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Wave extrapolation in the spatial wavelet domain with application to poststack reverse-time migration
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DOI：10.1190/1.1444358.png)
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A wavelet transformation is performed over each of the spatial coordinates of the scalar wave equation. This transformed equation is solved directly with a finite-difference scheme for both homogeneous and smooth inhomogeneous media. Wavefield extrapolation is performed completely in the spatial wavelet domain without transforming back into the space domain at each time step. The wavelet coefficients are extrapolated, rather than the wavefield itself. Thr numerical solution of the scalar wave equation in the spatial wavelet domain is closely related to the finite-difference method because of the compact support of the wavelet bases. Poststack reverse-time migration is implemented as an application. The resolution spaces of the wavelet transform provide a natural framework for multigrid analysis. Migrated images are constructed from various resolution spaces.
Keyword:
EQUATIONS
MEDIA
BASES
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