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Volume 10,     Number 2,     Summer 2002

 

APPROXIMATE FOURIER INTEGRAL WAVEFIELD EXTRAPOLATORS FOR HETEROGENEOUS, ANISOTROPIC MEDIA
G. F. MARGRAVE, R. J. FERGUSON AND M. P. LAMOUREUX

Abstract. Seismic imaging uses wavefield data recorded on the earth's surface to construct images of the internal structure. A key part of this process is the extrapolation of wavefield data into the earth's interior. An alternative to the commonly used ray theory approximation is to perform a plane-wave decomposition of the recorded data and extrapolate each plane wave independently. For homogeneous media, the Fourier transform can be used for the plane-wave decomposition and phase shifts propagate the plane waves. We explore an approximate extension of this concept to heterogeneous media that uses pseudodifferential operator theory. A derivation of a Fourier integral operator is presented, which implements the appropriate plane-wave mixing. We show the transpose of this operator is also a viable Fourier integral wavefield extrapolator with a rst order error that opposes the original operator. The symmetric average of these two extrapolators is shown to be more accurate than either of the original two. We present both numerical experiments and theoretical arguments to characterize our results and discuss their possible extensions.

 

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