Strategies for 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, such as noise, and create undesirable imaging artefacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable 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 reverse-time migration. A time-dependent imaging condition is derived by applying Q-compensation in the frequency domain, whereas a time-independent imaging condition is formed in the image space by calculating image normalisation weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high-frequency noise in the data.