Computing The Individual Seismic Phases Using Cagniard-de Hoop Method

Our research has been based on synthesizing seismograms in multi-layered half-space. Our method combines generalized R/T matrices method with generalized ray theory to offer an easy and efficient way to compute the individual seismic phases of synthetic seismogram. We try to get the solutions of seismic waves in Laplace domain by generalized R/T matrices method. Then, we introduce the concepts of reflection and transmission coefficients (shorten to R/T coefficients) which is different from the generalized R/T coefficients so that the whole seismic wavefield can be separated into different generalized rays according to different vertical traveling paths. The expression of each seismic phase in the time domain can be obtained by applying Cagniard-de Hoop method. Cagniard-de Hoop method has the merit that we can get solutions in the time domain by simple manipulation instead of complicated inverse Laplace transformation of seismic wave solution in the Laplace domain. As a result, the seismic phases have elegant form. Due to the difference of elastic properties between the media layers, seismic phases, which correspond to different generalized rays, differ from each other in their contributions to the whole seismic wave field. The property of the individual seismic phases may improve our understanding of the actual seismic records.