Seismic Waves in Laterally Inhomogeneous Media

Vlastislav Cerveny Ivan Psencik Academy of Sciences of the Czech Charles University Republic Faculty of Mathematics & Physics Geophysical Institute Dep. of Geophysics Bocni II, 1401 Ke Karlovu 3 14131 Praha 4 12116 Praha 2 Czech Republic Czech Republic e-mail: ip@ig. cas. cz e-mail: vcerveny@seis. karlov. mff. cuni. cz © Birkhauser Verlag, Basel, 2002 Pure appl. geophys. 159 (2002) 1403-1417 I Pure and Applied Geophysics 0033-4553/02/081403-15 $ 1. 50 + 0. 20/0 Coupled Anisotropic Shear-wave Ray Tracing in Situations where Associated Slowness Sheets Are Almost Tangent l P. M. BAKKER Summary- For shear waves in anisotropic media a frequency-dependent transport equation is derived, which involves coupling of both shear modes if the slowness vector points in adirection for which the associated slowness surfaces are (almost) tangent. This is achieved by averaging the Hamiltonians for both uncoupled shear modes. No assumption on weak anisotropy is made, and the shear polarisation is perpendicular to the P-wave polarisation for the actual slowness direction instead of an isotropically approximated P-wave polarisation. These are the main differences compared with the so-called zero-order quasi-isotropic approach. Key words: Anisotropy, ray tracing, shear wave. J. Introduction Reliable modelling of polarisations for shear waves in anisotropic media is relevant in the context of imaging mode-converted (OBCjOBS) data in cases where not only poSY, but also poSH conversions take place. In such situations it may be necessary to use the polarisation direction for consistent continuation of the different wave modes and for appropriate imaging.