Velocity, attenuation and the quality factor of waves propagating in homogenous media of arbitrary strength of anisotropy and attenuation are calculated in high-frequency asymptotics using a stationary slowness vector - the vector evaluated at the stationary point of the slowness surface. This vector is, in general, complex-valued and inhomogeneous, meaning that the real and imaginary parts of the vector have different directions. The slowness vector can be determined by solving three coupled polynomial equations of the 6th order or by a non–linear inversion. The procedure is simplified, if perturbation theory is applied. The elastic medium is viewed as a background medium, and the attenuation effects are incorporated as perturbations. In the first-order approximation, the phase and ray velocities and their directions remain unchanged being the same as those in the background elastic medium. The perturbation of the slowness vector is calculated by solving a system of three linear equations. The phase attenuation and phase quality factor are linear functions of the perturbation of the slowness vector. Calculating the ray attenuation and ray quality factor is even simpler than calculating the phase quantities, because they are expressed just in terms of perturbations of the medium without the necessity to evaluate the perturbation of the slowness vector. Numerical modeling indicates that the perturbations are highly accurate, the errors being less than 0.3% for a medium with a quality factor of 20 or higher. The accuracy can further be enhanced by a simple modification of the first-order perturbation formulas.
Anisotropy, attenuation, perturbation theory, ray theory, seismic waves, viscoelasticity.
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