The adjoint equations for thermochemical compressible mantle convection: derivation and verification by twin experiments.

The adjoint method is an efficient way to obtain gradient information in a mantle convection model relative to past flow structure, allowing one to retrodict mantle flow from observations of the present-day mantle state. While adjoint equations for isochemical mantle flow have been derived for both incompressible and compressible flows, here we extend the method to thermochemical mantle flow models, and present thermochemical adjoint equations in the elastic-liquid approximation. We verify the method with twin experiments, and retrodict the flow history of a thermochemical reference model (reference twin) assuming for the final state, either a consistent thermochemical interpretation, using the thermochemical adjoint equations, or an inconsistent purely thermal interpretation, using the isochemical adjoint equations. The consistent simulation correctly retrodicts the flow evolution of the reference twin. The inconsistent case, instead, restores a false flow history whereby internal buoyancy forces and convectively maintained topography are overestimated. Because the cost function is reduced in either case, our results suggest that the adjoint method can be used to link assumptions on the role of chemical mantle heterogeneity to geologic inferences of dynamic topography, thus providing additional means to test hypotheses on mantle composition and dynamics.

Mesozoic plate-motion history below the northeast Pacific Ocean from seismic images of the subducted Farallon slab

The high-resolution seismic imaging of subducted oceanic slabs has become a powerful tool for reconstructing palaeogeography. The images can now be interpreted quantitatively by comparison with models of the general circulation of the Earth's mantle. Here we use a three-dimensional spherical computer model of mantle convection to show that seismic images of the subducted Farallon plate provide strong evidence for a Mesozoic period of low-angle subduction under North America. Such a period of low-angle subduction has been invoked independently to explain Rocky Mountain uplift far inland from the plate boundary during the Laramide orogeny. The computer simulations also allow us to locate the largely unknown Kula-Farallon spreading plate boundary, the location of which is important for inferring the trajectories of 'suspect' terrain across the Pacific basin.

Time scales and heterogeneous structure in geodynamic earth models

Computer models of mantle convection constrained by the history of Cenozoic and Mesozoic plate motions explain some deep-mantle structural heterogeneity imaged by seismic tomography, especially those related to subduction. They also reveal a 150-million-year time scale for generating thermal heterogeneity in the mantle, comparable to the record of plate motion reconstructions, so that the problem of unknown initial conditions can be overcome. The pattern of lowermost mantle structure at the core-mantle boundary is controlled by subduction history, although seismic tomography reveals intense large-scale hot (low-velocity) upwelling features not explicitly predicted by the models.