Seismic Response of 2D Topographic Profiles for Incident SH Waves: Iterative Solution and Comparison of Direct and Indirect BEM

ABSTRACT The scattering and diffraction of waves by irregular surface profiles is of interest in seismology and in many other areas. Diverse techniques have been proposed to quantitatively study the problem. Among them, domain approaches such as finite differences, spectral elements and finite elements have been used. Because the reduction of dimensionality boundary formulations is widely used. Recently, the direct boundary-element method has been applied using some series approximations for surface scattering, including the preconditioned splitting series, for the numerical description of rough surface scattering. Extending further and simplifying this approach, we use the indirect boundary-element method. The ensuing Fredholm integral equation of the second kind that arises in IBEM leads to a very efficient iterative scheme based on the classical Jacobi method. A discussion of direct and indirect approaches is presented. Assuming incident SH waves, results are obtained with the various approaches and compared among them for both a canyon and a hill, both of semicircular shape. Besides, an example is presented of a surface profile that produces strong scattering. This was inspired by the diverse problems that arise in the emerging field of metamaterials.