An approach for attenuation-compensating multidimensional constant-Q viscoacoustic reverse time migration

Abstract

Simulation of wave propagation in a constant-[Formula: see text] viscoacoustic medium is an important problem, for instance, within [Formula: see text]-compensated reverse time migration (RTM). Processes of attenuation and dispersion influence all aspects of seismic wave propagation, degrading the resolution of migrated images. To improve the image resolution, we have developed a new approach for the numerical solution of the viscoacoustic wave equation in the time domain and we developed an associated viscoacoustic RTM ([Formula: see text]-RTM) method. The main feature of the [Formula: see text]-RTM approach is compensation of attenuation effects in seismic images during migration by separation of amplitude attenuation and phase dispersion terms. Because of this separation, we are able to compensate the amplitude loss effect in isolation, the phase dispersion effect in isolation, or both effects concurrently. In the [Formula: see text]-RTM implementation, an attenuation-compensated operator is constructed by reversing the sign of the amplitude attenuation and a regularized viscoacoustic wave equation is invoked to eliminate high-frequency instabilities. The scheme is tested on a layered model and a modified acoustic Marmousi velocity model. We validate and examine the response of this approach by using it within an RTM scheme adjusted to compensate for attenuation. The amplitude loss in the wavefield at the source and receivers due to attenuation can be recovered by applying compensation operators on the measured receiver wavefield. Our 2D and 3D numerical tests focus on the amplitude recovery and resolution of the [Formula: see text]-RTM images as well as the interface locations. Improvements in all three of these features beneath highly attenuative layers are evident.