Evaluation of poststack migration in terms of virtual source and partial derivative wavefields

Abstract

We show theoretically that reverse time migration using the one-way wave equation can be evaluated as poststack migration based on the exploding reflector model. An alternative for computing the subsurface image is to take the zero-lag value of cross-correlation between the surface seismogram and the partial derivative wavefield with respect to subsurface parameters such as velocity and density at a certain depth point. Reverse time migration can also be expressed by the zero-lag cross-correlation between the surface seismogram and the partial derivative wavefield. The partial derivative wavefield is computed by using the virtual source. Our numerical results show that when we use the one-way wave equation, the virtual source can be approximated by a delta function at time zero, which indicates that the virtual source computed by the one-way wave equation can be used for describing the exploding reflector model in the poststack migration. Reverse time migration and poststack migration are numerically identical, when we introduce the virtual source and the partial derivative wavefield in the imaging condition.