The phase-shift time-stepping equation (PSTS) is a wavefield propagator that allows two-way in time propagation for the acoustic wave equation. PSTS is based an an exact solution to the constant velocity acoustic wave equation. It is adapted to a variable velocity wave equation by a windowed Fourier transform where in each window a constant velocity solution is computed. We consider a correction to the phase-shift time-stepping equation that corrects the wave propagators for variable velocity. The correction is based on a similar Taylor-series expansion used to derive the split-step correction for one-way depth steppers or to derive higher-order in time pseudospectral methods using the modified equation approach or Lax-Wendroff method. The computational properties of the split-step correction to PSTS equation are similar to higher-order in time pseudospectral methods.
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