Adaptive-Dictionary-Regularized 3-D Direct Inversion of Surface-Wave Dispersion Data

Abstract

Conventional global smoothing regularization suppresses velocity anomaly amplitudes and blurs structural boundaries in regions of sparse ray coverage, limiting fine-scale crustal imaging under nonuniform observational conditions. This study introduces local sparse regularization based on adaptive-dictionary learning into the DSurfTomo 3-D direct inversion framework, yielding the DSurfTomo-local sparse tomography (LST) method, which simultaneously characterizes smooth velocity backgrounds and discontinuous structural boundaries. Under a Bayesian maximum a posteriori (MAP) formulation, the method couples the global $L_{2}$ constraint and a local dictionary sparsity prior in a unified objective function and jointly solves for the velocity model and sparse coefficients via alternating minimization. During the inversion iterations, dictionary atoms are updated in synchrony with the velocity model using the iterative thresholding and signed K-means (ITKM) algorithm, ensuring that the sparsity regularization remains consistent with the local structure of the current velocity field throughout the inversion. Synthetic data tests demonstrate that, relative to DSurfTomo, DSurfTomo-LST significantly improves velocity anomaly amplitude recovery and structural-boundary resolution under sparse ray-coverage conditions, with the overall root-mean-square error (RMSE) reduced by approximately 38% and 22% in the checkerboard and spike tests, respectively. Applications to the ChinArray data recover velocity structures consistent with regional tectonic features. The Luzhou dense-array results show velocity anomalies whose spatial distribution broadly corresponds to structural features observed in the seismic reflection profile.