Refining tomography using generative neural networks trained on geodynamic data

T. Santos, T. Bodin, F. Soulez, Y. Ricard, and Y. Capdeville

Geophysical Journal International, Volume 238, Issue 3, September 2024, Pages 1676–1695
https://doi.org/10.1093/gji/ggae240

Inverse problems occur in many fields of geophysics, wherein surface observations are used to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness inherent in these problems, a standard strategy is to incorporate a priori information regarding the unknown model. Sometimes a solution is obtained by imposing that the inverted model remains close to a reference model and with smooth lateral variations (e.g., a correlation length or a minimal wavelength are imposed). This approach precludes the presence of strong gradients or discontinuities in the recovered model. Admittedly, discontinuities—such as interfaces between layers, or the shapes of geological provinces or geological objects like slabs—can be a priori imposed or even suggested by the data themselves. This is, however, limited to a small set of possible constraints. For example, it would be very challenging and computationally expensive to perform a tomographic inversion where the subducting slabs might have top discontinuities with unknown shapes. The problem seems formidable because one cannot even imagine how to sample the prior space: is each specific slab continuous or broken into different portions with their own interfaces? No continuous set of parameters appears to describe all the possible interfaces we could consider. To address these challenges, we propose training a Generative Adversarial Network (GAN) to generate models from a geologically plausible prior distribution derived from geodynamic simulations. In a Bayesian framework, a Markov chain Monte Carlo algorithm is used to sample the low-dimensional model space representing the ensemble of potential geological models. This enables the integration of complex prior information, parameterized within a low-dimensional model space conducive to efficient sampling. The application of this approach is demonstrated in the context of a downscaling problem, where the objective is to infer small-scale geological structures from a smooth seismic tomographic image.