Shot-profile true amplitude crosscorrelation imaging condition

Abstract

The U/D imaging condition for shot profile migration can be used to estimate the angle dependent reflection coefficient, but is difficult to implement numerically because of the spectral division involved. Most techniques for stabilizing the division require a damping factor which might be difficult to estimate and which also introduces bias into the final result. A stable result can be achieved by approximating the imaging condition with a crosscorrelation of the up- and downgoing wavefields at zero time lag, but this will lead to incorrect amplitude-versus-angle (AVA) behavior of the estimated reflection coefficient. We use a simple model for wave propagation of primary reflections in the wavenumber frequency domain and invert the model with respect to the reflection coefficient. By using the properties of wavefield extrapolators it can then be shown that the reflection coefficients can be estimated by crosscorrelation of the upgoing wavefield and a downgoing wavefield where the initial wavefield is the inverse of the wavefield generated by a point source. The new imaging condition gives the correct AVA behavior for horizontal reflectors. For dipping reflectors it is shown that a postmigration correction factor can be used to recover the correct angle behavior of the reflection coefficient. The new imaging condition is numerically stable, does not involve damping factors, is simple to implement numerically, and is a simple modification of the classical crosscorrelation imaging condition. Numerical examples confirm the correct AVA behavior of the new imaging condition.