A Unified Framework for Forward and Inverse Problems in Subsurface Imaging using Latent Space Translations

TL;DR

This paper introduces a unified deep learning framework called GFI for solving both forward and inverse subsurface imaging problems, demonstrating state-of-the-art results and analyzing the impact of various model components.

Contribution

The paper proposes the GFI framework that unifies forward and inverse subsurface imaging, introduces two new architectures, and provides comprehensive analysis of their performance.

Findings

GFI encompasses previous deep learning methods as special cases.

Latent U-Net and Invertible X-Net achieve SOTA results on synthetic datasets.

Models show promising zero-shot performance on real-world-like datasets.

Abstract

In subsurface imaging, learning the mapping from velocity maps to seismic waveforms (forward problem) and waveforms to velocity (inverse problem) is important for several applications. While traditional techniques for solving forward and inverse problems are computationally prohibitive, there is a growing interest in leveraging recent advances in deep learning to learn the mapping between velocity maps and seismic waveform images directly from data. Despite the variety of architectures explored in previous works, several open questions still remain unanswered such as the effect of latent space sizes, the importance of manifold learning, the complexity of translation models, and the value of jointly solving forward and inverse problems. We propose a unified framework to systematically characterize prior research in this area termed the Generalized Forward-Inverse (GFI) framework, building on the assumption of manifolds and latent space translations. We show that GFI encompasses previous works in deep learning for subsurface imaging, which can be viewed as specific instantiations of GFI. We also propose two new model architectures within the framework of GFI: Latent U-Net and Invertible X-Net, leveraging the power of U-Nets for domain translation and the ability of IU-Nets to simultaneously learn forward and inverse translations, respectively. We show that our proposed models achieve state-of-the-art (SOTA) performance for forward and inverse problems on a wide range of synthetic datasets, and also investigate their zero-shot effectiveness on two real-world-like datasets. Our code is available at https://github.com/KGML-lab/Generalized-Forward-Inverse-Framework-for-DL4SI