Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity
2026-06-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors present a new method to create detailed 3D underground maps using a technique called full waveform inversion. They use a math trick called tensor train decomposition combined with special neural networks to save memory and keep accuracy when building these maps. Their method also uses a smart way to compare data that helps avoid common mistakes and makes the maps smoother and more reliable. Tests show their approach works well, even when starting with poor information or missing some data.
Full Waveform InversionTensor Train DecompositionImplicit Neural NetworksMulti-Scale Structural SimilarityVelocity ModelCycle SkippingInverse ProblemsLow-Rank ApproximationSeismic ImagingSubsurface Reconstruction
Authors
Liangsheng He, Chao Song, Tiansheng Chen, Tao Liu, Cai Liu
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.