Criteria for quasi‐shear wavefront triplication in a tranversely isotropic material

Triplication of a wavefront, also classically known as birefringence, can and does occur in transversely isotropic (TI) media. With the growing interest in shear waves, and in particular, converted shear waves, it becomes necessary to study this phenomenon, and the bright spots that accompany it. In a plane that includes the medium's rotational symmetry axis, there may exist a range of angles within which the qSV wave, whose polarization lies in that plane, may propagate at three distinct velocities. The region of the qSV wave curve where this can occur always corresponds to the region of the qSV slowness curve where the closed qSV curve about the origin is concave. When the range of angles is small and the three arrivals are close together, the usual situation, the qSV wave within that small range will be significantly brighter than in other directions. When the range of angles is large, the two cusps of the wave surface, on the borders of the region of triplication will both be bright spots.