Modeling of pure visco-qP-wave propagation in attenuating tilted transversely isotropic media based on decoupled fractional Laplacians

Abstract

The pseudoviscoacoustic anisotropic wave equation is widely used in the oil and gas industry for modeling wavefields in attenuating anisotropic media. Compared to the full viscoelastic anisotropic wave equation, it can greatly reduce the computational cost of wavefield modeling while maintaining the visco-qP-wave kinematics very well. However, even if we place the source in a thin isotropic layer, there will be some unwanted S-wave artifacts in the qP wavefield simulated by the pseudoviscoacoustic anisotropic wave equation due to the stepped approximation of inclined layer interfaces. Furthermore, the wavefield simulated by the pseudoviscoacoustic anisotropic wave equation may suffer from numerical instabilities when the anisotropy parameter epsilon is less than delta. To overcome these problems, we derive a pure-viscoacoustic tilted transversely isotropic (TTI) wave equation in media with anisotropy in velocity and attenuation based on the exact complex-valued phase velocity formula. The pure-viscoacoustic TTI wave equation has decoupled amplitude dissipation and phase dispersion terms, which is suitable for further reverse time migration with Q compensation. For numerical simulations, we adopt the second-order Taylor series expansion to replace the mixed-domain spatially variable fractional Laplacian operator, which guarantees the decoupling of the wavenumber from the space-related fractional order. Then, we use an efficient and stable hybrid finite-difference and pseudospectral method (HFDPSM) to solve the pure-viscoacoustic TTI wave equation. Numerical tests indicate that the simulation results of the newly derived pure-viscoacoustic TTI wave equation are stable, free from S-wave artifacts, and accurate. We further demonstrate that HFDPSM outperforms the pseudospectral method in terms of numerical simulation stability and computing efficiency.