A modified Levenberg-Marquardt algorithm for quasi-linear geostatistical inversing

Advances in Water Resources

Volumn 27, Issue 7, 2004, Pages 737-750

  Nowak, Wolfgang ^a   Cirpka, Olaf A ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Cokriging; Conditioning; Geostatistical inverse modeling; Levenberg; Marquardt

Indexed keywords

ALGORITHMS; AQUIFERS; HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELS; OPTIMIZATION; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS);

GEOSTATISTICS; MODELING; SUBSURFACE FLOWS;

HYDRAULICS;

ALGORITHM; AQUIFER; DATA INVERSION; GEOSTATISTICS; HYDRAULIC CONDUCTIVITY; KRIGING; SUBSURFACE FLOW;

EID: 3042559789     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2004.03.004     Document Type: Article

References (33)

1. Carrera J. Glorioso L. On geostatistical formulation of the groundwater flow inverse problem Adv. Water Resour. 14 5 1991 273-283
2. Cirpka O. Kitanidis P. Sensitivity of temporal moments calculated by the adjoint-state method, and joint inversing of head and tracer data Adv. Water Resour. 24 1 2001 89-103
3. Cirpka O, Nowak W. First-order variance of travel time in non-stationary formations. Water Resour. Res. (in press)
4. Dietrich C. Newsam G. A stability analysis of the geostatistical approach to aquifer transmissivity identification Stochast. Hydrol. Hydraul. 3 1989 293-316
5. Dietrich C. Newsam G. A fast and exact method for multidimensional Gaussian stochastic simulations Water Resour. Res. 29 8 1993 2861-2869
6. Dietrich C. Newsam G. A fast and exact method for multidimensional Gaussian stochastic simulations: extension to realizations conditioned on direct and indirect measurements Water Resour. Res. 32 6 1996 1643-1652
7. Gomez-Hernandez J. Sahuquillo A. Capilla J. Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data. 1. Theory J. Hydrol. 203 1997 162-174
8. Harter T. Gutjahr A. Yeh T.-J. Linearized cosimulation of hydraulic conductivity, pressure head, and flux in saturated and unsaturated, heterogenous porous media J. Hydrol. 183 1999 169-190
9. Kitanidis P. Parameter uncertainty in estimation of spatial functions: Bayesian analysis Water Resour. Res. 22 4 1986 499-507
10. Kitanidis P. Orthonormal residuals in geostatistics: model criticism and parameter estimation Math. Geol. 23 5 1991 741-758
11. Kitanidis P. Quasi-linear geostatistical theory for inversing Water Resour. Res. 31 10 1995 2411-2419
12. Kitanidis P. On the geostatistical approach to the inverse problem Adv. Water Resour. 19 6 1996 333-342
13. Kitanidis P. Analytical expressions of conditional mean, covariance, and sample functions in geostatistics Stochast. Hydrol. Hydraul. 12 1996 279-294
14. Kitanidis P. Comment on "a reassessment of the groundwater inverse problem" D. Mclaughlin and L.R. Townley Water Resour. Res. 33 9 1997 2199-2202
15. Kitanidis P. Vomvoris E. A geostatistical approach to the inverse problem in groundwater modeling (steady-state) and one-dimensional simulations Water Resour. Res. 19 3 1983 677-690
16. Levenberg K. A method for the solution of certain nonlinear problems in least squares Quart. Appl. Math. 2 1944 164-168
17. Marquardt D. An algorithm for least squares estimation of non-linear parameters J. Soc. Ind. Appl. Math. 11 1963 431-441
18. McLaughlin D. Townley L. A reassessment of the groundwater inverse problem Water Resour. Res. 32 5 1996 1131-1161
19. McLaughlin D. Townley L. Reply to comment by P. K. Kitanidis on "a reassessment of the groundwater inverse problem" by D. Mclaughlin and L.R. Townley Water Resour. Res. 33 9 1997 2203
20. Nowak W. Tenkleve S. Cirpka O. Efficient computation of linearized cross-covariance and auto-covariance matrices of interdependent quantities Math. Geol. 35 1 2003 53-66
21. Press W. Teukolsky B.F.S. Vetterling W. Numerical Recipes: The Art of Scientific Computing second ed. 1992 Cambridge University Press Cambridge
22. RamaRao B. La Venue A. de Marsily G. Marietta M. Pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields. 1. Theory and computational experiments Water Resour. Res. 31 3 1995 475-493
23. Schweppe F. Uncertain dynamic systems 1973 Prentice-Hall Englewood Cliffs, NJ
24. Sun N.-Z. Inverse problems in groundwater modeling Theory and applications of transport in porous media 1994 Kluwer Academic Publishers Dordrecht
25. Sun N.-Z. Yeh W.-G. Coupled inverse problems in groundwater modeling. 1. Sensitivity analysis and parameter identification Water Resour. Res. 26 10 1990 2507-2525
26. van Loan C. Computational frameworks for the fast Fourier transform 1992 SIAM Publications Philadelphia, PA
27. Vargas-Guzmán J. Yeh T.-J. Sequential kriging and cokriging: two powerful geostatistical approaches Stochast. Environ. Res. Risk Assess. 13 1999 416-435
28. Yeh T.-C. Gutjahr A. Jin M. An iterative cokriging-like technique for ground-water flow modeling Ground Water 33 1 1995 33-41
29. Yeh T.-C. Jin M. Hanna S. An iterative stochastic inverse method: conditional effective transmissivity and hydraulic head fields Water Resour. Res. 32 1 1996 85-92
30. Yeh T.-C. Ŝimůnek J. Stochstic fusion of information for characterizing and monitoring the vadose zone Vadose Zone J. 1 2002 207-221
31. Zhang J. Yeh T.-J. An iterative geostatistical inverse method for steady flow in the vadose zone Water Resour. Res. 33 1 1997 63-71
32. Zimmerman D. Computationally exploitable structure of covariance matrices and generalized covariance matrices in spatial models J. Statist. Computat. Simulat. 32 1/2 1989 1-15
33. Zimmerman D. de Marsily G. Gotway C. Marietta M. Axness C. Beauheim R., et-al. A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow Water Resour. Res. 34 6 1998 1373-1413