As a result of the numerical performance of finite-difference operators, reverse-time migration (RTM) images are typically low frequency. This occurs because finite-difference operators must be oversampled to control numerical dispersion. We consider a high-fidelity time-stepping equation based on the Fourier transform, which is exact if an aliasing condition is met. The technique is adapted to variable velocity using a localized Fourier transform (Gabor transform). The feasibility of using the time-stepping equation for RTM is demonstrated by studying its stability properties, its impulse response, and by migrating a synthetic example of a salt dome. We show that a high frequency wavefield can be time stepped with no loss and with a much larger time step than commonly used.
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