The accuracy of the real ray tracing approach developed by Vavrycuk (2008a) for waves propagating in smooth inhomogeneous viscoelastic media is tested. The complex eikonal equation in isotropic viscoelastic media is solved using three alternative ray approaches: the real viscoelastic ray tracing, the real elastic ray tracing and the complex ray tracing. The first two approaches are simple but approximate. The complex ray tracing is complicated but yields the most accurate results, which serve as the reference solution. Two models of a smoothly inhomogeneous viscoelastic medium with high velocity gradients and with strong attenuation are used to check the robustness of the approximate methods. The numerical modelling reveals that the real viscoelastic ray approach is unequivocally preferable to the real elastic ray approach. It is more accurate and works even in situations when the elastic ray tracing fails. In the studied models, the errors in the complex traveltime produced by the real viscoelastic ray approach were 15 to 30 times less than those of the real elastic ray approach. Also the ray fields calculated by the real viscoelastic ray approach were excellently reproduced even in the case when the elastic rays yielded completely distorted results. Compared with the complex ray tracing, which is limited to simple types of media, the real viscoelstic ray tracing offers a fast and computationally undemanding procedure for calculating the complex travel times in complicated 3-D inhomogeneous attenuating structures.
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