Coupling Deep Learning with Full Waveform Inversion

Abstract

Full waveform inversion (FWI) aims at reconstructing unknown physical coefficients in wave equations using the wave field data generated from multiple incoming sources. In this work, we propose an offline-online computational strategy for coupling classical least-squares based computational inversion with modern deep learning based approaches for FWI to achieve advantages that can not be achieved with only one of the components. In a nutshell, we develop an offline learning strategy to construct a robust approximation to the inverse operator and utilize it to design a new objective function for the online inversion with new datasets. We demonstrate through numerical simulations that our coupling strategy improves the computational efficiency of FWI with reliable offline training on moderate computational resources (in terms of both the size of the training dataset and the computational cost needed).

Waveform inversion via reduced order modeling

“…An explicit analysis of such a method, that minimizes the data misfit over both c(x) and f (t) in a very simple setting, can be found in [60]. There are various other ideas that have been tried, including machine learning [26,28]. Nevertheless, the state of the field remains far from satisfactory and theoretical guarantees that one method or another will work even in simple settings are rare.…”