Viscoacoustic anisotropic wave equations

The wave equation plays a central role in seismic modeling, processing, imaging and inversion. Incorporating attenuation anisotropy into the acoustic anisotropic wave equations provides a choice for acoustic forward and inverse modeling in attenuating anisotropic media. However, the existing viscoacoustic anisotropic wave equations are obtained for a specified viscoacoustic model. We have developed a relatively general representation of the scalar and vector viscoacoustic wave equations for orthorhombic anisotropy. We also obtain the viscoacoustic wave equations for transverse isotropy as a special case. The viscoacoustic orthorhombic wave equations are flexible for multiple viscoacoustic models. We take into account the classic visocoacoustic models such as the Kelvin-Voigt, Maxwell, standard-linear-solid and Kjartansson models, and we derive the corresponding viscoacoustic wave equations in differential form. To analyze the wave propagation in viscoacoustic models, we derive the asymptotic point-source solution of the scalar wave equation. Numerical examples indicate a comparison of the acoustic waveforms excited by a point source in the viscoacoustic orthorhombic models and the corresponding nonattenuating model, and the effect of the attenuation anisotropy on the acoustic waveforms.