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Shear-wave singularities in systems of anisotropic symmetry are comparatively well known, but it has not been generally realised that they may cause anomalies in shear-wave propagation for neighbouring directions due to the behaviour of the polarizations. Singularities are places where the two shear-wave slowness surfaces are continuous with each other through common points. The most frequent type, a point singularity, is a place where the two surfaces are continuous with each other through the vertices of cone-shaped projections from the surfaces. For directions of propagation in a plane, which cuts the slowness surfaces near a singularity, the velocities of the two shear-waves approach each other in a pinch and at the pinch exchange polarizations and velocity gradients. These singularities do not cause anomalies in plane waves propagating in a uniform medium, but may cause mode conversion and pulse-shape modification to waves with spherical wave-fronts, and to rays of shear-waves, in varying anisotropic media.
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