Boundary attenuation angles for inhomogeneous plane waves in anisotropic dissipative media

Abstract

We study behavior of attenuation (inhomogeneity) angles [Formula: see text], i.e., angles between real and imaginary parts of the slowness vectors of inhomogeneous plane waves propagating in isotropic or anisotropic, perfectly elastic or viscoelastic, unbounded media. The angle [Formula: see text] never exceeds the boundary attenuation angle [Formula: see text]. In isotropic viscoelastic media [Formula: see text]; in anisotropic viscoelastic media [Formula: see text] may be greater than, equal to, or less than [Formula: see text]. Plane waves with [Formula: see text] do not exist. Because [Formula: see text] in anisotropic viscoelastic media is usually not known a priori, the commonly used specification of an inhomogeneous plane wave by the attenuation angle [Formula: see text] may lead to serious problems. If [Formula: see text] is chosen close to [Formula: see text] or even larger, indeterminate, unstable or even nonphysical results are obtained. We study properties of [Formula: see text] and show that the approach based on the mixed specification of the slowness vector fully avoids the problems mentioned above. The approach allows exact determination of [Formula: see text] and removes instabilities known from the use of the specification of the slowness vector by [Formula: see text]. For [Formula: see text], the approach yields zero phase velocity, i.e., the corresponding wave is a nonpropagating wave mode. The use of the mixed specification leads to the explanation of the deviation of [Formula: see text] from [Formula: see text] as a consequence of different orientations of energy-flux and propagation vectors in anisotropic media. The approach is universal; it may be used for isotropic or anisotropic, perfectly elastic or viscoelastic media, and for homogeneous and inhomogeneous waves, including strongly inhomogeneous waves, like evanescent waves.