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A typical singularity of elastic wave propagation, often termed a shear-wavesingularity, takes place when the Christoffel equation has a double root or,equivalently, two out of three slowness or phase-velocity sheets share a commonpoint. We examine triple singularities, corresponding to triple degeneracies ofthe Christoffel equation, and establish their two notable properties: (i) ifmultiple triple singularities are present, the phase velocities along all ofthem are exactly equal, and (ii) a triple singularity maps onto a finite-sizeplanar patch shared by the group-velocity surfaces of the P-, S1-, andS2-waves. There are no other known mechanisms that create finite-size planarareas on group-velocity surfaces in homogeneous anisotropic media.

Triple singularities of elastic wave propagation in anisotropic media