[Paper Review] Auto-Linear Phenomenon in Subsurface Imaging

Yinan Feng, Yinpeng Chen+4 more|arXiv (Cornell University)|Apr 27, 2023

Seismic Imaging and Inversion TechniquesEarth and Planetary Sciences3 citations

TL;DR

This paper introduces SimFWI, a novel framework that simplifies full waveform inversion (FWI) by decoupling seismic data and velocity map modeling through domain-independent self-supervised learning using masked autoencoders. It discovers a linear relationship in latent spaces across domains, enabling a frozen, pre-trained encoder and decoder to be connected via a learnable linear mapping, achieving performance comparable to joint training with half the model size and superior few-shot and robustness performance.

ABSTRACT

Subsurface imaging involves solving full waveform inversion (FWI) to predict geophysical properties from measurements. This problem can be reframed as an image-to-image translation, with the usual approach being to train an encoder-decoder network using paired data from two domains: geophysical property and measurement. A recent seminal work (InvLINT) demonstrates there is only a linear mapping between the latent spaces of the two domains, and the decoder requires paired data for training. This paper extends this direction by demonstrating that only linear mapping necessitates paired data, while both the encoder and decoder can be learned from their respective domains through self-supervised learning. This unveils an intriguing phenomenon (named Auto-Linear) where the self-learned features of two separate domains are automatically linearly correlated. Compared with existing methods, our Auto-Linear has four advantages: (a) solving both forward and inverse modeling simultaneously, (b) applicable to different subsurface imaging tasks and achieving markedly better results than previous methods, (c)enhanced performance, especially in scenarios with limited paired data and in the presence of noisy data, and (d) strong generalization ability of the trained encoder and decoder.

Motivation & Objective

• To address the challenge of high model complexity and limited generalization in deep learning-based full waveform inversion (FWI).
• To investigate whether self-supervised pretraining in isolated domains can yield transferable representations for FWI.
• To simplify the mapping between seismic data and velocity maps by discovering a linear relationship in latent spaces.
• To enable model reuse across diverse FWI datasets through shared encoders, decoders, and dataset-specific linear mappings.
• To improve few-shot learning and robustness to noise and real-world data distribution shifts in subsurface imaging.

Proposed method

• Pre-train a seismic data encoder and velocity map decoder using masked autoencoders (MAE) in their respective domains without paired supervision.
• Train the models on multiple FWI datasets to learn domain-invariant representations via self-supervised learning.
• Discover a linear correlation between the latent spaces of seismic and velocity representations across datasets.
• Freeze the pre-trained encoder and decoder and train a learnable linear mapping layer to connect them using paired seismic-velocity data.
• Share the same encoder and decoder across multiple datasets within a family, while learning a unique linear converter per dataset.
• Use piecewise linear mapping to model global relationships across diverse subsurface structures.

Figure 1: Overview of SimFWI. Compared to the jointly trained encoder-decoder (top), SimFWI (bottom) decouples the encoder and decoder and self-supervised trains them separately in their own domains. Then, a linear converter is learned to connect the frozen, pre-trained encoder and decoder.

Experimental results

Research questions

• RQ1 Can self-supervised pretraining in isolated domains yield latent representations that exhibit a linear relationship across domains in FWI?
• RQ2 Does the discovered linear relationship enable effective and efficient mapping between seismic data and velocity maps without joint training?
• RQ3 Can the same pre-trained encoder and decoder be shared across multiple FWI datasets with different subsurface structures?
• RQ4 How does the performance of the proposed method compare to jointly trained models in few-shot and noisy data settings?
• RQ5 What is the relationship between the singular values of the learned linear layer and the complexity of the subsurface structure?

Key findings

• SimFWI achieves comparable performance to the jointly trained InversionNet, with only 12.3M parameters versus InversionNet’s 24.4M, demonstrating a 50% reduction in model size.
• In few-shot settings with limited paired data, SimFWI outperforms InversionNet, showing improved sample efficiency.
• The model demonstrates strong robustness to large noise in seismic data, maintaining high fidelity in velocity map reconstruction.
• Performance improves on complex datasets when sharing linear converters across families, due to broader coverage in latent space, while simpler datasets suffer from distribution shift.
• A correlation is observed between the singular values of the linear layer and dataset complexity, suggesting latent space geometry reflects subsurface structural complexity.
• Sharing the encoder and decoder across dataset families improves generalization, especially for complex subsurface structures, while maintaining high performance on realistic and noisy data.

Figure 2: Comparison between our SimFWI and InvLINT Feng et al. ( 2022 ) . The first row shows the similar framework of both methods. The second row indicates how our method trains each component. The third row shows how InvLINT trains each component.