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.

地震衰减通常由常数Q (CQ) 模型描述，该模型假设地震品质因数 ( Q ) 与频率无关。为了模拟地震波的衰减行为，我们开发了一种伪谱时域 (PSTD) 方法来求解 CQ 粘声波方程。这种方法在时间上接近四阶精度。与传统的时间二阶 PSTD 方法相比，新的 PSTD 方案被验证为更有效。在某些应用中，例如Q补偿逆时偏移（Q-RTM) 和时间反转成像，需要模拟抗衰减过程。为了实现这一目的，我们通过翻转支配幅度损失的算子的符号，将我们的粘声 PSTD 建模方案转换为幅度补偿 PSTD 建模方案。为了控制幅度提升建模中高频过度补偿引起的数值不稳定性，我们将时变滤波器集成到 PSTD 建模方案中以抑制高频噪声。均匀介质中的波场仿真示例验证了我们近四阶 PSTD 建模方案的时间精度。一个Q合成数据的-RTM测试也提出来证明我们振幅补偿PSTD建模方案的鲁棒性。