A novel approach to the model appraisal and resolution analysis of regularized geophysical inversion

Geophysics

Volumn 71, Issue 6, 2006, Pages

  Zhdanov, Michael S ^a   Tolstaya, Ekaterina ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Geophysical signal processing; Geophysical techniques; Inverse problems

Indexed keywords

IMAGING TECHNIQUES; INVERSE PROBLEMS; SIGNAL PROCESSING;

GEOPHYSICAL INVERSION; GEOPHYSICAL SIGNAL PROCESSING; GEOPHYSICAL TECHNIQUES; RESOLUTION ANALYSIS;

GEOPHYSICS;

ELECTROMAGNETIC SURVEY; IMAGE ANALYSIS; IMAGE RESOLUTION; INVERSE ANALYSIS; INVERSE PROBLEM; LEAST SQUARES METHOD; NUMERICAL MODEL; SIGNAL PROCESSING; SIGNAL-TO-NOISE RATIO;

CANADA; LABRADOR; NEWFOUNDLAND AND LABRADOR; NORTH AMERICA; VOISEY'S BAY;

EID: 33751060315     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.2336347     Document Type: Article

References (50)

1. Alumbaugh, D. L., and G. N. Newman, 2000, Image appraisal for 2D and 3D electromagnetic inversion: Geophysics, 65, 1455-1467. gpy GPYSA7 0016-8033 10.1190/1.1444834
2. Backus, G. E., 1970a, Inference from inadequate and inaccurate data, I: Proceedings of the National Academy of Sciences, 65, 1-7. pna PNASA6 0027-8424
3. 1970b, Inference from inadequate and inaccurate data, II: Proceedings of the National Academy of Sciences, 65, 281-287. pna PNASA6 0027-8424
4. 1970c, Inference from inadequate and inaccurate data, III: Proceedings of the National Academy of Sciences, 67, 282-289. pna PNASA6 0027-8424
5. Backus, G. E., and T. I. Gilbert, 1967, Numerical applications of a formalism for geophysical inverse problems: Geophysical Journal of the Royal Astronomical Society, 13, 247-276. gjr GEOJAN 0016-8009
6. 1968, The resolving power of gross earth data: Geophysical Journal of the Royal Astronomical Society, 16, 169-205. gjr GEOJAN 0016-8009
7. Balch, S. J., T. J. Crebs, A. King, and M. Verbiski, 1998, Geophysics of the Voisey's Bay Ni-Cu-Co deposits: 68th Annual International Meeting, SEG, Expanded Abstracts, 784-787.
8. Berdichevsky, M. N., and V. I. Dmitriev, 2002, Magnetotellurics in the context of the theory of ill-posed problems: SEG.
9. Cagniard, L., 1953, Theory of magnetotelluric method of geophysical prospecting: Geophysics, 18, 605-635. gpy GPYSA7 0016-8033 10.1190/ 1.1437915
10. V. I. Dmitriev, M. S. Zhdanov, V. A. Morozov, A. A. Nikitin, and H. P. Brusnetsov, eds., 1990, Computational mathematics and techniques in exploration geophysics (in Russian): Nedra Press.
11. Druskin, V., and L. Knizhnerman, 1994, Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains: Radio Science, 29, 937-953. ras RASCAD 0048-6604 10.1029/94RS00747
12. Druskin, V., L. Knizhnerman, and P. Lee, 1999, New spectral Lanczos decomposition method for induction modeling in arbitrary 3D geometry: Geophysics, 64, 701-706. gpy GPYSA7 0016-8033 10.1190/1.1444579
13. Foster, M., 1961, An application of the Wiener-Kolmogorov smoothing theory to matrix inversion: Journal of the Society for Industrial and Applied Mathematics, 9, 387-392. jsh JSIMAV 0368-4245
14. Franklin, J. N., 1970, Well-posed stochastic extensions of ill-posed linear problems: Journal of Mathematical Analysis and Applications, 31, 682-716. jma JMANAK 0022-247X 10.1016/0022-247X(70)90017-X
15. Golub, G. H., and C. F. Van Loan, 1996, Matrix computations, 3rd ed.: Johns Hopkins Univ. Press.
16. Hursán, G., and M. S. Zhdanov, 2002, Contraction integral equation method in 3D electromagnetic modeling: Radio Science, 37, 1089 doi:10.1029/2001RS002513. ras RASCAD 0048-6604 10.1029/2001RS002513
17. Jackson, D. D., 1972, Interpretation of inaccurate, insufficient and inconsistent data: Geophysical Journal of the Royal Astronomical Society, 28, 97-110. gjr GEOJAN 0016-8009
18. Lanczos, C., 1961, Linear differential operators: D. van Nostrand Co.
19. Marquardt, D. W., 1963, An algorithm for least-squares estimation of nonlinear parameters: Journal of the Society for Industrial and Applied Mathematics, 11, 431-441. jsh JSIMAV 0368-4245 10.1137/0111030
20. 1970, Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation: Technometrics, 12, 591-612. thn TCMTA2 0040-1706
21. McGillivray, P. R., and D. W. Oldenburg, 1990, Methods for calculating Fréchet derivatives and sensitivities for the nonlinear inverse problem: A comparative study: Geophysical Prospecting, 38, 499-524. 8uc GPPRAR 0016-8025 10.1111/j.1365-2478.1990.tb01859.x
22. McGillivray, P. R., D. W. Oldenburg, R. G. Ellis, and T. M. Habashy, 1994, Calculation of sensitivities for the frequency-domain electromagnetic problem: Geophysical Journal International, 116, 1-4. gji GJINEA 0956-540X
23. Mehanee, S., and M. S. Zhdanov, 2002, Two-dimensional magnetotelluric inversion of blocky geoelectrical structures: Journal of Geophysical Research, 107, B4, 2065, doi:10.1029/2001JB000191. jgr JGREA2 0148-0227
24. Menke, W., 1989, Geophysical data analysis: Discrete inverse theory: Academic Press Inc.
25. Naldrett, A. J., H. Keats, K. Sparkes, and S. Moore, 1996, Geology of the Voisey's Bay Ni-Cu-Co deposit, Labrador, Canada: Exploration and Mining Geology, 5, 169-179.
26. Oldenburg, D. W., 1983, Funnel functions in linear and nonlinear appraisal: Journal of Geophysical Research, 88, B9 7387-7398. jgr JGREA2 0148-0227
27. Parker, R. L., 1975, The theory of ideal bodies for gravity interpretation: Geophysical Journal of the Royal Astronomical Society, 42, 315-334. gjr GEOJAN 0016-8009
28. Portniaguine, O., and M. S. Zhdanov, 1999, Focusing geophysical inversion images: Geophysics, 64, 874-887. gpy GPYSA7 0016-8033 10.1190/ 1.1444596
29. Ramirez, A. L., W. D. Daily, and R. L. Newmark, 1995, Electrical resistance tomography for steam injection monitoring and control: Journal of Environmental and Engineering Geophysics, 0, 39-52. gpy GPYSA7 0016-8033
30. Rodi, W. L., 1976, A technique for improving the accuracy of finite element solutions for magnetotelluric data: Geophysical Journal of the Royal Astronomical Society, 44, 483-506. gjr GEOJAN 0016-8009
31. Sabatier, P. C., 1977a, On geophysical inverse problems and constraints: Journal of Geophysical Research, 43, 115-137. jgr JGREA2 0148-0227
32. 1977b, Positivity constraints in linear inverse problems - I. General theory: Geophysical Journal of the Royal Astronomical Society, 48, 415-441. gjr GEOJAN 0016-8009
33. 1977c, Positivity constraints in linear inverse problems - II. Applications: Geophysical Journal of the Royal Astronomical Society, 48, 443-459. gjr GEOJAN 0016-8009
34. Sambridge, M., and K. Mosegaard, 2002, Monte Carlo methods in geophysical inverse problems: Reviews of Geophysics, 40, 3, 1-29. abl RVGPB4 8755-1209
35. Spies, B. R., and T. M. Habashy, 1995, Sensitivity analysis of cross-well electromagnetics: Geophysics, 60, 834-845. gpy GPYSA7 0016-8033 10.1190/1.1443821
36. Stark, P. B., and R. L. Parker, 1987, Velocity bounds from statistical estimates of t (p) and X (p): Journal of Geophysical Research, 92, B3, 2713-2719. jgr JGREA2 0148-0227
37. Stark, P. B., R. L. Parker, G. Masters, and L. A. Orcutt, 1986, Strict bounds on seismic velocity in the spherical earth: Journal of Geophysical Research, 91, B14, 13892-13902. jgr JGREA2 0148-0227
38. Tarantola, A., 1987, Inverse problem theory: Elsevier Science Publ. Co. Inc.
39. Tarantola, A., and B. Valette, 1982, Generalized nonlinear inverse problem solved using the least squares criterion: Reviews of Geophysics and Space Physics, 20, 219-232. rgh RGPSBL 0034-6853
40. Tikhonov, A. N., 1950, On determining electric characteristics of the deep layers of the earth's crust: Doklady Akademii Nauk SSSR, 73, 295-297. dbl DBLRAC 0002-354X
41. Tikhonov, A. N., and V. Y. Arsenin, 1977, Solution of ill-posed problems: W. H. Winston and Sons.
42. Xiong, Z., 1992, EM modeling of three-dimensional structures by the method of system iteration using integral equations: Geophysics, 57, 1556-1561. gpy GPYSA7 0016-8033 10.1190/1.1443223
43. Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Elsevier Science Publ. Co., Inc.
44. Zhdanov, M. S., and A. Chernyavskiy, 2004, Rapid three-dimensional inversion of multi-transmitter electromagnetic data using the spectral Lanczos decomposition method: Inverse Problems, 20, S233-S256. inp INPEEY 0266-5611 10.1088/0266-5611/20/6/S14
45. Zhdanov, M. S., V. I. Dmitriev, S. Fang, and G. Hursán, 2000, Quasi-analytical approximations and series in electromagnetic modeling: Geophysics, 65, 1746-1757. gpy GPYSA7 0016-8033 10.1190/1.1444859
46. Zhdanov, M. S., and N. G. Golubev, 2003, Three-dimensional inversion of magnetotelluric data in complex geological structures, in J. Macnae and G. Liu, eds., Three-dimensional electromagnetics III, Australian Society of Exploration Geophysics.
47. Zhdanov, M. S., and G. Hursán, 2000, 3D electromagnetic inversion based on quasi-analytical approximation: Inverse Problems, 16, 1297-1322. inp INPEEY 0266-5611 10.1088/0266-5611/16/5/311
48. Zhdanov, M. S., and G. W. Keller, 1994, The geoelectrical methods in geophysical exploration: Elsevier Science Publ. Co., Inc.
49. Zhdanov, M. S., and E. Tartaras, 2002, Inversion of multi-transmitter 3D electromagnetic data based on the localized quasi-linear approximation: Geophysical Journal International, 148, 506-519. gji GJINEA 0956-540X 10.1046/j.1365-246x.2002.01591.x
50. Zhdanov, M. S., and E. Tolstaya, 2004, Minimum support nonlinear parameterization in the solution of 3D magnetotelluric inverse problem: Inverse Problems, 20, 937-952. inp INPEEY 0266-5611 10.1088/0266-5611/20/ 3/017