A pure-viscoacoustic wave equation for anisotropic attenuating media

Abstract Attenuation and anisotropy are intrinsic properties of the Earth that require accurate governing equations for quantitative description. In our previous work, we introduced a spatially independent decoupled fractional Laplacian (DFL) viscoelastic wave equation in velocity- and attenuation-anisotropic media. This formulation decouples amplitude attenuation from phase dispersion and avoids mixed-domain limitations, making it effective for strongly heterogeneous media. Although the complete viscoelastic wave equation offers greater theoretical rigor, its mathematical complexity and high computational demands render it presently infeasible for industrial-scale seismic imaging and inversion. To overcome these challenges, we introduce a pure-viscoacoustic wave equation tailored for simulating pure anisotropic P-wave wavefields. The proposed approach eliminates S-wave artifacts and employs a fixed-order anisotropic fractional Laplacian operator to simultaneously capture directional velocity and attenuation variations. A series of 2D numerical examples demonstrate that the proposed scheme accurately characterizes anisotropic attenuation in scalar wavefields. Excellent agreement with benchmark solutions confirms the numerical accuracy of the simulated wavefields. Validation using the 3D Salton Trough model further demonstrates the method's feasibility for crustal-scale simulations. Owing to its concise form and computational efficiency, the proposed equation offers strong potential for advancing imaging and inversion in complex anisotropic attenuating media.