Robust Inferences About the Lower Mantle |
Don L. Anderson Caltech, MS 252-21, Pasadena, CA 91125 USA, dla@gps.caltech.edu |
Mineral physicists are quite familiar with the trade-offs between temperature, mineralogy and composition when discussing the state of the lower mantle. Seismologists realize that the red areas on their tomographic maps could have causes other than high temperature. Debates about layered convection and locations of geochemical reservoirs generally ignore these ambiguities and consider only temperature. However, there are some robust conclusions regarding the state of the deep mantle and the nature of mantle convection that can be derived from simple and classical solid state physics and anharmonic theory. Material properties such as elastic moduli, thermal conductivity, expansivity and viscosity depend to first order on interatomic distances. This is reflected in Birch’s Law, the law of corresponding states, the seismic equation of state and the quasi-harmonic approximation. Given that volume decreases with pressure we know how these parameters are related. Temperature effects, over and above the effect on volume, are small, particularly at high pressure. Equations of state based on such considerations are quite different from the ones used in fluid dynamic modeling (Boussinesq, anelastic) and in tomographic and geodynamic interpretations (simple velocity-density scalings). Thermodynamically self-consistent calculations are yet to be attempted by numerical modelers outside of the ab initio community. The calculated material properties at the base of the mantle imply that heat is conducted efficiently out of the core, thermal expansion and buoyancy are small, rheology is sluggish and the effective Rayleigh number is very low. Thermal instabilities in the lowermost mantle must be gigantic, as observed in tomography, and slow to develop. Modest intrinsic density and compositional contrasts irreversibly stratify the mantle, and the thermal effects on seismic velocities are low. Boundaries between chemical layers must have enormous relief and little seismic velocity contrast (stealth layers). Visually impressive contrasts in deep mantle tomographic cross-sections are likely due to chemical and mineralogical contrasts. Boundary layer scalings that are are consistent with the thickness and time scales of surface plates suggest that equivalent features at the base of the mantle have dimensions of thousands of kilometers and lifetimes of billions of years. These conclusions can be drawn even if we cannot know the composition or temperature. |