## Real ray tracing in anisotropic viscoelastic media

**Vaclav Vavrycuk**
### Summary

Ray tracing equations applicable to smoothly inhomogeneous anisotropic
viscoelastic media are derived. The equations produce real rays, in contrast
to previous ray-theoretical approaches, which deal with complex rays. The real
rays are defined as the solutions of the Hamilton equations, with
the Hamiltonian modified for viscoelastic media, and physically correspond to
trajectories of high-frequency waves characterized by a real stationary phase.
As a consequence, the complex eikonal equation is satisfied only approximately.
The ray tracing equations are valid for weakly and moderately attenuating
media. The rays are frequency-dependent and must be calculated for each
frequency, separately.

Solving the ray tracing equations in viscoelastic
anisotropy is more time consuming than in elastic anisotropy. The main
difficulty is with determining the stationary slowness vector, which is
generally complex-valued and inhomogeneous and must be computed at each time
step of the ray tracing procedure. In viscoelastic isotropy, the ray tracing
equations considerably simplify, because the stationary slowness vector is
homogeneous. The computational time for tracing rays in isotropic elastic
and viscoelastic media is the same. Using numerical examples, it is shown
that ray fields in weakly attenuating media (Q higher than about 30) are
almost indistinguishable from those in elastic media. For moderately
attenuating anisotropic media (Q between 5-20), the differences in ray fields
can be visible and significant.

### Keywords

Elasticity and anelasticity, body waves, seismic anisotropy,
seismic attenuation, wave propagation.

### Whole paper

The reprint is available in
PDF (594 kB).

*Geophys. J. Int.*, **175** (2008), 617-626.

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