A visual based connection between seismic inversion and seismic migration

John C. Bancroft

doi:10.1071/ASEG2003ab008

ISSN: 2202-0586
E-ISSN:

oa A visual based connection between seismic inversion and seismic migration
Authors John C. Bancroft^a
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^a University of Calgary/CREWES, [email protected]
Publisher: Australian Society of Exploration Geophysicists
Source: ASEG Extended Abstracts, Volume 2003, Issue ASEG2003 - 16th Geophysical Conference, Aug 2003, p. 1 - 4
DOI: https://doi.org/10.1071/ASEG2003ab008
- Published online: 01 Aug 2003

Abstract

The Kirchhoff migration algorithm is heuristically derived using the mathematics of least squares inversion and the concept of matched filters. These concepts are visualized with cartoon descriptions that describe inversion using linear algebra and time-varying deconvolution. The time varying wavelets are then replaced with diffractions, to form a diffraction matrix that is used to model seismic data. The product of the transpose of this diffraction matrix with the seismic data produces a band-limited inversion that is identical to a Kirchhoff migration. Simple modification to the diffraction matrix illustrate the use of variable velocities and constant offset prestack migration.

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2003-08-01

2026-01-14

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References

Bleistein, N., Cohen, J. K., and Stockwell, Jr., J. W., 2001, Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion, Springer
Claerbout, J. R, 1992, "Earth Soundings Analysis: Processing versus inversion", Blackwell Scientific Publications
Lindseth, R. O., 1979, Synthetic sonic logs-a process for stratigraphic interpretation, Geophysics, 44, 3-26
Lines, L. R., and Levin, F. K., 1992 Inversion of Geophysical Data, Geophysical reprint series, No. 9, SEG
Lines, L. R., and Treitel, S., 1984, Tutorial: a review of least-squares inversion and its application to geophysical problems, Geophysical Prospecting, 32, 159-186
Margrave, G E, 1998, Theory of non-stationary linear filtering in the Fourier domain with applications to time-variant filtering, Geophysics, 63, 255-259
Schneider, W. A., 1978, Integral formulation for migration in two and three dimensions, Geophysics, 43, 49-76

/content/journals/10.1071/ASEG2003ab008

Article Type: Research Article

Keyword(s): Inversion; least-squares; migration; modelling; visualization

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