An exploration of the theory of nonstationary filters as applied to seismic wavefield extrapolation is presented. Depth imaging methods based on nonstationary filters are developed and shown to be suitable for imaging media that are strongly heterogeneous and anisotropic.
Two elementary nonstationary filters arise naturally when deriving recursive explicit wavefield extrapolators from Taylor series or directly from the Helmholtz equation. One of them, a nonstationary combination filter, is the limiting form of more commonly implemented extrapolators such as: Split-step Fourier, Phase screen, PSPI and recursive explicit finite difference.
The elementary nonstationary filters belong to the more general class of pseudodifferential operators. An analysis based on the mathematics of pseudo-differential operators suggests two new extrapolators that are more accurate and more stable than the elementary extrapolators. They also have the desirable property of being symmetric.
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