Method of discontinuities and integral representation in theanalysis of wave field dynamics

摘要

We analyze the dynamics of seismic waves in a ray seriesapproximation in the time domain. The aims of the research are: todescribe the wave field in a first approximation of ray series (that isto take into account two first terms) and to consider singularsituations of the ray propagation. We suggest a new technique of elasticwave field calculation in the ray series approximation. Some explicitformulas were received for regular cases of wave propagation. It wasshown that on the simple and cusp caustics a conventional ray series(orders: q, q+1,…) which is valid far from caustics splits intotwo ray series (orders: q-α, q+1-α,… and q+α,q+1+α,…). For cusp caustics a uniform wave fielddescription was developed that is valid on the caustic itself and out ofit