## The Snell's laws at interfaces in anisotropic viscoelastic media

**Vaclav Vavrycuk**
### Summary

The behaviour of rays at interfaces in anisotropic viscoelastic media is studied using three
different approaches: the real elastic ray theory, the real viscoelastic ray theory and the
complex ray theory. In solving the complex eikonal equation, the highest accuracy is
achieved by the complex ray theory. The real elastic and viscoelastic ray theories are less
accurate but computationally more effective. In all three approaches, the rays obey Snell's
law at the interface, but its form is different for each approach. The complex Snell's law
constrains the complex tangential components of the slowness vector. The real viscoelastic
and elastic Snell's laws constrain the real tangential components of the slowness vector. In
the viscoelastic ray theory, besides Snell's law, the condition of stationary slowness vector
is imposed in calculating the rays of scattered waves. The accuracy of all three ray
theoretical approaches is numerically tested by solving the complex eikonal equation. The
models of the medium consist of attenuating isotropic and anisotropic homogeneous
halfspaces. The level of attenuation ranges from extremely strong (*Q* = 2.5-3) to moderate
attenuation (*Q* = 25-30). Numerical modelling shows that the real viscoelastic ray approach
is highly accurate being at least 20 times more accurate than the real elastic ray approach.

### Keywords

Anisotropy, attenuation, complex eikonal equation, ray theory, seismic waves,
wave propagation.

### Whole paper

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In: Seismic Waves in Complex 3-D Structures, Report 19,
pp. 237-261, Dep. Geophys., Charles Univ., Prague, 2009.

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