| Abstract: | We present a semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (andacoustic) waves in multi-layered media with irregular interfaces. The method worksrecursively starting from the top-most free surface at which a stress-free boundarycondition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrixformulation of the propagation matrix (PM) or more recently the reflectivity methodas wide used in the geophysics community for the computation of synthetic seismograms in stratified media. The reflected and transmitted wave-fields between arbitraryshapes of layers can be computed using the indirect boundary element method (BEM,sometimes called IBEM). Like any standard BEM, the primary task of the BEM-basedpropagation matrix method (thereafter called PM-BEM) is the evaluation of elementboundary integral of the Green's function, for which there are standard method thatcan be adapted. In addition, effective absorbing boundary conditions as used in thefinite difference numerical method is adapted in our implementation to suppress thespurious arrivals from the artificial boundaries due to limited model space. To ourknowledge, such implementation has not appeared in the literature. We present several examples in this paper to demonstrate the effectiveness of this proposed PM-BEMfor modelling elastic waves in media with complex structure. |
