Constant-Q wave propagation and compensation by pseudo-spectral time-domain methods

Seismic attenuation is usually described by a constant -Q (CQ) model that assumes the seismic quality factor (Q) is independent of the frequency. To simulate the attenuation behaviors of seismic waves, we develop a pseudo-spectral time-domain (PSTD) method to solve a CQ viscoacoustic wave equation. This method is nearly fourth-order accurate in time. Compared to the conventional temporal second-order PSTD method, the new PSTD scheme is verified to be more efficient. In some applications such as Q-compensated reverse time migration (Q-RTM) and time-reversal imaging, one requires to simulate an anti-attenuation process. To realize this purpose, we switch our viscoacoustic PSTD modeling scheme into an amplitude-compensated PSTD modeling scheme by flipping the signs of the operators that dominate the amplitude loss. To control the numerical instability caused by high-frequency overcompensation in the amplitude-boosted modeling, we integrate a time-variant filter to the PSTD modeling scheme to suppress the high-frequency noise. Wavefield simulation examples in homogeneous media verify the temporal accuracy of our nearly fourth-order PSTD modeling scheme. A Q-RTM test of synthetic data is also presented to demonstrate the robustness of our amplitude-compensated PSTD modeling scheme.