Modified pure-viscoacoustic wave propagation and compensated reverse-time migration in transversely isotropic media

Abstract

Previous studies demonstrated that seismic attenuation and anisotropy can significantly affect the kinematic and dynamic characteristics of wavefields. If these effects are not incorporated into seismic migration, the resolution of the imaging results will be reduced. Considering the anisotropy of velocity and attenuation, we derive a new pure-viscoacoustic wave equation to simulate P wave propagation in transversely isotropic (TI) attenuating media by combining the complex dispersion relation and modified complex modulus. Compared to the conventional complex modulus, the modified modulus is derived from the optimized relationship between angular frequency and wavenumber, which can improve the modeling accuracy in strongly attenuating media. Wavefield comparisons illustrate that our pure-viscoacoustic wave equation can simulate stable P wavefields in complex geological structures without S-wave artifacts and generate similar P wave information to the pseudo-viscoacoustic wave equation. During the implementation, we introduce two low-rank decompositions to approximate the real and imaginary parts and then use the pseudo-spectral method to solve this new equation. Since the proposed equation can simulate decoupled amplitude attenuation and phase dispersion effects, it is used to perform Q-compensated reverse-time migration (Q-RTM). Numerical examples demonstrate the accuracy and robustness of the proposed method for pure-viscoacoustic wavefield simulations and migration imaging in transversely isotropic attenuating media.