Physically based regularization of hydrogeophysical inverse problems for improved imaging of process-driven systems

Water Resources Research

Volumn 49, Issue 10, 2013, Pages 6238-6247

  Oware, E K ^a   Moysey, S M J ^a   Khan, T ^b  

^a Clemson University   (United States)

^b CLEMSON UNIVERSITY   (United States)

Author keywords

coupled inversion; electrical resistivity imaging; flow and transport; inverse theory; prior models; proper orthogonal decomposition

Indexed keywords

COUPLED INVERSION; ELECTRICAL RESISTIVITY IMAGING; FLOW AND TRANSPORT; INVERSE THEORY; PROPER ORTHOGONAL DECOMPOSITIONS;

GEOPHYSICS; IMAGING TECHNIQUES; INVERSE PROBLEMS; MEAN SQUARE ERROR; MONTE CARLO METHODS; PRINCIPAL COMPONENT ANALYSIS;

RESEARCH;

CONCEPTUAL FRAMEWORK; ERROR ANALYSIS; GEOPHYSICAL METHOD; HYDROGEOLOGY; IMAGING METHOD; INVERSE PROBLEM; MONTE CARLO ANALYSIS; SIMULATION;

EID: 84884859265     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/wrcr.20462     Document Type: Article

References (27)

1. Banks, H. T., M. L. Joyner, B. Wincheski, and, W. P. Winfree, (2000), Nondestructive evaluation using a reduced-order computational methodology, Inverse Probl., 16, 929-945.
2. Coleman, T. F., and, Y. Li, (1996), An interior, trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim. 6, 418-445.
3. Daily, W., and, A. Ramirez, (1995), Electrical-resistance tomography during in-situ trichloroethylene remediation at the Savanna river site, J. Appl. Geophys., 33, 239-249.
4. De Josselin De Jong, G., (1958), Longitudinal and transverse diffusion in granular deposits, Trans. AGU, 39, 1-6.
5. Deutsch, C. V., and, A. G. Journel, (1998), GSLIB: Geostatistical Software Library and User's Guide, Oxford Univ. Press, New York.
6. Ferré, T., L. Bentley, A. Binley, N. Linde, A. Kemna, K. Singha, K. Holliger, J. A. Huisman, and, B. Minsley, (2009), Critical steps for the continuing advancement of hydrogeophysics, EOS Trans. AGU, 90 (23), 200, doi: 10.1029/2009Eo230004.
7. Fowler, D. E., and, S. M. J. Moysey, (2011), Estimation of aquifer transport parameters from resistivity monitoring data within a coupled inversion framework, J. Hydrol., 409, 545-554, doi: 10.1016/j.jhydrol.2011.08.063.
8. Freeze, R. A., and, J. A. Cherry, (1979), Groundwater, 604 pp., Prentice-Hall, Englewood Cliffs, N. J.
9. Freyberg, D. L., (1986), A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers, Water Resour. Res., 22 (13), 2031-2046, doi: 10.1029/WR022i013p02031.
10. Greenhalgh, S. A., Z. Bing, and, A. Green, (2006), Solutions, algorithms and inter-relationshi (Pubitemid 43970077)
11. Hinnell, A. C., T. P. A. Ferre, J. A. Vrugt, J. A. Huisman, S. Moysey, J. Rings, and, M. B. Kowalsky, (2010), Improved extraction of hydrologic information from geophysical data through coupled hydrogeophysical inversion, Water Res. Res., 46, W00D40, doi: 10.1029/2008WR007060.
12. Jin, B., T. Khan, and, P. Maass, (2011), A reconstruction algorithm for electrical impedance tomography based on sparsity regularization, Int. J. Num. Meth. Eng., 89, 337-353, doi: 10.1002/nme.3247.
13. Kemna, A., J. Vanderborght, 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, 125-146. (Pubitemid 35180814)
14. Kunisch, K., and, S. Volkwein, (2003), Galerkin proper orthogonal decomposition for a general equation in fluid dynamics, SIAM J. Numer. Anal., 40 (2), 492-515.
15. LaBrecque, D. J., and, X. Yang, (2001), Difference inversion of ERT data: A fast inversion method for 3-D in-situ monitoring, J. Environ. Eng. Geophys., 6 (2), 83-89.
16. Lehikoinen, A., J. M. J. Huttunen, S. Finsterle, M. B. Kowalsky, and, J. P. Kaipio, (2010), Dynamic inversion for hydrogeophysical process monitoring with electrical resistance tomography under model uncertainties, Water Resour. Res., 46, W04513, doi: 10.1029/2009WR008470.
17. Lesmes, D. P., and, S. P. Friedman, (2005), Relationships between the electrical and hydrogeological properties of rocks and soils, in Hydrogeophysics, edited by, Y. Rubin, and, S. S. Hubbard, pp. 87-128, Springer, Dordrecht, Netherlands.
18. 1-norm regularization of wavelet coefficients, Geophys. J. Int., 170, 359-370, doi: 10.1111/j.1365-246X.2007.03409.x. (Pubitemid 47039672)
19. Moysey, M. S., K. Singha, and, R. Knight, (2005), A framework for inferring field-scale rock physics relationship through numerical simulation, Geophys. Res. Lett., 32, L08304, doi: 10.1029/2004GL022152. (Pubitemid 41043242)
20. Pidlisecky, A., E. Haber, and, R. Knight, (2007), RESINVM3D: A 3D resistivity inversion package, Geophysics, 72 (2), H1-H10, doi: 10.1190/1.2402499. (Pubitemid 46403872)
21. Pidlisecky, A., K. Singha, and, F. D. Day-Lewis, (2011), A distribution-based parameterization for improved tomographic imaging of solute plumes, Geophys. J. Int., 187, 214-224, doi: 10.1111/j.1365-246X.2011.05131.x.
22. Pinnau, R., (2008), Model reduction via proper orthogonal decomposition, in Model Order Reduction: Theory, Research Aspects and Applications, edited by, W. H. A. Schilder, and, H. van der Vorst, pp. 96-109, Springer, New York.
23. Rathinam, M., and, L. R. Petzold, (2004), A new look at proper orthogonal decomposition, SIAM J. Numer. Anal., 41 (5), 1893-1925.
24. Rucker, D. F., and, T. P. A. Ferré, (2004), Parameter estimation for soil hydraulic properties using zero-offset borehole radar: Analytical method, Soil Sci. Soc. Am. J., 68, 1560-1567. (Pubitemid 39218920)
25. Singha, K., and, S. M. Gorelick, (2005), Saline tracer visualized with three-dimensional electrical resistivity tomography: Field-scale spatial moment analysis, Water Resour. Res., 41, W05023, doi: 10.1029/2004WR003460. (Pubitemid 40856473)
26. Strebelle, S., 2000, Sequential simulation drawing structures from training images, PhD dissertation, 187 pp., Stanford Univ., Stanford, Calif.
27. Tikhonov, A. N., and, V. Y. Arsenin, (1977), Solutions of Ill-Posed Problems, John Wiley and Sons, New York.