The two-component representation of time-harmonic elastic body waves in the high- and intermediate-frequency regimes

Abstract

Propagation and diffraction of time-harmonic elastic body waves through homogeneous and isotropic materials is revisited. The two-component representation of body waves is given which is applicable in the high- and intermediate-frequency regimes when the family of rays is (i) regular or (ii) possesses an irregularity due to the presence of a wedge, an acoustic point source located on the boundary, simple caustic, or focal line. Both physical and mathematical description of the phenomena under consideration is offered. The resulting expressions are asymptotic in character and easy to compute. They should prove useful in producing algorithms for describing acoustic fields in homogeneous and isotropic materials with isolated defects and in providing benchmark cases for testing numerical codes designed to solve elastic wave equations in more complicated situations.