ADI plus interpolation on 3D Fourier finite-difference migration

Conventional two-way splitting FFD migration for 3D complex media yields azimuthal anisotropy where an additional phase correction is needed with much increase of computational cost. We incorporate the alternating-direction-implicit scheme plus interpolation (ADIPI) into the conventional FFD method to reduce azimuthal anisotropy. The new method retains the high-order remnants ignored by the two-way splitting in the form of a wavefield interpolation in the wavenumber domain. The wavefield interpolation for each step of downward extrapolation is implemented between the wavefields before and after the conventional FFD extrapolation. By using a 2D array to memorize the wavefield in the latest step of downward extrapolation, we save two Fourier transforms needed in the ADIPI scheme, and the resulting method keeps most of the efficiency of the two-way splitting FFD method. Formal error analyses show that the presented method is superior to the original ADIPI scheme in handling complex media with large velocity contrasts and steep dips. Impulse responses show that the presented method reduces the azimuthal anisotropy at almost no extra cost.