Q-compensated reverse time migration in tilted transversely isotropic media

Abstract

Anisotropy and absorption are critical to the modeling and analysis of seismic amplitude,phase, and traveltime data. To neglect any of these phenomena, which are often bothoperating simultaneously, degrades the resolution and interpretability of migrated images.However, a full accounting of anisotropy and anelasticity is computationally complex andexpensive. One strategy for accommodating these aspects of wave propagation, while keepingcost and complexity under control, is to do so within an acoustic approximation. Weset up a procedure for solving the time-domain viscoacoustic wave equation for tilted transverselyisotropic (TTI) media, based on a standard linear solid model and, from this, developa viscoacoustic reverse time migration (Q-RTM) algorithm. In this approach, amplitudecompensation occurs within the migration process through a manipulation of attenuationand phase dispersion terms in the time domain differential equations. Specifically, theback-propagation operator is constructed by reversing the sign only of the amplitude lossoperators, but not the dispersion-related operators, a step made possible by reformulatingthe absorptive TTI equations such that the loss and dispersion operators appear separately.The scheme is tested on synthetic examples to examine the capacity of viscoacoustic RTM to correct for attenuation, and the overall stability of the procedure.