SEISMIC-WAVE-FORM EFFECTS OF CONICAL POINTS IN GRADUALLY VARYING ANISOTROPIC MEDIA

We describe the effects of anisotropic slowness-surface conical points (acoustic axes) on quasi-shear wavefronts and waveforms in variable e lastic media. Conical points have quite complicated geometrical conseq uences even for a point source in or a wave refracting into a homogene ous anisotropic medium. A hole develops in the fast quasi-shear wavefr ont and the swallowtail catastrophe plays an important role in the geo metry of the slow quasi-shear front, which becomes folded with numerou s self-intersections, The two fronts are joined along the rim of the h ole. This geometry influences the waveforms, which show Hilbert-transf orm and diffraction effects. Therefore, standard ray theory is inappli cable even for a uniform medium and the Maslov method is needed to des cribe waveforms. The introduction of elastic gradients further complic ates the geometry of the problem, because rays bend sharply as their s lowness approaches that of the axis. An initially smooth, single-value d slow quasi-shear front will evolve in the gradient region into a fro nt which is folded and multivalued and once again the swallowtail is i mportant. However, in contrast to a homogeneous medium, no 'hole' deve lops in the fast quasi-shear front and the slow and fast fronts separa te completely, While such geometrical factors are included in the Masl ov method, waveforms are also affected by coupling of the fast and slo w waves on nearing the axis, where the rays and polarizations rotate m ost rapidly and their slownesses differ by very little. Numerical exam ples are presented for a cubic and an orthorhombic material. The diffe rences between these two examples show that the fine structure of 'con tinuously varying internal conical refraction' can vary considerably f rom material to material, though its basic principles are clearly defi ned. Waveforms are presented for a point source in a uniform medium an d for fast and slow shear waves in a gradient, with and without coupli ng. Overall, we conclude that the wavefront-folding effects cause the most drastic waveform distortions. Coupling becomes most important whe n signals merge, as at cuspidal edges or at lower frequencies, since t he net waveform could be altered significantly if its components are v aried. Conical refraction complicates and yet could be decisive for th e identification of seismic anisotropy and rock properties.