Predicting seismic anisotropy in the upper mantle using supervised deep-learning

Both elastic and viscoplastic behaviors of the Earth’s upper mantle are highly anisotropic, because olivine, which composes 60-80% of the mantle, has a strong intrinsic anisotropy and develops strong crystal preferred orientations (CPO). Predicting the evolution of anisotropy with strain is essential to: (1) probe indirectly the deformation in the mantle based on seismic measurements and (2) accounting for the deformation history when simulating the long-term dynamics of the Earth. However, traditional micro-mechanical approaches to model the evolution of CPO-induced elastic and viscous anisotropies are too memory-costly and time-consuming for coupling into geodynamical simulations. To speed up the prediction of seismic anisotropy in the mantle, we developed deep-learning (DL) surrogates trained on a synthetic database built with viscoplastic self-consistent simulations of texture evolution of olivine polycrystals in typical 2D geodynamical flows. A first challenge was the choice of memory-saving representations of the CPO. Training the DL models on the evolution of the elastic tensor components avoided the need of storing the CPOs. However, the major challenge has been to prevent error compounding in a recursive-prediction scheme – where a model prediction at a given time step becomes the input for the next one - to evaluate the anisotropy evolution along a flow line. We implemented multilayer feed-forward (FFNN), ensemble, and transformer neural networks, obtaining the best efficiency/accuracy ratio for the FFNN. The results highlight the importance of (1) the standardization of the outputs in the training stage to avoid overfitting in predictions, (2) the statistical characteristics of the strain histories in the training database, and (3) the influence of non-monotonic strain histories on error propagation. Predictions for complex unseen strain histories are accurate, much more time-efficient and memory-costly than the traditional micro-mechanical models. Our work opens thus new avenues for modeling the strain-controlled evolution of mechanical anisotropy in the Earth’s mantle. This work was supported by the European Research Council (ERC) under the European Union Horizon 2020 Research and Innovation programme [grant agreement No 882450 – ERC RhEoVOLUTION.