Auto-Linear Phenomenon in Subsurface Imaging

TL;DR

This work introduces the Auto-Linear Phenomenon in subsurface imaging, showing that independently learned encoders and decoders from seismic data and velocity maps can be connected through a simple linear converter to solve both forward and inverse problems. By training two masked autoencoders in a self-supervised fashion and then learning a low-rank linear bridge between latent spaces, the approach achieves robust performance with limited paired data and exhibits strong generalization across datasets and even across imaging modalities (including EM inversion). The method outperforms the previous decoupled InvLINT and matches or exceeds joint-training methods like InversionNet while using fewer supervised parameters, and it extends to forward modeling and other PDE-driven tasks. Overall, Auto-Linear provides a modular, data-efficient paradigm that reveals a near-linear cross-domain alignment in latent representations, with practical implications for few-shot learning, noise tolerance, and cross-domain applicability in subsurface imaging.

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.

Figures (10)

• Figure 1: Overview of the jointly trained encoder-decoder (top), InvLINT (middle), and Auto-Linear (bottom). The orange color indicates that components need to be trained with paired data. Auto-Linear decouples both the encoder and decoder and self-supervised trains them separately in their own domains. Linear converters are learned to connect the frozen, pre-trained encoders and decoders.
• Figure 2: Illustration of results evaluated on OpenFWI, compared with InversionNet and InvLINT.
• Figure 3: Illustration of forward results on "Fault Family".
• Figure 4: Illustration of results from Forward-Inverse process on CurveFault-A.
• Figure 5: Normalized Singular Value of the linear layers.