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 QS 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.

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