Decoupled approximate qP- and qSV-wave equations in attenuated transversely isotropic media

Accurate seismic models with anisotropy and attenuation characteristics are crucial to accurately imaging subsurface structures. However, the anisotropic viscoelastic equations are complex and require significant computational resources. In addition, the single-mode waves have been sufficient for most practical exploration needs. However, separating the qP- and qSV-waves in anisotropic viscoelastic wavefields is challenging. Thus, we propose a new method to approximate and efficiently separate the qP- and qSV-waves in attenuated transversely isotropic media. First, we obtain the decoupled approximate phase velocities of qP- and qSV-waves by a curve-fitting method. Consequently, based on the average and maximum relative error analysis, our approximate qP- and qSV-wave phase velocities are more accurate than the existing approximations. Additionally, our approximations have broader applicability, resulting in acceptable errors during their application. Second, based on the approximate qP- and qSV-wave phase velocities, we derive the corresponding qP- and qSV-wave equations for a complete decoupling of the qP- and qSV-wave components in transversely isotropic media. Third, to combine the attenuation and anisotropy characteristics, we incorporate the Kelvin–Voigt attenuation model and obtain the decoupled qP- and qSV-wave equations in attenuated transversely isotropic media. Then, we use an efficient and stable hybrid finite-difference and pseudo-spectral method to solve the new decoupled qP- and qSV-wave equations. Finally, several numerical examples demonstrate the separability and high accuracy of the proposed qP- and qSV-wave equations. We obtain a qP-wave wavefield entirely devoid of SV-wave artefacts. In addition, the decoupled approximate qP- and qSV-wave equations are accurate and stable in heterogeneous media with different velocities and attenuation. The decoupled, approximated qP-wave and qSV-wave equations proposed in this paper can effectively separate the qP-wave and qSV-wave components, resulting in fully decoupled qP- and qSV-wave wavefields in attenuated transversely isotropic media.