Seismic waves propagating through attenuating media induce amplitude loss and phase dispersion. Neglecting the attenuation effects during seismic processing results in the imaging profiles with weakened energy, mispositioned interfaces and reduced resolution. To obtain high‐quality imaging results, Q‐compensated reverse time migration is developed. The kernel of the Q‐compensated reverse time migration algorithm is a viscoacoustic wave equation with decoupled amplitude loss and phase dispersion terms. However, the majority of current decoupled viscoacoustic wave equations are solved using the computationally expensive pseudo‐spectral method. To enhance computational efficiency, we initiate our approach from the dispersion relation of a single standard linear solid model. Subsequently, we derive a novel decoupled viscoacoustic wave equation by separating the amplitude loss and phase dispersion terms, previously coupled in the memory variable. The newly derived decoupled viscoacoustic wave equation can be efficiently solved using the finite‐difference method. Then, we reverse the sign of the amplitude loss term of the newly derived viscoacoustic wave equation to implement high‐efficient Q‐compensated reverse time migration based on the finite‐difference method. In addition, we design a regularization term to suppress the high‐frequency noise for stabilizing the wavefield extrapolation. Forward modelling tests validate the decoupled amplitude loss and phase dispersion characteristics of the newly derived viscoacoustic wave equation. Numerical examples in both two‐dimensional and three‐dimensional confirm the effectiveness of the Q‐compensated reverse time migration based on the finite‐difference algorithm in mitigating the attenuation effects in subsurface media and providing high‐quality imaging results.

中文翻译：

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使用高效解耦粘声波方程的多维 Q 补偿逆时偏移

通过衰减介质传播的地震波会引起振幅损失和相位色散。忽略地震处理过程中的衰减效应会导致成像剖面能量减弱、界面错位和分辨率降低。为了获得高质量的成像结果，问‐开发了补偿逆时偏移。其内核为问‐补偿逆时偏移算法是一种具有解耦幅度损失和相位色散项的粘声波方程。然而，当前大多数解耦粘声波方程都是使用计算成本昂贵的伪谱方法求解的。为了提高计算效率，我们从单个标准线性实体模型的色散关系开始我们的方法。随后，我们通过分离先前耦合在记忆变量中的振幅损失和相位色散项，导出了一个新颖的解耦粘声波方程。新推导的解耦粘声波方程可以使用有限差分法有效求解。然后，我们反转新推导的粘声波方程的振幅损失项的符号以实现高效问‐基于有限差分法的补偿逆时偏移。此外，我们设计了一个正则化项来抑制高频噪声，以稳定波场外推。正演模型测试验证了新推导的粘声波方程的解耦幅度损失和相位色散特性。二维和三维的数值例子证实了该方法的有效性问‐基于有限差分算法的补偿逆时偏移，可减轻地下介质的衰减效应并提供高质量的成像结果。