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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