| | AbstractThe split-step Fourier
propagator is a one-way wave propagation method that has been widely
used to simulate primary forward and backward (reflected)
deterministic/random wave propagation due to its fast computational
speed and limited computer memory requirement. The method is useful for
rapid modeling of seismic-wave propagation in heterogeneous media where
forward scattered waveforms can be considered to be dominant or
reverberations can be ignored. The method is based on a solution to the
one-way wave equation that requires expanding the square root of an
operator and splitting of the resulting noncommutative operators to
allow calculation by transferring wave fields between the space and
wavenumber domains. Previous analysis of the accuracy of the method has
focused on the error related to only a portion of the approximations
involved in the propagator. To better understand the accuracy of the
propagator, we present a complete formal and numerical accuracy
analyses. Our formal analysis indicates that the dominant error of the
propagator increases as the first order in the marching interval. We
show that nonsymmetrically and symmetrically split-step marching
solutions have the same first-order error term. Their second- and
third-order error terms are similar. Therefore, the differences between
the accuracy of different split-step marching solutions are
insignificant. This conclusion is confirmed by our numerical tests. The
relation among the phase error of the split-step Fourier propagator,
relative velocity perturbation, and propagation angle is numerically
studied. The results suggest that the propagator is accurate for up to a
60o propagation angle from the main propagation direction for
media with small relative velocity perturbations
(10%).Return to Table
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