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

• Published in: Journal of geophysical research. Machine learning and computation Vol. 1; no. 1
• Main Authors: Taufik, Mohammad H., Wang, Fu, Alkhalifah, Tariq
• Format: Journal Article
• Language: English
• Published: Wiley 01.03.2024
• Subjects: coherent scattering radar; equatorial electrojet; equatorial spread F; E‐region irregularities; F‐region irregularities; occurrence rate
• DOI: 10.1029/2024JH000125
• ISSN: 2993-5210

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. Plain Language Summary Full waveform inversion (FWI) attempts to utilize the complete information of the recorded seismic waves to estimate the Earth's properties by iteratively minimizing the difference between the recorded and simulated data. Often, in practice, the acoustic assumption of the Earth is made, and we invert for a single parameter. This has worked well with offshore data. However, for land data, the acoustic assumption has not fared well, and often we end up with poor results. To account for a more representative simulation, the elastic assumption can be employed during the simulation yielding an elastic variant of FWI (EFWI). Practically, however, EFWI often encounters many challenges. First, EFWI requires a more sophisticated recording apparatus. Even in the presence of multi‐component recordings, empirical formulations that relate the elastic parameters are usually needed to avoid parameter trade‐offs. Moreover, inadequacy in accounting for this relationship causes interdependency between the parameters. To overcome these limitations, we introduce an adaptive regularization framework using generative deep learning models. Numerical experiments, ranging from synthetic to land field data, show that our framework solves imperfect acquisition setups, provides more realistic elastic parameter ratios compared to the conventional EFWI, and converges to better model estimates fitting the observed data better. Key Points Introduce a novel regularization for multi‐parameter elastic full waveform inversion that also improves the data fitting accuracy Demonstrate that the proposed regularization preserves the elastic parameter structure and relationship with negligible additional cost Showcase the proposed regularization on regional land seismic data