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Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

Inverse AVO problem for a stack of layers

Liliya Malovichko
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Department of Exploration Geophysics, Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia. Email: liliya.malovichko@curtin.edu.au

Exploration Geophysics 46(3) 261-266 https://doi.org/10.1071/EG13020
Submitted: 20 February 2013  Accepted: 2 July 2014   Published: 4 September 2014

Abstract

The problem of estimating thin layered model parameters by amplitude variation with offset (AVO) inversion has been studied. The motivation was resolving of the thin layers in inverted prestack seismic data as it contains more information on elastic properties of the subsurface than poststack seismic data.

In this paper, an algorithm for solving the prestack inverse AVO problem in the case of multilayered media is derived. This algorithm is based on iterative corrections to the parameters of the initial model which tend to minimise the misfits between observed and synthetic seismograms. The synthetic seismograms are calculated using the reflection–transmission (RT)-matrices method, assuming a plane-wave with respect to the source position.

A regularised Gauss-type algorithm for the inversion of prestack seismic data has been used. A differential seismogram computation algorithm to characterise the sensitivity of the seismic signal to the variations of a model parameter was used. The derived solution of the inverse problem is constructed in the time domain. This gives a slight advantage because it allows for visual control of the solution process. One can monitor the amplitude reduction of the data residual (difference between observed and synthetic seismograms) during the iteration process. Numerical examples show the accuracy and efficiency of the method.

Key words: AVO, forward and inverse problems, reflection coefficient, RT-matrices method.


References

Aki, K., and Richards, P. G., 2002, Quantitative seismology (2nd edition): University Science Books.

Blyas, E.A., 2005, A linearized approach to the computation of the P- and S-wave impedances from reflected P-wave seismograms (AVO-inversion): Seismic Exploration Technologies, 1, 5–15

Booth, A. D., Clark, R. A., Kulessa, B., Murray, T., and Hubbard, A., 2012, Thin-layer effects in glaciological seismic amplitude-versus-angle (AVA) analysis: implications for characterising a subglacial till unit, Russell Glacier, West Greenland: The Cryosphere Discussions, 6, 759–792
Thin-layer effects in glaciological seismic amplitude-versus-angle (AVA) analysis: implications for characterising a subglacial till unit, Russell Glacier, West Greenland:Crossref | GoogleScholarGoogle Scholar |

Buzlukov, V., and Nefedkina, T., 2001, AVO-analysis for the thin layered reflecting objects by the PP+PS waves: Mathematics and Geophysics: Second Russian National Meeting, Perm, 19–30 [in Russian].

Buzlukov, V., Nefedkina, T., and Volkov, G., 2005, Multi-wave AVO in thing layered environment: Seismic Exploration Technologies, 1, 16–23

Castagna, J. P., and Backus, M. M., 1993, Offset-dependent reflectivity: theory and practice of AVO analysis: SEG Books.

Haskell, N. A., 1953, The dispersion of surface waves on multilayered media: Bulletin of the Seismological Society of America, 43, 17–34

Kennett, B. L. N., 1980, Seismic waves in a stratified half space II - theoretical seismograms: Geophysical Journal of the Royal Astronomical Society, 61, 1–10
Seismic waves in a stratified half space II - theoretical seismograms:Crossref | GoogleScholarGoogle Scholar |

Kennett, B. L. N., 2009, Seismic wave propagation in stratified media (4th edition): Australian National University Press.

Kennett, B. L. N., and Kerry, N. J., 1979, Seismic waves in a stratified half space: Geophysical Journal of the Royal Astronomical Society, 57, 557–583
Seismic waves in a stratified half space:Crossref | GoogleScholarGoogle Scholar |

Kormendi, F., and Dietrich, M., 1991, Nonlinear waveform inversion of plane-wave seismograms in stratified elastic media: Geophysics, 56, 664–674
Nonlinear waveform inversion of plane-wave seismograms in stratified elastic media:Crossref | GoogleScholarGoogle Scholar |

Larsen, S., and Grieger, J., 1998, Elastic modeling initiative, part III: 3-D computational modeling: 68th Annual International Meeting, SEG, Expanded Abstracts, 68, 1803–1806.

Luco, J. E., and Apsel, R. J., 1983, On the Green’s functions for a layered half-space. Part I: Bulletin of the Seismological Society of America, 73, 909–929

Pan, G. S., and Phinney, R. A., 1989, Full-waveform inversion of plane wave seismograms in stratified acoustic media: applicability and limitations: Geophysics, 54, 368–380
Full-waveform inversion of plane wave seismograms in stratified acoustic media: applicability and limitations:Crossref | GoogleScholarGoogle Scholar |

Randall, G. E., 1994, Efficient calculation of complete differential seismograms for laterally homogeneous earth models: Geophysical Journal International, 118, 245–254
Efficient calculation of complete differential seismograms for laterally homogeneous earth models:Crossref | GoogleScholarGoogle Scholar |

Sen, M. K., and Roy, I. G., 2003, Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion: Geophysics, 68, 2026–2039
Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion:Crossref | GoogleScholarGoogle Scholar |

Shuey, R. T., 1985, A simplification of the Zoeppritz equations: Geophysics, 50, 609–614
A simplification of the Zoeppritz equations:Crossref | GoogleScholarGoogle Scholar |

Tarantola, A., 1987, Inverse problem theory: Elsevier Science Publ. Co., Inc.

Thomson, W. T., 1950, Transmission of elastic waves through a stratified solid medium: Journal of Applied Physics, 21, 89–93
Transmission of elastic waves through a stratified solid medium:Crossref | GoogleScholarGoogle Scholar |

Zhang, R., Sen, M. K., and Srinivasan, S., 2013, A prestack basis pursuit seismic inversion: Geophysics, 78, R1–R11
A prestack basis pursuit seismic inversion:Crossref | GoogleScholarGoogle Scholar |