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

2024-10-15

arXiv.org

AI Summary

In subsurface imaging, modeling the forward and inverse mappings between velocity fields and seismic waveforms faces challenges including high computational cost, latent-space misalignment, and poor generalization. To address these, this paper proposes a Generalized Forward-Inverse (GFI) imaging framework—unifying deep-learning-based imaging methods for the first time under the manifold hypothesis and latent-space translation. We design two complementary architectures: Latent U-Net for forward mapping and Invertible X-Net for invertible backward mapping, enabling end-to-end bidirectional translation and zero-shot cross-domain transfer. The framework is trained jointly on synthetic and realistic synthetic-like data. Evaluated on multiple synthetic benchmarks, it achieves state-of-the-art performance; critically, it demonstrates effective zero-shot generalization on two unseen real-world datasets. These results empirically validate the necessity and superiority of jointly modeling forward and inverse problems with explicit manifold alignment.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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

Problem

• Develop unified framework for subsurface imaging problems
• Improve deep learning for velocity-waveform mapping
• Evaluate latent space and model architecture effects

Innovation

• Unified GFI framework for subsurface imaging
• Latent U-Net and Invertible X-Net architectures
• Jointly solves forward and inverse problems