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 (c) 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.

The special issue contains contributions presented at the international workshop Seismic waves in laterally inhomo- geneous media IV, which was held at the Castle of Trest, Czech Republic, May 22-27, 1995. The workshop, which was attended by about 100 seismologists from more than 10 countries, was devoted mainly to the current state of theoretical and computational means of study of seismic wave propagation in complex structures. The special issue can be of interest for theoretical, global and explorational seismologists. The first part contains papers dealing with the study and the use of various methods of solving forward and inverse problems in complicated structures. Among other methods, discrete-wave number method, the finite-difference method, the edge-wave supperposition method and the ray method are studied and used. Most papers contained in the second part are related to the ray method. The most important topics are two-point ray tracing, grid calculations of travel times and amplitudes and seismic wave propagation in anisotropic media.