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For the second-order approximation (*m*=1,*n*=1), equation (9) is the following
cascaded partial differential equation in the space domain:
| |
(11) |

| (12) |

In isotropic migration, and are constant. In VTI media, and are
functions of the anisotropy parameters and . For laterally varying media, the value of and
also vary laterally. It is too expensive to calculate and for each grid point during the
wavefield extrapolation. I calculate and for a range of and and store them
in a table before the migration. I then generate maps of and from the table.
With the map of the coefficents and , the finite-difference scheme for VTI media can be performed in the same way as an isotropic migration.

** Next:** Phase correction filter
** Up:** Shan: Implicit migration for
** Previous:** Optimized one-way wave equation
Stanford Exploration Project

4/5/2006