The phase-shift time-stepping equation (PSTS) is a wavefield propagator that allows two-way in time propagation for the acoustic wave equation. The PSTS is based an an exact solution to the acoustic wave equation. It is adapted to 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 inhomogeneity velocity variations. 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. Its computational properties are similar to higher-order in time pseudospectral methods.
We present techniques developed for numerical modeling of wave propagation, and source-signature removal in seismic imaging, based on a class of linear operators known as Gabor multipliers.
