Data-driven Methods for Solving Large-scale Inverse Problems with Applications to Subsurface Imaging

Abstract

Seismic full-waveform inversion is a typical non-linear and ill-posed large-scale inverse problem. It is an important and widely used geophysical exploration method to obtain subsurface structures. The existing computational methods for solving full-waveform inversion are not only computationally expensive but also yield low-resolution results because of the ill-posedness and cycle skipping issues of full-waveform inversion. To resolve those issues, we employ machine-learning techniques to solve the full-waveform inversion. Specifically, we focus on applying convolutional neural network˜(CNN) to directly derive the inversion operator so that the velocity structure can be obtained without knowing the forward operator. We build a convolutional neural network with an encoder-decoder structure to model the correspondence from seismic data to subsurface velocity structures. To evaluate the performance of our inversion technique, we compare it to both existing physics-driven methods and other data-driven methods. Our numerical examples using synthetic seismic reflection data show that our CNN model significantly improves the accuracy of the velocity inversion while the computational time is reduced. Through numerical tests, we also study the robustness of our CNN model and show that our model yields some weak generalization ability.