The propagation of seismic waves in attenuating and anisotropic earth media is accompanied by amplitude attenuation and phase distortion. If these adverse effects are not addressed in seismic imaging, we may end up with inaccurate reflector positions, dimming amplitudes, and reduced spatial resolution in the imaging results. We use a pure pseudo-viscoacoustic TTI wave equation as a forward engine to implement Q-compensated TTI reverse time migration (RTM) because the wavefields simulated by the conventional coupled pseudo-viscoacoustic tilted transversely isotropic (TTI) wave equation contain shear wave artifacts and are unstable when the anisotropic parameters ε < δ. The high-frequency noise in the wavefield will be amplified exponentially during amplitude-compensated extrapolation, resulting in numerical instability when using Q-compensated TTI RTM. To eliminate the destabilizing effect of boosted high-frequency noise, we introduce a complex velocity that can be used to describe amplitude compensation over the limited frequency band. Then, based on this complex velocity, we derive a stable amplitude-compensated operator and apply it to the Q-compensated TTI RTM. The numerical simulation results show that, in comparison with the coupled pseudo-viscoacoustic TTI wave equation, the pure pseudo-viscoacoustic TTI wave equation is free from shear wave artifacts and is not restricted by anisotropic parameters. In addition, the pure pseudo-viscoacoustic TTI wave equation has high accuracy in describing velocity anisotropy and attenuation isotropy. Synthetic and field data examples demonstrate the effectiveness of our Q-compensated TTI RTM in compensating amplitude dissipation and correcting phase distortion.

地震波在衰减和各向异性地球介质中的传播伴随着振幅衰减和相位失真。如果在地震成像中没有解决这些不利影响，我们最终可能会导致反射器位置不准确、振幅变暗以及成像结果的空间分辨率降低。我们使用纯伪粘声 TTI 波动方程作为正向引擎来实现Q补偿 TTI 逆时偏移 (RTM)，因为传统耦合伪粘声倾斜横向各向同性 (TTI) 波动方程模拟的波场包含剪切波伪影和当各向异性参数ε  <  δ时不稳定. 在幅度补偿外推期间，波场中的高频噪声将呈指数级放大，导致使用Q补偿 TTI RTM 时数值不稳定。为了消除增强的高频噪声的不稳定效应，我们引入了一种复数速度，可用于描述有限频带上的幅度补偿。然后，基于这个复速度，我们推导出一个稳定的幅度补偿算子，并将其应用于Q-补偿的 TTI RTM。数值模拟结果表明，与耦合拟粘声TTI波动方程相比，纯拟粘声TTI波动方程没有横波伪影，不受各向异性参数的限制。此外，纯拟粘声TTI波动方程在描述速度各向异性和衰减各向同性方面具有较高的精度。合成和现场数据示例证明了我们的Q补偿 TTI RTM 在补偿幅度耗散和校正相位失真方面的有效性。