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Receiver function is important for imaging crustal and upper mantle discontinuities. However, sparsely scattered stations would introduce imaging artifacts or even lead to misinterpretation on comp...

The Fourier finite-difference propagator and the generalized-screen propagator are two general high-order forms of one-way dual-domain methods. We compare these two propagators mainly on phase accuracy, computational efficiency and 3D extension. A comparison of phase accuracy shows that the high-order generalized-screen propagator is preferable to the Fourier finite-difference propagator for heterogeneous media with a weak velocity contrast and wide dip angle. With increasing velocity contrast, the accuracy improvement gained by the high-order generalized-screen propagator declines rapidly. The Fourier finite-difference propagator is more robust and flexible to lateral velocity variations than the generalized-screen propagator. The 2D Fourier finite-difference propagator is superior to the 2D generalized-screen propagator when the velocity contrast is stronger than 23%. Despite the two-way splitting error, the 3D Fourier finite-difference propagator is more accurate than the second-order generalized-screen propagator when the velocity contrast is stronger than 20% and is more accurate than the fourth-order generalized-screen propagator when the velocity contrast is stronger than 40%. Numerical experiments on the SEG/EAGE salt model demonstrate that the Fourier finite-difference propagator behaves better than the generalized-screen propagator when imaging steep salt boundary and faults beneath the salt body. Under the same hardware and software conditions, the computational cost of the Fourier finite-difference propagator in our implementation is greater than that of the second-order generalized-screen propagator but smaller than that of the third-order generalized-screen propagator. Compared with the Fourier finite-difference propagator, the generalized-screen propagator requires fewer grid points per wavelength and has more potential to improve running speed in the presence of a much faster Fourier transform. These analyses are applicable for both forward modelling and depth migration.

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.