3D Fourier finite-difference migration by alternating-direction-implicit plus interpolation

Conventional two-way splitting Fourier finite-difference 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 plus interpolation scheme into the conventional Fourier finite-difference method to reduce azimuthal anisotropy. This scheme 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 Fourier finite-difference extrapolation. As the Fourier finite-difference migration is implemented in the space and wavenumber dual space, the Fourier transforms between space and wavenumber domain that were needed for the alternating-direction-implicit plus interpolation in frequency domain (FD) migration are saved in Fourier finite-difference migration. Since the azimuth anisotropy in Fourier finite-difference is much less than that in FD, the application of the alternating-direction-implicit plus interpolation scheme in Fourier finite-difference migration is superior to that in FD migration 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.