 Elastic wave surface

The unit-time elastic wave surface is the locus of group velocities on the three branches of a homogeneous elastic wave. At time $t$, its scaled sheets describe the propagating wavefronts from an impulsive point source when that source excites the corresponding modes. Homogeneity of the dispersion relation gives $\mathbf{p}\cdot \mathbf{g}=1$, so each regular sheet is the envelope of planes $\mathbf{p}\cdot \mathbf{x}=1$. It is generally different from the radial reciprocal of the elastic slowness surface.