We analyze how time migration mispositions events in the presence of lateral velocity variation by examining the impulse response of depth modeling followed by time migration. By examining this impulse response, we lay the groundwork for the development of a remedial migration operator which links time and depth migration. A simple theory by Black and Brzostowski (1994) predicted that the response of zero-offset time migration to a point diffractor in a v(x,z) medium would be a distinctive, cusp-shaped curve called a plume. We have constructed these plumes by migrating synthetic data using several time-migration methods. We have also computed the shape of the plumes by two geometrical construction methods. These two geometrical methods compare well and explain the observed migration results.
The plume response is strongly influenced by migration velocity. We have studied this dependency by migrating synthetic data with different velocities. The observed velocity dependence is confirmed by geometrical construction. A simple first-order theory qualitatively explains the behavior of zero-offset time migration, but a more complete understanding of migration velocity dependence in a v(x,z) medium requires a higher order finite-offset theory.