High-resolution three-term AVO inversion by means of a Trivariate Cauchy probability distribution

Geophysics

Volumn 76, Issue 3, 2011, Pages

  Alemie, Wubshet ^a   Sacchi, Mauricio D ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE VELOCITY; ITERATIVE METHODS; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS; SEISMIC WAVES; SEISMOLOGY; SHEAR WAVES; WAVE PROPAGATION;

BAYESIAN INVERSION; BAYESIAN PROCEDURES; CAUCHY DISTRIBUTION; DENSITY PERTURBATION; INVERSION PROBLEMS; ITERATIVE ALGORITHM; PRIOR DISTRIBUTION; REFLECTION SEISMIC;

INVERSE PROBLEMS;

ALGORITHM; AVO METHOD; BAYESIAN ANALYSIS; INVERSE PROBLEM; MULTIVARIATE ANALYSIS; P-WAVE; PROBABILITY; S-WAVE; SEISMIC DATA; SEISMIC REFLECTION; WAVE VELOCITY;

EID: 84857296741     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.3554627     Document Type: Article

References (38)

1. Aki, K., and P. G. Richards, 1980, Quantitative seismology: theory and methods: W. H. Freeman.
2. Alemie, W. M., 2010, Regularization of the AVO inverse problem by means of a multivariate Cauchy probability distribution: MSc thesis, University of Alberta.
3. BulA., and H. Omre, 2003, Bayesian linearized AVO inversion: Geophysics, 68, no. 1, 185-198. 10.1190/1.1543206
4. Castagna, J. P., M. L. Batzle, and R. L. Eastwood, 1985, Relationships between compressional and shear-wave velocities in clastic silicate rocks: Geophysics, 50, 334.
5. Charbonnier, P., L. Blanc-Feraud, G. Aubert, and M. Barlaud, 1997, Deterministic edgepreserving regularization in computed imaging: IEEE Transactions on Image Processing, 6, no. 2, 298-311. 10.1109/83.551699
6. Chauanhai, L., 1994, Statistical analysis using the multivariate t-distribution: Phd thesis, Harvard University.
7. Clapp, R. G., B. Biondi, and J. F. Claerbout, 2004, Incorporating geologic information into reflection tomography: Geophysics, 69, no. 2, 533-546. 10.1190/1.1707073
8. Daubechies, I., R. DeVore, M. Fornasier, and C. S. Gunturk, 2010, Iteratively re-weighted least squares minimization for sparse recovery: Communications on Pure and Applied Mathematics, 63, no. 1, 1-38 10.1002/cpa.20303
9. Downton, J. E., 2005, Seismic parameter estimation from AVO inversion: Ph.D. Thesis, University of Calgary.
10. Downton, J. E., and L. R. Lines, 2004, Three term AVO waveform inversion: SEG, Expanded Abstracts, 23, 215-218.
11. Fatti, J. L., G. C. Smith, P. J. Vail, P. J. Strauss, and P. R. Levitt, 1994, Detection of gas in sandstone reservoirs using avo analysis: A 3-d seismic case history using the Geostack technique: Geophysics, 59, no. 9, 1362-1376 10.1190/1.1443695
12. Fomel, S., 2003, Time-migration velocity analysis by velocity continuation: Geophysics, 68, no. 5, 1662-1672 10.1190/1.1620640
13. Gardner, G. H. F., L. W. Gardner, and A. R. Gregory, 1974, Formation velocity and density: the diagnostic basics for stratigraphic traps: Geophysics, 39, no. 6, 770-780. 10.1190/1.1440465
14. Johnson, N. L., and S. Kotz, 1972, Distribution in Statistics: continuous multi-variate distribution: John Willey and Sons.
15. Levy, S., and P. K. Fullagar, 1981, Reconstruction of a sparse spike train from a portion of its spectrum and application to high-resolution deconvolution: Geophysics, 46, no. 9, 1235-1243 10.1190/1.1441261
16. Li, Y., 2005, A study on applicability of density inversion in defining reservoirs: SEG, Expanded Abstracts, 24, 1646-1649.
17. Lines, L., 1999, Density and AVO: Canadian Society of Exploration Geophysics, 35, 32-35.
18. Mahmoudian, F. and G. F., Margrave, 2007, P-wave impedance, S-wave impedance and density from linear AVO inversion: Application to VSP data from Alberta: CSPG CSEG convention.
19. Moon, T. K., 1996, The expectation-maximization algorithm: Signal Processing Magazine, IEEE, 13, no. 6, 47-60 10.1109/79.543975
20. Pilkington, M., 2009, 3d magnetic data-space inversion with sparseness constraints: Geophysics, 74, no. 1, L7-L15 10.1190/1.3026538
21. Portniaguine, O., and J. Castagna, 2004, Inverse spectral decomposition: 74th Annual International Meeting, SEG, Expanded Abstracts, 23, 1786-1789.
22. Potter, C. C., A. K. Dey, and R. R. Stewart, 1998, Density prediction using P-and S-wave sonic velocities: Geotriad, CSPG, CSEG, CWLS joint convention.
23. Richards, P. G., and W. Frasier, 1976, Scattering of elastic waves from depth-depenendent inhomogeneities: Geophysics, 41, no. 3, 441-458. 10.1190/1.1440625
24. Røislien, J., H. Omre, 2006, T-distributed radom fields:a parametric modell for heavy-tailed well-log data: Mathematical Geology, 38, no. 7, 821-849 10.1007/s11004-006-9050-z
25. Sacchi, M. D., 1997, Reweighting strategies in seismic deconvolution: Geophysical Journal International, 129, no. 3, 651-656 10.1111/j.1365-246X.1997.tb04500.x
26. Sacchi, M. D., and T. J. Ulrych, 1995, High-resolution velocity gathers and offset space reconstruction: Geophysics, 60, no. 4, 1169-1177 10.1190/1.1443845
27. Scales, J. A., and L. Tenorio, 2001, Prior information and uncertainty in inverse problems: Geophysics, 66, no. 2, 389-397 10.1190/1.1444930
28. Shuey, R. T., 1985, A simplication of the Zoeppritz equations: Geophysics, 50, no. 4, 609-614. 10.1190/1.1441936
29. Smith, G. C., and M. Gidlow, 2003, The fluid factor angle and the crossplot angle: SEG Technical Program Expanded Abstracts, 22, 185-188.
30. Soldo, J., 2009, Fluid to lithology discrimination approach using simultaneous AVO inversion: Puesto Peter Field, Austral Basin, Argentina: The Leading Edge, 28, no. 6, 698-701. 10.1190/1.3148411
31. Tarantola, A., 1987, Inverse problem theory, method for data fitting and model parameter estimation: Elsevier Science Publishers.
32. Theune, U., I. Jensås, and J. Eidsvik, 2010, Analysis of prior models for a blocky inversion of seismic AVA data: Geophysics, 75, no. 3, C25-C35.
33. Tikhonov, A. N., 1963, Solution of incorrectly formulated problems and the regularizationmethod: Soviet Mathematical Doklady, 4, 1035-1038.
34. Trad, D., T. Ulrych, and M. D. Sacchi, 2003, Latest views of the sparse Radon transform: Geophysics, 68, no. 1, 386-399 10.1190/1.1543224
35. Ulrych, T. J., M. D. Sacchi, and A. Woodbury, 2001, A Bayes tour of inversion: A tutorial: Geophysics, 66, no. 1, 55-69 10.1190/1.1444923
36. Wang, J., and M. D. Sacchi, 2007, High-resolution wave-equation amplitude-variation withray-parameter (avp) imaging with sparseness constraints: Geophysics, 72, no. 1, S11-S18. 10.1190/1.2387139
37. Wang, J., Y. Zheng, and M. Perz, 2007, High-resolution deconvolution with sparsity and lateral continuity constraints: CSEG, Expanded Abstracts, 509-512.
38. Zwartjes, P., and M. Sacchi, 2007, Fourier reconstruction of nonuniformly sampled, aliased seismic data: Geophysics, 72, no. 1, V21-V32 10.1190/1.2399442