Viscoacoustic anisotropic wave equations

Abstract

Running head: Viscoacoustic anisotropic wave equations ABSTRACT The wave equation plays a central role in seismic modeling, processing and inversion. Incorporating the attenuation anisotropy into the acoustic anisotropic wave equations provides a choice for acoustic modeling and imaging in fluid-filled anisotropic reservoirs. However, the existing viscoacoustic anisotropic wave equations are obtained for a specified viscoacoustic model. In this paper, we present a relatively general representation of the scalar and vector viscoacoustic wave equations for orthorhombic anisotropy. We also show 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 1 and Kjartansson models, and derive the corresponding viscoacoustic wave equations in differential form. To analyze the wave propagation in viscoacoustic models, we derive the asymptotic acoustic point-source radiation. Numerical examples show 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.

Thomsen-type parameters and attenuation coefficients for constant-Q transverse isotropy

“…Next, we consider the so-called "viscoacoustic" constant-Q media described by the Thomsen-type notation. The acoustic approximation is implemented by setting ṼS0 = A S0 = 0 in equations 18, 40, and 29 [20,21,22] . The parameters δ, η, and δ Q then reduce to:…”