Geostatistical inversing for large-contrast transmissivity fields

Stochastic Environmental Research and Risk Assessment

Volumn 23, Issue 5, 2009, Pages 565-577

  Zanini, Andrea ^a   Kitanidis, Peter K ^b  

^a UNIVERSITY OF PARMA   (Italy)

^b Stanford University   (United States)

Author keywords

Geostatistics; MCMC; Quasilinear; Tranmissivity estimation

Indexed keywords

BEST ESTIMATES; COMPUTATIONAL COSTS; DERIVATIVE-FREE; ESTIMATION VARIANCE; FIELD PARAMETERS; GAUSS-NEWTON ITERATION; GEOSTATISTICAL; GEOSTATISTICS; GROUNDWATER MODELING; HIGH CONTRAST; HYDRAULIC HEADS; INVERSE APPROACH; LINE SEARCHES; MARKOV CHAIN MONTE CARLO; MCMC; METROPOLIS-HASTINGS ALGORITHM; NUMERICAL RESULTS; POLISHING STEPS; QUASILINEAR; TRANMISSIVITY ESTIMATION; TRANSMISSIVITY; TRANSMISSIVITY FIELD;

APPROXIMATION ALGORITHMS; GROUNDWATER; HYDROGEOLOGY; ITERATIVE METHODS; LINEARIZATION; MARKOV PROCESSES;

PARAMETER ESTIMATION;

GEOSTATISTICS; HYDRAULIC HEAD; INVERSE PROBLEM; MARKOV CHAIN; MODELING; MONTE CARLO ANALYSIS; TRANSMISSIVITY;

EID: 67349145692     PISSN: 14363240     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00477-008-0241-7     Document Type: Article

References (49)

1. Bates BC, Campbell EP (2001) A Markov Chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling. Water Resour Res 37(4):937-947
2. Brent RP (1973) Algorithms for minimization without derivatives. Prentice-Hall, Englewood Cliffs
3. Carrera J (1987) State of the art of the inverse problem applied to the flow and solute transport problems. In: Curtodio E, Gurgui A, Lobo-Ferreira JP (eds) Groundwater flow and quality modeling (NATO ASI Series). Reidel, Hingham, pp 549-585
4. Chen J, Hubbard S, Rubin Y, Murray C, Roden E, Majer E (2004) Geochemical characterization using geophysical data and Markov Chain Monte Carlo methods: A case study at the South Oyster bacterial transport site in Virginia. Water Resour Res 40, doi: 10.1029/ 2003WR002883
5. Chib S, Greenberg E (1995) Understanding the Metropolis-Hastings algorithm. Am Stat 49(4):327-335
6. Dagan G (1985) Stochastic modeling of groundwater-flow by unconditional and conditional probabilities: The inverse problem. Water Resour Res 21(1):65-72
7. Feyen L, Ribeiro Jr PJ, Gòmez-Hernández JJ, Beven KJ, De Smedt F (2003) Bayesian methodology for stochastic capture zone delineation incorporating transmissivity measurements and hydraulic head observations. J Hydrol 271:156-170
8. Forsythe GE, Malcom MA, Moler CB (1976) Computer methods for mathematical computations. Prentice-Hall, New Jersey
9. Fritz J, Nowak W, Neuweiler I (2008) FFT-based algorithms for Kriging (Submitted to Mathematical Geology)
10. Ginn TR, Cushman JH (1990) Inverse methods for subsurface flow: A critical review of stochastic techniques. Stoch Hydrol Hydraul 4:1-26
11. Gòmez-Hernández JJ, Sahuquillo A, Capilla JE (1997) Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data-1 theory. J Hydrol 203:162-174
12. Gutjahr AL, Wilson JL (1989) Co-kriging for stochastic models. Transp Porous Media 4(6):585-598
13. Gutjahr AL, Bulard B, Hatch S, Hughson L (1994) Joint conditional simulations and the spectral approach for flow modeling. Stoch Hydrol Hydraul 8(1):79-108
14. Hanna S, Yeh TCJ (1998) Estimation of co-conditional moments of transmissivity, hydraulic head, and velocity fields. Adv Water Resour 22(1):87-95
15. Harter T, Yeh TCJ (1996a) Stochastic analysis of solute transport in heterogeneous, variability saturated soils. Water Resour Res 32(6):1585-1595
16. Harter T, Yeh TCJ (1996b) Conditional stochastic analysis of solute transport in heterogeneous, variably saturated soils. Water Resour Res 32(6):1597-1609
17. Harvey CF, Gorelick S (1995) Mapping hydraulic conductivity: Sequential conditioning with measurements of solute arrival time, hydraulic head, and local conductivity. Water Resour Res 31(7):1615-1626
18. Hill MC, Tiedeman C (2007) Effective groundwater model calibration, Wiley, London
19. Hoeksema RJ, Kitanidis PK (1984) An application of the geostatistical approach to the inverse problem in two-dimensional groundwater modeling. Water Resour Res 20(7):1003-1020
20. Hoeksema RJ, Kitanidis PK (1989) Prediction of transmissivities, heads, and seepage velocities using mathematical modeling and geostatistics. Adv Water Resour 12:90-101
21. Kitanidis PK (1991) Orthonormal residuals in geostatistics: Model criticism and parameter estimation. Math Geol 23:741-758
22. Kitanidis PK (1995) Quasi-linear geostatistical theory for inversing. Water Resour Res 31(10):2411-2419
23. Kitanidis PK (1996) On the geostatistical approach to the inverse problem. Adv Water Resour 19(6):333-342
24. Kitanidis PK (1997) Introduction to geostatistics, applications in hydrogeology. Cambridge University Press, New York
25. Kitanidis PK, Vomvoris EG (1983) A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations. Water Resour Res 19(3):677-690
26. Li B, Yeh TCJ (1999) Cokriging estimation of the conductivity field under variably saturated flow conditions. Water Resour Res 35(12):3663-3674
27. Marshall L, Nott D, Sharma A (2004) A comparative study of Markov Chain Monte Carlo methods for conceptual rainfall-runoff modeling. Water Resour Res 40:W02501
28. Mathworks (2002), MATLAB
29. McLaughlin D, Townley LR (1996) A reassessment of the groundwater inverse problem. Water Resour Res 32(5):1131-1161
30. Michalak AM (2003) Application of Bayesian inference methods to inverse modeling for contaminant source identification. Phd Thesis, Stanford University, Stanford
31. Michalak AM, Kitanidis PK (2003) A method for enforcing parameter non-negativity in Bayesian inverse problems with an application to contaminant source identification. Water Resour Res 39(2) SBH 7-1, pp 7-14
32. Michalak AM, Kitanidis PK (2004) Application of geostatistical inverse modeling to contaminant source identification at Dover AFB, Delaware. J Hydraul Res 42 Extra issue, pp 9-18
33. Nowak W (2005) Geostatistical methods for the identification of flow and transport parameters in the subsurface. Phd Thesis, Stuttgart University, Stuttgart
34. Nowak W, Tenklenve S, Cirpka OA (2003) Efficient computation of linearized cross-covariance matrices of interdependent quantities. Math Geol 35(1):53-66
35. Rubin Y, Dagan G (1987a) Stochastic identification of transmissivity and effective recharge in steady groundwater flow, 1, Theory. Water Resour Res 23(7):1185-1192
36. Rubin Y, Dagan G (1987b) Stochastic identification of transmissivity and effective recharge in steady groundwater flow, 2, case-study. Water Resour Res 23(7):1193-1200
37. Rubin Y, Dagan G (1988) Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, 1, constant head boundary. Water Resour Res 24(10):1689-1697
38. Rubin Y, Dagan G (1989) Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers, 2, impervious boundary. Water Resour Res 25(4):707-712
39. Sun NZ (1994) Inverse problems in groundwater modeling. Kluwer, Norwell
40. Tamminen J, Kyrölä E (2001) Bayesian solution for nonlinear and non-Gaussian inverse problems by Markov chain Monte Carlo method? J Geophys Res 106(14):377-390
41. Vrugt JA, Gupta HV, Bouten W, Sorooshian S (2003) A suhffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resour Res 39:8
42. Yeh WWG (1986) Review of parameter identification procedures in groundwater hydrology: The inverse problem. Water Resour Res 22(1): 95-108
43. Yeh TCJ, Zhang J (1996) A geostatistical inverse method for variably saturated flow in the vadose zone. Water Resour Res 32(9):2757-2766
44. Yeh TCJ, Gutjahr AL, Jin M (1995) An iterative cokriging-like technique for groundwater flow modeling. Ground Water 33:33-41
45. Yeh TCJ, Minghui J, Hanna S (1996) An iterative stochastic inverse method: Conditional effective transmissivity and hydraulic head fields. Water Resour Res 32(1):85-92
46. Yeh TCJ, Liu S, Glass RJ, Baker K, Brainard JR, Alumbaugh D, LaBrecque D (2002) A geostatistically based inverse model for electrical resistivity surveys and its applications to vadose zone hydrology. Water Resour Res 38:12
47. Zanini A (2006) Geostatistical approach for solving inverse problems in groundwater: Applications and improvements. Phd Thesis, Parma University, Parma, Italy
48. Zhang J, Yeh TCJ (1997) An iterative geostatistical inverse method for steady flow in the vadose zone. Water Resour Res 33:63-71
49. Zimmerman DA, DeMarsily G, Gotway CA, Marietta MG, Axness CL, Beauheim RL, Bras RL, Carrera J, Dagan G, Davies PB, Gallegos DP, Galli A, Gòmez-Hernánde JJ, Grindrod P, Gutjahr AL, Kitanidis PK, Lavenue AM, McLaughlin D, Neuman SP, RamaRao BS, Ravenne C, Rubin Y (1998) A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow. Water Resour Res 34(6):1373-1413