메뉴 건너뛰기




Volumn 50, Issue 7, 2014, Pages 5410-5427

Large-scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA)

Author keywords

matrix free; PCGA; Principal Component Geostatistical Approach; randomized eigen decomposition; randomized SVD

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; COVARIANCE MATRIX; DIFFERENTIAL EQUATIONS; DIGITAL STORAGE; INVERSE PROBLEMS; ITERATIVE METHODS; JACOBIAN MATRICES; SCALABILITY; STOCHASTIC SYSTEMS; TOMOGRAPHY; UNCERTAINTY ANALYSIS;

EID: 84906101878     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2014WR015483     Document Type: Article
Times cited : (104)

References (43)
  • 1
    • 84890566434 scopus 로고    scopus 로고
    • Large-scale stochastic linear inversion using hierarchical matrices
    • Ambikasaran, S., J. Y. Li, P. K. Kitanidis, and, E. Darve, (2013), Large-scale stochastic linear inversion using hierarchical matrices, Comput. Geosci., 17 (6), 913-927.
    • (2013) Comput. Geosci. , vol.17 , Issue.6 , pp. 913-927
    • Ambikasaran, S.1    Li, J.Y.2    Kitanidis, P.K.3    Darve, E.4
  • 2
    • 84877696912 scopus 로고    scopus 로고
    • Extreme-scale UQ for Bayesian inverse problems governed by PDEs, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, IEEE Computer Society Press.
    • Bui-Thanh, T., C. Burstedde, O. Ghattas, J. Martin, G. Stadler, and, L. C. Wilcox, (2012), Extreme-scale UQ for Bayesian inverse problems governed by PDEs, in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pp. 1-11, IEEE Computer Society Press.
    • (2012) , pp. 1-11
    • Bui-Thanh, T.1    Burstedde, C.2    Ghattas, O.3    Martin, J.4    Stadler, G.5    Wilcox, L.C.6
  • 3
    • 84055188748 scopus 로고    scopus 로고
    • 3-D transient hydraulic tomography in unconfined aquifers with fast drainage response
    • doi: 10.1029/2010WR010367.
    • Cardiff, M., and, W. Barrash, (2011), 3-D transient hydraulic tomography in unconfined aquifers with fast drainage response, Water Resour. Res., 47, W12518, doi: 10.1029/2010WR010367.
    • (2011) Water Resour. Res. , vol.47
    • Cardiff, M.1    Barrash, W.2
  • 6
    • 0034306672 scopus 로고    scopus 로고
    • Sensitivity of temporal moments calculated by the adjoint-state method and joint inversing of head and tracer data
    • Cirpka, O. A., and, P. K. Kitanidis, (2000), Sensitivity of temporal moments calculated by the adjoint-state method and joint inversing of head and tracer data, Adv. Water Resour., 24 (1), 89-103.
    • (2000) Adv. Water Resour. , vol.24 , Issue.1 , pp. 89-103
    • Cirpka, O.A.1    Kitanidis, P.K.2
  • 7
    • 2942653250 scopus 로고    scopus 로고
    • Algorithm 832: Umfpack v4.3 - An unsymmetric-pattern multifrontal method
    • Davis, T. A., (2004), Algorithm 832: Umfpack v4.3-An unsymmetric-pattern multifrontal method, ACM Trans. Math. Software, 30 (2), 196-199.
    • (2004) ACM Trans. Math. Software , vol.30 , Issue.2 , pp. 196-199
    • Davis, T.A.1
  • 8
    • 84864777094 scopus 로고    scopus 로고
    • Reverse flow routing in open channels: A Bayesian geostatistical approach
    • D'Oria, M., and, M. G. Tanda, (2012), Reverse flow routing in open channels: A Bayesian geostatistical approach, J. Hydrol., 460, 130-135.
    • (2012) J. Hydrol. , vol.460 , pp. 130-135
    • D'Oria, M.1    Tanda, M.G.2
  • 9
    • 0029657366 scopus 로고    scopus 로고
    • A geostatistical approach to the conditional estimation of spatially distributed solute concentration and notes on the use of tracer data in the inverse problem
    • Ezzedine, S., and, Y. Rubin, (1996), A geostatistical approach to the conditional estimation of spatially distributed solute concentration and notes on the use of tracer data in the inverse problem, Water Resour. Res., 32 (4), 853-861.
    • (1996) Water Resour. Res. , vol.32 , Issue.4 , pp. 853-861
    • Ezzedine, S.1    Rubin, Y.2
  • 10
    • 70349778650 scopus 로고    scopus 로고
    • Obtaining parsimonious hydraulic conductivity fields using head and transport observations: A bayesian geostatistical parameter estimation approach
    • doi: 10.1029/2008WR007431.
    • Fienen, M., R. Hunt, D. Krabbenhoft, and, T. Clemo, (2009), Obtaining parsimonious hydraulic conductivity fields using head and transport observations: A bayesian geostatistical parameter estimation approach, Water Resour. Res., 45, W08405, doi: 10.1029/2008WR007431.
    • (2009) Water Resour. Res. , vol.45
    • Fienen, M.1    Hunt, R.2    Krabbenhoft, D.3    Clemo, T.4
  • 11
    • 79952307064 scopus 로고    scopus 로고
    • Fast algorithms for bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial hessian approximations
    • Flath, H. P., L. C. Wilcox, V. Akcelik, J. Hill, B. V. Waanders, and, O. Ghattas, (2011), Fast algorithms for bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial hessian approximations, SIAM J. Sci. Comput., 33 (1), 407-432.
    • (2011) SIAM J. Sci. Comput. , vol.33 , Issue.1 , pp. 407-432
    • Flath, H.P.1    Wilcox, L.C.2    Akcelik, V.3    Hill, J.4    Waanders, B.V.5    Ghattas, O.6
  • 12
    • 70349731909 scopus 로고    scopus 로고
    • The black-box fast multipole method
    • Fong, W., and, E. Darve, (2009), The black-box fast multipole method, J. Comput. Phys., 229 (23), 8712-8725.
    • (2009) J. Comput. Phys. , vol.229 , Issue.23 , pp. 8712-8725
    • Fong, W.1    Darve, E.2
  • 13
    • 10444261986 scopus 로고    scopus 로고
    • Finite elements for elliptic problems with stochastic coefficients
    • DOI 10.1016/j.cma.2004.04.008, PII S0045782504003299
    • Frauenfelder, P., C. Schwab, and, R. A. Todor, (2005), Finite elements for elliptic problems with stochastic coefficients, Comput. Methods Appl. Mech. Eng., 194 (2-5), 205-228. (Pubitemid 39637479)
    • (2005) Computer Methods in Applied Mechanics and Engineering , vol.194 , Issue.25 , pp. 205-228
    • Frauenfelder, P.1    Schwab, C.2    Todor, R.A.3
  • 14
    • 0007510129 scopus 로고
    • Computing forward-difference intervals for numerical optimization
    • Gill, P. E., W. Murray, M. A. Saunders, and, M. H. Wright, (1983), Computing forward-difference intervals for numerical optimization, SIAM J. Sci. Stat. Comput., 4 (2), 310-321.
    • (1983) SIAM J. Sci. Stat. Comput. , vol.4 , Issue.2 , pp. 310-321
    • Gill, P.E.1    Murray, W.2    Saunders, M.A.3    Wright, M.H.4
  • 15
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulations
    • Greengard, L., and, V. Rokhlin, (1987), A fast algorithm for particle simulations, J. Comput. Phys., 73 (2), 325-348.
    • (1987) J. Comput. Phys. , vol.73 , Issue.2 , pp. 325-348
    • Greengard, L.1    Rokhlin, V.2
  • 16
    • 79960425522 scopus 로고    scopus 로고
    • Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
    • Halko, N., P. G. Martinsson, and, J. A. Tropp, (2011), Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions, SIAM Rev., 53 (2), 217-288.
    • (2011) SIAM Rev. , vol.53 , Issue.2 , pp. 217-288
    • Halko, N.1    Martinsson, P.G.2    Tropp, J.A.3
  • 17
    • 84906101909 scopus 로고    scopus 로고
    • Modflow-2000, the US geological survey modular ground-water model: User guide to modularization concepts and the ground-water flow process, Tech. Rep. 2000-92, U.S. Geol. Surv.
    • Harbaugh, A. W., E. R. Banta, M. C. Hill, and, M. G. McDonald, (2000), Modflow-2000, the US geological survey modular ground-water model: User guide to modularization concepts and the ground-water flow process, Tech. Rep. 2000-92, U.S. Geol. Surv.
    • (2000)
    • Harbaugh, A.W.1    Banta, E.R.2    Hill, M.C.3    McDonald, M.G.4
  • 18
    • 0029413203 scopus 로고
    • Mapping hydraulic conductivity: Sequential conditioning with measurements of solute arrival time, hydraulic head, and local conductivity
    • DOI 10.1029/95WR00547
    • Harvey, C. F., and, S. M. Gorelick, (1995), Mapping hydraulic conductivity-Sequential conditioning with measurements of solute arrival time, hydraulic-head, and local conductivity, Water Resour. Res., 31 (7), 1615-1626. (Pubitemid 26443157)
    • (1995) Water Resources Research , vol.31 , Issue.7 , pp. 1615-1626
    • Harvey, C.F.1    Gorelick, S.M.2
  • 19
    • 33748749612 scopus 로고    scopus 로고
    • Statistical inverse problems: Discretization, model reduction and inverse crimes
    • DOI 10.1016/j.cam.2005.09.027, PII S0377042705007296
    • Kaipio, J., and, E. Somersalo, (2007), Statistical inverse problems: Discretization, model reduction and inverse crimes, J. Comput. Appl. Math., 198 (2), 493-504. (Pubitemid 44402950)
    • (2007) Journal of Computational and Applied Mathematics , vol.198 , Issue.2 , pp. 493-504
    • Kaipio, J.1    Somersalo, E.2
  • 20
    • 0029413779 scopus 로고
    • Quasi-linear geostatistical theory for inversing
    • DOI 10.1029/95WR01945
    • Kitanidis, P. K., (1995), Quasi-linear geostatistical theory for inversing, Water Resour. Res., 31 (10), 2411-2419. (Pubitemid 26475164)
    • (1995) Water Resources Research , vol.31 , Issue.10 , pp. 2411-2419
    • Kitanidis, P.K.1
  • 22
    • 0032169156 scopus 로고    scopus 로고
    • How observations and structure affect the geostatistical solution to the steady-state inverse problem
    • Kitanidis, P. K., (1998), How observations and structure affect the geostatistical solution to the steady-state inverse problem, Ground Water, 36 (5), 754-763. (Pubitemid 28448120)
    • (1998) Ground Water , vol.36 , Issue.5 , pp. 754-763
    • Kitanidis, P.K.1
  • 23
    • 84885506735 scopus 로고    scopus 로고
    • Bayesian and geostatistical approaches to inverse problems
    • in, edited by L. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, Y. Marzouk, L. Tenorio, B. van Bloemen Waanders, and K. Willcox, Wiley, Chichester, West Sussex, U. K.
    • Kitanidis, P. K., (2010), Bayesian and geostatistical approaches to inverse problems, in Large-Scale Inverse Problems and Quantification of Uncertainty, edited by L. Biegler, G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, B. Mallick, Y. Marzouk, L. Tenorio, B. van Bloemen Waanders, and K. Willcox, pp. 71-85, Wiley, Chichester, West Sussex, U. K.
    • (2010) Large-Scale Inverse Problems and Quantification of Uncertainty , pp. 71-85
    • Kitanidis, P.K.1
  • 24
    • 84884926040 scopus 로고    scopus 로고
    • Towards optimal allocation of computer resources: Trade-offs between uncertainty quantification, discretization and model reduction
    • Leube, P. C., F. P. J. de Barros, W. Nowak, and, R. Rajagopal, (2013), Towards optimal allocation of computer resources: Trade-offs between uncertainty quantification, discretization and model reduction, Environ. Modell. Software, 50, 97-107.
    • (2013) Environ. Modell. Software , vol.50 , pp. 97-107
    • Leube, P.C.1    De Barros, F.P.J.2    Nowak, W.3    Rajagopal, R.4
  • 25
    • 34249112258 scopus 로고    scopus 로고
    • Two-dimensional characterization of hydraulic heterogeneity by multiple pumping tests
    • doi: 10.1029/2006WR005333.
    • 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.
    • (2007) Water Resour. Res. , vol.43
    • Li, W.1    Englert, A.2    Cirpka, O.A.3    Vanderborght, J.4    Vereecken, H.5
  • 26
    • 40149107029 scopus 로고    scopus 로고
    • Three-dimensional geostatistical inversion of flowmeter and pumping test data
    • DOI 10.1111/j.1745-6584.2007.00419.x
    • Li, W., A. Englert, O. A. Cirpka, and, H. Vereecken, (2008), Three-dimensional geostatistical inversion of flowmeter and pumping test data, Ground Water, 46 (2), 193-201. (Pubitemid 351326727)
    • (2008) Ground Water , vol.46 , Issue.2 , pp. 193-201
    • Li, W.1    Englert, A.2    Cirpka, O.A.3    Vereecken, H.4
  • 27
    • 79551664076 scopus 로고    scopus 로고
    • Large-scale inverse modeling with an application in hydraulic tomography
    • doi: 10.1029/2010WR009144.
    • Liu, X., and, P. K. Kitanidis, (2011), Large-scale inverse modeling with an application in hydraulic tomography, Water Resour. Res., 47, W02501, doi: 10.1029/2010WR009144.
    • (2011) Water Resour. Res. , vol.47
    • Liu, X.1    Kitanidis, P.K.2
  • 28
    • 84885490127 scopus 로고    scopus 로고
    • Geostatistical reduced-order models in underdetermined inverse problems
    • Liu, X., Q. Zhou, J. Birkholzer, and, W. A. Illman, (2013), Geostatistical reduced-order models in underdetermined inverse problems, Water Resour. Res., 49, 6587-6600.
    • (2013) Water Resour. Res. , vol.49 , pp. 6587-6600
    • Liu, X.1    Zhou, Q.2    Birkholzer, J.3    Illman, W.A.4
  • 29
    • 0029667847 scopus 로고    scopus 로고
    • A reassessment of the groundwater inverse problem
    • McLaughlin, D., and, L. R. Townley, (1996), A reassessment of the groundwater inverse problem, Water Resour. Res., 32 (5), 1131-1161.
    • (1996) Water Resour. Res. , vol.32 , Issue.5 , pp. 1131-1161
    • McLaughlin, D.1    Townley, L.R.2
  • 30
    • 4544378364 scopus 로고    scopus 로고
    • Estimation of historical groundwater contaminant distribution using the adjoint state method applied to geostatistical inverse modeling
    • doi: 10.1029/2004WR003214.
    • Michalak, A. M., and, P. K. Kitanidis, (2004), Estimation of historical groundwater contaminant distribution using the adjoint state method applied to geostatistical inverse modeling, Water Resour. Res., 40, W08302, doi: 10.1029/2004WR003214.
    • (2004) Water Resour. Res. , vol.40
    • Michalak, A.M.1    Kitanidis, P.K.2
  • 32
    • 3042559789 scopus 로고    scopus 로고
    • A modified Levenberg-Marquardt algorithm for quasi-linear geostatistical inversing
    • DOI 10.1016/j.advwatres.2004.03.004, PII S0309170804000594
    • Nowak, W., and, O. A. Cirpka, (2004), A modified Levenberg-Marquardt algorithm for quasi-linear geostatistical inversing, Adv. Water Resour., 27 (7), 737-750. (Pubitemid 38836430)
    • (2004) Advances in Water Resources , vol.27 , Issue.7 , pp. 737-750
    • Nowak, W.1    Cirpka, O.A.2
  • 33
    • 33749374162 scopus 로고    scopus 로고
    • Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data
    • doi: 10.1029/2005WR004832.
    • Nowak, W., and, O. A. Cirpka, (2006), Geostatistical inference of hydraulic conductivity and dispersivities from hydraulic heads and tracer data, Water Resour. Res., 42, W08416, doi: 10.1029/2005WR004832.
    • (2006) Water Resour. Res. , vol.42
    • Nowak, W.1    Cirpka, O.A.2
  • 34
    • 0242617471 scopus 로고    scopus 로고
    • Efficient Computation of Linearized Cross-Covariance and Auto-Covariance Matrices of Interdependent Quantities
    • DOI 10.1023/A:1022365112368
    • Nowak, W., S. Tenkleve, and, O. A. Cirpka, (2003), Efficient computation of linearized cross-covariance and auto-covariance matrices of interdependent quantities, Math. Geol., 35 (1), 53-66. (Pubitemid 38149279)
    • (2003) Mathematical Geology , vol.35 , Issue.1 , pp. 53-66
    • Nowak, W.1    Tenkleve, S.2    Cirpka, O.A.3
  • 36
    • 72449140504 scopus 로고    scopus 로고
    • A randomized algorithm for principal component analysis
    • Rokhlin, V., A. Szlam, and, M. Tygert, (2009), A randomized algorithm for principal component analysis, SIAM J. Matrix Anal. Appl., 31 (3), 1100-1124.
    • (2009) SIAM J. Matrix Anal. Appl. , vol.31 , Issue.3 , pp. 1100-1124
    • Rokhlin, V.1    Szlam, A.2    Tygert, M.3
  • 37
    • 84861357098 scopus 로고    scopus 로고
    • Efficient methods for large-scale linear inversion using a geostatistical approach
    • doi: 10.1029/2011WR011778.
    • Saibaba, A. K., and, P. K. Kitanidis, (2012), Efficient methods for large-scale linear inversion using a geostatistical approach, Water Resour. Res., 48, W05522, doi: 10.1029/2011WR011778.
    • (2012) Water Resour. Res. , vol.48
    • Saibaba, A.K.1    Kitanidis, P.K.2
  • 38
    • 33746346426 scopus 로고    scopus 로고
    • Karhunen-Loeve approximation of random fields by generalized fast multipole methods
    • DOI 10.1016/j.jcp.2006.01.048, PII S0021999106000349
    • Schwab, C., and, R. A. Todor, (2006), Karhunen-loeve approximation of random fields by generalized fast multipole methods, J. Comput. Phys., 217 (1), 100-122. (Pubitemid 44111671)
    • (2006) Journal of Computational Physics , vol.217 , Issue.1 , pp. 100-122
    • Schwab, C.1    Todor, R.A.2
  • 39
    • 0030619775 scopus 로고    scopus 로고
    • A geostatistical approach to contaminant source identification
    • Snodgrass, M. F., and, P. K. Kitanidis, (1997), A geostatistical approach to contaminant source identification, Water Resour. Res., 33 (4), 537-546.
    • (1997) Water Resour. Res. , vol.33 , Issue.4 , pp. 537-546
    • Snodgrass, M.F.1    Kitanidis, P.K.2
  • 40
    • 77956530760 scopus 로고    scopus 로고
    • A geostatistical synthesis study of factors affecting gross primary productivity in various ecosystems of North America
    • Yadav, V., K. L. Mueller, D. Dragoni, and, A. M. Michalak, (2010), A geostatistical synthesis study of factors affecting gross primary productivity in various ecosystems of North America, Biogeosci. Discuss., 7 (1), 2655-2671.
    • (2010) Biogeosci. Discuss. , vol.7 , Issue.1 , pp. 2655-2671
    • Yadav, V.1    Mueller, K.L.2    Dragoni, D.3    Michalak, A.M.4
  • 41
    • 43049138027 scopus 로고    scopus 로고
    • A view toward the future of subsurface characterization: Cat scanning groundwater basins
    • et al., doi: 10.1029/2007WR006375.
    • Yeh, T. C. J., et al. (2008), A view toward the future of subsurface characterization: Cat scanning groundwater basins, Water Resour. Res., 44, W03301, doi: 10.1029/2007WR006375.
    • (2008) Water Resour. Res. , vol.44
    • Yeh, T.C.J.1
  • 42
    • 67349145692 scopus 로고    scopus 로고
    • Geostatistical inversing for large-contrast transmissivity fields
    • Zanini, A., and, P. K. Kitanidis, (2009), Geostatistical inversing for large-contrast transmissivity fields, Stochastic Environ. Res. Risk Assess., 23 (5), 565-577.
    • (2009) Stochastic Environ. Res. Risk Assess. , vol.23 , Issue.5 , pp. 565-577
    • Zanini, A.1    Kitanidis, P.K.2
  • 43
    • 84906100935 scopus 로고    scopus 로고
    • MT3DMS: A modular three-dimensional multispecies transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems; documentation and user's guide, Tech. Rep. SERDP-99-1, U.S. Army Engineer Research and Development, Vicksburg, Miss.
    • Zheng, C., and, P. P. Wang, (1999), MT3DMS: A modular three-dimensional multispecies transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems; documentation and user's guide, Tech. Rep. SERDP-99-1, U.S. Army Engineer Research and Development, Vicksburg, Miss.
    • (1999)
    • Zheng, C.1    Wang, P.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.