Tensor-Train-Based Elastic Wavefield Decomposition in VTI Media

Abstract

Elastic wavefield decomposition into quasi-compressional (qP) and quasi-shear-vertical (qSV) modes is essential for elastic imaging and inversion in VTI media, but becomes computationally expensive when polarization vectors vary strongly in space. I propose a tensor-train (TT) representation of mixed-domain decomposition projectors, constructed via TT-cross with a single user-specified tolerance and applied efficiently using FFT-based operations. A residual-orthogonal strategy extracts qSV from the residual wavefield after qP removal to suppress mode leakage. The method is implemented in Python/PyTorch with GPU acceleration. Numerical experiments on three 2D VTI models (a two-layer benchmark, a BP 2007 benchmark subset, and an Overthrust-based structurally complex model) demonstrate reconstruction errors of 0.094-0.89% for TT, compared to 1.67-6.44% for a conventional CUR low-rank approach (4-46x improvement), with consistently lower cross-talk and near-unity energy ratios. Time-domain receiver traces further confirm that TT yields smaller reconstruction residual spikes and reduced cross-mode leakage than CUR. Runtime tests show that CUR can be faster on smaller grids, whereas TT with GPU acceleration becomes competitive and can outperform CUR for larger models. The TT representation scales linearly with tensor Od Ns r2-enabling practical extension to higher-dimensional projector tensors where conven-tional methods become impractical.