Berkeley -- With a simple but controversial assumption and lots of supercomputer time, two UC Berkeley geophysicists have solved a long-standing problem in geology -- why the jigsaw puzzle of crustal plates on the Earth's surface looks the way it does.
The problem, which has bedeviled the theory of plate tectonics since it
was proposed nearly a half century ago, is that basic theories of fluid
heating and convection say the surface should be broken into many small
puzzle pieces, none larger than about 3,000 kilometers across.
Instead we see a smaller number of huge plates. One of these, the Pacific plate, spans nearly 13,000 kilometers at its widest, more than four times larger than predicted.
The University of California at Berkeley scientists found that a simple but fundamental assumption -- that the viscosity or stiffness of the hot rock in the Earth's interior increases by a factor of 30 from top to bottom -- predicts exactly what is observed on the surface.
In their new model, upwelling of hot rock from the deep mantle and downwelling of cool rock from near the surface -- analogous to the upward movement of hot air and the downward flow of cool air in the atmosphere -- create a cyclic flow or convection cell with dimensions close to the dimensions of the tectonic plates. Because convection in the mantle is assumed to nudge the continents around on the the surface of the Earth and break them up into plates of roughly the same size as the convection cell, this model provides an explanation for why the plates are the size they are.
"This is a fundamental discovery of fluid dynamics which brings us very close to solving a major problem of geodynamics," says Mark Richards, professor of geophysics at the University of California at Berkeley.
The landmark feat was achieved by monopolizing a massively parallel computer at Los Alamos National Laboratory in New Mexico for nearly three weeks to perform calculations on a three-dimensional model of the Earth's mantle. The mantle, composed of rock at high temperature and pressure, underlies the surface crust or lithosphere and extends 2,700 kilometers down to the Earth's core.
Richards and UC Berkeley graduate student Hans-Peter Bunge, currently working at Los Alamos, will describe their model in a cover article scheduled for publication in the Oct. 1 issue of Geophysical Research Letters. They described a more idealized model -- though one that nevertheless duplicated the behavior of the Earth's mantle -- in the Feb. 8, 1996, issue of Nature.
Over the decades scientists have created extremely complex models of the the Earth's molten interior and calculated the motions in the mantle using the world's largest supercomputers, yet still have failed to reproduce the Earth's large crustal plates. Basic physics, for example, predicts that convection cells in a heated liquid will be roughly the same size as the depth of the fluid, which in the case of the Earth is about 3,000 kilometers.
Faced with such failure, the fallback explanation has been that the crust of the Earth is just sticky enough to make it clump together in continents of the size we see today.
"Until now the explanation has been that the plates are stiff and have high strength, so they make big rafts that only sink in a few places," Richards says. "We've turned that whole argument on its head. If you try to model that, it doesn't really work out."
What Richards and Bunge did was simplify the model of the interior to include only one major physical effect -- that the viscosity or stiffness of the mantle increases with depth.
This effect has only recently been established from seismic studies, Richards says, and many geophysicists remain skeptical. Others, however, say the viscosity could increase by as much as a factor of 100 from the top, where it borders the lithosphere, to the bottom, where it borders the Earth's core.
Richards and Bunge adopted the more conservative figure of 30, and assumed that the viscosity jumps rapidly to that figure at a depth of approximately 660 kilometers. Seismic reflections and also the shape of the Earth's gravity field suggest that the viscosity increases dramatically at that depth.
Bunge constructed a three-dimensional computer model, based on an earlier model by postdoctoral fellow John Baumgardner, with this as the primary assumption. Then he used a massively parallel supercomputer at Los Alamos -- a Cray T3D -- to calculate what the convection cells in the Earth's interior would look like.
"Assuming a 30-times increase in viscosity causes a dramatic change over what you get when you assume a uniform viscosity in the mantle," Bunge says. "Instead of isolated point-like cold blobs dropping into the interior, the pattern changes to long, linear structures sliding into the interior that look like subduction zones.
Subduction zones are places where tectonic plates dive under one another into the mantle.
These results, which Richards terms "a fundamental discovery of fluid
dynamics," were reported in Nature Feb. 8.
"Once we included the effects of changing viscosity, we got pretty much the Earth," Richards says. "The deep mantle is perfectly happy with that scale of convection, and the surface plates follow the convecting system in the mantle, rather than vice versa."
Because this model lacked a realistic lithosphere, the scale of the convection was off by a factor of two. Richards and Bunge remedy that with a report in an upcoming issue of Geophysical Research Letters, in which they show what happens if you combine that earlier model of the mantle with a slightly sticky lithosphere floating on top.
The net prediction of the model is large plates on the surface and long linear plate boundaries, analagous to the linear subduction zones where plates dive under one another and the linear midocean ridges and mountain ranges where molten mantle wells up.
"The amazing thing is that such a simple effect, a viscosity contrast
between the upper and lower mantle, has such profound influence on what
we find at the surface," Richards says. "The size of the continents
is governed by this effect and not by the structure and stickiness of the
Their model also explains the stability of the Earth's hotspots -- upwellings of hot molten rock in spots that remain constant for billions of years. The Hawaiian and Reunion Islands, as well as Yellowstone and Iceland, are examples of hot spots that have remained in the same place for a large portion of the Earth's history.
The reason, Richards says, is that these upwellings are rooted solidly in the very viscous deep mantle, near where it borders the core, and can't move.
"Our model explains why the rotation axis is static with respect to the deep mantle and to the hot spots," he says. Bunge and Richards will continue to improve their model so that it more accurately reflects the physical details of the Earth's interior. Also, while the most recent calculations were for a mantle modeled on a scale of about 50 kilometers, they hope soon to increase the resolution to 25 kilometers.
Bunge is also developing a way to calculate the model using a cluster of inexpensive workstations, rather than using 64 parallel computers of the very expensive Cray T3D toroidal supercomputer, which are available at only a few places in the world.
The work was supported by a grant from National Science Foundation and by the Institute of Geophysics and Planetary Physics at Los Alamos. Computer time was provided by the Advanced Computing Laboratory at LANL.
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