Introduction

In practice, it is usually difficult to choose the correct velocity for migration. For depth migration, it is generally accepted that the best choice is the velocity that optimally focuses the image. But what happens when we use time migration to focus the image? We often employ time migration to image events when there are lateral velocity variations present. In these situations, it is generally impossible to completely focus the image even when the correct velocity is used. For example, in Black et. al. 1992 we showed that time migration with the correct migration velocity collapses a point diffractor not to a point but to a cusp-shaped curve that we called a ``plume''. It is therefore interesting to study the effect of migration velocity on the plume response in a v(x) medium, and that is the purpose of this paper. Here we use both a geometrical construction and actual migrations of synthetic data to demonstrate the diffractor response of time migration in such a medium. The plume response described in Black et. al. 1992 is shown to rotate and change shape with changing migration velocity. We gain some insight into this behavior by developing a simple first-order theory of plume rotation analogous to Black and Brzostowski 1993.

Since we will be building on the material presented in Black et. al. 1992, we will refer to that paper as Paper 1.