Implementation aspects of attenuation compensation in reverse-time migration

Attenuation compensation in reverse-time migration has been shown to improve the resolution of the seismic image. In this paper, three essential aspects of implementing attenuation compensation in reverse-time migration are studied: the physical justification of attenuation compensation, the choice of imaging condition, and the choice of a low-pass filter. The physical illustration of attenuation compensation supports the mathematical implementation by reversing the sign of the absorption operator and leaving the sign of the dispersion operator unchanged in the decoupled viscoacoustic wave equation. Further theoretical analysis shows that attenuation compensation in reverse-time migration using the two imaging conditions (cross-correlation and source-normalized cross-correlation) is able to effectively mitigate attenuation effects. In numerical experiments using a simple-layered model, the source-normalized cross-correlation imaging condition may be preferable based on the criteria of amplitude corrections. The amplitude and phase recovery to some degree depend on the choice of a low-pass filter. In an application to a realistic Marmousi model with added Q, high-resolution seismic images with correct amplitude and kinematic phase are obtained by compensating for both absorption and dispersion effects. Compensating for absorption only can amplify the image amplitude but with a shifted phase.