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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.
Next: VARIATION OF MIGRATION VELOCITY
Up: Black et. al.: Plume
Previous: Black et. al.: Plume
Stanford Exploration Project
11/17/1997