Construction of shallow shear wave velocity structure model via trans-dimensional Bayesian inversion of Rayleigh wave dispersion curves

Summary Rayleigh wave dispersion curves inversion is an important method for shallow shear wave velocity structure imaging, which can be achieved through different frameworks such as deterministic inversion and Bayesian inversion. The deterministic methods with fixed parametrization usually require pre-set model complexity, and are difficult to directly provide posterior uncertainty estimation. In contrast, trans-dimensional Bayesian method can probabilistically estimate the dimensions of the model during the sampling process and quantify the uncertainty of the inversion results. However, in the inversion of multimode Rayleigh wave dispersion curves, the posterior space usually has high-dimensional, multi-modal, and strongly nonlinear characteristics. How to achieve efficient posterior exploration and stable trans-dimensional mixing is still a key issue in practical applications. In response to this issue, we constructed and evaluated a trans-dimensional Parallel Tempering reversible jump Markov Chain Monte Carlo (PT-rjMCMC) inversion workflow for multi-modal Rayleigh wave dispersion curves in shear wave velocity imaging, denoted as All-Pair-Sweep PT-rjMCMC (APS-PT-rjMCMC). The method integrated Voronoi trans-dimensional parameterization, multi-modal dispersion likelihood function, reversible jump model update, and parallel tempering sampling into a unified framework. In the replica exchange stage, it adopted an all-pair-sweep replica-exchange schedule with randomized ordering to enhance the inter chain information propagation and trans-dimensional mixing ability under a limited number of temperature chains. The inversion results of synthesized model and measured data indicated that compared with the benchmark implementation, the workflow exhibited better performance in convergence behavior, posterior structure recovery, and layer identification. Our technology provides a solution that combines adaptability and reliability for fine survey of shallow geological structures. It is effectively improving the inversion accuracy of shear wave velocity structures under complex geological conditions. It has broad application space and significant application value in fields such as engineering survey, geological hazard assessment, and water resources investigations.