Conclusion

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 $60^\circ$. The migrations for the synthetic and real datasets show that this implicit finite-difference method can extrapolate the wavefield accurately in laterally varying media.