Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop

TL;DR

This paper presents an unsupervised learning approach for full-waveform inversion that integrates PDE modeling with CNNs, enabling seismic data reconstruction without requiring expensive velocity map labels, and introduces a new benchmark dataset.

Contribution

It introduces a novel PDE-CNN loop for unsupervised FWI, eliminating the need for labeled velocity maps and providing a large-scale dataset for evaluation.

Findings

Unsupervised model achieves accuracy comparable to supervised methods.

The approach outperforms supervised models with more seismic data.

The method reduces reliance on expensive velocity map labels.

Abstract

This paper investigates unsupervised learning of Full-Waveform Inversion (FWI), which has been widely used in geophysics to estimate subsurface velocity maps from seismic data. This problem is mathematically formulated by a second order partial differential equation (PDE), but is hard to solve. Moreover, acquiring velocity map is extremely expensive, making it impractical to scale up a supervised approach to train the mapping from seismic data to velocity maps with convolutional neural networks (CNN). We address these difficulties by integrating PDE and CNN in a loop, thus shifting the paradigm to unsupervised learning that only requires seismic data. In particular, we use finite difference to approximate the forward modeling of PDE as a differentiable operator (from velocity map to seismic data) and model its inversion by CNN (from seismic data to velocity map). Hence, we transform the supervised inversion task into an unsupervised seismic data reconstruction task. We also introduce a new large-scale dataset OpenFWI, to establish a more challenging benchmark for the community. Experiment results show that our model (using seismic data alone) yields comparable accuracy to the supervised counterpart (using both seismic data and velocity map). Furthermore, it outperforms the supervised model when involving more seismic data.