On the estimation of reflectivity in reverse time migration: Implementational forms of the inverse-scattering imaging condition

Abstract

The inverse-scattering imaging condition (ISIC) for reverse time migration (RTM) aims at recovering amplitudes proportional to seismic reflectivity. It has been derived as the high-frequency asymptotic inverse of Born modeling, which justifies its being called a true-amplitude imaging condition. It involves the temporal and spatial derivatives of the up- and downgoing wavefields, in this way generalizing the conventional crosscorrelation imaging condition. The temporal derivations can be redistributed between different wavefield contributions, in this way deriving a set of different implementational forms of the ISIC. By making use of the wave equation for the up- and downgoing wavefields, one can substitute the time derivatives by the Laplacian operator. This provides a theoretical foundation for a popular filter for reducing the backscattering artifacts in RTM. Using Born data from a simple three-layer model and the Marmousi II model as well as the Sigsbee2b data, we have determined that the theoretical equivalence of the equations leads to similar but not identical images. Our numerical tests indicate that the ISIC versions using spatial derivatives are the most economical approach, and that the images obtained with the second time derivative of the source wavefield indicate slightly improved resolution over the other implementations, making the combination of these two characteristics the best choice.