Properties of inhomogeneous plane waves propagating in a viscoelastic anisotropic medium are investigated. The slowness vector p is described by the so-called mixed specification. In it, the vector p is expressed in terms of two given real-valued, mutually perpendicular vectors (one of them specifying the direction of propagation), and of a free complex-valued parameter sigma. The parameter sigma must be determined so that the slowness vector p satisfies a constraint relation following from an equation of motion for viscoelastic media. In this contribution, sigma 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 media 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 pi/2 even for very weakly inhomogeneous plane waves.
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