Teleseismic Rayleigh Wave Helmholtz Tomography in Northeastern Tibet Using Physics-Informed Neural Networks

In this study, we apply a physics-informed neural network (PINN)-based teleseismic Rayleigh wave Helmholtz tomography (pinnTHT) to investigate the crustal and upper mantle structure beneath the northeastern Tibetan Plateau. The method incorporates the Helmholtz equation directly into the loss function, allowing phase velocity, amplitude, and traveltime fields to be jointly constrained. We represent the physical fields as continuous, grid-free functions whose spatial derivatives are evaluated by automatic differentiation rather than by finite differences on a fixed grid. We apply this approach to teleseismic surface wave data recorded by a dense seismic array and analyze Rayleigh wave phase velocities at periods of 20–80 s. Our results reveal significant lateral heterogeneity in velocity structure that correlates well with major tectonic features across the study area. The method achieves reliable resolution using only approximately 20% of the observational data compared to traditional approaches, and a synthetic ground-truth test confirms that pinnTHT recovers a known velocity model more accurately than conventional Helmholtz tomography applied to the full data set. Comparisons with ambient noise tomography results at overlapping periods show consistent velocity anomaly patterns, indicating that the combination of earthquake and ambient noise data provides a systematic understanding of phase velocity structure across multiple periods. These results demonstrate that PINN-based teleseismic Helmholtz tomography offers a memory efficient and robust approach for investigating deep Earth structure, particularly beneficial in regions with sparse or unevenly distributed data.