Stable attenuation compensation in reverse-time migration

Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high-frequency components and create undesirable imaging artifacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using smooth division. The operator relies on a constant-Q wave equation with decoupled fractional Laplacians, and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reversetime migration (RTM). A time-dependent imaging condition is derived by applying Q-compensation at each time step, while a time-independent imaging condition is formed in the image space by calculating image normalization weights. Synthetic examples demonstrate an improved illumination of seismic images by applying the proposed method.