High-Temporal-Accuracy Viscoacoustic Wave Propagation Based on k -Space Compensation and the Fractional Zener Model

The acoustic behavior in fluid attenuating media can be effectively simulated using a fractional Zener model (FZM). Because of the fractional time derivatives of both stress and strain in the constitutive relationship, this mechanism is very realistic and flexible in describing seismic attenuation. However, using conventional FZM wave equations to propagate seismic waves requires storing large amounts of previous wavefield information to calculate the fractional time derivatives, which is unacceptable in practice. In this paper, we derive a new time-domain viscoacoustic wave equation in the framework of the FZM. This new equation does not contain any fractional time derivatives; thus, it is more economical in computational costs. Furthermore, the amplitude attenuation and phase dispersion effects are separated in the newly proposed equation, which is very favorable to compensate for energy loss and correct phase dispersion in reverse-time migration. To improve the accuracy, we incorporate a wave number ( k )-space operator into the decoupled FZM wave equation to compensate for temporal dispersion errors caused by the second-order finite-difference discretization. Therefore, a high-temporal-accuracy viscoacoustic wave equation is derived to simulate nearly constant- Q wavefields in attenuating media. In the implementation, a low-rank decomposition method is introduced to solve the mixed-domain operators. Numerical analysis and modeling results demonstrate the effectiveness and applicability of the proposed method for simulating the decoupled viscoacoustic wavefield with high accuracy.