid offers. It is a lot easier to
swim through a substance like water than it is through honey or treacle. The amount of
resistance that a fluid offers to an object moving through it is called the viscosity of the
fluid. Higher viscosity leads to more resistance and slower motion for a given force.
Alternatively, you need to supply a more force for a given speed if the viscosity is higher.
Viscosity is also a material property, and it depends (often strongly) on temperature.
Compare for example the viscosity of honey out of the fridge with that on a hot pancake.
Let’s reverse our train of thought now and make the lava lamp go slower.
Q: What do you need to do in order to slow down the convection in the lava lamp?
Q: Can you completely stop motion in the lava lamp by changing thermal expansivity or
viscosity, even if you leave the light on at full?
These thought experiments lead us to important conclusions about the nature of thermal
convection.
1. You need a source of heat to drive mantle convection.
2. The speed of mantle convection depends on how much heat you supply, and what
the material properties (in particular thermal expansivity and viscosity) of the
fluid are.
3. If the fluid is viscous enough, there is no convection.
Thermal convection is a very important process for anything from industrial processes to
the structure of stars and is consequently very extensively studied. For convection in
fluids we can make a number of generalizations that actually allow us to simplify the
description and make some simple modeling possible. One important generalization is
that we can describe the vigor of convection as proportional to the ratio of driving to
resistive forces. This ratio is called the Rayleigh number in honor of Lord Rayleigh who
performed a large number of fluid dynamics experiments in the early parts of the 20th
century. This number is often identified by the symbol Ra. We can further identify that
the driving forces are proportional to the amount of heat and the thermal expansivity and
inversely proportional to the viscosity of the fluid.
The details of the dynamics of thermal convection can be studied in various ways. We
can follow our own example by using analogues and thought experiments to come to a
better qualitative understanding of the dominant processes. We can get quantitative
estimates (how much faster does convection go if viscosity is reduced by half?) by doing
detailed measurements in our experiments. For example, we can measure the speed of the
wax bubbles as a function of lamp power. Scientists have often relied on experiments that
can be better controlled than lava lamps, but the experimental setup is quite similar in
spirit.
Figure: laboratory tank set up.
The figure below shows such as fluid dynamical ‘tank’ that is filled with corn syrup and
heated from below by an electric heating pad, and cooled from above by running cold
water over the fixed top surface. The physics of thermal convection is now well
understood and we can also formulate the physical problem in terms of equations that can
be solved numerically on a computer. An example of a set of simulations that was
obtained by modeling thermal convection is shown in the figure below.
Figure: model simulations of convection with increasing vigor
The speed of convection (along the top surface) and the heat flow are plotted as a
function of Rayleigh number. Note that our main conclusions seem to work well!
Q: Estimate from the graph at which Ra the fluid stops moving.
Note also that the speed of convection or surface heat loss does not increase as a linear
function of Rayleigh number. This is one of the reasons it is difficult to make predictions
about the evolution of a convecting system without having to do quantitative models.
Note also that we can use this type of models to provide (relatively) quantitative
relationships between heat loss and Rayleigh number. For the given example we find
(powerlaw relationship of q with Ra).
Putting it all together
We now have all the necessary knowledge to make quantitative predictions about the
speed of plate tectonics in relation to the heat that is supplied. Let’s summarize the
important points:
1. The energy to drive plate tectonics through thermal convection is provided
dominantly by radiogenic heating and cooling of the mantle
2. The speed of convection depends on the Rayleigh number, which in turn depends
on the amount of thermal energy, but also on material properties such as thermal
expansivity and viscosity
3. The faster the flow, the more rapid heat is lost from the Earth’s mantle to space.
4. If the Rayleigh number becomes smaller than some critical number, convection
ceases.
In order to put this all together we need to make a heat balance, in which we account for
the heat that goes into the mantle and the heat that goes out. The difference is used to
warm up the mantle (if more heat goes in than out) or used to cool the mantle. In equation
form this reads:
Change in mantle temperature is proportional to heat in
minus heat loss at surface
This is an equation that we can actually solve! First, we can use our estimates of the
amount of radioactive elements in the mantle to find the amount of ‘heat in’. If we know
the temperature (which is representative of the total heat in the mantle) and the material
properties we can calculate the Rayleigh number and find the amount of heat that is lost.
At any given instant we can then calculate how much heat is left to heat up the Earth, or
how much heat must be given off by cooling.
Q: Apply the idea of a heat balance to the cooling of a cup of tea. Is there any heat that
goes into the cup of tea once the hot water is poured into the cup? What is your prediction
for the temperature of the tea? Will it go up, stay the same or only go down? Is the heat
loss constant as a function of the temperature of the tea? Does the heat loss ever become
zero? What will happen in that case to the temperature of the cup of tea?
Project
In a separate spreadsheet program the heat balance equation can now be solved. We have
provided the main equipment and made sure that all the parameters apply to the Earth. If
you open the spreadsheet program you will see an example for a calculation of the
Earth’s temperature as a function of time since the formation of the planet 4.6 billion
years ago. In this case, we have assumed that the Earth started hot (with average mantle
temperature of 5000 K), that there is no internal heating (no radiogenic heating at all!)
and that the mantle silicates behave like a fluid with a viscosity that does not depend on
temperature. It is a model that leaves things to be wished for, but it will suffice for the
initial investigation.
Have a look at the graph of temperature, heat flow at the surface and Rayleigh number.
Does the mantle behave the way you expect it to do? In order to quantitatively test this
model we will use a number of constraints about the present day thermal state of the
mantle.
Q: We have good reasons to believe that the average temperature of the Earth is between
2000 and 3000 K at present. Does this model satisfy this constraint?
Q: We have better constraints on the heat flow (as explored in the very first exercise).
Does this model satisfy the heat flow constraint?
Q: The melting temperature of the Earth varies with depth, but on average we can assume
that large portions of the mantle were molten if the mantle was on average hotter than
about 4000 K. If large parts of the Earth melt we would likely see massive volcanism and
heat loss by different processes than plate tectonics. In effect, we can see 4000 K as a
realistic upper limit of the mantle temperature at any point in Earth’s history. Does the
predicted evolution show that the Earth was always cooler than this maximum value?
Let’s keep these three constraints in mind when we explore how the model assumptions
affect the predicted thermal evolution of the Earth.
We can start changing the model assumptions to see if we can make a better fit. First, it is
not very realistic to assume that there is no radiogenic heating at all. Change the amount
of radiogenic heating in the spreadsheet. Try out a few values and record what happens.
Is there any model run that satisfies all three constraints? What happens if you use the
same amount of radiogenic heating that corresponds to our estimates of the heat
producing elements in the mantle?
The temperature of the early Earth is not well known. Most observations suggest that the
Earth was hotter in the past, but most information about the very early Earth (before 4.0
billion years ago) is lost. Set the heat production to our best estimate for the ‘real’ heat
radiogenic heat production. Then, try different values for the initial temperature (from
cold to very hot). What happens? Can you explain the shape of the curves?
The assumption that the viscosity of mantle silicates doesn’t change with time is not very
realistic. Scientists who study the deformation of rock under the high temperatures and
pressures of the Earth’s interior have actually shown that there is a strong dependence of
the viscosity of rock with temperature. This has rather profound implications for the
evolution of the Earth.
Q: predict what happens to the vigor of convection as a function of increasing
temperature. Does the speed of convection increase more rapidly than in the case in
which viscosity doesn’t change? What happens to heat flow?
You have predicted an important feedback mechanism. On the one hand, high
temperatures lead to low viscosity and rapid convection, but on the other the high
convective speed cause rapid cooling and reduction in temperature. Let’s see if we can
see what happens quantitatively by making the viscosity of the mantle in our model
temperature dependent. Use the correct estimate for heat producing elements. Test the
evolution of the model now for different estimates of the initial temperature of the Earth
(say between 1000 and 5000 K). What happens? Does it matter whether or not the Earth
started ‘hot’ or ‘cold’?
As a final experiment, we can use our best model to predict what will happen to plate
tectonics on Earth in the future. The Moon and Mars are examples of Earthlike planets
that at some point in the past were a lot more active (as seen by the large amounts of lava
that were extruded to the surface on those planets) but are now either quiescent (Mars) or
non-tectonic (the Moon). The Earth so far has escaped this fate because it is much larger
and loses its heat less efficiently to space. Yet, a glance at any of the temperature and
velocity curves you have made make it easy to predict that at some point Earth dynamics
too will slow down and eventually cease. When will this be? You can answer this
question by taking the best model estimate (one with a realistic mantle viscosity that
depends on temperature, with realistic heat production and a present day mantle
temperature and surface heat flow that corresponds reasonably well to the observed
values). Take this model and let it run for 15 billion years (3x the age of the Earth). What
happens to the heat flow and temperature? What happens to the Rayleigh number? When
does it become smaller than what you predicted to be the critical Rayleigh number? Will
plate tectonics still be active then?
Conclusions
In this project we have investigated the dynamics of plate tectonics. We have learned that
volcanoes, earthquakes and continental drift are all expressions of the Earth functioning
as a heat engine, where the Earth’s internal heat is converted into mechanical work. Most
of the Earth’s internal heat comes from the present-day decay of radiogenic elements and
secular cooling. We can explore the physics of Earth’s dynamics in more detail by using
analogue experiments (like a lava lamp) or by numerical calculations that use the
fundamental principle of energy conservation. The convective vigor of the Earth is
determined in part by the average temperature of the mantle and material properties such
as viscosity and thermal expansivity. Spreadsheet calculations can be used to model the
convective vigor as a function of initial temperature, radiogenic heating and the
dependence of viscosity on temperature. Such calculations also allow for a prediction of
how the dynamics of the Earth change as the main sources of energy are depleted.
Lecture 16: Driving the Lithosphere - the Forces Behind
Plate Tectonics
Plate tectonics is a kinematic theory that best describes the interactions
of simple, oceanic plates. The forces that drive plate tectonics are poorly
understood, and probably vary in space and time. The most likely
driving mechanisms can be grouped into edge-driven or bottom-driven
categories. Edge-driven forces arise due to buoyancy contrasts between
lithosphere and asthenosphere, and tend to push or pull the plates from
their edges. Bottom-driven forces arise due to drag exerted on the base
of the lithosphere by convecting asthenosphere, and move the plates
from below. Both categories are ultimately driven by gravity.
In Lecture 15 we discussed the nuts and bolts of plate tectonics - what it is, what it
predicts. ItÕs time now to think about what makes it go. What are the forces that move
plates around?
Caveats
But first, a few qualifications. Plate tectonics is what is known as a kinematic theory,
meaning that it describes the relative motions of different parts of the lithosphere. It is
NOT a dynamic theory, meaning that it does not predict - or even tell you anything about
- the detailed ways in which the plates interact, or the ways in which those interactions
change through time.
In addition, itÕs important to remember that plate tectonics originated through efforts to
describe the kinematics of oceanic lithosphere, which is a relatively simple,
homogeneous system. This is because oceanic crust and mantle is uniform in
composition, is thin, and is fairly young. In contrast, continental lithosphere tends to be
older, to have a lengthy and varied tectonic history, and to be more chemically
complicated.
Thus the simple predictions of plate tectonics donÕt tell the whole story of continental
deformation. The boundaries between oceanic plates are sharp and distinct - ridges,
trenches, transform faults. The boundaries between continental plates tend to be much
broader and more diffuse. Think of the Himalaya and Tibetan plateau (warning: 600 kb),
a 1000 km wide mountain range that marks the destructive boundary between the Indian
and Eurasian plates.
What Makes Plates Go?
Remarkably (to me), we still donÕt know exactly why the plates move. A glance at any
introductory geology textbook (and Plummer & McGeary is no exception) will show you
nice cartoons of plates that are driven by convection currents in the mantle. These make
nice art, but in reality the situation is a lot more complicated.
However, we can make some educated guesses. Broadly speaking, we can divide plate
driving forces into two kinds:
1) Edge-driven: imagine two dinner plates on a table. If you push on the edge of one, it
will smack into the other and slide past it. The plate movement is thus driven from the
edge.
2) Bottom-driven: now imagine that the table is covered by a tablecloth. If you shear or
slide the tablecloth, and if the plates are coupled to it, they will slide past one another
without any force being exerted on the plates themselves.
Specifically, there are 5 different forces that have been invoked to drive plate tectonics:
1) Ridge push. Oceanic lithosphere cools and thickens through time, meaning that areas
of oceanic lithosphere far from a mid-ocean ridge will be bathymetrically lower than the
ridge itself. Thus there is a gravity gradient - a slope - and the plate slides downhill,
away from the ridge. Formally, the actual ridge push force is the pressure gradient from
ridge to trench (remember, pressure is force/area) integrated over the area of the plate.
In reality, the plate doesnÕt really cool much after about 90 Myr, so the ridge push is
only generated by the younger (<90 Myr) parts of the plate.
2) Slab pull. As a plate is subducted, the downgoing part, or slab, is negatively buoyant
relative to the surrounding asthenosphere. The slab thus feels a downward force that pulls
on the rigid plate as a whole. The downward motion of the slab is resisted by the viscous
mantle, and so the force that matters is the net slab force. This depends mostly on the size
of the slab (length and thickness) and the angle at which it subducts (steeper angle = less
viscous resistance).
There does seem to be a strong correlation between subduction velocity and slab age (i.e.,
old dense slabs pull the plate down rapidly), which would imply that this is an important
driving force.
3) Trench suction. The subducting slab may set up a small convection cell in the
ÔwedgeÕ of mantle above it, which would drag or suck the overriding plate toward the
trench. While theoretically possible, itÕs hard to separate this from the other forces,
mostly because we have such a poor understanding of shallow mantle convection.
4) Plate contact resistance. As a plate is subducted, it comes in contact with the
overriding plate along a huge fault (sometimes called a megathrust, because the
overriding plate is being thrust up and over the subducting plate). The friction along this
interface can produce a substantial resisting force.
5) Basal drag. This is what you see in intro textbooks. As asthenospheric material is
driven upwards in a convection cell, it hits the base of the lithosphere at mid-ocean ridges
and flows outward along the base of the plate. As it does so, it drags the overlying plate
along. For this to work, two things must be true:


the asthenosphere must in fact be moving as it does in the cartoons, and
it must be viscous enough, or the lithosphere/asthenosphere boundary rough
enough, to transmit stress across the boundary.
There is little direct evidence to support either of these conditions, but numerical models
suggest that basal drag is certainly possible. However, one problem is this: if basal drag is
important, then big plates should move faster than little plates because the drag is exerted
over a greater area. But no such correlation exists, implying to some that edge-driven,
rather than bottom-driven, processes are more important.
How to Tell the Difference?
To unravel the mystery, people have looked at plate motions or kinematics. For example:


South America is not attached to any downgoing slabs, so slab pull should be
non-existent and other mechanisms (specifically ridge push, trench suction, and
basal drag) must be important. South America doesnÕt seem to be moving
particularly slowly, relative to other plates, meaning that slab pull is generally
NOT orders of magnitude greater than any other forces.
Africa is surrounded on three sides (west, south, and east) by spreading ridges,
and so it too cannot be moving in response to slab pull. We would expect Africa
to be squeezed by all that seafloor spreading, but instead we find that Africa is in
tension - the plate is literally trying to pull itself apart. Therefore, some other
force must be overcoming the ridge push.
The Role of Plumes
Mantle plumes (remember those from Lecture 12) introduce a wild card into the mix.
Plume heads spread out radially when they hit the base of the lithosphere, which will tend
to put the lithosphere in tension and try to rift it apart. Even medium-size plumes are
theoretically capable of rifting a continent in two. ItÕs thought that a very large plume
beneath equatorial Africa is responsible for the tensional stresses observed in that region.
Things get even more complicated when a plume hits a mid-ocean ridge. The hot material
in the plume causes the ridge to be even more buoyant than normal, which increases its
elevation and increases the magnitude of the ridge push force (the plate falls down a
steeper slope). Also, the plume material can exert basal drag on the plates at the same
time, adding to the plate velocity.
Supercontinents: Aggregation and Dispersal
Plate reconstructions over geologic time show a striking thing: the continents periodically
gather together into a supercontinent, surrounded by a single superocean. The last
iteration of this, called Pangaea, began to break up in the mid-Jurassic, about 170 Myr
ago.
If you imagine the plates randomly moving about the earth, it makes sense that continents
will occasionally collide. If those collisions weld the two plates together, as is currently
happening with India and Asia, then sooner or later the continents should all aggregate
into one giant mass that sweeps up all the scraps. But if so, why should it ever disperse?
An interesting idea has to do with the escape of heat from the mantle:
1) A supercontinent aggregates. Some or most of its margins are likely to be destructive,
in order to balance the seafloor spreading in the superocean.
2) That seafloor spreading locally releases heat in the mantle beneath the superocean. But
heat below the supercontinent canÕt escape, and so it builds up, increasing the mantle
temperatures beneath the supercontinent.
3) In time, either (a) hot mantle material rises as a plume and rifts the supercontinent
apart, or (b) the convection system reorganizes, with upwelling beneath the
supercontinent and downwelling beneath the superocean. Either way, the continents
disperse.
Gravity Always Wins
By now it should be clear that the single most important driving mechanism behind plate
tectonics is gravity. Gravity gives rise to buoyancy forces that drive convection, and
plates slide off ridges and into trenches under the force of gravity. Gravity also controls
the maximum thickness of the crust and lithosphere. Q: Why is the highest point on Earth
only 8.8 km above sealevel, and not 20 or 50 km? A: Because Earth materials arenÕt
strong enough to support the weight of a 20 or 50 km high mountain. At heights above 5
or 6 km, the rocks begin to fail and the mountain falls apart, sliding off to the side - all
under the force of gravity. Similarly, we donÕt see lithosphere that is much thicker than
about 250 km - any thicker and the stresses at the base of the lithosphere would exceed its
strength, causing it to fail.
MyClassroom • About Visionlearning
Plate Tectonics II:
Plates, plate boundaries, and driving forces
by Anne E. Egger, M.S.
News &
Events
Drilling the San
Andreas Fault
Stanford Report
By 1962, the idea that pieces of the earth's surface moved around no
longer seemed radical. As we saw in Plate Tectonics I, the concepts of
continental drift and seafloor spreading had revolutionized geology,
and researchers excitedly began to revise their interpretations of
existing data. For example, geologists had long recognized that
earthquakes are not randomly distributed on the earth.
The Effects of
the Mt.
Pinatubo
Eruption
U.S. Geological
Survey
Experiment!
Plate Tectonics
Activity
PBS - An
interactive plate
tectonics animation
that illustrates the
processes
occurring at plate
boundaries.
Reconstructing
Pangaea
Cornell University You can move and
rotate the
continents to
reconstruct
Pangaea.
Earthquakes are shown in red. This image was generated using QUEST, the
interactive mapping tool operated online through Discover Our Earth at
Cornell University.
Questions?
Ask-a-Tutor
Online Tutoring
Program
Ask-a-Friend
Visionlearning
Discussion Board
Ask-a-Scientist
Argonne National
Lab
Ask-a-Scientist
MAD Scientist Net
Biography
In fact, earthquakes are concentrated
along the plate boundaries drawn by
Harry Hess. Not all earthquakes occur
at the same depth, however. Where
Hess had postulated that the rocks of
the ocean floor were diving down into
subduction zones, earthquakes occur
at shallow depths of 0-33 km below
Cross-section of earthquakes in the
the surface near the trenches, and
Tonga region. The blue line
depths of almost 700 km below the
represents the plate boundary.
surface further inland. On the other
hand, only shallow earthquakes (depths of 0-33 km) are recorded at the
spreading ridges. These data helped geologists draw more detailed
cross-sections showing that plates are thin at spreading ridges, and that
subduction extends long distances, taking plates deep beneath the
continents.
Similar to earthquakes, volcanoes are located preferentially on or near
plate boundaries.
J. Tuzo Wilson
Used with
permission
University of Toronto
Archives and Robert
Lansdale
Photography Ltd.
Classics
1906 San
Francisco
Earthquake
San Francisco
Museum - This
site offers
eyewitness
accounts of the
Great 1906 San
Francisco quake.
"Geologists have
a new game of
chess to play,
using a spherical
board and
strange new
rules."
-Patrick M.
Hurley,
1968
Historically active volcanoes are shown in red. This image was generated using
QUEST, the interactive mapping tool operated online through Discover Our Earth
at Cornell University.
Also similar to earthquakes, different kinds of volcanoes occur along
different types of plate boundaries. Most of the volcanic eruptions that
make the news, like the 1980 Mount St. Helens eruption, take place
near subduction zones. These devastating, explosive eruptions reflect
the composition of the magma - it is extremely viscous and thus cannot
flow easily. In contrast, the volcanic eruptions that occur along
spreading ridges are much gentler, in part because most of these
eruptions occur under 2-3 kilometers of water, but also because the
magma is far less viscous.
Plate boundaries
These observations about the distribution of earthquakes and volcanoes
helped geologists define the processes that occur at spreading ridges
and subduction zones. In addition, they helped scientists recognize that
there are other types of plate boundaries. In general, plate boundaries
are the scene of a lot of geologic action - earthquakes, volcanoes, and
dramatic topography such as mountain ranges like the Himalayas are
all concentrated where two or more plates meet along a boundary.
There are three major ways that plates interact along boundaries: they
can move away from each other (diverge), they can move towards each
other (converge), or they can slide by each other (transform). Each of
these interactions produces a different, characteristic pattern of
earthquakes, volcanism, and topography:
Divergent boundaries
Divergent boundaries are the mid-ocean
ridges that launched the plate tectonics
revolution - the Mid-Atlantic Ridge is a
classic example. Shallow earthquakes and
minor lava flows characterize mid-ocean
ridges. The seafloor at the ridges is higher
than the surrounding abyssal plain
Earthquakes are shown as
because the rocks are hotter (and less
yellow squares on this diagram
of a divergent boundary.
dense) - they cool and condense as they
This image modified from This Dynamic
move away from the spreading center.
Earth, a publication from the U.S.
Geological Survey
Spreading has been occurring along the
Mid-Atlantic Ridge for 180 million years,
resulting in a large ocean basin - the Atlantic Ocean.
Convergent boundaries
Convergent boundaries are the most geologically active, with different
features depending on the type of crust involved. There are two types
of crust: oceanic and continental. Continental crust is thick and
buoyant; oceanic crust is thin, dense, and forms at mid-ocean ridges.
The activity that takes place at convergent boundaries depends on the
type of crust involved, as explained below.
• Oceanic crust meets continental crust: these are the subduction
zones first imagined by Hess, where dense oceanic crust is diving
beneath more buoyant continental crust. These boundaries are
characterized by: a) a very deep ocean trench next to a high
continental mountain range, b) large numbers of earthquakes which
progress from shallow to deep, and c) large numbers of intermediate
composition volcanoes. The Andes owe their existence to a
subduction zone on the western edge of the South American plate; in
fact, this type of boundary is often called an Andean margin.
Earthquakes are shown
as yellow squares.
This image modified from This
Dynamic Earth, a publication
from the U.S. Geological Survey
• Oceanic crust meets more oceanic crust: where two oceanic plates
converge, a subduction zone also occurs, but the result is slightly
different than an Andean margin. Since the densities of the two
plates are similar, it is usually the older oceanic crust that is
subducted because it is colder and slightly denser. Earthquakes
progress from shallow to deep like in the oceanic-continental
convergence, and volcanoes form an island arc, like Mt. Fuji in
Japan and Pinatubo in the Philippines. These volcanoes are slightly
different from those that form the Andes because the magma is
produced from the melting of oceanic crust rather than the melting of
continental crust.
Earthquakes are shown
as yellow squares.
This image modified from This
Dynamic Earth, a publication
from the U.S. Geological Survey
• Continental crust meets more continental crust: when two pieces of
continental crust converge, the result is a great pile-up of continental
material. Both pieces of crust are buoyant and are not easily
subducted. Continental convergence is exemplified by the
Himalayan mountain range, where the Indian plate runs into the
Asian plate. Numerous shallow earthquakes occur, but there is very
little volcanism.
Earthquakes are shown
as yellow squares.
This image modified from This
Dynamic Earth, a publication
from the U.S. Geological Survey
Transform boundaries
Most boundaries are either convergent or
divergent, transform boundaries are by far
the rarest. The San Andreas Fault in
California is an example of a continental
transform boundary - frequent, shallow
earthquakes occur (like the famous 1906
and 1989 San Francisco earthquake), but
there is little associated volcanism or
topographic relief. The Alpine Fault in
New Zealand is very similar. Most
transform boundaries occur not on land,
however, but in short segments along midocean ridges.
A few boundaries defy simple
classification and are referred to as "plate
boundary zones." For example, a
complicated earthquake pattern is produced
by a wide, poorly understood plate
boundary zone between the Eurasian and
African plates in the Mediterranean region.
In this topographic image of
the seafloor, spreading ridges
are shown in red, while
transform boundaries are
shown in yellow.
Geologic activity away from plate boundaries
The boundaries described above account for the vast majority of
seismic and volcanic activity on the earth. The more data that began to
fit into the plate tectonics scheme, however, the more the exceptions
stood out. What could account for Hawaii, for example, a scene of
long-lived volcanic activity in the middle of the Pacific plate where
there is no subduction or spreading to generate magma?
There had to be something else. In 1963, J. Tuzo Wilson, a Canadian
geophysicist, theorized that the mantle contained immobile hotspots,
thin plumes of hot magma that acted like Bunsen burners as plates
moved over them. The Hawaiian Islands form a long, linear chain, with
ongoing volcanic eruptions on the island of Hawaii and extinct, highly
eroded volcanic islands to the northwest. According to Wilson's hotspot
theory, the chain of islands represents the southeastward motion of the
Pacific plate over a mantle plume.
One important
implication of
Wilson's theory
was that, since
hotspots were
stationary, hotspot
tracks could be
used to trace plate
motion history.
J. Tuzo Wilson's original sketch of the Hawaiian hot spot.
For example, the
(Used with the permission of the Canadian Journal of
track of the
Physics.)
Hawaiian chain
continues to the northwest as an underwater chain of progressively
older, no longer active volcanoes. Once the volcanic eruptions stop,
ocean waves begin to take their toll, eroding the islands down to just
below sea level, at which point they are called seamounts. The islands
and seamounts associated with the Hawaiian hotspot provide a history
of motion for the Pacific plate, which appears to have taken an
eastward turn around 28 million years ago. Other hotspot tracks around
the world can be used in a similar manner to reconstruct a global plate
tectonic history.
What are the driving forces?
Hotspots added further proof to confirm that plates moved constantly
and steadily. Ironically, however, the question that incited ridicule for
Wegener continues to launch heated debate today: what ultimately
drives plate motion? Plates are constantly shifting and rearranging
themselves in response to each other. Eventually, a new Pangaea (or
single supercontinent) will form, break apart, and form again on Earth.
What keeps these plates moving?
Hess assumed that mantle convection was the main driving force - hot,
less dense material rises along mid-ocean ridges, cools, and subsides at
subduction zones, and the plates "ride" these convection cells (see the
lesson on Density for more information). While there is little doubt that
convection does occur in the mantle, current modeling suggests that it
is not so simple. Many geologists argue that the force of convection is
not enough to push enormous lithospheric plates like the North
American plate. They suggest instead that gravity is the main driving
force: cold, dense oceanic crust sinks at subduction zones, pulling the
rest of the plate with it. According to this theory, magmatic intrusions
at spreading ridges are passive - the magma merely fills a hole created
by pulling two plates apart.
"Ridge push" and "slab pull" are both ways that gravity
can act to keep a plate in motion. Note that arrows on
convection cells and overlying plate are going in the same
direction.
Figure modified from This Dynamic Earth, a publication from the U.S.
Geological Survey.
Undoubtedly, gravity and convection both supply energy to keep plates
moving. Their relative contributions, however, are a matter of debate
and ongoing research.
The strength of plate tectonic theory lies in its ability to explain
everything about the processes we see both in the geologic record and
in the present. Our understanding of the subtleties continues to evolve
as we learn more about our planet, but plate tectonics is truly the
foundation upon which the science of geology is built.
Resources
Further Exploration
Plate Tectonics II Quiz
Discover Our Earth
Visionlearning - an interactive practice
exercise.
Cornell University - This site allows you to
explore the concepts of plate tectonics in
more detail, even including an interactive
mapping tool called QUEST.
Overhead - Convergent & Divergent
Boundaries
Visionlearning - Illustration formatted for
printing on transparencies or display with
projector.
Visionlearning Glossary
Visionlearning - an alphabetical glossary of
relevant scientific terms .
Global Volcanism Program
Smithsonian Institute - The Global
Volcanism Program (GVP) has up to the
minute information about volcanic eruptions
worldwide and a downloadable database of
recent eruptions.
USGS Earthquake Site
U.S. Geological Survey - The USGS hosts a
real-time earthquake map and a
downloadable database of all earthquakes
since 1990.
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