Integrating Physics of the Problem into Data-Driven Methods to Enhance Elastic Full-Waveform Inversion with Uncertainty Quantification

TL;DR

This paper combines elastic wave physics with deep learning to improve seismic full-waveform inversion accuracy and uncertainty quantification, addressing nonlinearity and local minima issues.

Contribution

It introduces a physics-informed deep learning approach for elastic FWI and modifies Variational Autoencoders to quantify uncertainties in seismic imaging.

Findings

Enhanced FWI accuracy over traditional methods

Effective uncertainty quantification through modified VAEs

Comprehensive dataset for method evaluation

Abstract

Full-Waveform Inversion (FWI) is a nonlinear iterative seismic imaging technique that, by reducing the misfit between recorded and predicted seismic waveforms, can produce detailed estimates of subsurface geophysical properties. Nevertheless, the strong nonlinearity of FWI can trap the optimization in local minima. This issue arises due to factors such as improper initial values, the absence of low frequencies in the measurements, noise, and other related considerations. To address this challenge and with the advent of advanced machine-learning techniques, data-driven methods, such as deep learning, have attracted significantly increasing attention in the geophysical community. Furthermore, the elastic wave equation should be included in FWI to represent elastic effects accurately. The intersection of data-driven techniques and elastic scattering theories presents opportunities and challenges. In this paper, by using the knowledge of elastic scattering (physics of the problem) and integrating it with machine learning techniques, we propose methods for the solution of time-harmonic FWI to enhance accuracy compared to pure data-driven and physics-based approaches. Moreover, to address uncertainty quantification, by modifying the structure of the Variational Autoencoder, we introduce a probabilistic deep learning method based on the physics of the problem that enables us to explore the uncertainties of the solution. According to the limited availability of datasets in this field and to assess the performance and accuracy of the proposed methods, we create a comprehensive dataset close to reality and conduct a comparative analysis of the presented approaches to it.