OTG: A Physics-Informed Hybrid Interpolation Framework for High-Precision 3D S-Wave Velocity Modeling

Three-dimensional (3D) S-wave velocity field modeling is a critical task in seismic exploration, but balancing modeling accuracy and geological rationality remains challenging due to sparse observation data and inherent limitations of existing methods. To address this issue, we propose an Ordinary Kriging-Thin Plate Spline-Graph Convolutional Network (OTG) fusion model. It dynamically integrates the global trend capture capability of Ordinary Kriging, the local smooth processing ability of Thin Plate Spline, and the nonlinear feature fitting performance of Graph Convolutional Network (GCN) via an adaptive gating fusion mechanism. A multi-dimensional physical constraint loss function is further designed to ensure the geophysical plausibility of interpolation results. Validated on a dataset from 105 seismic stations in Southwest China using spatial cross-validation and random repeated experiments, the full OTG model achieves a root mean square error (RMSE) of 0.1148 km/s, a mean absolute percentage error (MAPE) of 1.9614%, and a Pearson correlation coefficient (PCC) of 0.9801. Compared with the optimal traditional method (OK) and the state-of-the-art hybrid method (DeepKriging), the proposed model reduces the root mean square error (RMSE) by 42.8% and 8.2%, respectively. This study demonstrates that the OTG model realizes the complementary advantages of traditional geoscientific methods and deep learning, providing a reliable engineering solution for high-precision 3D S-wave velocity structure interpolation in seismic exploration.