Automatic generation of the adjoint of the StagYY mantle convection model

Motions within the Earth mantle and tectonics constitute a single self-organized system which is cooling the planet over its geological history. Since the end of the XXth century, models of mantle convection self-generating plate tectonic behavior have progressed to a state that makes them applicable to global tectonic problems. The possibility of combining geological and geophysical data with dynamic models to retrieve the recent history of mantle flow and tectonics becomes realistic. Therefore, it is a challenge to build inverse methods to study inverse and sensitivity problems in the Earth's mantle convection. We have automatically generated the tangent-linear and the adjoint source code from the StaggYY code (Tackley, Phys. Earth Planet. Int. 171, 7-18, 2008). The Fortran code of the model was translated to the corresponding derivative codes using TAF (Transformation of Algorithms in Fortran), source-to-source translator. All codes run in parallel mode, using MPI (Message Passing Interface). The economic taping strategy of TAF, including re-computations, and checkpointing, helps to keep the memory footprint of the adjoint code low and the performance high. We highlight some key features of the automatic differentiation, evaluate the performance of the adjoint code, and show first results from 2D and 3D sensitivity fields, focusing on the relationships between temperature in the mantle and tectonics. Ultimately the addjoint code shall be applied to inversion and assimilation problems using a bayesian framework.