Learned Regularizations for Multi‐Parameter Elastic Full Waveform Inversion Using Diffusion Models

Abstract Elastic full waveform inversion (EFWI) promises to account for the Earth's elastic nature and corresponding reflectivity, which is often disregarded in the commonly used acoustic FWI. However, EFWI usually requires a more sophisticated recording apparatus (beyond the usual single‐component data). Even in the presence of multicomponent recordings, an empirical formulation that relates the elastic parameters is usually employed. Such approximations, thus, render the inverted elastic parameters (and their relationship) hostage to our assumptions. To overcome these limitations, we introduce learned regularization using diffusion models. Specifically, we first train the (unsupervised) diffusion model to understand the coupling relationship of the distribution of the elastic parameters and use the trained model in the inversion process with a negligible additional computational cost. To fully realize the effect of our regularization and to mimic a realistic scenario, the vertical component of the particle velocity is used to invert the elastic parameters. Unlike other learned (deep) regularizers, diffusion models offer a unique conditional capability that suits the nature of an FWI process (going from low to high frequency) while maintaining the problem‐agnostic feature of such regularizers. Numerical experiments, ranging from synthetic to land field data, show that our framework solves the illumination effects from an imperfect acquisition setup and provides more realistic elastic parameter ratios than the conventional EFWI. We also empirically demonstrate that, unlike traditional regularization schemes, our framework converges to better model estimates that fit the observed data better.