Localized Boundary Integral Equation-Discrete Wavenumber Method for Simulating Wave Propagation in Irregular Multiple Layers, Part I: Theory

摘要

We present a new method of synthesizing seismograms for irregular multilayered problems. It is an extension of the local (lo) boundary integral equation (BIE) discrete wavenumber method (DWM) topography problem. Following similar procedures as those developed in solving the P-SV waves of topography problems, we first provide the formulation of Bouchon and Campillo's BIE-DWM (Bouchon, 1985; Campillo and Bouchon, 1985) for the multilayered problem. By orthogonally decomposing the forces on irregular and flat parts of each interface and applying a discrete Fourier transform (DFT) we derive their relation. Finally, considering the continuity of displacement and traction on each interface, we get a linear equation only involving the unknown forces on irregular parts of interfaces and discuss its solution. In this algorithm the dimension of the lineal equation is decided by the sampling number on irregular parts of interfaces. Therefore, its computation efficiency increases dramatically, particularly for the problem in which the corrugated part of the layer is highly localized.