The behaviour of parabolic lines and caustics in anisotropic solids can be, in general, very complicated, but it considerably simplifies under weak anisotropy. Supposing sufficiently weak anisotropy, no parabolic lines appear on the S1 slowness sheet. Consequently, the S1 wave sheet displays no caustics and triplications. Parabolic lines and caustics can appear for the S2 wave, but only in the directions close to conical or wedge singularities. Each conical and wedge singularity in weakly anisotropic solids 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. For decreasing strength of anisotropy, the size of caustics and anticaustics decreases. For infinitesimally weak anisotropy, the caustics and anticaustics contract into one joint point. No parabolic lines, caustics, anticaustics and triplications can appear in transversely isotropic solids, provided the strength of anisotropy is sufficiently weak.
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