The real geological medium is close to viscoelastic media in which seismic wave propagate with dispersion and attenuation. It is important to compensate the unwanted viscous effects in seismic processing. It is more accurate and physically more consistent to mitigate these effects in a wave-equation-based prestack depth migration. Historically, reverse time migration (RTM) based on directly solving the two-way wave equation has provided a superior way to image complex geologic regions. However, instability usually arises when considering compensation for absorption. Most researchers conduct high frequency filtering in wavenumber domain before or during wavefield extrapolate in RTM to ensure stability. In this paper, we use viscoacoustic wave equation derived by Bai et al. (2013) to do Q-RTM and stabilize extrapolate by adding a regularization term. Compared with direct filtering, the regularization parameter can be space-varying. So this is suitable for severely variational regions. And we also find that source normalized cross-correlation imaging condition is more suitable in Q-RTM.
It has been broadly observed that real earth media attenuate and disperse seismic waves, which indicates earth is not an ideal elastic body. Large anelastic effects are found for instance in shallow sediments, fractured rocks, saturated rocks. In migrating such data sets, we usually obtain poor seismic images of the structure within and below such high-attenuation area. So it is important to correct these unwanted effects in seismic processing and make the final image more interpretable.
Early efforts to compensate for the seismic attenuation were performed in the unmigrated data domain with an inverse Q-filter (Wang, 2006). These method were based on a one-dimensional backward propagation and cannot correctly handle real geological complexity. Because anelastic attenuation and phase dispersion effects on wavefields occur during the wave propagation, it is more accurate and physically more consistent to mitigate these effects in a wave-equation-based prestack depth migration (Zhu et al., 2014).
Much effort has been put forth in developing an inverse Qmigration using one-way wave equation migration (Yu et al., 2002). One-way wave equation migration is implemented in the frequency domain, so it is natural to incorporate attenuation in imaging. Historically, reverse time migration (RTM) based on directly solving the twoway wave equation has provided a superior way to image complex geologic regions. And some researchers have tried to compensate viscoacoustic effects in RTM, and obtained better results (Zhang et al., 2010, Suh et al., 2012, Bai et al., 2013, Zhu et al., 2014).