We introduce a novel technique for seismic wave extrapolationin time. The technique involves cascading a Fouriertransform operator and a finite-difference operator to form achain operator: Fourier finite differences (FFD). We derivethe FFD operator from a pseudoanalytical solution of theacoustic wave equation. Two-dimensional synthetic examplesdemonstrate that the FFD operator can have high accuracyand stability in complex-velocity media. Applying theFFD method to the anisotropic case overcomes some disadvantagesof other methods, such as the coupling of qP-wavesand qSV-waves. The FFD method can be applied to enhanceaccuracy and stability of seismic imaging by reverse timemigration.
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