The Analysis of Surface Wave Spectra Using a Reciprocity Theorem for Surface Waves

Summary By the use of a reciprocity theorem for surface waves, the mathematical expression for the spectrum of surface waves from a point source in a plane layered solid medium can be factorized into a component involving the transmission path and a component involving the source mechanism and depth. This second component can be easily constructed from expressions for the displacement and stress in a propagating surface wave. The factorization has been used to study the effect of source mechanism and depth on the magnitude of the surface waves generated from point sources. In particular this study shows how holes may appear in the surface wave spectra due to the principle that it is impossible to excite a mode of oscillation by action at a node; it also throws doubt on the applicability of the depth correction terms currently used in the formula for Ms.