The Green's function for homogeneous anisotropic elastic media can be expressed as an integral over the slowness surface S (1). For fixed position the singularities of the Green's function as a function of time arise as contributions to the integral from arbitrarily small neighbourhoods of certain usually isolated points on S, and the nature of the surface near these points determines the kind of singularity. It is the aim of this paper to examine the contribution from the neighbourhoods of the conical points of S for media with cubic symmetry. Since the wave surface and slowness surface are related by polar reciprocation in a sphere, these conical points of S give rise to flat ‘lids’ on the wave surface. The contributions from near non-singular points of S have been discussed by Buchwald (9) for harmonic waves. We briefly develop the corresponding theory for the time-dependent wave equation before concentrating on the conical points.
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Robert Burridge (1967) studied this question.