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As the World Churns:
Modeling Convection in the Earth's Mantle

Paul Tackley
Assistant Professor, Department of Earth and Space Sciences, UCLA

The Earth's outer crust is only a few miles thick--thinner, in proportion, than the shell of an egg. Between the crust and the molten core lies the mantle, nearly 3,000 kilometers of rock at temperatures and pressures so high that it behaves like a thick liquid. Carrying heat from the core to the surface, the mantle creeps like tar on a hot day. The mantle's movement reveals itself through such forces as volcanoes, earthquakes, and continental drift. To better understand the behavior of the mantle, UCLA geophysicist Paul Tackley and colleagues use NPACI computers to perform increasingly complex and realistic 3-D simulations.

"The thermal convection within the Earth's mantle is the driving force behind the geological processes that shape our planet," Tackley said. "A thorough understanding of this process is essential to understanding the Earth's dynamics, structure, and evolution, from earthquakes and volcanoes to the forces that broke up the great Pangean land mass 160 million or so years ago."


Tackley-sphere_cold-cmykFigure 1. Going Down

Cold downwellings from a mantle simulation with a phase change at 670 kilometers depth. Downwellings are deflected at the phase boundary, forming pools of cold material that grow, destabilize, and eventually fall into the lower mantle in cylindrical "avalanches."


The general process of thermal convection is well-understood--it's the method of heat transfer in action when a pot of stew simmers on the stove. Currents of heated, less-dense material rise to the surface, cool off, and sink in an endless cycle. But the mantle is no ordinary stew, and modeling the mantle's convection process is extremely challenging.

The numerical model must deal with complex material properties, including solid-state phase transitions, chemical composition differences, and thermodynamic properties that depend on both pressure and temperature. One of the worst complications is that rock viscosity depends strongly on temperature and changes by several orders of magnitude across the mantle's boundary layers, which are less than 100 kilometers thick.

Because of these complexities, most previous simulations had used a highly simplified version of the mantle. Accurate modeling of the Earth's interior convection requires resolution of less than 25 kilometers within a sphere 12,800 kilometers in diameter. Until recently, most numerical work had been performed in two dimensions.

Using the processing power provided by supercomputers at NPACI sites, Tackley and his colleagues have been able to perform 3-D simulations of unprecedented realism and complexity. Under NSF and NASA funding, Tackley has been simulating mantle convection on the Intel supercomputers at SDSC and at Caltech's Center for Advanced Computational Research since the early 1990s, and more recently on SDSC's CRAY T3D, CRAY T3E, and IBM SP. His first work used a spherical-shell convection model based on a spectral transform method, while recent research uses a 3-D finite-volume code. The models have been growing more and more complex as his work advances.

A useful simulation allows researchers to discover things that are not obvious from the model inputs or from observations, and Tackley's simulations are proving to be useful indeed. His spherical geometry simulations yield data sets that can be compared statistically to geophysical observations, such as 3-D maps of long-wavelength seismic velocity variations in the Earth's interior obtained by seismic tomography. The results strongly resemble what can be inferred of our planet's interior from geological and seismological observations.

Tackley-plumes-cmykFigure 2. The Original Lava Lamp

A "flat-Earth" representation of convection with temperature-dependent viscosity. The low viscosity of the hot plumes makes them narrow and relatively fast-moving. This model results in a single tectonic plate at the surface, rather than the many moving plates of the Earth's crust.


Seismologists have detected a discontinuity in the mantle at a depth of 670 kilometers, and experiments in high-pressure mineral physics indicate that a phase transition occurs at this depth as the intense pressure causes rocks to collapse into a denser state. The pressure-temperature relationship of this transition creates buoyancy forces that tend to keep the material from crossing the boundary between the lower and upper mantle. When this complexity is added to the model, a form of partially layered convection appears: downwelling cold material within the mantle accumulates into pools above the phase transition boundary. At periodic intervals, "avalanches" occur that flush great masses of this cold material into the lower mantle (Figure 1). The true picture seems to lie between the extremes of layered and whole-mantle convection, and provides a way to reconcile various pieces of seemingly contradictory geophysical evidence.

The Earth's tectonic plates consist mostly of lithosphere, the cold, strong top part of the mantle. The crust is just a thin layer of buoyant rock embedded in lithospheric plates. Some plates have continents embedded in part of them, so they are part ocean and part continent, while others are entirely oceanic with only a very thin crust--six-kilometers thick.

"In my opinion, self-consistent generation of plate tectonics is the most important issue facing mantle modelers right now," Tackley said. Researchers who have included lithospheric plates in 3-D models have always had to impose them by hand. The effects of temperature-dependent viscosity alone simply result in an immobile, rigid lid--analogous to a single, world-girdling tectonic plate (Figure 2).

Tackley is investigating the possible role of complex stress-dependent deformations and material flows and horizontal compositional variations, such as non-subducting continental material, in giving rise to our planet's three different types of plate boundaries: mid-ocean ridges, subduction zones and transform faults.

In his current strain-rate weakening model, material stress increases with strain rate to a critical point, past which the stress decreases and the material weakens--not unlike a snapping twig. Strain-induced shearing causes the lithosphere to "break" into a number of very high-viscosity plates; these are separated by sharply defined weak zones with viscosity orders of magnitude lower. Broad weak zones with dominant convergent/divergent motion above upwellings and downwellings are interconnected by a network of narrow weak zones with dominant strike-slip motion (Figure 3).

The model results are similar to rigid plates separated by broad weak zones analogous to subduction zones and mid-ocean spreading centers and narrow weak zones that resemble strike-slip faults such as the San Andreas Fault. This is something of a breakthrough, since for the first time separate plates are the result of a 3-D model rather than an initial assumption. "Although the features are not fully realistic, these results show that self-consistent plate generation is a realizable goal in 3-D mantle convection and provide a promising avenue for future research," Tackley said.

Tackley-plates_T-cmykFigure 3. Making Plates

A visualization of the temperature field in one of Tackley's strain-rate weakening models. This model assumes compressible mantle material, heated at the base. The temperature field shows long linear downwellings and a broad "megaplume" similar to those observed by seismic tomography. (See back cover of magazine.)


Recently, Tackley has been applying this model to Venus, a planet similar in size, mass, and composition to the Earth, but much different in its surface expression of mantle convection since it lacks plate tectonics. The two planets seem to have strikingly different geophysical processes operating in their interiors. "Understanding why these differences occur is essential to a complete theory of mantle convection," Tackley said. "Recent detailed mapping of Venus by the Magellan spacecraft make this an ideal time for such a study."

Tackley also has been doing convection calculations for Io, the innermost of Jupiter's large moons and probably the most volcanically active body in the solar system Figure 4). "Io is interesting because its heating comes from tidal dissipation, not from decay of radioactive isotopes or heat left over from planetary formation as with all other bodies that have been modeled. We will present these results in early July at the Study of the Earth's Deep Interior (SEDI) conference in Tours, France, and we think the planetary science community will be intrigued." --MG


Figure 4. Io, Inside and Out

Left: Calculated convection model for Io, the innermost of Jupiter's large moons. Red indicates hot upwellings; blue indicates cold downwellings. Right: Photograph of Io taken by NASA's Galileo probe. Most of the mottled areas are recently active volcanos.