Comparison between the Fourier finite-difference method and the generalized-screen method

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.