Bayesian inversion of shear wave velocity profile based on dispersion curve

Dispersion curve inversion is a key step of analyzing data from multichannel surface wave method (MASW) for investigating the shear wave velocity-depth (v_s-h) profile. The profile is usually simplified to be a stratification model consisting of horizontal and homogenous layers. Model parameters include the number (N) and thicknesses (h) of layers and shear wave velocity (v_s) in each layer. The N represents model complexity. The larger N value is, the more complex the model is. A model that is too complex is prone to overfitting. The opposite is true for too simple models that underfit. Mathematically, the dispersion curve inversion problem is ill-posed, that is, there are a number of stratification models of the v_s-h profile with different N, h, and v_s values resulting in identical, or at least, similar dispersion curves. Because the N value is usually unknown during the inversion, the model selection is necessary in which a model fitting well with data and proper model complexity is identified in a pool of competitive models.

Nonetheless, research is rare that addresses the model selection issue in dispersion curve inversion problems. Bayesian framework can be used in model selection by quantifying the uncertainty in the stratification model. In this study, critical issues of Bayesian frameworks for quantifying the uncertainty in stratification model selection are discussed, including Bayesian inversion with a variable or a fixed number of layers in stratification models. Then, the major difficulties in computing the posterior distribution and Bayesian model evidence for determining N are demonstrated and discussed, which are mainly caused by the high-dimensional and highly nonlinear likelihood function. Finally, the sensitivity of model complexity to the error associated with the dispersion curve is explored preliminarily.