Boundary attenuation angles for inhomogeneous plane waves in anisotropic dissipative media

Vlastislav Cerveny and Ivan Psencik


Attenuation angles γ of inhomogeneous plane waves propagating in isotropic or anisotropic, perfectly elastic or viscoelastic media are investigated. In isotropic viscoelastic media, the attenuation angle always varies between 00 and 900. In anisotropic viscoelastic media, however, the attenuation angle varies in the range <00, γ*>, where the boundary attenuation angle γ* may be greater than, equal to, or less than 900. The boundary attenuation angle depends on the viscoelastic moduli of the medium and on the properties of the plane wave under consideration, mainly on the direction of propagation of the wave.

In the plane-wave attenuation analysis, the attenuation angle γ is often considered as a parameter of the inhomogeneous plane wave under consideration, which can be chosen arbitrarily. It is shown in this paper that such parameterization of the inhomogeneous plane wave may lead to serious errors and problems, particularly if the attenuation angle is chosen greater than or close to the boundary attenuation angle. For γ > γ*, such approach yields non-physical results (forbidden directions), for γ < γ* but close to γ, it yields inaccurate, unstable and even indefinite expressions. As the boundary attenuation angle is usually not known a priori, the attenuation angle should not be chosen freely.

A simple approach to compute quantities characterizing propagation of inhomogeneous plane waves, used in this paper is based on the so-called mixed specification of the slowness vector. The mixed specification does not use the attenuation angle γ as a free parameter of the inhomogeneous plane wave, and avoids the problems mentioned above. It makes possible to compute exactly the phase velocity of the wave, the attenuation angle, the boundary attenuation angle, the propagation and attenuation vectors, etc. The derived equations may be used quite generally, for isotropic or anisotropic, perfectly elastic or viscoelastic media, and for homogeneous and inhomogeneous waves (including evanescent waves).

Numerical examples are presented and discussed.

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In: Seismic Waves in Complex 3-D Structures, Report 20, pp. 169-192, Dep. Geophys., Charles Univ., Prague, 2010.