Sensitivity Analysis of Global Kinematics on Mantle Structure Using Automatically Generated Adjoint Thermochemical Convection Codes

Within the past 30 years, numerical models of mantle convection have been able to predict observations on Earth and planets, and among them tectonics. The possibility of building inverse problems in global geodynamics became concrete, and often involve the development of adjoint codes. Such tools provide efficient ways to estimate sensitivities of misfit functions relative to control parameters, like errors on predicted velocities relative to mantle 3D structure. One issue to build an adjoint code is that such code is problem specific in many cases, while forward codes are versatile. We propose here a way to build adjoint codes that are exact adjoints of forward codes through an automated process. Using the automatic differentiation translator TAF \cite{giering2003} and incorporating specific implementations for MPI communications, we generate two adjoint codes of the 3D spherical thermomechanical mantle convection code StagYY \cite{tackley2008}. We first present a benchmarking example computing the sensitivities of a thermal state to initial conditions with a 3D spherical thermochemical model. We then compute the sensitivities of present-day plate velocities relative to guessed temperature distribution in the mantle. The sensitivities reflect either the intrinsic sensitivity of the problem (sensitivity to upper mantle structure) and the errors made in reconstructing the thermal structure of the mantle (deepest mantle structure). Both codes successfully pass the rigorous and demanding gradient test, also called Taylor test. We show that our workflow for automatic generation of adjoint codes for StagYY provides a sustainable and adaptive method to engage in inverse modelling and sensitivity computations of 3D global geodynamics.