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Seismic depth migration with the Dirac equation

Ketil Hokstad and Rune Mittet
Seismic depth migration with the Dirac equation
Geophysics (June 1999) 64 (3): 925-933

Abstract

We demonstrate the applicability of the Dirac equation in seismic wavefield extrapolation by presenting a new explicit one-way prestack depth migration scheme. The method is in principle accurate up to 90 degrees from the vertical, and it tolerates lateral velocity variations. This is achieved by performing the extrapolation step of migration with the Dirac equation, implemented in the space-frequency domain. The Dirac equation is an exact linearization of the square-root wave equation and is equivalent to keeping infinitely many terms in a Taylor series or continued-fraction expansion of the squareroot operator. An important property of the new method is that the local velocity and the spatial derivatives decouple in separate terms within the extrapolation operator. Therefore, we do not need to precompute and store large tables of convolutional extrapolator coefficients depending on velocity. The main drawback of the explicit scheme is that evanescent energy must be removed at each depth step to obtain numerical stability. We have tested two numerical implementations of the migration scheme. In the first implementation, we perform depth stepping using the Taylor series approximation and compute spatial derivatives with high-order finite difference operators. In the second implementation, we perform depth stepping with the Rapid expansion method and numerical differentiation with the pseudospectral method. The imaging condition is a generalization of Claerbout's U/D principle. For both implementations, the impulse response is accurate up to 80 degrees from the vertical. Using synthetic data from a simple fault model, we test the depth migration scheme in the presence of lateral velocity variations. The results show that the proposed migration scheme images dipping reflectors and the fault plane in the correct positions.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 64
Serial Issue: 3
Title: Seismic depth migration with the Dirac equation
Affiliation: SINTEF Group, IKU Petroleum Research, Trondheim, Norway
Pages: 925-933
Published: 199906
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 19
Accession Number: 2000-041392
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 1 table
Secondary Affiliation: Sting Research, NOR, Norway
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute.
Update Code: 200014
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