Estimation of Interface Geometry for Three-Dimensional Layered Basin Structure Using a Random Search Method

Construction of detailed three-dimensional underground velocity structure models is an important requirement for strong motion prediction. The deep subsurface structure, i.e. the region from the top of upper crust to the surface of the earth, has large influence on the ground motion because the heterogeneity of medium property changes drastically in horizontal and vertical directions especially in the sedimentary basins and plains. The deep subsurface velocity structure models are often modeled as layered structure for the purpose of use in ground motion simulation. Among various methods for modeling the layered structure, Aoi (2000) proposed a waveform inversion method to estimate the 3D topography of sediment/bedrock interface with least-squares criterion. The problem is pseudo-linearized and solved iteratively on the assumption of weak nonlinearity. Iwaki and Iwata (2011) extended the method to apply it to the real observed ground motion data, and proposed a refined velocity structure model of the Osaka sedimentary basin, Japan. The waveform inversion method can potentially be a useful tool to construct or calibrate the deep subsurface velocity structure models worldwide. However, despite the fact that solving a nonlinear least-squares problem by pseudo-linearization requires an appropriate initial model that is close enough to the global optimum, such appropriate initial model is not always available; even if a well-calibrated model is available, it is difficult to judge whether it is appropriate enough. In this study, we investigate the potential of Monte Carlo (random) methods, for the waveform inversion of interface topography. Monte Carlo methods are often used in inverse problems to search the global model space. Although they require a larger amount of computation, the inverse process is more robust and it depends less on the initial model. In addition, the models explored during the search can be reanalyzed to construct the posterior probability density function based on Bayesian theorem (e.g. Sambridge, 1999) so that resolution and uncertainties can be studied. We conducted a preliminary analysis using a virtual basin model as a target in order to examine the applicability of the method. We will apply the method to the Osaka basin using a very simple initial model, on the assumption that only little information on the velocity structure is available.