Learned regularizations for multi-parameter elastic full waveform inversion using diffusion models

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 often requires a more sophisticated recording apparatus. Even in the presence of multi-component 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 first train a (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 cost. Only the vertical particle velocity data is used to invert the elastic parameters. Unlike other learned 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 data to land field data, show that our framework not only solves the illumination effects from imperfect acquisition setups and provides more realistic elastic parameter ratios compared to the conventional EFWI but also converges to better model estimates that fit the observed data better.