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I present an implicit finite-difference migration method for VTI media. The scheme is designed by approximating
the dispersion relation with rational functions and solving the coefficients by least-squares methods.
The coefficients of finite-difference are obtained from a table, which is calculated before the wavefield extrapolation.
This implicit finite-difference method guarantees stability, and its computational cost is almost the same as isotropic
implicit finite-difference migration. Both dispersion-error analysis and impulse response indicate that the
implicit finite-difference operator is accurate to . The migrations for the synthetic and real datasets
show that this implicit finite-difference method can extrapolate the wavefield accurately in laterally varying media.

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** Up:** Shan: Implicit migration for
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Stanford Exploration Project

4/5/2006