As a result of the numerical performance of finite-difference operators, reverse-time migration (RTM) produces images which are typically low frequency or require large computational resources. We consider an alternative to wavefield propagation with finite differences, a two-way high-fidelity time-stepping equation based on the Fourier transform which is exact for homogeneous media 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, and by migrating the Marmousi data set. We show that a high frequency wavefield can be time-stepped with no loss of frequency content and with a much larger time step than is commonly used.
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