Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity

2026-06-22

AI Summary

This work addresses the challenges of high memory consumption, computational cost, and cycle-skipping sensitivity in three-dimensional full-waveform inversion (FWI) by proposing a novel modeling approach that integrates tensor-train (TT) decomposition with axial implicit neural representations (INRs). The 3D velocity model is represented as low-rank TT core tensors, whose elements are jointly predicted by three axial INRs, substantially reducing memory requirements while preserving high resolution. To mitigate cycle skipping, especially under poor initial models or scarce low-frequency data, the method employs multi-scale structural similarity (M-SSIM) as the objective function, effectively leveraging ultra-low-frequency information. This is the first study to combine TT decomposition with axial INRs for 3D velocity inversion, achieving accurate and continuous velocity reconstructions on both synthetic and complex land datasets, with robust performance even in adverse initialization or data conditions.

Abstract

Three-dimensional full waveform inversion (3DFWI) is a powerful technique for reconstructing high-resolution subsurface velocity models. However, its application is often limited by high memory requirements, computational costs, and sensitivity to cycle skipping. To overcome these challenges, we propose a novel tensor train (TT) decomposition-based 3D implicit full waveform inversion framework (TT-3DIFWI) combined with a multi-scale structural similarity (M-SSIM) objective function. In this framework, the 3D velocity model is represented by TT decomposition as a product of a series of low-rank core tensors. Then, three axis-specific implicit neural network representations (INR) based on one-dimensional vector coordinates as input are constructed to predict these core tensors, rather than directly predicting the velocity model. This INR reparameterization method based on TT decomposition can significantly reduce the memory consumption of INR training while maintaining the accuracy and resolution of the 3D velocity model reconstruction. Meanwhile, the low-rank structure of TT decomposition also ensures the structural consistency of the reconstruction velocity, thereby improving the accuracy and continuity of the inversion result. Furthermore, the M-SSIM objective function can compare the multi-scale structural differences between predicted and observed data, and utilize the ultra-low frequency features to reduce cycle skipping. Numerical experiments on synthetic and challenging land datasets demonstrate that TT-3DIFWI with M-SSIM achieves accurate and continuous velocity reconstruction, even with poor initial models or missing low-frequency data.

Problem

• 3D full waveform inversion
• memory requirements
• computational cost
• cycle skipping
• velocity model reconstruction

Innovation

• Tensor Train Decomposition
• Implicit Neural Representation
• Full Waveform Inversion
• Multi-scale Structural Similarity
• Low-rank Modeling