Simulating Shear Wave Propagation in Two-Dimensional Fractured Heterogeneous Media by Coupling Boundary Element and Finite Difference Methods

Abstract

A hybrid method to model the shear wave (SH) scattering from 2D fractures embedded in a heterogeneous medium is developed by coupling Boundary Element Method (BEM) and Finite Different Method (FDM) in the frequency domain. FDM is used to propagate an SH wave from a source through heterogeneities to localized homogeneous domains where fractures are embedded within artificial boundaries. According to Huygens’ Principle, the boundary points can be regarded as “secondary” point sources and their values are determined by FDM. Given the incident fields from these point sources, BEM is applied to model scatterings from fractures and propagate them back to the artificial boundaries. FDM then takes the boundaries as secondary sources and continues propagating the scattered field into the heterogeneous medium. The hybrid method utilizes both the advantage of BEM and FDM. A numerical iterative scheme is also presented to account for the multiple scattering between different sets of fractures. The results calculated from this hybrid method with pure BEM method are first compared to show the accuracy of the hybrid approach and the iterative scheme. This method is then applied to calculate the wave scattered from fractures embedded in complex media.