Accuracy analysis of the phase-screen propagator: Implications for modeling and migration

We present formal and numerical error analyses of the phase-screen (or split-step Fourier) propagator. Numerical results suggest that the propagator is accurate up to 60 degrees propagation angle relative the main propagation direction for media with small velocity perturbations. We investigate the errors from various approaches for splitting the exponential operator of the phase-screen propagator. The symmetrically split equations are slightly more accurate than the one-step split equations. Numerical examples show that the differences among splitting approaches are not significant. Therefore, relative to the symmetrically split equations, the one-step-free one-stepperturbation split equation is more efficient for migration in which wavefields in the space domain at all depth levels must be calculated. However, the half-step-free one-step-perturbation half-step-free split equation has almost the same efficiency as the one-step split equations for forward wave simulations.