Open AccessParabolic lines and caustics in homogeneous weakly anisotropic solids
Author(s) -
Vavryčuk Václav
Publication year - 2003
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.2003.01845.x
Subject(s) - singularity , gravitational singularity , caustic (mathematics) , anisotropy , conical surface , isotropy , slowness , transverse isotropy , wedge (geometry) , physics , geometry , classical mechanics , transverse plane , mathematical analysis , mathematics , optics , quantum mechanics , structural engineering , engineering
SUMMARY The form of parabolic lines and caustics in homogeneous generally anisotropic solids can be very complicated, but simplifies considerably in homogeneous weakly anisotropic solids. Assuming sufficiently weak anisotropy, no parabolic lines appear on the S 1 slowness sheet. Consequently, the corresponding wave sheet displays no caustics or triplications. Parabolic lines and caustics can appear on the S 2 slowness and wave sheets, respectively, but only in directions close to conical or wedge singularities. Each conical and wedge singularity generates parabolic lines, caustics and anticaustics in its vicinity. The parabolic lines cannot touch or pass through a conical singularity, but they touch each wedge singularity. The size of the caustics and anticaustics decreases with decreasing strength of anisotropy. For infinitesimally weak anisotropy, the caustics and anticaustics contract into a single point. No parabolic lines, caustics, anticaustics and triplications can appear in transversely isotropic solids, provided the transverse isotropy is sufficiently weak.