Method of discontinuities and integral representation in the analysis of wave field dynamics

We analyze the dynamics of seismic waves in a ray series approximation in the time domain. The aims of the research are: to describe the wave field in a first approximation of ray series (that is to take into account two first terms) and to consider singular situations of the ray propagation. We suggest a new technique of elastic wave field calculation in the ray series approximation. Some explicit formulas were received for regular cases of wave propagation. It was shown that on the simple and cusp caustics a conventional ray series (orders: q, q+1,…) which is valid far from caustics splits into two ray series (orders: q-α, q+1-α,… and q+α, q+1+α,…). For cusp caustics a uniform wave field description was developed that is valid on the caustic itself and out of it