Scalable uncertainty estimation for nonlinear inverse problems using parameter reduction, constraint mapping, and geometric sampling: Marine controlled-source electromagnetic examples

Geophysics

Volumn 76, Issue 4, 2011, Pages

  Tompkins, Michael J ^a   Fernández Martínez, Juan L ^b   Alumbaugh, David L ^a   Mukerji, Tapan ^c  

^a SCHLUMBERGER   (United States)

^b UNIVERSITY OF OVIEDO   (Spain)

^c STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COVARIANCE MATRIX; DIGITAL STORAGE; GEOMETRY; MAPPING; PRINCIPAL COMPONENT ANALYSIS; SINGULAR VALUE DECOMPOSITION;

COMPRESSION METHODS; CONTROLLED SOURCE ELECTRO-MAGNETIC; METROPOLIS-HASTINGS SAMPLINGS; NON-LINEAR INVERSE PROBLEM; PARAMETER CONSTRAINTS; PARAMETER REDUCTION; UNCERTAINTY ESTIMATION; UNCERTAINTY MEASURES;

INVERSE PROBLEMS;

COVARIANCE ANALYSIS; DATA INVERSION; ELECTROMAGNETIC METHOD; ESTIMATION METHOD; GEOMETRY; INVERSE PROBLEM; MAPPING; PRINCIPAL COMPONENT ANALYSIS; SAMPLING; UNCERTAINTY ANALYSIS;

EID: 84857313916     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.3581355     Document Type: Article

References (39)

1. Abubakar, A., T. M. Habashy, V. L. Druskin, L. Knizhnerman, and D. Alumbaugh, 2008, 2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurements: Geophysics, 73, no. 4, F165-F177.
2. Alumbaugh, D. L., 2002, Linearized and nonlinear parameter variance estimation for two-dimensional electromagnetic induction inversion: Inverse Problems, 16, 1323-1341.
3. Alumbaugh, D. L., and G. A. Newman, 2000, Image appraisal for 2-D and 3-D electromagnetic inversion: Geophysics, 65, 1455-1467.
4. Avis, D., and K. Fukuda, 1992, A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra: Journal of Discrete Computational Geometry, 8, 295-313.
5. Barthelmann, V., E. Novak, and K. Ritter, 2000, High dimensional polynomial interpolation on sparse grids: Advances in Computational Mathematics, 12, 273-288.
6. De Lathauwer, L., B. De Moor, and J. Vandewalle, 2000, A multilinear singular value decomposition: SIAM Journal on Matrix Analysis and Applications, 21, 1253-1278.
7. Echeverria, D., T. Mukerji, and E. T. F. Santos, 2009, Robust scheme for inversion of seismic and production data for reservoir facies modeling: 79th Annual International Meeting, SEG, Expanded Abstracts, 2432-2436.
8. Fernández-Álvarez, J. P., J. L. Fernández Martínez, and C. O. Menéndez-Pérez, 2008, Feasibility analysis of the use of binary genetic algorithms as importance samplers application to a geoelectrical VES inverse problem: Mathematical Geosciences, 40, 375-408.
9. Fernández Martínez, J. L., E. García Gonzalo, J. P. Fernández Álvarez, H. A. Kuzma, and C. O. Menéndez Pérez, 2010a, PSO: A powerful algorithm to solve geophysical inverse problems. Application to a 1D-DC resistivity case: Journal of Applied Geophysics, 71, 13-25.
10. Fernández Martínez, J. L., E. García Gonzalo, and V. Naudet, 2010b, Particle swarm optimization applied to solving and appraising the streaming-potential inverse problem: Geophysics, 75, no. 4, WA3-WA15.
11. Fernández Martínez, J. L., T. Mukerji, E. García Gonzalo, A. Suman, 2010c, Reservoir characterization and inversion uncertainty via a family of particle swarm optimizers: Application to the synthetic Stanford VI reservoir: 80th Annual International Meeting, SEG, Expanded Abstracts, 2334-2339.
12. Fernández Martínez, J. L., M. J. Tompkins, Z. Fernández Muñiz, T. Mukerji, 2010d, Inverse problems and model reduction techniques, in C. Borgelt, G. González-Rodríguez, W. Trutschnig, M. Asuncíon Lubiano, M. Ángeles Gil, P. Grezegorzewski, and O. Hryniewicz, eds., Advances in intelligent and soft computing: Combining soft computing and statistical methods in data analysis: Springer, 255-262.
13. Fukuda, K., and A. Prodon, 1996, Double description method revisited: Combinatorics and computer science: Lecture Notes in Computer Science, 1120, 91-111.
14. Ganapathysubramanian, B., and N. Zabaras, 2007, Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method: Journal of Computational Physics, 226, 326-353.
15. Haario, H., E. Saksman, and J. Tamminen, 2001, An adaptive Metropolis algorithm: Bernoulli, 7, 223-242.
16. Jolliffe, I. T., 2002, Principal component analysis, 2nd ed.: Springer.
17. Key, K., 2009, 1D inversion of multicomponent, multifrequency marine CSEM data: Methodology and synthetic studies for resolving thin resistive layers: Geophysics, 74, no. 2, F9-F20.
18. Malinverno, A., 2002, Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem: Geophysical Journal International, 151, 675-688.
19. Matarese, J. R., 1995, Nonlinear traveltime tomography: Ph.D. thesis, Massachusetts Institute of Technology.
20. Meju, M. A., 1994, Geophysical data analysis: Understanding inverse problem theory and practice: Course notes series, SEG.
21. Meju, M. A., 2009, Regularized extremal bounds analysis (REBA):An approach to quantifying uncertainty in nonlinear geophysical inverse problems: Geophysical Research Letters, 36, L03304.
22. Menke, W., 1994, Geophysical data analysis: Discrete inverse theory: Academic.
23. Mosegaard, K., and A. Tarantola, 1995, Monte Carlo sampling of solutions to inverse problems: Journal of Geophysical Research, 100, 12431-12447.
24. Oldenburg, D. W., 1983, Funnel functions in linear and nonlinear appraisal: Journal of Geophysical Research, 88, 7387-7398.
25. Osypov, K., D. Nichols, M. Woodward, O. Zdraveva, and C. E. Yarman, 2008, Uncertainty and resolution analysis for anisotropic tomography using iterative eigendecomposition: 78th Annual International Meeting, SEG, Expanded Abstracts, 3244-3249.
26. Pearson, K., 1901, On lines and planes of closest fit to systems of points in space: Philosophical Magazine, 2, no. 6, 559-572.
27. Sambridge, M., 1999, Geophysical inversion with a neighborhood algorithm - I. Searching a parameter space: Geophysical Journal International, 138, 479-494.
28. Sambridge, M., K. Gallagher, A. Jackson, and P. Rickwood, 2006, Trans-dimensional inverse problems, model comparison and the evidence: Geophysical Journal International, 167, 528-542, doi:10.1111/j.1365-246X.2006.03155.x
29. Scales, J. A., and L. Tenorio, 2001, Prior information and uncertainty in inverse problems: Geophysics, 66, 389-397.
30. Sen, M., and P. L. Stoffa, 1995, Global optimization methods in geophysical inversion: Elsevier.
31. Smolyak, S., 1963, Quadrature and interpolation formulas for tensor products of certain classes of functions: Doklady Mathematics, 4, 240-243.
32. Tarantola, A., 2005, Inverse problem theory: SIAM.
33. Tarantola, A., and B. Valette, 1982, Inverse problems = quest for information: Journal of Geophysics, 50, 159-170.
34. Tompkins, M. J., 2003, Quantitative analysis of borehole electromagnetic induction logging responses using anisotropic forward modeling and inversion: Ph.D. thesis, University of Wisconsin-Madison.
35. Tompkins, M. J., and D. L. Alumbaugh, 2002, A transversely isotropic 1D electromagnetic inversion scheme requiring minimal a priori information: 72nd Annual International Meeting, SEG, Expanded Abstracts, 676-679.
36. Tompkins, M. J., and J. L. Fernández Martínez, 2010, Scalable solutions for nonlinear inverse uncertainty using model reduction, constraint mapping, and sparse sampling: 72nd EAGE Conference and Exhibition, Extended Abstracts, 3882-3887.
37. Trainor, W., and G. M. Hoversten, 2009, Practical challenges of stochastic inversion implementation for geophysical problems: 79th Annual International Meeting, SEG, Expanded Abstracts, 734-738.
38. Xiu, D., and J. S. Hesthaven, 2005, High-order collocation methods for differential equations with random inputs: SIAM Journal of Scientific Computing, 27, 1118-1139.
39. Zhang, H., and C. H. Thurber, 2007, Estimating the model resolution matrix for large seismic tomography problems based on Lanczos bidiagonalization with partial reorthogonalization: Geophysical Journal International, 170, 337-435.