When a seismic wave propagates in the subsurface of the earth, its energy can be attenuated. This has a negative influence on both the amplitude and the phase of an image, especially when a geological body with large attenuation coefficients presents in the target survey area. Therefore, we need to compensate for the attenuation effect in wave propagation. The attenuation effect is generally frequency-dependent, so it is natural to incorporate the attenuation formula into the Fourier finite-difference wave-equation migration (FFD WEM) that also works in the frequency domain. The FFD WEM in tilted transversely isotropic (TTI) media involves three parts: a phase-shift, a thin-lens, and an FFD term. Compared to the traditional method that compensates the Q effect only in the thin-lens term, this paper involves two innovative parts: First, we incorporate a frequency-dependent velocity in all the three parts of the
FFD WEM. As a result, the FFD coefficients are frequency-dependent and a complex-valued velocity is also included in the FFD term. Second, to obtain a stable Q-compensated wavefield, we design a filter in the frequency domain by comparing two propagating wavefields. The method aims at improving the Q-compensation accuracy for the FFD WEM in Q-TTI media, especially at relatively large propagation
angles. Examples show that the proposed method can provide high-quality images for Q-TTI media.