Plumes: Response of time migration to lateral velocity
variation
#### D. Bevc, J. L. Black, and G. Palacharla

####

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.

#### Geophysics, Vol. 60, no. 4 (July-August 1995), P. 1118-1127