Characterization and analysis of attenuation anisotropy in viscoelastic vertical transverse isotropic media

Due to the intrinsic attenuation of the earth, the study of wave propagation characteristics, considering seismic attenuation plays an important role in high-precision reservoir prediction. Therefore, we investigate the propagation and reflection characteristics of seismic waves in viscoelastic vertical transverse isotropic media in the complex frequency domain. Specifically, we analyse the response characteristics of velocity, propagation vector and attenuation vector with respect to viscosity media with different attenuation intensities. Furthermore, based on the quasi-Zoeppritz equation, the variation of reflection coefficient amplitude with offset at different attenuation angles and different attenuation intensities is studied. We also compare the trends in the amplitude variation of reflection coefficients with offset in elastic isotropic, elastic anisotropic and viscoelastic anisotropic media. Due to the complexity of the exact reflection coefficient expression, we first propose the approximate expression of the attenuation-anisotropy parameters and then derive the approximate expression of the reflection coefficient. The numerical simulation results show that the approximate expression of the reflection coefficient is still accurate, even in media with strong anisotropy. Finally, the accuracy evaluations of the reflection coefficient formulas using four typical theory models demonstrate that the approximate reflection coefficient formulas are highly accurate in both weak and strong anisotropic media.