Geodynamicists have made substantial progress over the past years in developing sophisticated mantle convection models, including chemical heterogeneity, temperature and strain-rate dependent rheology, realistic 3-D spherical shell geometry and convective vigor that is nearly Earthlike. In to apply the new modeling capability to study the flow history of Earth's mantle, mantle convection models must be properly initialized, i.e. one must constrain initial conditions into the past. This is an inverse problem and the PI proposes to evaluate the potential of adjoint fluid dynamic inverse theory to track mantle heterogeneity back into the relatively recent Cenozoic and Mesozoic history of our planet. To this end, a novel 3-D spherical high-resolution adjoint model of mantle convection will be developed. The PI will apply the adjoint method in idealized mantle convection models for time periods of less than one convective overturn, in order to explore the feasibility of the method to estimate unknown initial conditions back in time. The PI will constrain unknown initial conditions in mantle convection calculation through a series of coupled forward-in-time and adjoint backward-in-time integrations, a difficult task facilitated by the rapid advance in supercomputer capabilities. The outcome of the work will be to explore the utility of adjoint fluid-dynamic inverse theory in retrieving flow structure back in time in mantle convection models. (Code benchmark is available at www.geophysics.princeton.edu/Geodynamics/TERRA/HTML/page5.top.html)
