Mode-Free Wave Equation Tomography of Surface Waves via GPU-Accelerated Automatic Differentiation

Surface wave inversion traditionally relies on layered Earth assumptions and modal dispersion analysis, which can be inadequate in complex geological settings and require subjective mode identification. Full-waveform inversion (FWI), while more accurate, is computationally intensive and highly sensitive to the initial model. These limitations underscore the need for a robust, efficient, and mode-independent approach to surface wave tomography.

This work presents a differentiable wave equation tomography (WET) framework implemented in PyTorch, leveraging automatic differentiation and GPU acceleration for efficient optimization. The method combines two complementary misfit strategies: cross-correlation lag minimization of dispersion spectra and full-spectrum comparison. Both are formulated to avoid mode picking and enable end-to-end differentiability.

Synthetic experiments on 1D and 2D models demonstrate accurate recovery of velocity structures and dispersion characteristics, even in the presence of velocity reversals and lateral heterogeneities. The approach achieves rapid convergence within practical runtimes, offering a viable alternative to traditional surface wave analysis.

This framework provides a flexible foundation for advanced seismic imaging and is readily extensible to incorporate other seismic phases, such as guided waves and reflections, for future joint inversion applications.