Representation of an extended seismic source in a propagator-based formalism

Abstract

Abstract A method is presented for the computation of synthetic seismograms for an arbitrary seismic source embedded in a stratified medium. The technique is applied to a source extending in three space dimensions for which the radiation has been decoupled into P, SV, and SH motions. A matrix formulation is given in which the displacements and stresses due to individual plane wave components of the P-SV and SH radiations from the source are separated into contributions at the upper and lower interfaces of the source layer where they are subtracted from the displacement-stress vector due to the total wave field. With this method, the propagator in the source layer connects only the reverberated components of the waves at the upper and lower layer interfaces, and there are no discontinuities in the displacements and stresses at the source depth. An application of Dunkin's formulation of the Thompson-Haskell algorithm is given for the solution of the P-SV problem, along with a brief summary of the well-known propagator matrix formulation for the associated SH problem. The formulation is extended to the case of a shallow source penetrating two layers, and examples are presented for both shear and tensile sources.