Behaviour of rays at interfaces in anisotropic viscoelastic media

Abstract

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, the Snell's law is supplemented by the condition of the stationary slowness vector of scattered waves. The accuracy of all three ray theoretical approaches is numerically tested by solving the complex eikonal equation and by calculating the R/T coefficients. The models of the medium consist of attenuating isotropic and anisotropic homogeneous half-spaces with attenuation ranging from extremely strong (Q= 2.5–3) to moderate (Q= 25–30). Numerical modelling shows that solving the complex eikonal equation by the real viscoelastic ray approach is at least 20 times more accurate than solving it by the real elastic ray approach. Also the R/T coefficients are reproduced with a higher accuracy by the real viscoelastic ray approach than by the elastic ray approach.