Asymptotic wave quantities in anisotropic viscoelastic media such as ray velocity and ray attenuation are calculated using a stationary slowness vector defined as the slowness vector that predicts the complex energy velocity parallel to a ray. The stationary slowness vector is, in general, complex-valued and inhomogeneous. Its computation involves finding two independent unit vectors, which specify the directions of its real and imaginary parts. The wave inhomogeneity affects the asymptotic quantities and complicates their computation. The critical quantities are attenuation and the Q-factor, which can significantly vary with the slowness vector inhomogeneity. If the inhomogeneity is neglected, the directional variation of attenuation and the Q-factor can distinctly be distorted. The errors can attain values commensurate to strength of velocity anisotropy, so up to tens of percent for sedimentary rocks. This applies to strongly as well as weakly attenuative media. On the contrary, the ray velocity, which defines the wavefronts and physically corresponds to the energy velocity of a high-frequency signal propagating along a ray, is almost insensitive to the slowness vector inhomogeneity and thus can be calculated in a simplified way except for media with extremely strong anisotropy and attenuation.
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