The computation of the slowness vector of an inhomogeneous plane wave propagating in a homogeneous viscoelastic anisotropic medium is based on the solutions of an eigenvalue problem for 3 x 3 or 6 x 6 complex-valued matrices. Individual approaches leading to these eigenvalue problems differ in the specification of the slowness vector (directional specification, componental specification, mixed specification). In two important cases, complete analytical solutions for the slowness vector are obtained. This applies to P and S inhomogeneous plane waves propagating in an isotropic viscoelastic medium, and to qSH inhomogeneous plane waves propagating in the plane of symmetry of a monoclinic (orthorhombic, hexagonal) anisotropic viscoelastic medium. The analytical solutions for these two cases are derived and discussed in this paper. These solutions offer a simple physical insight into the problem of inhomogeneous plane waves, and a valuable comparison of advantages and drawbacks of the individual approaches. For isotropic viscoelastic media, all the three specifications of the slowness vector yield analogous results, and can be used fully alternatively. For qSH inhomogeneous plane waves propagating in the plane of symmetry of a monoclinic anisotropic viscoelastic medium, however, the situation is different. The approaches based on the componental and mixed specifications of the slowness vector offer simpler and more powerful analytical solutions than the approach based on the directional specification. They yield explicit equations for the slowness vector, the phase velocity, the attenuation amplitude factor and the attenuation angle, and avoid fully the problems of forbidden directions.
Viscoelastic media, inhomogeneous plane waves, phase velocity, attenuation angle, slowness vector.
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