Reflection/transmission laws for slowness vectors in viscoelastic anisotropic media

Abstract

The reflection/transmission laws (R/T laws) of plane waves at a plane interface between two homogeneous anisotropic viscoelastic (dissipative) halfspaces are discussed. Algorithms for determining the slowness vectors of reflected/transmitted plane waves from the known slowness vector of the incident wave are proposed. In viscoelastic media, the slowness vectors of plane waves are complex-valued, p = P + iA, where P is the propagation vector, and A the attenuation vector. The proposed algorithms may be applied to bulk plane waves (A = 0), homogeneous plane waves (A ≠ 0, P and A parallel), and inhomogeneous plane waves (A ≠ 0, P and A non-parallel). The manner, in which the slowness vector is specified, plays an important role in the algorithms. For unrestricted anisotropy and viscoelasticity, the algorithms require an algebraic equation of the sixth degree to be solved in each halfspace. The degree of the algebraic equation decreases to four or two for simpler cases (isotropic media, plane waves in symmetry planes of anisotropic media). The physical consequences of the proposed algorithms are discussed in detail.