Dynamical inversion of geophysical ERT data: State estimation in the vadose zone

Inverse Problems in Science and Engineering

Volumn 17, Issue 6, 2009, Pages 715-736

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

^a UNIVERSITY OF EASTERN FINLAND   (Finland)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^c UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Dynamical inversion; Kalman filter; State estimation

Indexed keywords

COMPLETE ELECTRODE MODEL; CONDUCTIVE FLUIDS; DRY SOIL; DYNAMIC INVERSE PROBLEMS; DYNAMICAL INVERSION; ELECTRICAL CONDUCTIVITY; ELECTRICAL CONDUCTIVITY DISTRIBUTION; ELECTRICAL RESISTANCE TOMOGRAPHY; EVOLUTION MODELS; GROUND SURFACES; PETROPHYSICAL RELATIONSHIP; POINT SOURCES; POROUS MEDIA; SIMULATED EXPERIMENTS; TARGET REGIONS; TIME-DEPENDENT; UNSATURATED FLOWS; VADOSE ZONE; WATER SATURATIONS;

CONTROL THEORY; ELECTRIC CONDUCTIVITY; ESTIMATION; INVERSE PROBLEMS; KALMAN FILTERS; POROUS MATERIALS; RADIATIVE TRANSFER; TOMOGRAPHY;

STATE ESTIMATION;

EID: 70349751563     PISSN: 17415977     EISSN: 17415985     Source Type: Journal    
DOI: 10.1080/17415970802475951     Document Type: Article

References (58)

1. W.H. Gardner, Water content, in Methods of Soil Analysis. Part 1. Physical and Mineralogic Methods, Agronomy Monograph No. 9, 2nd ed., A. Klute, ed., American Society of Agronomy- Soil Science Society of America, Madison, Wisconsin, 1986, pp. 493-544.
2. K. Noborio, Measurement of soil water content and electrical conductivity by time domain reflectometry: A review, Comput. Electron. Agric. 31 (2001), pp. 213-237.
3. W.D. Daily, A.L. Ramirez, A. Binley, and D. LaBrecque, Electrical resistance tomography, Leading Edge 23 (2004), pp. 438-442.
4. K.-S. Cheng, D. Isaacson, J.C. Newell, and D.G Gisser, Electrode models for electric current computed tomography, IEEE Trans. Biomed. Eng. 36 (1989), pp. 918-924.
5. K. Singha and S.M. Gorelick, Effects of spatially variable resolution on field-scale estimates of tracer concentration from electrical inversions using Archie's law, Geophysics 71 (2006), pp. G83-G91.
6. J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Applied Mathematical Sciences, Vol. 160, Springer-Verlag, New York, 2004.
7. A. Seppänen, M. Vauhkonen, P.J. Vauhkonen, E. Somersalo, and J.P. Kaipio, State estimation with fluid dynamical evolution models in process tomography - EIT application. Technical Report 6/2000, University of Kuopio, Department of Applied Physics.
8. A. Seppänen, M. Vauhkonen, P.J. Vauhkonen, E. Somersalo, and J.P. Kaipio, State estimation with fluid dynamical models in process tomography - An application to impedance tomography, Inverse Probl. 17 (2001), pp. 455-471.
9. M. Vauhkonen, P.A. Karjalainen, and J.P. Kaipio, Dynamical electrical impedance tomography, IEEE Trans. Biomed. Eng. 45 (1998), pp. 486-493.
10. B.D.O. Anderson and J.B. Moore, Optimal Filtering, Prentice-Hall, Eaglewood Cliffs, NJ, 1979.
11. A. Seppäynen, State estimation in process tomography, PhD Thesis, University of Kuopio, Kuopio, Finland, 2005.
12. P.J. Vauhkonen, M. Vauhkonen, T. Mäkinen, P.A. Karjalainen, and J.P. Kaipio, Dynamic electrical impedance tomography - phantom studies, Inv. Probl. Eng. 8 (2000), pp. 495-510.
13. D. Baroudi, J. Hietaniemi, and E. Somersalo, Dynamical electric tomography: A time series approach, Inverse Probl. 14 (1998), pp. 799-814.
14. S.G. Diamond, T.J. Huppert, V. Kolehmainen, M.A. Franceschini, J.P. Kaipio, S.R. Arridge, and D.A. Boas, Dynamic physiological modelling for functional diffuse optical tomography, Neuroimage 30 (2006), pp. 88-101.
15. S. Prince, V. Kolehmainen, J.P. Kaipio, M.A. Franceschini, D.A. Boas, and S.R. Arridge, Timeseries estimation of biological factors in optical diffusion tomography, Phys. Med. Biol. 48 (2003), pp. 1491-1504.
16. A. Voutilainen and J.P. Kaipio, Estimation of time-varying aerosol size distributions - Exploitation of modal aerosol dynamic models, J. Aerosol. Sci. 33 (2002), pp. 1181-1200.
17. E. Somersalo, A. Voutilainen, and J.P. Kaipio, Non-stationary magnetoencephalography by bayesian filtering of dipole models, Inverse Probl. 19 (2003), pp. 1047-1063.
18. A. Voutilainen, T. Pyhälahti, K.Y. Kallio, J. Pulliainen, H. Haario, and J.P. Kaipio, A filtering approach for estimating lake water quality from remote sensing data, Inter. J. Appl. Earth Obser. Geoinform. 9 (2007), pp. 50-64.
19. G.E. Archie, The electrical resistivity logs as an aid determining some reservoir characteristics, Trans. AIME 146 (1942), pp. 54-61.
20. A. Kemna, J. Vanderboroght, B. Kulessa, and H. Vereecken, Imaging and characterisation of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models, J. Hydrol. 267 (2002), pp. 174-198.
21. W.D. Daily and A.L. Ramirez, Electrical imaging of engineered hydraulic barriers, Geophysics 65 (2000), pp. 83-94.
22. A. Ramirez, W. Daily, A. Binley, D. LaBrecque, and D. Roelant, Detection of leaks in underground storage tanks using electrical resistance methods, J. Environ. Eng. Geophys. 1 (1996), pp. 189-203.
23. A. Binley, G. Cassiani, R. Middleton, and P. Winship, Vadose zone flow model parametcrisation using cross-borehole radar and resistivity imaging, J. Hydrol. 267 (2002), pp. 147-159.
24. W.D. Daily, A.L. Ramirez, D.J. LaBrecque, and J. Nitao, Electrical resistivity tomography of vadose water movement, Water Resour. Res. 28 (1992), pp. 1429-1442.
25. T.-C. Jim Yeh, S. Liu, R.J. Glass, K. Baker, J.R. Brainard, D. Alumbaugh, and D. LaBrecque, A geostatistically based inver model for electrical resistivity surveys and its applications to vadose zone hydrology, Water Resour. Res. 38 (2002), p. 1278.
26. Q.Y Zhou, J. Shimada, and A. Sato, Three dimensional spatial and temporal monitoring of soil water content using electrical resistivity tomography, Water Resour. Res. 37 (2001), pp. 273-285.
27. W.D. Daily and A.L. Ramirez, Electrical resistance tomography during in-situ trichloroethylene remediation at the Savannah River site, J. Appl. Geophys. 33 (1995), pp. 1429-1442.
28. P.K. Kitanidis, A unified approach to the parameters estimation of groundwater models, MSc Thesis, Massachusetts Institute of Technology 1976.
29. D.B. McLaughlin, Application of Kalman filtering to groundwater basin modelling and prediction, in Real-Time Forecasting/Control of Water Resource Systems, IIASA Proc. Ser, EF. Wood, ed., Pergamon, New York, 1976, pp. 109-123.
30. M.J. Eppstein and D.E. Dougherty, Simultaneous estimation of transmissivity values and zonation, Water Resour. Res. 32 (1996), pp. 3321-3336.
31. A. Furman, T. Ferré and A. Warrick, Optimization of ERT surveys for monitoring transient hydrological events using perturbation sensitivity and genetic algorithms, Vadose Zone J. 3 (2004), pp. 1230--1239.
32. S.R. Arridge, J.P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, Approximation errors and model reduction with an application in optical diffusion tomography, Inverse Probl. 22 (2006), pp. 175-195.
33. J.P. Kaipio and E. Somersalo, Statistical inverse problems: Discretization model reduction and inverse crime, J. Comput. Appl. Math. 189 (2007), pp. 493-504.
34. J. Heino, E. Somersalo, and J.P. Kaipio, Compensation for geometric mismodelling by anisotropies in optical tomography, Optic. Exp. 13 (2005), pp. 296-308.
35. A. Lehikoinen, S. Finsterle, A. Voutilainen, L.M. Heikkinen, M. Vauhkonen, and J.P. Kaipio, Approximation errors and truncation of computational domains with application to geophysical tomography, Inverse Probl. Imaging 1 (2007), pp. 371-389.
36. A. Seppänen, M. Vauhkonen, P.J. Vauhkonen, E. Somersalo, and J.P. Kaipio, Fluid dynamical models and state estimation in process tomography: Effect due to inaccuracies in flow fields, J. Electr. Imaging 10 (2001), pp. 630-640.
37. H.K. Pikkarainen, A mathematical model for electrical impedance process tomography, PhD Thesis, Helsinki University of Technology 2005.
38. H.K. Pikkarainen, State estimation approach to nonstationary inverse problems: Discretization error and filtering problem, Inverse Probl. 22 (2007), pp. 365-379.
39. J.M.J. Huttunen and J.P. Kaipio, Approximation errors in nonstationary inverse problems, Inverse Probl. Imaging 1 (2007), pp. 77-93.
40. J.M.J Huttunen and J.P. Kaipio, Approximation error analysis in non-linear state estimation with an application to state-space identification, Inverse Probl. 23 (2007), pp. 2141-2157.
41. J.M.J. Huttunen and J.P. Kaipio, Model reduction in state identification problems with an application to determination of thermal parameters, Appl. Num. Math. (2008), in press.
42. J.A. Vrugt, C.G.H. Diks, H.V. Gupta, W. Bouten, and J.M. Verstaten, Improved treatment of uncertainty in hydrologic modelling: Combining the strengths of global optimization and data assimilation, Water Resour. Res. 41 (2005), p. W01017.
43. N. Sun and W.W.G. Yeh Yeh, Identification of parameter structure in groundwater inverse problems, Water Resour. Res. 21 (1985), pp. 869-883.
44. A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice, Springer, New York, 2001.
45. L.A. Richards, Capillary conduction of liquids through porous medium, Physics 1 (1931), pp. 318-313.
46. M.T. van Genuchten, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil. Sci. Soc. Am. J. 44 (1980), pp. 892-898.
47. K. Pruess, C. Oldenburg, and G. Moridis, TOUGH2 User's Guide, Version 2.0, Report LBNL- 43134, 1999, Lawrence Berkeley National Laboratory, Berkeley, California.
48. E. Somersalo, M. Cheney, and D. Isaacson, Existence and uniqueness for electrode models for electric current computed tomography, SIAM J. Appl. Math. 52 (1992), pp. 1023-1040.
49. M. Vauhkonen, Electrical impedance tomography and prior information, PhD Thesis, University of Kuopio, Kuopio, Finland, 1997.
50. R.P. Ewing and A.G. Hunt, Dependence of the electrical conductivity on saturation in real porous media, Vadose Zone J. 5 (2006), pp. 731-741.
51. L.M. Heikkinen, J. Kourunen, J. Rastas, T. Savolainen, P.J. Vauhkonen, J.P. Kaipio, and M. Vauhkonen, Real time three-dimensional electrical impedance tomography applied to multiphase flow imaging, in 4th World Congress on Industrial Process Tomography, Aizu, Japan, September 2005, pp. 5-8.
52. K. Singha and S.M. Gorelick, Hydrogeophysical tracking of three-dimensional tracer migration: The concept and application of apparent petrophysical relations, Water Resour. Res. 42 (2006), p. W06422.
53. R.E. Kalman, A new approach to linear filtering and prediction problems, Trans. ASME J. Basic Eng. 82D (1960), pp. 3520-1345.
54. P.J. Vauhkonen, Image reconstruction in three dimensional electrical impdedance tomography, PhD Thesis, University of Kuopio, Kuopio, Finland, 2004.
55. RH. Reichle, WT. Crow, and CL. Keppenne, An adaptive ensemble Kalman filter for soil moisture data assimilation, Water Resour. Res. 44 (2008), p. W03423.
56. T. Savolainen, Modular adaptive impedance tomography system, PhD Thesis manuscript, University of Kuopio, Finland, 2008.
57. G.G. Katul, O. Wendroth, M.B. Parlange, C.E. Puente, M.V. Folegatti, and D.R. Nielsen, Estimation of in situ hydraulic conductivity function from non-linear filtering theory, Water Resour. Res. 29 (1993), pp. 1063-1070.
58. K. Singha and S.M. Gorelick, Saline tracer visualized with three-dimensional electrical resisitivity tomography: Field-scale spatial moment analysis, Water Resour. Res. 41 (2005), p. W05023.