The nonstationary phase-shift extrapolator provides a highly accurate wavefield extrapolator in laterally inhomogeneous media. However, because the operator depends on both the lateral spatial variable and its wavenumber, the transform between space and wavenumber cannot be implemented with the fast Fourier transform technique and therefore, the computational effort is greater than that of the stationary phase shift method. In this paper, a method is developed that applies the windowed Fourier transform to the Helmholtz equation to obtain a local wavefield expression, which leads to the windowed version of nonstationary phase-shift. Numerical results show that the computational efficiency is improved with little loss of accuracy.
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