Solving Forward and Inverse Problems for Seismic Imaging using Invertible Neural Networks

Abstract

Full Waveform Inversion (FWI) is a widely used optimization technique for subsurface imaging where the goal is to estimate the seismic wave velocity beneath the Earth's surface from the observed seismic data at the surface. The problem is primarily governed by the wave equation, which is a non-linear second-order partial differential equation. A number of approaches have been developed for FWI including physics-based iterative numerical solvers as well as data-driven machine learning (ML) methods. Existing numerical solutions to FWI suffer from three major challenges: (1) sensitivity to initial velocity guess (2) non-convex loss landscape, and (3) sensitivity to noise. Additionally, they suffer from high computational cost, making them infeasible to apply in complex real-world applications. Existing ML solutions for FWI only solve for the inverse and are prone to yield non-unique solutions. In this work, we propose to solve both forward and inverse problems jointly to alleviate the issue of non-unique solutions for an inverse problem. We study the FWI problem from a new perspective and propose a novel approach based on Invertible Neural Networks. This type of neural network is designed to learn bijective mappings between the input and target distributions and hence they present a potential solution to solve forward and inverse problems jointly. In this thesis, we developed a data-driven framework that can be used to learn forward and inverse mappings between any arbitrary input and output space. Our model, Invertible X-net, can be used to solve FWI to obtain high-quality velocity images and also predict the seismic waveforms data. We compare our model with the existing baseline mod- els and show that our model outperforms them in velocity reconstruction on the OpenFWI dataset. Additionally, we also compare the predicted waveforms with a baseline and ground truth and show that our model is capable of predicting highly accurate seismic waveforms simultaneously.