The absorption (anelastic attenuation) and anisotropy properties of subsurface media jointly affect the seismic wave propagation and the quality of migration imaging. Anisotropic viscoelastic model can effectively describe seismic velocity and attenuation anisotropy effects. To reduce the computational cost and complexity of elastic wave modes decoupling for seismic imaging in anisotropic attenuating media, we have developed a pure-viscoacoustic transversely isotropic (TI) wave equation starting from the complex-valued velocity dispersion relation of quasi-compressional (qP) wave. The wave equation involving fractional Laplacians has advantages of being able to describe the constant-Q (frequency-independent quality factor) attenuation, arbitrary TI velocity and attenuation, decoupled amplitude loss and velocity dispersion effects. Numerical analyses showed that the simplified equation can accurately hold the velocity and attenuation anisotropy of qP-wave in viscoelastic anisotropic media in the range of moderate anisotropy. Compared to previous pseudo-viscoacoustic equations, the pure-viscoacoustic equation can be completely free from undesirable S-wave artifacts and behaves good numerical stability in tilted transversely isotropic (TTI) attenuating media. There are obvious wavefield differences between isotropic attenuation and anisotropic attenuation cases especially in the direction perpendicular to the axis of symmetry. Furthermore, to mitigate the influences of velocity and attenuation anisotropy on migrated seismic images, we have developed an anisotropic attenuation (Q) compensated reverse time migration (AQ-RTM) approach based on the new propagator. The compensation can be implemented by reversing the sign of the dissipation terms and keeping the dispersion terms unchanged during wavefields extrapolation. Synthetic example from a Graben model illustrated that the anisotropic Q-compensated RTM scheme can produce images with more balanced amplitude and accurate position of reflecters compared with conventional RTM methods under assumptions of acoustic anisotropic (uncompensated) and isotropic attenuating media. Results from a Marmousi-II model demonstrated that the new methodology is applicable for complicated geological model to significantly improve imaging resolution of the target area and deep layers.

地下介质的吸收（非弹性衰减）和各向异性特性共同影响地震波的传播和偏移成像的质量。各向异性粘弹性模型可以有效地描述地震速度和衰减的各向异性效应。为了降低各向异性衰减介质中地震成像的弹性波模式解耦的计算成本和复杂性，我们从准压缩（qP）的复值速度色散关系开始开发了纯粘声横向各向同性（TI）波动方程海浪。涉及分数拉普拉斯算子的波动方程具有能够描述常数Q的优点（与频率无关的品质因数）衰减、任意 TI 速度和衰减、解耦幅度损失和速度色散效应。数值分析表明，简化方程可以准确地保持qP波在中等各向异性范围内的粘弹性各向异性介质中的速度和衰减各向异性。与以前的伪粘声方程相比，纯粘声方程可以完全没有不良的S波伪影，并且在倾斜的横向各向同性（TTI）衰减介质中表现出良好的数值稳定性。各向同性衰减和各向异性衰减情况之间存在明显的波场差异，特别是在垂直于对称轴的方向上。此外，Q ) 基于新传播子的补偿反向时间偏移 (AQ-RTM) 方法。补偿可以通过反转耗散项的符号并在波场外推期间保持色散项不变来实现。来自 Graben 模型的合成示例表明，在声学各向异性（未补偿）和各向同性衰减介质的假设下，与传统 RTM 方法相比，各向异性Q补偿 RTM 方案可以产生具有更平衡的幅度和反射器位置准确的图像。Marmousi-II模型的结果表明，新方法适用于复杂的地质模型，显着提高了目标区域和深层的成像分辨率。