Abstract
An analytic method is proposed for Love wave field generated at a vertical interface between two 2-D elastic quater-spaces; one homogeneous and the other multi-layered (see Fig. 1). The incident field is a plane SH-wave whose amplitude varies with depth, propagating horizontally in the first quarter. The Love wave transmitted into the second quarter is expressed using the Representation Theorem and the normal mode solution of the Love wave. When imposing continuity condition for displacement and traction at the vertical interface, the diffracted waves in the first quarter and the body waves in the second quarter are neglected. The integration along the vertical interface is analytically performed, assuming constant amplitude of the incident wave within each layer at the interface, and using the fact that the amplitude of the normal mode solution decreases exponentially, which guarantees rapid, convergence of the intergral. To check the accuracy of our solution, we have computed theoretical seismograms at stations along the free surface of two sedimentary basins embedded in a homogeneous half-space for the case of incident SH-waves from a shallow dislocation source (see Fig. 2). Results are in excellent agreement with the corresponding results by the boundary element method, with the advantage that the proposed method requires much less computational time (see Figs. 4 and 6).
