Fast model updates using wavelets

Multiscale Modeling and Simulation

Volumn 3, Issue 1, 2004, Pages 106-130

  Bennett, Nicholas N ^a   Malinverno, Alberto ^a  

^a SCHLUMBERGER DOLL RESEARCH   (United States)

Author keywords

Cholesky decomposition; Covariance matrix; Kalman filter; Model averaging; Model update; Multiwavelets; Uncertainty; Wavelets

Indexed keywords

INVERSE PROBLEMS; KALMAN FILTERING; MATRIX ALGEBRA; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; WAVELET TRANSFORMS;

CHOLESKY DECOMPOSITION; COVARIANCE MATRIX; MODEL AVERAGING; MODEL UPDATE; MULTIWAVELETS; UNCERTAINTY;

MATHEMATICAL MODELS;

EID: 17644375499     PISSN: 15403459     EISSN: None     Source Type: Journal    
DOI: 10.1137/030601466     Document Type: Article

References (27)

1. B. Alpert, G. Beylkin, R. Coifman, and V. Rokhlin, Wavelet-like bases for the fast solution of second-kind integral equations, SIAM J. Sci. Comput., 14 (1993), pp. 159-184.
2. T. Anderson, An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, New York, 1958.
3. N. Bennett, Wavelet Model Updates in Nonlinear Inverse Problems, manuscript.
4. G. Beylkin, On wavelet-based algorithms for solving differential equations, in Wavelets: Mathematics and Applications, CRC Press, Boca Raton, FL, 1994, pp. 449-466.
5. G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Coram. Pure Appl. Math., 44 (1991), pp. 141-183.
6. G. Christakos, Random Field Models in Earth Sciences, Academic Press, San Diego, 1992.
7. A. Cohen, I. Daubechies, and P. Vial, Wavelets on the interval and fast wavelet transforms, Appl. Comput. Harmon. Anal., 1 (1993), pp. 54-81.
8. R. Coifman and D. Donoho, Translation invariant de-noising, in Lecture Notes in Statistics: Wavelets and Statistics, Springer-Verlag New York, 1995, pp. 125-150.
9. J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Stewart, LINPACK User's Guide, SIAM, Philadelphia, 1979.
10. S. Gortler, P. Schroder, M. Cohen, and P. Hanrahan, Wavelet Radiosity Comput. Graphics, 27 (1993), pp. 221-230.
11. W. Gouveia and J. Scales, Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis, J. Geophys. Res., 103 (1998), pp. 2759-2779.
12. P. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, 82 (1995), pp. 711-732.
13. W. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57 (1970), pp. 97-109.
14. J. Hoeting, D. Madigan, A. Raftery, and C. Volinsky, Bayesian model averaging: A tutorial, Statist. Sci., 14 (1999), pp. 382-417.
15. D. Jackson, The use of a priori data to resolve non-uniqueness in linear inversion, Geophys. J. Royal Astron. Soc., 57 (1979), pp. 137-157.
16. E. Jaynes, Probability Theory: The Logic of Science, Cambridge University Press, Cambridge, UK, 2003.
17. A. Malinverno, A Bayesian criterion for simplicity in inverse parameterization, Geophys. J. Int., 140 (2000), pp. 267-285.
18. A. Malinverno, Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem, Geophys. J. Int., 151 (2002), pp. 675-688.
19. A. Malinverno and V. Briggs, Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes, Geophysics, to appear.
20. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Physics, 21 (1953), pp. 1087-1092.
21. C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, 2000.
22. R. L. Parker, Geophysical Inverse Theory, Princeton University Press, Princeton, NJ, 1994.
23. W. H. Press, B.P. Flannery, S. A. Teukolsky, and W. T. Vertterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed., Cambridge University Press, New York, 1992.
24. A. Tarantola, Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam, 1988.
25. A. Tarantola and B. Valette, Generalized nonlinear inverse problems solved using the least squares criterion, Rev. Geophys. Space Phys., 20 (1982), pp. 219-232.
26. G. Welch and G. Bishop, An Introduction to the Kalman Filter, Technical report TR 95-041, Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC, 2002, http://www.cs.unc.edu/~welch.
27. A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions, Springer Series in Statistics, Springer-Verlag, New York, 1986.