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 planewave decomposition of the recorded
data and extrapolate each
plane wave independently. For homogeneous media, the Fourier
transform can be used for the planewave 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 planewave 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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