Velocity dispersion and attenuation in anisotropic linear viscoelastic media

Rocks are far from being isotropic and elastic. Thus, an accurate description of wave propagation requires a constitutive relation that accounts for the anisotropic and viscoelastic behavior of rocks. This work establishes a new constitutive relation on the azimuthally anisotropic linear viscoelastic media with an arbitrary azimuthal angle for the fractured strata. Probing the medium with a time-harmonic homogeneous plane wave gives the Christoffel equation. Then the complex velocities for homogeneous viscoelastic waves are calculated from it, while the attenuation factor and phase velocity and quality factor are obtained from the complex velocity. The examples show simulations in azimuthally an isotropic clay shale and sandstone. And the relations between the attenuation and frequency, azimuthal angle, incidence angle are explicitly worked out.