Dynamic inversion for hydrological process monitoring with electrical resistance tomography under model uncertainties

Water Resources Research

Volumn 46, Issue 4, 2010, Pages

  Lehikoinen, A ^a   Huttunen, J M J ^a,b   Finsterle, S ^c   Kowalsky, M B ^c   Kaipio, J P ^a,d  

^a UNIVERSITY OF EASTERN FINLAND   (Finland)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^d UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMIC INVERSION; ELECTRICAL RESISTANCE TOMOGRAPHY; HYDROLOGICAL PROCESS; MODEL UNCERTAINTIES;

EID: 80054972011     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1029/2009WR008470     Document Type: Article

References (49)

1. Anderson, B. D. O., and J. B. Moore (1979), Optimal Filtering, Prentice Hall, Englewood Cliffs, N. J.
2. Archie, G. E. (1942), The electrical resistivity logs as an aid determining some reservoir characteristics, Trans. Am. Inst. Min. Metall. Pet. Eng., 146, 54-61.
3. Arridge, S. R., J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen (2006), Approximation errors and model reduction with an application in optical diffusion tomography, Inverse Probl., 22, 175-195.
4. Binley, A., G. Cassiani, R. Middleton, and P. Winship (2002), Vadose zone flow model parametrisation using cross-borehole radar and resistivity imaging, J. Hydrol., 267, 147-159.
5. Cheng, K.-S., D. Isaacson, J. C. Newell, and D. G. Gisser (1989), Electrode models for electric current computed tomography, IEEE Trans. Biomed., 36, 918-924.
6. Daily, W. D., and A. L. Ramirez (2000), Electrical imaging of engineered hydraulic barriers, Geophysics, 65, 83-94.
7. Daily, W. D., A. L. Ramirez, D. J. LaBrecque, and J. Nitao (1992), Electrical resistivity tomography of vadose water movement, Water Resour. Res., 28, 1429-1442.
8. Dennis, J. E., and R. B. Schnabel (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Englewood Cliffs, N. J.
9. Deutsch, C., and A. Journel (1992), GSLIB-Geostatistical Software Library and User's Guide, Oxford Univ. Press, New York.
10. Dobson, D. C., and F. Santosa (1996), Recovery of blocky images from noisy and blurred data, SIAM J. Appl. Math., 56(4), 1181-1198.
11. Doucet, A., N. de Freitas, and N. Gordon (2001), Sequential Monte Carlo Methods in Practice, Springer, New York.
12. Eppstein, M. J., and D. E. Dougherty (1998), Efficient three-dimensional data inversion: Soil characterization and moisture monitoring from cross-well ground-penetrating radar at a Vermont test site, Water Resour. Res., 34, 1889-1900.
13. Evensen, G. (1994), Sequential data assimilation with a non-linear quasigeostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99(C5), 10143-10162.
14. Ferre, T. P. A., A. C. Hinnell, and J. B. Blainey (2006), Examining the potential for inferring hydraulic properties using surface-based electrical resistivity during infiltration, Leading Edge, 25(6), 720-723.
15. Finsterle, S. (2004), Multiphase inverse modeling: Review and iTOUGH2 applications, Vadose Zone J., (3), 747-762.
16. French, H. K., C. Hardbattle, A. Binley, P. Winship, and L. Jakobsen (2002), Monitoring snowmelt induced unsaturated flow and transport using electrical resistivity tomography, J. Hydrol., 267, 273-284.
17. Hughson, D. L., and T.-C. J. Yeh (2000), An inverse model for three dimensional flow in variably saturated porous media, Water Resour. Res., 36, 829-839.
18. Huttunen, J. M. J., and J. P. Kaipio (2007a), Approximation errors in nostationary inverse problems, Inverse Probl. Imaging, 1(1), 77-93.
19. Huttunen, J. M. J., and J. P. Kaipio (2007b), Approximation error analysis in nonlinear state estimation with an application to state-space identification, Inverse Probl., 23, 2141-2157.
20. Järvenpää, S. (1996), Finite element model for inverse conductivity problem, Ph.D. thesis, Univ. of Helsinki, Helsinki.
21. Kaipio, J., and E. Somersalo (1999), Nonstationary inverse problems and state estimation, Inverse Ill Posed Probl., 7, 273-282.
22. Kaipio, J., and E. Somersalo (2004), Statistical and Computational Inverse Problems, Appl. Math. Sci., vol. 160, Springer, New York.
23. Kaipio, J., and E. Somersalo (2007), Statistical inverse problems: Discretization, model reduction, and inverse crimes, J. Comput. Appl. Math., 198, 493-504.
24. Kaipio, J. P., M. Vauhkonen, and E. Somersalo (1999), Inverse problems with structural prior information, Inverse Probl., 15, 713-729.
25. Kaipio, J. P., V. Kolehmainen, E. Somersalo, and M. Vauhkonen (2000), Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography, Infrared Phys., 16, 1487-1522.
26. Kalman, R. E. (1960), A new approach to linear filtering and prediction problems, J. Basic Eng., 82D, 35-45.
27. Kemna, A., J. Vanderboroght, B. Kulessa, and H. Vereecken (2002), Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models, J. Hydrol., 267, 174-198.
28. Lehikoinen, A., S. Finsterle, A. Voutilainen, and J. P. Kaipio (2007), Approximation errors and truncation of computational domains with application to geophysical tomography, Inverse Probl. Imaging, 1(2), 371-389.
29. Lehikoinen, A., S. Finsterle, A. Voutilainen, M. B. Kowalsky, and J. P. Kaipio (2009), Water saturation estimation by dynamical filtering of geophysical data using an unsaturated flow evolution model, Inverse Probl. Sci. Eng., in press.
30. Linde, H., S. Finsterle, and S. Hubbard (2006a), Inversion of hydrological tracer test data using tomographic constraints, Water Resour. Res., 42, W04410, doi:10.1029/2004WR003806.
31. Linde, N., A. Binley, A. Tryggvason, L. B. Pedersen, and A. Revil (2006b), Improved hydrogeophysical characterization using joint inversion of cross-hole electrical resistance and ground penetrating radar traveltime data, Water Resour. Res., 42, W12404, doi:10.1029/2006WR005131.
32. Nissinen, A., L. M. Heikkinen, and J. P. Kaipio (2008), Approximation errors in electrical impedance tomography-Experimental study, Meas. Sci. Technol., 19, 015501, doi:10.1088/0957-0233/19/1/015501.
33. Park, S. K. (1998), Fluid migration in the vadoze zone from 3-D inversion of resistivity monitoring data, Geophysics, 63, 41-51.
34. Pruess, K., C. Oldenburg, and G. Moridis (1999), Tough2 user's guide, version 2.0, Rep. LBNL-43134, Lawrence Berkeley Natl. Lab., Berkeley, Calif.
35. Ramirez, A., W. Daily, D. LaBrecque, E. Owen, and D. Chesnut (1993), Monitoring an underground steam injection process using electrical resistance tomography, Water Resour. Res., 29, 73-87.
36. Ramirez, A., W. Daily, A. Binley, D. LaBrecque, and D. Roelant (1996), Detection of leaks in underground storage tanks using electrical resistance methods, J. Environ. Eng. Geophys., 1(3), 189-203.
37. Richards, L. A. (1931), Capillary conduction of liquids through porous medium, Physics, 1, 318-333.
38. Seppänen, A., M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, and J. P. Kaipio (2001), State estimation with fluid dynamical models in process tomography-An application to impedance tomography, Inverse Probl., 17, 455-471.
39. Slater, L., A. Binley, W. Daily, and R. Johnson (2000), Cross-hole electrical imaging of a controlled saline tracer injection, J. Appl. Geophys., 44, 85-102.
40. van Genuchten, M. T. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil. Sci. Soc. Am. J., 44, 892-898.
41. Vauhkonen, P. J. (2004), Image reconstruction in three dimensional electrical impedance tomography, Ph.D. thesis, Univ. of Kuopio, Kuopio, Finland.
42. Vauhkonen, P. J., M. Vauhkonen, T. Savolainen, and J. P. Kaipio (1999), Three dimensional electrical impedance tomography based on the complete electrode model, IEEE Trans. Biomed. Eng., 46, 1150-1160.
43. Voutilainen, A., and J. P. Kaipio (2009), Model reduction and pollution source identification from remote sensing data, Inverse Probl. Imaging, in press.
44. Voutilainen, A., T. Pyhälahti, K. Y. Kallio, J. Pulliainen, H. Haario, and J. P. Kaipio (2007), A filtering approach for estimating lake water quality from remote sensing data, Int. J. Appl. Earth Obs. Geoinf., 9, 50-64.
45. Vrugt, J. A., B. A. Robinson, and V. V. Vesselinov (2005), Improved inverse modeling for flow and transport in subsurface media: Combined parameter and state estimation, Geophys. Res. Lett., 32, L18408, doi:10.1029/2005GL023940.
46. Yeh, T.-C., and J. Simunek (2002), Stochastic fusion of information for characterizing and monitoring the vadose zone, Vadose Zone J., 1, 207-221.
47. Yeh, T.-C. J., S. Liu, R. J. Glass, K. Baker, J. R. Brainard, D. Alumbaugh, and D. LaBrecque (2002), A geostatistically based inverse model for electrical resistivity surveys and its applications to vadose zone hydrology, Water Resour. Res., 38(12), 1278, doi:10.1029/2001WR001204.
48. Zhang, J., and T.-C. J. Yeh (1997), An iterative geostatistical inverse method for steady flow in the vadose zone, Water Resour. Res., 33, 63-71.
49. Zhou, Q. Y., J. Shimada, and A. Sato (2001), Three dimensional spatial and temporal monitoring of soil water content using electrical resistivity tomography, Water Resour. Res., 37, 273-285.