The effect of noise and Tikhonov's regularization in inverse problems. Part II: The nonlinear case

Journal of Applied Geophysics

Volumn 108, Issue , 2014, Pages 186-193

  Fernandez Martinez J L ^a   Pallero, J L G ^b   Fernandez Muniz Z ^a   Pedruelo Gonzalez L M ^a  

^a UNIVERSITY OF OVIEDO   (Spain)

^b UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Noise; Nonlinear inversion; Regularization; Uncertainty analysis

Indexed keywords

DIFFERENTIAL EQUATIONS; NONLINEAR PROGRAMMING; UNCERTAINTY ANALYSIS;

INVERSE PROBLEM SOLUTION; LOCAL OPTIMIZATION METHODS; NOISE; NON LINEAR INVERSION; NON-LINEAR INVERSE PROBLEM; NONLINEAR UNCERTAINTIES; REGULARIZATION; REGULARIZATION TECHNIQUE;

INVERSE PROBLEMS;

DATA INVERSION; GEOPHYSICAL METHOD; INVERSE PROBLEM; NOISE; NONLINEARITY; OPTIMIZATION; UNCERTAINTY ANALYSIS;

EID: 84905503978     PISSN: 09269851     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jappgeo.2014.05.005     Document Type: Article

References (20)

1. Aster R.C., Borchers B., Thurber C.H. Parameter Estimation and Inverse Problems 2012, Academic Press, New York. 2nd ed.
2. Barhen J., Berryman J.G., Borcea L., Dennis J., de Groot-Hedlin C., Gilbert F., Gill P., Heinkenschloss M., Johnson L., McEvilly T., Moré J., Newman G., Oldenburg D., Parker P., Porto B., Sen M., Torczon V., Vasco D., Woodward N.B. Optimization and Geophysical Inverse Problems 2000, Technical Report. Ernest Orlando Lawrence Berkeley National Laboratory, San Jose, California.
3. Blackman R.B., Tukey J.W. The measurement of power spectra from the point of view of communications engineering-part I. Bell Syst. Tech. J. 1958, 37:185-282.
4. Blackman R.B., Tukey J.W. The measurement of power spectra from the point of view of communications engineering-part II. Bell Syst. Tech. J. 1958, 37:485-569.
5. Engl H.W., Hanke M., Neubauer A. Regularization of inverse problems. Number 375 in Mathematics and its Applications 1996, Kuwler Academic Publishers, Dordrecht.
6. Fernández-Martínez J.L., Fernández Muñiz Z., Tompkins M.J. On the topography of the cost functional in linear and nonlinear inverse problems. Geophysics 2012, 77:W1-W15. 10.1190/geo2011-0341.1.
7. Fernández-Martínez J.L., Fernández Muñiz Z., Pallero J.L.G., Pedruelo-González L.M. From Bayes to Tarantola: new insights to understand uncertainty in inverse problems. J. Appl. Geophys. 2013, 98:62-72. 10.1016/j.jappgeo.2013.07.005.
8. Fernández-Martínez J.L., Pallero J.L.G., Fernández Muñiz Z., Pedruelo-González L.M. The effect of the noise and Tikhonov's regularization in inverse problems. Part I: the linear case. J. Appl. Geophys 2014, 10.1016/j.jappgeo.2014.05.005.
9. Kaltenbacher B., Neubauer A., Scherzer O. Iterative Regularization Methods for Nonlinear Ill-Posed Problems 2008, Walter de Gruyter, Berlin.
10. Osypov K., Nichols D., Woodward M., Zdraveva O., Yarman C.E. Uncertainty and resolution analysis for anisotropic tomography using iterative eigendecomposition. SEG Technical Program Expanded Abstracts 2008, 3244-3249. 10.1190/1.3064019.
11. Tarantola A. Popper, Bayes and the inverse problem. Nat. Phys. 2006, 2:492-494.
12. Tarantola A., Valette B. Generalized nonlinear inverse problems solved using the least squares criterion. Rev. Geophys. Space Phys. 1982, 20:219-232.
13. Tarantola A., Valette B. Inverse problems=quest for information. J. Geophys. 1982, 50:159-170.
14. Tibshirani R. Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Methodol. 1996, 58:267-288. 10.1190/1.1442303.
15. Tikhonov A.N., Arsenin V.Y. Solutions of Ill-Posed Problems 1977, V. H, Winston and Sons, Washington, D. C.
16. Tompkins M.J., Fernández-Martínez J.L., Alumbaugh D.L., Mukerji T. Scalable uncertainty estimation for nonlinear inverse problems using parameter reduction, constraint mapping, and geometric sampling: marine controlled-source electromagnetic examples. Geophysics 2011, 76:F263-F281. 10.1190/1.3581355.
17. Tompkins M.J., Fernández-Martínez J.L., Fernández-Muñiz Z. Marine electromagnetic inverse solution appraisal and uncertainty using model-derived basis functions and sparse geometric sampling. Geophys. Prospect. 2011, 59:947-965. 10.1111/j.1365-2478.2011.00955.x.
18. Tompkins M.J., Fernández-Martínez J.L., Fernández-Muñiz Z. Comparison of sparse-grid geometric and random sampling methods in nonlinear inverse solution uncertainty estimation. Geophys. Prospect. 2013, 61:28-41. 10.1111/j.1365-2478.2012.01057.x.
19. Vugrin K.E. On the Effects of Noise on Parameter Identification Optimization Problems 2005, Ph.D. thesis, (Virginia, USA).
20. Zhdanov M.S. Geophysical inverse theory and regularization problems. Number 36 in Methods in Geochemistry and Geophysics 2002, Elsevier.