Wavefront singularities associated with the conical point in elastic solids with cubic symmetry

TL;DR

This paper analyzes wavefront singularities in elastic solids with cubic symmetry, focusing on the conical points of the slowness surface, and develops a uniform asymptotic solution capturing complex wavefront interactions.

Contribution

It introduces a uniform asymptotic solution for wavefronts near conical points in cubic elastic solids, unifying different wavefront contributions including singularities.

Findings

Identifies a $H(t) t^{-3/4}$ singularity at the cone edge.

Derives a uniform solution encompassing plane lid and regular wavefronts.

Provides insight into wavefront behavior in cubic elastic solids.

Abstract

The wavefronts from a point source in a solid with cubic symmetry are examined with particular attention paid to the contribution from the conical points of the slowness surface. An asymptotic solution is developed that is uniform across the edge of the cone in real space, the interior of which contains the plane lid wavefront analyzed by Burridge \cite{Burridge67}. The uniform solution also contains the regular wavefronts away from the cone edge, a delta pulse on one side and its Hilbert transform on the other. In the direction of the cone edge the three wavefronts merge to produce a singularity of the form $H(t) t^{-3/4}$.