Slowness vectors of harmonic plane waves in viscoelastic anisotropic media

Abstract

Properties of inhomogeneous plane waves propagating in a viscoelastic anisotropic medium are investigated. The slowness vector p is described by the so-called mixed speci cation. In it, the vector p is expressed in terms of two given real-valued, mutually perpendic-ular vectors (one of them specifying the direction of propagation), and of a free complex-valued parameter σ. The parameter σ must be determined so that the slowness vector p satis es a constraint relation following from an equation of motion for viscoelastic media. In this contribution, σ is determined by solving a complex-valued polynomial equation of the sixth degree. The used algorithm is quite general. It can be used for homogeneous as well as inhomogeneous plane waves propagating in elastic or viscoelastic, isotropic or anisotropic media. It is shown that the inhomogeneous plane waves propagating in anisotropic viscoelastic me- dia exhibit certain phenomena, not known from elastic anisotropic or viscoelastic isotropic media. For example, the inhomogeneous plane qP wave may propagate with the same phase velocity as one of inhomogeneous plane qS wave. It is also shown that the attenuation angles of inhomogeneous plane waves can attain values greater than /2 even for very weakly inhomogeneous plane waves.