A pattern-search-based inverse method

Water Resources Research

Volumn 48, Issue 3, 2012, Pages

  Zhou, Haiyan ^a   Gómez Hernández, J Jaime ^a   Li, Liangping ^a  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW AND TRANSPORT; FLOW DATA; HYDRAULIC HEADS; IDENTIFICATION OF MODEL; INVERSE METHODS; MAIN STRUCTURE; MODEL PARAMETERS; MODEL PREDICTION; MULTIPOINT; NON-LINEAR RELATIONSHIPS; OBJECTIVE FUNCTIONS; REFERENCE FIELD; SIMULATED MODEL; UNKNOWN PARAMETERS; UPDATED MODEL;

AQUIFERS; HYDROGEOLOGY; INVERSE PROBLEMS; PATTERN MATCHING;

COMPUTER SIMULATION;

ALGORITHM; AQUIFER CHARACTERIZATION; GAUSSIAN METHOD; GROUNDWATER FLOW; HETEROGENEITY; HYDRAULIC HEAD; MODEL VALIDATION; NONLINEARITY; OPTIMIZATION; UNCERTAINTY ANALYSIS;

EID: 84863246925     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011WR011195     Document Type: Article

References (54)

1. Alcolea, A., and P. Renard (2010), Blocking moving window algorithm: Conditioning multiple-point simulations to hydrogeological data, Water Resour. Res., 46, W08511, doi:10.1029/2009WR007943.
2. Alcolea, A., J. Carrera, and A. Medina (2006), Pilot points method incorporating prior information for solving the groundwater flow inverse problem, Adv. Water Resour., 29(11), 1678-1689. (Pubitemid 44341083)
3. Arpat, G. B., and J. Caers (2007), Conditional simulation with patterns, Math. Geol, 39(2), 177-203, doi:10.1007/s11004-006-9075-3. (Pubitemid 46760071)
4. Borg, I., and P. J. Groenen (2005), Modern Multi-dimensional Scaling: Theory and Application, 2nd ed., Springer, New York.
5. Caers, J. (2002), Geostatistical history matching under training-image based geological model constraints, paper SPE 77429 presented at SPE Annual Technical Conference and Exhibition, Soc. of Pet. Eng., San Antonio, Tex.
6. Caers, J. (2003), Efficient gradual deformation using a streamline-based proxy method, J. Pet. Sci. Eng., 39(1-2), 57-83, doi:10.1016/S0920-4105(03) 00040-8. (Pubitemid 36914834)
7. Caers, J., and T. Hoffman (2006), The probability perturbation method: A new look at Bayesian inverse modeling, Math. Geol, 38(1), 81-100, doi:10.1007/s11004-005-9005-9. (Pubitemid 43899127)
8. Capilla, J., and C. Llopis-Albert (2009), Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 1. Theory, J. Hydrol, 371(1-4), 66-74, doi:10.1016/j.jhydrol.2009.03.015.
9. Carrera, J., and S. P. Neuman (1986), Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information, Water Resour. Res., 22(2), 199-210. (Pubitemid 16477839)
10. Chen, Y., and D. Zhang (2006), Data assimilation for transient flow in geologic formations via ensemble Kalman filter, Adv. Water Resour., 29(8), 1107-1122, doi:10.1016/j.advwatres.2005.09.007. (Pubitemid 44089284)
11. Christiansen, L., P. J. Binning, D. Rosbjerg, O. B. Andersen, and P. Bauer- Gottwein (2011), Using time-lapse gravity for groundwater model calibration: An application to alluvial aquifer storage, Water Resour. Res., 47, W06503, doi:10.1029/2010WR009859.
12. de Marsily, G., F. Delay, J. Gonçalvés, P. Renard, V. Teles, and S. Violette (2005), Dealing with spatial heterogeneity, Hydrogeol. J., 13(1), 161-183, doi:10.1007/s10040-004-0432-3. (Pubitemid 40517751)
13. Deutsch, C., and T. Tran (2002), FLUVSIM: A program for object-based stochastic modeling of fluvial depositional systems, Comput. Geosci., 28(4), 525-535, doi:10.1016/S0098-3004(01)00075-9. (Pubitemid 34577639)
14. Dubuisson, M.-P., and A. K. Jain (1994), A modified Hausdorff distance for object matching, Proc. 17th IAPR Int. Conf. Pattern Recognition, 566-568, IEEE, Jerusalem, doi:10.1109/ICPR.1994.576361.
15. Duda, R. O., P. E. Hart, and D. G. Stork (2001), Pattern Classification, 2nd ed., John Wiley, New York.
16. Emsellem, Y., and G. de Marsily (1971), An automatic solution for the inverse problem, Water Resour. Res., 7(5), 1264-1283.
17. Evensen, G. (2003), The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dyn., 53(4), 343-367, doi:10.1007/ s10236-003-0036-9.
18. Falivene, O., P. Cabello, P. Arbués, J. A. Muñoz, and L. Cabrera (2009), A geostatistical algorithm to reproduce lateral gradual facies transitions: Description and implementation, Comput. Geosci, 35(8), 1642-1651, doi:10.1016/j.cageo.2008.12.003.
19. Fernàndez-Garcia, D., T. Illangasekare, and H. Rajaram (2005), Differences in the scale dependence of dispersivity and retardation factors estimated from forced-gradient and uniform flow tracer tests in threedimensional physically and chemically heterogeneous porous media, Water Resour. Res., 41, W03012, doi:10.1029/2004WR003125. (Pubitemid 40589254)
20. 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.
21. Fu, J., and J. J. Gómez-Hernández (2009), A blocking Markov chain Monte Carlo method for inverse stochastic hydrogeological modeling, Math. Geosci., 41(2), 105-128, doi:10.1007/s11004-008-9206-0.
22. Gómez-Hernández, J. J., A. Sahuquillo, and J. E. Capilla (1997), Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data-I. Theory, J. Hydrol, 203(1-4), 162-174. (Pubitemid 28118236)
23. Guardiano, F., and R. Srivastava (1993), Multivariate geostatistics: Beyond bivariate moments, in Geostatistics-Troia, edited by A. Soares, pp. 133-144, Kluwer Acad., Dordrecht, Netherlands. (Pubitemid 24391874)
24. Harbaugh, A. W., E. R. Banta, M. C. 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, Tech. Rep. Open-File Rep. 00-92, U. S. Dept. Inter., U. S. Geol. Surv., Reston, Va., 121 pp.
25. Hendricks Franssen, H. J., and W. Kinzelbach (2008), Real-time groundwater flow modeling with the ensemble Kalman filter: Joint estimation for states and parameters and the filter inbreeding problem, Water Resour. Res., 44, W09408, doi:10.1029/2007WR006505.
26. Hendricks Franssen, H. J., J. J. Gómez-Hernández, and A. Sahuquillo (2003), Coupled inverse modelling of groundwater flow and mass transport and the worth of concentration data, J. Hydrol, 281(4), 281-295, doi:10.1016/S0022-1694(03)00191-4. (Pubitemid 37332124)
27. Henrion, V., G. Caumon, and N. Cherpeau (2010), ODSIM: An objectdistance simulation method for conditioning complex natural structures, Math. Geosci., 42(8), 911-924, doi:10.1007/s11004-010-9299-0.
28. Hoeksema, R. J., and P. K. Kitanidis (1984), An application of the geostatistical approach to the inverse problem in two-dimensional groundwater modeling, Water Resour. Res., 20(7), 1003-1020.
29. Hoeksema, R. J., and P. K. Kitanidis (1985), Analysis of the spatial structure of properties of selected aquifers, Water Resour. Res., 21(4), 563-572. (Pubitemid 17269167)
30. Hu, L. Y. (2000), Gradual deformation and iterative calibration of Gaussian-related stochastic models, Math. Geol, 32(1), 87-108. (Pubitemid 30222082)
31. Hu, L. Y., and T. Chugunova (2008), Multiple-point geostatistics for modeling subsurface heterogeneity: A comprehensive review, Water Resour. Res., 44, W11413, doi:10.1029/2008WR006993.
32. Huysmans, M., and A. Dassargues (2009), Application of multiple-point geostatistics on modelling groundwater flow and transport in a crossbedded aquifer (Belgium), Hydrogeol. J., 17(8), 1901-1911, doi:10. 1007/s10040-009- 0495-2.
33. Jafarpour, B., and M. Khodabakhshi (2011), A probability conditioning method (PCM) for nonlinear flow data integration into multipoint statistical facies simulation, Math. Geosci., 43(2), 133-164, doi:10.1007/ s11004-011-9316-y.
34. Journel, A., and T. Zhang (2006), The necessity of a multiple-point prior model, Math. Geol., 38(5), 591-610, doi:10.1007/s11004-006-9031-2. (Pubitemid 44963556)
35. Kerrou, J., P. Renard, H. J. Hendricks Franssen, and I. Lunati (2008), Issues in characterizing heterogeneity and connectivity in non-multi-Gaussian media, Adv. Water Resour., 31(1), 147-159, doi:10.1016/j.advwatres.2007.07.002. (Pubitemid 350082681)
36. Kim, K. I., M. O. Franz, and B. Schölkppf (2005), Iterative kernel principal component analysis for image modeling, IEEE Trans. Pattern Anal. Mach. Intell., 27(9), 1351-1366, doi:10.1109/TPAMI. 2005.181. (Pubitemid 41387769)
37. Kitanidis, P. K. (2007), On stochastic inverse modeling, in Subsurface Hydrology: Data Integration for Properties and Processes, Geophys. Monogr. Ser., vol. 171, edited by D. W. Hyndman, F. D. Day-Lewis, and K. Singha, pp. 19-30, AGU, Washington, D. C.
38. Kitanidis, P. K., and E. G. Vomvoris (1983), A geostatistical approach to the inverse problem in groundwater modeling (steady state) and onedimensional simulations, Water Resour. Res., 19(3), 677-690. (Pubitemid 15253236)
39. Li, L., H. Zhou, H. J. Hendricks Franssen, and J. J. Gómez- Hernández (2011a), Groundwater flow inverse modeling in non-multiGaussian media: Performance assessment of the normal-score ensemble Kalman filter, Hydrol. Earth Syst. Sci. Discuss., 8(4), 6749-6788, doi:10.5194/hessd-8-6749- 2011.
40. Li, L., H. Zhou, and J. J. Gómez-Hernández (2011b), Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media, Adv. Water Resour., 34(4), 478-489, doi:10.1016/j. advwatres.2011.01.001.
41. Li, L., H. Zhou, and J. J. Gómez-Hernández (2011c), A comparative study of three-dimensional hydraulic conductivity upscaling at the macrodispersion experiment (MADE) site, Columbus Air Force Base, Mississippi (USA), J. Hydrol, 404(3-4), 278-293, doi:10.1016/j.jhydrol.2011. 05.001.
42. Mariethoz, G., P. Renard, and J. Straubhaar (2010a), The direct sampling method to perform multiple-point geostatistical simulations, Water Resour. Res., 46, W11536, doi:10.1029/2008WR007621.
43. Mariethoz, G., P. Renard, and J. Caers (2010b), Bayesian inverse problem and optimization with iterative spatial resampling, Water Resour. Res., 46, W11530, doi:10.1029/2010WR009274.
44. Mika, S., B. Schölkopf, A. J. Smola, K. R. Müller, M. Scholz, and G. Rätsch (1999), Kernel PCA and de-noising in feature spaces, Adv. Neural Inf. Process. Syst., 11(1), 536-542.
45. Neuman, S. P. (1973), Calibration of distributed parameter groundwater flow models viewed as a multiple-objective decision process under uncertainty, Water Resour. Res., 9(4), 1006-1021.
46. Oliver, D. S., L. B. Cunha, and A. C. Reynolds (1997), Markov chain Monte Carlo methods for conditioning a permeability field to pressure data, Math. Geol., 29(1), 61-91.
47. RamaRao, B., A. LaVenue, G. de Marsily, and M. Marietta (1995), Pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields: 1. Theory and computational experiments, Water Resour. Res., 31(3), 475-493. (Pubitemid 26437835)
48. Rubin, Y., X. Chen, H. Murakami, and M. Hahn (2010), A Bayesian approach for inverse modeling, data assimilation, and conditional simulation of spatial random fields, Water Resour. Res., 46, W10523, doi:10.1029/2009WR008799.
49. Strebelle, S. (2002), Conditional simulation of complex geological structures using multiple-point statistics, Math. Geol, 34(1), 1-21. (Pubitemid 41444773)
50. Suzuki, S., and J. Caers (2008), A distance-based prior model parameterization for constraining solutions of spatial inverse problems, Math. Geosci., 40(4), 445-469, doi:10.1007/s11004-008-9154-8.
51. Wen, X. H., J. E. Capilla, C. V. Deutsch, J. J. Gómez- Hernández, and A. S. Cullick (1999), A program to create permeability fields that honor singlephase flow rate and pressure data, Comput. Geosci, 25(3), 217-230. (Pubitemid 29294537)
52. Zhang, T., P. Switzer, and A. Journel (2006), Filter-based classification of training image patterns for spatial simulation, Math. Geol., 38(1), 63-80, doi:10.1007/s11004-005-9004-x. (Pubitemid 43899126)
53. Zhou, H., J. J. Gómez-Hernández, H.-J. Hendricks Franssen, and L. Li (2011), An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filter, Adv. Water Resour., 34(7), 844-864, doi:10.1016/j.advwatres.2011.04.014.
54. Zhou, H., L. Li, H.-J. Hendricks Franssen, and J. J. Gómez- Hernández (2012), Pattern recognition in a bimodal aquifer using the normal-score ensemble Kalman filter, Math. Geosci., 44(2), 169-185, doi:10.1007/s11004-011-9372-3.