@article {GrechkaWA45,
author = {Grechka, Vladimir},
title = {Algebraic degree of a general group-velocity surface},
volume = {82},
number = {4},
pages = {WA45--WA53},
year = {2017},
doi = {10.1190/geo2016-0523.1},
publisher = {Society of Exploration Geophysicists},
abstract = {Three algebraic surfaces {\textemdash} the slowness surface, the phase-velocity surface, and the group-velocity surface {\textemdash} play fundamental roles in the theory of seismic wave propagation in anisotropic elastic media. While the slowness (sometimes called phase-slowness) and phase-velocity surfaces are fairly simple and their main algebraic properties are well understood, the group-velocity surfaces are extremely complex; they are complex to the extent that even the algebraic degree, D, of a system of polynomials describing the general group-velocity surface is currently unknown, and only the upper bound of the degree (D<=150) is available. This paper establishes the exact degree (D=86) of the general group-velocity surface along with two closely related to D quantities: the maximum number, B, of body waves that may propagate along a ray direction in a homogeneous anisotropic elastic solid (B=19) and the maximum number, H, of isolated, singularity-unrelated cusps of a group-velocity surface (H=16).},
issn = {0016-8033},
URL = {http://geophysics.geoscienceworld.org/content/82/4/WA45},
eprint = {http://geophysics.geoscienceworld.org/content/82/4/WA45.full.pdf},
journal = {Geophysics}
}