Introduction

At first glance, shot-profile migration and source-receiver migration seem to be completely different. They are performed on different data geometry and use different equations to extrapolate wavefields. Shot-profile migration downward continues source and receiver wavefields independently, and produces an image through a cross-correlation between these two wavefields along the time axis. Source-receiver migration extrapolates the CMP gathers with the Double Square Root equation, and creates an image by extracting the wavefield at zero time and zero subsurface offset.

However, shot-profile migration and source-receiver migration obtain the same migration result. Wapenaar and Berkhout (1987) proves that identical stacked images will be obtained from these two methods. Biondi (2002) proves that an equivalent image cube will be obtained, given the assumptions that the source is an impulse function, the imaging condition is cross-correlation, and the source and receiver wavefields are downward propagated by a one-way wave equation. The cross-correlation imaging condition and one-way wave equation downward continuation are the key points for the equivalence between shot-profile migration and source-receiver migration. In this paper, we give a new proof for the equivalence between shot-profile migration and source-receiver migration for an arbitrary source.

Before demonstrating the equivalence between them, we first present an overview of shot-profile migration and source-receiver migration.