Parabolic lines and caustics in homogeneous weakly anisotropic solids

Abstract

The form of parabolic lines and caustics in homogeneous generally anisotropic solids can be very complicated, but simplifies considerably in homogenous weakly anisotropic solids. Assuming sufficiently weak anisotropy, no parabolic lines appear on the S1 slowness sheet. Consequently, the corresponding wave sheet displays no caustics or triplications. Parabolic lines and caustics can appear on the S2 slowness and wave sheets, respectively, but only in directions close to conical or wedge singularities. Each conical and wedge singularity generates parabolic lines, caustics and anticaustics in its vicinity. The parabolic lines cannot touch or pass through a conical singularity, but they touch each wedge singularity. The size of the caustics and anticaustics decreases with decreasing strength of anisotropy. For infinitesimally weak anisotropy, the caustics and anticaustics contract into a single point. No parabolic lines, caustics, anticaustics and triplications can appear in transversely isotropic solids, provided the transverse isotropy is sufficiently weak.