CONCLUSION

The response of time migration to a point diffractor in a v(x) medium is a cusp-shaped curve called a plume. Migration velocity analysis is strongly influenced by the behavior of the plume as the migration velocity is changed. We have examined the dependence of the zero-offset plume on migration velocity by migrating synthetic data. The observed velocity dependence is confirmed by the common-tangent construction. A simple first-order theory qualitatively explains the behavior of zero-offset time migration. It is clear that a more complete understanding of migration velocity analysis with time migration in a v(x) medium requires a finite-offset theory.