$Q$-compensated reverse time migration (Q-RTM) is effective for improving the seismic imaging quality degraded by low-$Q$ anomalies. However, it is difficult to apply existing pseudospectral-based Q-RTM methods to large-scale problems due to the obstacles to high-efficient parallelization posed by the global pseudospectral operators. On the other hand, finite-difference Q-RTM is intrinsically appropriate for domain decomposition and parallel computation, thus being suitable for industrial-sized problems but facing a twofold challenge: (1) to effectively compensate the phase in a broad-bandwidth sense during the wave back-propagation process and (2) to accurately handle the tilted transverse isotropic (TTI) medium with attenuation. We have developed a new framework of finite-difference Q-RTM algorithm by expanding the linear viscoacoustic constitutive relation to a series of integer-order differential terms and a unique integral term that can decouple the amplitude and the phase to allow accurate compensation in a broader frequency range. This framework has two typical implementations: (1) optimizing the frequency-dependent phase velocity (while fixing the negative constant $Q$) and (2) optimizing the $Q$ value (while fixing the frequency-dependent phase velocity). We generalize this broadband finite-difference Q-RTM algorithm to TTI media, where an artificial $Q_{\mathrm{S}}$ is applied to suppress the shear-wave artifacts induced by the acoustic TTI approximation. Numerical examples demonstrate that this Q-RTM method accurately compensates the phase and amplitude in a broad frequency range of 5–70 Hz and produces high-quality images. Due to the local nature of finite-difference operators, this algorithm is expected to outperform the existing pseudospectral-based Q-RTM methods in terms of computational efficiency and implementation convenience for real-world Q-RTM projects.

中文翻译：

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倾斜横观各向同性介质的宽带有限差分Q补偿逆时偏移算法

$问$补偿的逆时偏移（Q-RTM）有效地改善了因低速而退化的地震成像质量$问$异常。然而，由于全局伪谱算子对高效并行化的障碍，很难将现有的基于伪谱的Q-RTM方法应用于大规模问题。另一方面，有限差分Q-RTM本质上适用于域分解和并行计算，因此适用于工业规模的问题，但面临双重挑战：（1）在运行期间以宽带方式有效补偿相位波反向传播过程和（2）精确处理倾斜的横向各向同性（TTI）介质并进行衰减。我们通过将线性粘声本构关系扩展为一系列整数阶微分项和一个唯一的积分项，从而可以将幅度和相位解耦，从而在更广泛的范围内进行精确补偿，从而开发了一种新的有限差分Q-RTM算法框架频率范围。该框架有两种典型的实现方式：（1）优化频率相关的相速度（同时固定负常数）$问$）和（2）优化 $问$值（同时确定频率相关的相速度）。我们将这种宽带有限差分Q-RTM算法推广到TTI媒体，${问}_{\mathrm{小号}}$应用来抑制由声学TTI近似引起的剪切波伪像。数值示例表明，这种Q-RTM方法可以在5–70 Hz的宽频率范围内准确补偿相位和幅度，并可以产生高质量的图像。由于有限差分算子的局部性质，在现实世界中Q-RTM项目的计算效率和实现便利性方面，该算法有望优于现有的基于伪谱的Q-RTM方法。