Introduction

Prestack Stolt residual migration has recently gained a new momentum because of its usefulness in imaging and migration velocity analysis Biondi and Sava (1999); Sava and Biondi (2000). The method's main merit is that instead of requiring an assumption about the magnitude of the target velocity model to which we want to residually migrate, it only calls for an assumption about the ratio of the reference velocity to the target velocity Sava (1999a,b). Since the method is, in essence, a Stolt-stretch technique, it inherits Stolt's speed and convenience.

As for other Stolt-type techniques, the derivation of the method is based on the assumption of constant velocity. However, if we start from a depth-migrated image, the residual migration process can be shown not to depend on the actual velocities anymore, but rather on the ratio of the reference (v₀) and correct (v) velocities.

Strictly speaking, the ratio corresponds to two constant velocities. This would imply, however, that we obtain the original image using constant velocity as well, which is normally not the case. In this paper, I investigate the applicability of the residual migration method to images obtained using variable velocity models. I begin with a brief review of the theory and continue with three synthetic examples and one real-data example, which demonstrate that, although not theoretically accurate, the method can still be used in cases of variable velocity media.