Application of automatic differentiation to the inversion of nonlinear mantle rheology using plate motion and topography

The rheological properties of the mantle govern plate tectonics and mantle convection, yet constraining the rheological parameters remains a significant challenge. Laboratory experiments are usually performed under different temperature-pressure-strain-rate conditions than those of natural environments, leading to substantial uncertainties when extrapolating the parameters to real-world conditions. While traditional Bayesian inversion with Monte Carlo sampling methods offers sufficient exploration of the parameter space and accurate inversion results, the excessive computational cost limits its practical application to complex nonlinear problems. To address these limitations, we integrate finite-difference-based geodynamic forward modeling with Automatic Differentiation (AD) to build a framework to invert non-linear rheological parameters. By incorporating multisource observational data, including surface velocities and topography, we are able to invert critical rheological parameters of the lithosphere and mantle, including the viscosity pre-exponential factor, activation energy, stress exponent, yield stress, and plate-interface viscosity. To validate the method, a series of models with different levels of complexity from single- to multiple-subduction systems and consideration of data noises are designed to generate synthetic data that are further used for inversion. Our method can successfully restore the rheological parameters under various conditions, with minimal errors between predicted and true values, underscoring its stability and broad applicability. In general, this study introduces a highly efficient and practical geodynamic forward and inverse modeling approach that can be used to infer the rheology of the mantle.