An interactive bayesian geostatistical inverse protocol for hydraulic tomography

Water Resources Research

Volumn 44, Issue 12, 2008, Pages

  Fienen, Michael N ^a   Clemo, Tom ^b   Kitanidis, Peter K ^c  

^a WISCONSIN WATER SCIENCE CENTER   (United States)

^b BOISE STATE UNIVERSITY   (United States)

^c Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ECONOMIC AND SOCIAL EFFECTS; HYDROGEOLOGY; IMAGE SEGMENTATION; TOMOGRAPHY;

CROSS VALIDATION; HYDRAULIC PARAMETERS; HYDRAULIC TOMOGRAPHIES; HYDROGEOLOGIC PARAMETER; INTERACTIVE PROTOCOLS; PARAMETER COVARIANCE; PRIOR INFORMATION; REGION OF INTEREST;

INVERSE PROBLEMS;

EID: 84981720392     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1029/2007WR006730     Document Type: Article

References (57)

1. Batu, V. (1998), Aquifer Hydraulics: A Comprehensive Guide to Hydrogeologic Data Analysis, John Wiley, New York.
2. Bohling, G. C. (1993), Hydraulic tomography in two-dimensional, steadystate groundwater flow, Eos Trans. AGU, 74(16), Spring Meet. Suppl., 141.
3. Bohling, G. C., X. Zhan, J. J. Butler Jr., and L. Zheng (2002), Steady shape analysis of tomographic pumping tests for characterization of aquifer heterogeneities, Water Resour. Res., 38(12), 1324 doi:10.1029/2001WR001176.
4. Bohling, G. C., J. J. Butler Jr., X. Zhan, and M. D. Knoll (2007), A field assessment of the value of steady shape hydraulic tomography for characterization of aquifer heterogeneities, Water Resour. Res., 43, W05430 doi:10.1029/2006WR004932.
5. Brauchler, R. (2005), Characterization of fractured porous media using multivariate statistics and hydraulic travel time tomography, Ph.D. dissertation, Univ. Tübingen, Tübingen, Germany.
6. Butler, J. J., Jr., C. D. McElwee, and G. C. Bohling (1999), Pumping tests in networks of multilevel sampling wells: Motivation and methodology, Water Resour. Res., 35(11), 3553-3560 doi:10.1029/1999WR900231.
7. Caers, J., and T. Zhang (2004), Multiple-point geostatistics: A quantitative vehicle for integrating geologic analogs into multiple reservoir models, in Integration of Outcrop and Modern Analogs in Reservoir Modeling, edited by G. M. Grammer, P. M. Harris, and G. P. Eberli, AAPG Mem., 80, 383-394.
8. Clemo, T. (2007), MODFLOW-2005 ground water model—User guide to the adjoint state based sensitivity process (ADJ), Tech. Rep. BSU CGISS 07-01, Boise State Univ., Boise, Idaho.
9. Fetter, C. (1994), Applied Hydrogeology, 3rd ed., Prentice-Hall, Upper Saddle River, N. J.
10. Feyen, L., and J. Caers (2006), Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations, Adv. Water Resour., 29(6), 912-929 doi:10.1016/j.advwatres.2005.08.002.
11. Fienen, M. N. (2007), Inverse methods for nearfield hydrogeologic characterization, Ph.D. dissertation, Stanford Univ., Stanford, Calif.
12. Fienen, M. N., P. K. Kitanidis, D. Watson, and P. Jardine (2004), An application of Bayesian inverse methods to vertical deconvolution of hydraulic conductivity in a heterogeneous aquifer at Oak Ridge National Laboratory, Math. Geol., 36(1), 101-126 doi:10.1023/B:MATG.0000016232.71993.bd.
13. Fienen, M. N., J. Luo, and P. K. Kitanidis (2006), A Bayesian geostatistical transfer function approach to tracer test analysis, Water Resour. Res., 42, W07426 doi:10.1029/2005WR004576.
14. 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.
15. Gaganis, P., and L. Smith (2001), A Bayesian approach to the quantification of the effect of model error on the predictions of groundwater models, Water Resour. Res., 37(9), 2309-2322 doi:10.1029/2000WR000001.
16. Gallagher, M. R., and J. Doherty (2007), Parameter interdependence and uncertainty induced by lumping in a hydrologic model, Water Resour. Res., 43, W05421 doi:10.1029/2006WR005347.
17. Giudici, M., G. Morossi, G. Parravicini, and G. Ponzini (1995), A new method for the identification of distributed transmissivities, Water Resour. Res., 31(8), 1969-1988 doi:10.1029/95WR01205.
18. Gottlieb, J., and P. Dietrich (1995), Identification of the permeability distribution in soil by hydraulic tomography, Inverse Probl., 11(2), 353-360 doi:10.1088/0266-5611/11/2/005.
19. Harbaugh, A. W., E. W. Banta, M. Hill, and M. G. McDonald (2000), MODFLOW-2000, the U.S. Geological Survey modular ground-water model—User guide to modularization concepts and the ground-water flow process, U. S. Geol. Surv. Open File Rep., 00-92.
20. Hoeksema, R. J., and P. K. Kitanidis (1984),An application of the geostatistical approach to the inverse problemin two-dimensional groundwater modeling, Water Resour. Res., 20(7), 1003-1020 doi:10.1029/WR020i007p01003.
21. Hyndman, D. W., J. M. Harris, and S. M. Gorelick (2000), Inferring the relation between seismic slowness and hydraulic conductivity in heterogeneous aquifers, Water Resour. Res., 36(8), 2121-2132 doi:10.1029/2000WR900112.
22. Illman, W. A., X. Liu, and A. Craig (2007), Steady-state hydraulic tomography in a laboratory aquifer with deterministic heterogeneity: Multimethod and multiscale validation of hydraulic conductivity tomograms, J. Hydrol., 341(3-4), 222-234 doi:10.1016/j.jhydrol.2007.05.011.
23. Journel, A. G. (1983), Nonparametric estimation of spatial distributions, Math. Geol., 15(3), 445-468 doi:10.1007/BF01031292.
24. Kitanidis, P. K. (1991), Orthonormal residuals in geostatistics:Model criticism and parameter estimation, Math. Geol., 23(5), 741-758 doi:10.1007/BF02082534.
25. Kitanidis, P. K. (1995), Quasi-linear geostatistical theory for inversing, Water Resour. Res., 31(10), 2411-2419 doi:10.1029/95WR01945.
26. Kitanidis, P. K. (1997), Introduction to Geostatistics: Applications in Hydrogeology, Cambridge Univ. Press, New York.
27. Kitanidis, P. K. (1998), How observations and structure affect the geostatistical solution to the steady-state inverse problem, Ground Water, 36(5), 754-763 doi:10.1111/j.1745-6584.1998.tb02192.x.
28. Kruseman, G. P., and N. A. De Ridder (1990), Analysis and Evaluation of Pumping Test Data, 2nd ed., Int. Inst. for Land Reclam. and Impr., Wageningen, Netherlands.
29. Kunstmann, H., W. Kinzelbach, P. Marschall, and G. Li (1997), Joint inversion of tracer tests using reversed flow fields, J. Contam. Hydrol., 26(1-4), 215-226 doi:10.1016/S0169-7722(96)00070-8.
30. Li, W., and O. A. Cirpka (2006), Efficient geostatistical inverse methods for structured and unstructured grids, Water Resour. Res., 42, W06402 doi:10.1029/2005WR004668.
31. Li, W., W. Nowak, and O. A. Cirpka (2005), Geostatistical inverse modeling of transient pumping tests using temporal moments of drawdown, Water Resour. Res., 41, W08403 doi:10.1029/2004WR003874.
32. Li, W., A. Englert, O. A. Cirpka, J. Vanderborght, and H. Vereecken (2007), Two-dimensional characterization of hydraulic heterogeneity by multiple pumping tests, Water Resour. Res., 43, W04433 doi:10.1029/2006WR005333.
33. Liu, S., T.-C. J. Yeh, and R. Gardiner (2002), Effectiveness of hydraulic tomography: Sandbox experiments, Water Resour. Res., 38(4), 1034 doi:10.1029/2001WR000338.
34. Liu, X., W. A. Illman, A. J. Craig, J. Zhu, and T.-C. J. Yeh (2007), Laboratory sandbox validation of transient hydraulic tomography, Water Resour. Res., 43, W05404 doi:10.1029/2006WR005144.
35. Mackay, D. M., D. L. Freyberg, P. V. Roberts, and J. A. Cherry (1986), A natural gradient experiment on solute transport in a sand aquifer: 1. Approach and overview of plume movement, Water Resour. Res., 22(13), 2017-2029 doi:10.1029/WR022i013p02017.
36. Michalak, A. M., and P. K. Kitanidis (2003), A method for enforcing parameter nonnegativity in Bayesian inverse problems with an application to contaminant source identification, Water Resour. Res., 39(2), 1033 doi:10.1029/2002WR001480.
37. Nowak, W., and O. A. Cirpka (2004), A modified Levenberg-Marquardt algorithm for quasi-linear geostatistical inversing, Adv. Water Resour., 27(7), 737-750 doi:10.1016/j.advwatres.2004.03.004.
38. Oliver, D. S., and S. Aramco (1990), The averaging process in permeability estimation from well-test data, SPE Form. Eval., 5(3), 319-324 doi:10.2118/19845-PA.
39. Portniaguine, O., and M. S. Zhdanov (1999), Focusing geophysical inversion images, Geophysics, 64(3), 874-887 doi:10.1190/1.1444596.
40. Portniaguine, O., and M. S. Zhdanov (2002), 3-D magnetic inversion with data compression and image focusing, Geophysics, 67(5), 1532-1541 doi:10.1190/1.1512749.
41. Sharma, P. V. (1997), Environmental and Engineering Geophysics, Cambridge Univ. Press, Cambridge, U. K.
42. Slichter, C. S. (1899), Theoretical investigation of the motion of ground waters, in 19th Annual Report of the U.S. Geological Survey, Part II, pp. 295-384, Washington, D. C.
43. Snodgrass, M. F., and P. K. Kitanidis (1998), Transmissivity identification through multi-directional aquifer stimulation, Stochastic Hydrol. Hydraul., 12(5), 299-316 doi:10.1007/s004770050023.
44. Straface, S., T.-C. J. Yeh, J. Zhu, S. Troisi, and C. H. Lee (2007), Sequential aquifer tests at a well field, Montalto Uffugo Scalo, Italy, Water Resour. Res., 43, W07432 doi:10.1029/2006WR005287.
45. Sun, N.-Z. (1994), Inverse Problems in Groundwater Modeling, Theor. Appl. Transp. Porous Media, vol. 6, Kluwer Acad., Dordrecht, Netherlands.
46. Sykes, J. F., J. L. Wilson, and R. W. Andrews (1985), Sensitivity analysis for steady state groundwater flow using adjoint operators, Water Resour. Res., 21(3), 359-371 doi:10.1029/WR021i003p00359.
47. Theis, C. V. (1935), The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage, Eos Trans. AGU, 2, 519-524.
48. Thiem, G. (1906), Hydrologische Methoden, 56 pp., Gebhart, Leipzig, Germany.
49. Tiedeman, C. R., and P. A. Hsieh (2004), Evaluation of longitudinal dispersivity estimates from simulated forced-and natural-gradient tracer tests in heterogeneous aquifers, Water Resour. Res., 40, W01512 doi:10.1029/2003WR002401.
50. Tosaka, H., K. Masumoto, and K. Kojima (1993), Hydropulse tomography for identifying 3-D permeability distribution, paper presented at 4th Annual International Conference on High Level Radioactive Waste Management, Am. Soc. of Civ. Eng., Las Vegas, Nev., 26-30 April.
51. Tronicke, J., K. Holliger, W. Barrash, and M. D. Knoll (2004), Multivariate analysis of cross-hole georadar velocity and attenuation tomograms for aquifer zonation, Water Resour. Res., 40, W01519 doi:10.1029/2003WR002031.
52. Vasco, D. W., and A. Datta-Gupta (1999), Asymptotic solutions for solute transport: A formalism for tracer tomography, Water Resour. Res., 35(1), 1-16 doi:10.1029/98WR02742.
53. Vasco, D. W., H. Keers, and K. Karasaki (2000), Estimation of reservoir properties using transient pressure data: An asymptotic approach, Water Resour. Res., 36(12), 3447-3465 doi:10.1029/2000WR900179.
54. Yeh, T.-C. J., and C.-H. Lee (2007), Time to change the way we collect and analyze data for aquifer characterization, Ground Water, 45(2), 116-118 doi:10.1111/j.1745-6584.2006.00292.x.
55. Yeh, T.-C. J., and S. Liu (2000), Hydraulic tomography: Development of a new aquifer test method, Water Resour. Res., 36(8), 2095-2105 doi:10.1029/2000WR900114.
56. Zanini, A., and P. K. Kitanidis (2008), Geostatistical inversing for largecontrast transmissivity fields, Stochastic Environ. Res. Risk Assess., in press.
57. Zhu, J., and T.-C. J. Yeh (2006), Analysis of hydraulic tomography using temporal moments of drawdown recovery data, Water Resour. Res., 42, W02403 doi:10.1029/2005WR004309.