Non-linear model error and resolution properties from two-dimensional single and joint inversions of direct current resistivity and radiomagnetotelluric data

Geophysical Journal International

Volumn 182, Issue 3, 2010, Pages 1174-1188

  Kalscheuer, Thomas ^a   de los Ángeles García Juanatey, María ^b   Meqbel, Naser ^c   Pedersen, Laust B ^b  

^a ETH ZURICH   (Switzerland)

^b UPPSALA UNIVERSITY   (Sweden)

^c OREGON STATE UNIVERSITY   (United States)

Author keywords

Electromagnetic theory; Instability analysis; Inverse theory; Magnetotelluric; Numerical approximations and analysis

Indexed keywords

ELECTROMAGNETIC THEORIES; INSTABILITY ANALYSIS; INVERSE THEORY; MAGNETOTELLURIC; NUMERICAL APPROXIMATIONS;

ELECTRIC CONDUCTIVITY; ELECTRIC FIELDS; ELECTROMAGNETISM; LINEARIZATION; MAGNETOTELLURICS; SINGULAR VALUE DECOMPOSITION;

ERRORS;

DATA SET; EIGENVALUE; ELECTRICAL RESISTIVITY; ELECTROMAGNETIC METHOD; ESTIMATION METHOD; INVERSE ANALYSIS; MAGNETOTELLURIC METHOD; NONLINEARITY; NUMERICAL METHOD; RADIOMETRIC METHOD;

EID: 77955747950     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2010.04686.x     Document Type: Article

References (47)

1. Alumbaugh DL, Newman GA. Image appraisal for 2-D and 3-D electromagnetic inversion. Geophysics 2000, 65(5):1455-1467.
2. Anderson E. LAPACK Users' Guide: Society for Industrial and Applied Mathematics 1999, 3rd edn, Philadelphia, PA, USA
3. Aprea C, Booker JR, Smith JT. The forward problem of electromagnetic induction: accurate finite-difference approximations for two-dimensional discrete boundaries with arbitrary geometry. Geophys. J. Int. 1997, 129(1):29-40.
4. Candansayar ME, Tezkan B. Two-dimensional joint inversion of radiomagnetotelluric and direct current resistivity data. Geophys. Prospect. 2008, 56(5):737-749.
5. Christensen NB. Difficulties in determining electrical anisotropy in subsurface investigations. Geophys. Prospect. 2000, 48(1):1-19.
6. Christensen-Dalsgaard J, Hansen PC, Thompson MJ. Generalized singular-value decomposition analysis of helioseismic inversions. Mon. Not. R. astr. Soc. 1993, 264(3):541-564.
7. Constable SC, Parker RL, Constable CG. Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 1987, 52(3):289-300.
8. de Groot-Hedlin C, Constable S. Occam's inversion to generate smooth, two-dimensional models for magnetotelluric data. Geophysics 1990, 55(12):1613-1624.
9. Dey A, Morrison HF. Resistivity modelling for arbitrarily shaped two-dimensional structures. Geophys. Prospect. 1979, 27(1):106-136.
10. Friedel S. Resolution, stability and efficiency of resistivity tomography estimated from a generalized inverse approach. Geophys. J. Int. 2003, 153(2):305-316.
11. Golub G, van Loan C. Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences 1996, 3rd edn, Johns Hopkins University Press, Baltimore and London
12. Gómez-Trevino E, Edwards RN. Electromagnetic soundings in the sedimentary basin of southern Ontario: a case history. Geophysics 1983, 48(3):311-330.
13. Haber E, Oldenburg D. Joint inversion: a structural approach. Inverse Probl. 1997, 13(1):63-77.
14. Hohmann GW. Numerical modeling for electromagnetic methods in geophysics. Electromagnetic Methods in Applied Geophysics 1987, Vol. 1:313-363. Nabighian MN. Theory, ed., SEG, Tulsa
15. Hohmann GW, Raiche AP. Inversion of controlled-source electromagnetic data. Electromagnetic Methods in Applied Geophysics 1987, Vol. 1:469-503. Nabighian MN, Theory, ed., SEG, Tulsa
16. Jackson DD. Marginal solutions to quasilinear inverse problems in geophysics: the edgehog method. Geophys. J. R. astr. Soc. 1973, 35(1-3):121-136.
17. Jackson DD. Most squares inversion. J. geophys. Res. 1976, 81(5):1027-1030.
18. Johansen HK. A man/computer interpretation system for resistivity soundings over a horizontally stratified earth. Geophys. Prospect. 1977, 25(4):667-691.
19. Jupp DLB, Vozoff K. Simple iterative methods for the inversion of geophysical data. Geophys. J. R. astr. Soc. 1975, 42(3):957-976.
20. Kalscheuer T, Pedersen LB. A non-linear truncated SVD variance and resolution analysis of two-dimensional magnetotelluric models. Geophys. J. Int. 2007, 169(2):435-447.
21. Kalscheuer T, Pedersen LB, Siripunvaraporn W. Radiomagnetotelluric two-dimensional forward and inverse modelling accounting for displacement currents. Geophys. J. Int. 2008, 175(2):486-514.
22. LaBrecque DJ, Morelli G, Daily W, Ramirez A, Lundegard P. Occam's inversion of 3D ERT data. Three-Dimensional Electromagnetics 1999, 575-590. Spies B, ed., SEG, Tulsa
23. Lines LR, Treitel S. Tutorial: a review of least-squares inversion and its application to geophysical problems. Geophys. Prospect. 1984, 32(2):159-186.
24. Lines LR, Treitel S. Inversion with a grain of salt. Geophysics 1985, 50(1):99-109.
25. Meju MA. Biased estimation: a simple framework for inversion and uncertainty analysis with prior information. Geophys. J. Int. 1994, 119(2):521-528.
26. Meju MA. Regularized extremal bounds analysis (REBA): an approach to quantifying uncertainty in nonlinear geophysical inverse problems. Geophys. Res. Lett. 2009, 36(3):L03304.
27. Meju MA, Hutton VRS. Iterative most-squares inversion: application to magnetotelluric data. Geophys. J. Int. 1992, 108(3):758-766.
28. Menke W. Geophysical data analysis: discrete inverse theory 1989, Vol. 45 of, Academic Press, London
29. Miller CR, Routh PS. Resolution analysis of geophysical images: comparison between point spread function and region of data influence measures. Geophys. Prospect. 2007, 55(6):835-852.
30. Monteiro Santos FA, Afonso ARA, Dupis A. 2D joint inversion of dc and scalar audio-magnetotelluric data in the evaluation of low enthalpy geothermal fields. J. geophys. Eng. 2007, 4:53-62.
31. Muñoz G, Rath V. Beyond smooth inversion: the use of nullspace projection in MT. Geophys. J. Int. 2006, 164(2):301-311.
32. Oldenburg DW, Li YG. Estimating depth of investigation in dc resistivity and IP surveys. Geophysics 1999, 64(2):403-416.
33. Ory J, Pratt RG. Are our parameter estimators biased? The significance of finite-difference regularization operators. Inverse Probl. 1995, 11(2):397-424.
34. Parker RL. Understanding inverse theory. Ann. Rev. Earth Planet. Sci. 1977, 5:35-64.
35. Parker RL. The inverse problem of resistivity sounding. Geophysics 1984, 49(12):2143-2158.
36. Pedersen LB. Constrained inversion of potential field data. Geophys. Prospect. 1979, 27(4):726-748.
37. Pedersen LB, Rasmussen TM. Inversion of magnetotelluric data: a non-linear least squares approach. Geophys. Prospect. 1989, 37(6):669-695.
38. Raiche AP, Jupp DLB, Rutter H, Vozoff K. The joint use of coincident loop transient electromagnetic and Schlumberger sounding to resolve layered structures. Geophysics 1985, 50(10):1618-1627.
39. Rodi W, Mackie RL. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics 2001, 66(1):174-187.
40. Rodi WL. A technique for improving the accuracy of finite element solutions for magnetotelluric data. Geophys. J. R. astr. Soc. 1976, 44(2):483-506.
41. Sasaki Y. Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data. Geophysics 1989, 54(2):254-262.
42. Schwalenberg K, Rath V, Haak V. Sensitivity studies applied to a two-dimensional resistivity model from the Central Andes. Geophys. J. Int. 2002, 150(3):673-686.
43. Siripunvaraporn W, Egbert G. An efficient data-subspace inversion method for 2-D magnetotelluric data. Geophysics 2000, 65(3):791-803.
44. Vozoff K, Jupp DLB. Joint inversion of geophysical data. Geophys. J. R. astr. Soc. 1975, 42(3):977-991.
45. Weaver JT, Le Quang BV, Fischer G. A comparison of analytical and numerical results for a two-dimensional control model in electromagnetic induction - I: B-polarization calculations. Geophys. J. R. astr. Soc. 1985, 82(2):263-277.
46. Weaver JT, Le Quang BV, Fischer G. A comparison of analytical and numerical results for a two-dimensional control model in electromagnetic induction - II: E-polarization calculations. Geophys. J. R. astr. Soc. 1986, 87(3):917-948.
47. Xu S, Duan B, Zhang D. Selection of the wavenumbers k using an optimization method for the inverse Fourier transform in 2.5D electrical modelling. Geophys. Prospect. 2000, 48(5):789-796.