The Snell's laws at interfaces in anisotropic viscoelastic media

Vaclav Vavrycuk


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.


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

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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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