On the geostatistical characterization of hierarchical media

Water Resources Research

Volumn 44, Issue 2, 2008, Pages

  Neuman, Shlomo P ^a   Riva, Monica ^b   Guadagnini, Alberto ^b  

^a UNIVERSITY OF ARIZONA   (United States)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELS; PARAMETER ESTIMATION; SOLUTE TRANSPORT;

GEOSTATISTICAL CHARACTERIZATION; STATIONARY VARIOGRAM MODEL;

POROUS MATERIALS;

HYDRAULIC CONDUCTIVITY; MATHEMATICAL MODELS; PARAMETER ESTIMATION; POROUS MATERIALS; SOLUTE TRANSPORT;

AQUIFER; ARTIFACT; GEOSTATISTICS; HYDRAULIC CONDUCTIVITY; HYDRAULIC PROPERTY; MEASUREMENT METHOD; MODEL; SAMPLING; VARIOGRAM;

BADEN-WURTTEMBERG; CENTRAL EUROPE; EURASIA; EUROPE; GERMANY; TUBINGEN;

EID: 41149164101     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2007WR006228     Document Type: Article

References (37)

1. Abramowitz, M., and I. A. Stegun (1967), Handbook of Mathematical Functions, Appl. Math. Ser., vol. 55, Natl. Bur. of Stand., Washington, D. C.
2. Barton, C. C. (1995), Fractal analysis of the scaling and spatial clustering of fractures in rock, in Fractals in the Earth Sciences, edited by C. C. Barton and P. R. La Pointe, pp. 141-177, Plenum, New York.
3. Barton, C. C., and P. R. La Pointe (Eds.) (1995), Fractals in the Earth Sciences, Plenum, New York.
4. Chen, K.-C., and K.-C. Hsu (2007), A general fractal model of flow and transport in randomly heterogeneous porous media, Water Resour. Res., 43, W12501, doi:10.1029/2007WR005934.
5. Cintoli, S., S. P. Neuman, and V. Di Federico (2005), Generating and scaling fractional Brownian motion on finite domains, Geophys. Res. Lett., 32, L08404, doi:10.1029/2005GL022608.
6. Cushman, J. H. (1990), Dynamics of Fluids in Hierarchical Porous Media, Academic, London.
7. Dai, Z., R. W. Ritzi Jr., and D. F. Dominic (2005), Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies, Water Resour. Res., 41, W07032, doi:10.1029/2004WR003515.
8. Deutsch, C. V., and A. G. Journel (1998), GSLIB: Geostatistical Software Library and User's Guide, 2nd ed., Oxford Univ. Press, New York.
9. Di Federico, V., and S. P. Neuman (1997), Scaling of random fields by means of truncated power variograms and associated spectra, Water Resour. Res., 33(5), 1075-1085.
10. Di Federico, V., and S. P. Neuman (1998a), Flow in multiscale log conductivity fields with truncated power variograms, Water Resour. Res., 34(5), 975-987.
11. Di Federico, V., and S. P. Neuman (1998b), Transport in multiscale log conductivity fields with truncated power variograms, Water Resour. Res., 34(5), 963-973.
12. Di Federico, V., S. P. Neuman, and D. M. Tartakovsky (1999), Anisotropy, lacunarity, upscaled conductivity, and its covariance in multiscale fields with truncated power variograms, Water Resour. Res., 35(10), 2891-2908.
13. Frantziskonis, G., and A. Hansen (2000), Wavelet-based multiscaling in self-affine random media, Fractals, 8(4), 403-411.
14. Gelhar, L. W. (1993), Stochastic Subsurface Hydrology, Prentice-Hall, Upper Saddle River, N. J.
15. Jacob, C. E. (1944), Notes on determining permeability by pumping tests under water-table conditions, mimeographed report, U.S. Geol. Surv., Reston, Va.
16. Liu, H. H., and F. J. Molz (1997), Multifractal analyses of hydraulic conductivity distributions, Water Resour. Res., 33(11), 2483-2488.
17. Mandelbrot, B. B., and J. W. Van Ness (1968), Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10, 422-437.
18. Molz, F. J., H. Rajaram, and S. Lu (2004), Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions, Rev. Geophys., 42, RG1002, doi:10.1029/2003RG000126.
19. Neuman, S. P. (1990), Universal scaling of hydraulic conductivities and dispersivities in geologic media, Water Resour. Res., 26(8), 1749-1758.
20. Neuman, S. P. (1994), Generalized scaling of permeabilities: Validation and effect of support scale, Geophys. Res. Lett., 21(5), 349-352.
21. Neuman, S. P. (2003), Relationship between juxtaposed, overlapping, and fractal representations of multimodal spatial variability, Water Resour. Res., 9(8), 1205, doi:10.1029/2002WR001755.
22. Neuman, S. P. (2006a), Comment on "Spatial correlation of permeability in cross-stratified sediment with hierarchical architecture" by Robert W. Ritzi, Zhenxue Dai, David F. Dominic, and Yoram N. Rubin, Water Resour. Res., 42, W05601, doi:10.1029/2005WR004256.
23. Neuman, S. P. (2006b), Blueprint for perturbative solution of flow and transport in strongly heterogeneous composite media using fractal and variational multiscale decomposition, Water Resour. Res., 42, W06D04, doi:10.1029/2005WR004315.
24. Neuman, S. P., and V. Di Federico (2003), Multifaceted nature of hydrogeologic scaling and its interpretation, Rev. Geophys., 41(3), 1014, doi:10.1029/2003RG000130.
25. Neuman, S. P., A. Guadagnini, and M. Riva (2004), Type-curve estimation of statistical heterogeneity, Water Resour. Res., 40, W04201, doi:10.1029/2003WR002405.
26. Neuman, S. P., A. Blattstein, M. Riva, D. M. Tartakovsky, A. Guadagnini, and T. Ptak (2007), Type curve interpretation of late-time pumping test data in randomly heterogeneous aquifers, Water Resour. Res., 43, W10421, doi:10.1029/2007WR005871.
27. Painter, S. (1996a), Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations, Water Resour. Res., 32(5), 1183-1195.
28. Painter, S. (1996b), Stochastic interpolation of aquifer properties using fractional Levy motion, Water Resour. Res., 32(5), 1323-1332.
29. Painter, S., and L. Paterson (1994), Fractional Levy motion as a model for spatial variability in sedimentary rocks, Geophys. Res. Lett., 21, 2857-2860.
30. Ritzi, R.W., and R. M. Allen-King (2007), Why did Sudicky [1986] find an exponential-like spatial correlation structure for hydraulic conductivity at the Borden research site?, Water Resour. Res., 43, W01406, doi:10.1029/2006WR004935.
31. Ritzi, R. W., Z. Dai, D. F. Dominic, and Y. N. Rubin (2004), Spatial correlation of permeability in cross-stratified sediment with hierarchical architecture, Water Resour. Res., 40, W03513, doi:10.1029/2003WR002420.
32. Riva, M., L. Guadagnini, A. Guadagnini, T. Ptak, and E. Martac (2006), Probabilistic study of well capture zones distribution at the Lauswiesen field site, J. Contam. Hydrol., 88(1-2), 92-118.
33. Samorodnitsky, G., and M. S. Taqqu (1994), Stable Non-Gaussian Random Processes, Chapman and Hall, New York.
34. Sposito, G. (1998), Scale Dependence and Scale Invariance in Hydrology, Cambridge Univ. Press, Cambridge, U. K.
35. Sudicky, E. A. (1986), A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process, Water Resour. Res., 22, 2069-2082.
36. Turcotte, D. L. (1997), Fractals and Chaos in Geology and Geophysics, Cambridge Univ. Press, Cambridge, U. K.
37. Voss, R. F. (1985), Random fractals: Characterization and measurement, in Scaling Phenomena in Disordered Systems, NATO ASI Ser., edited by R. Pynn and A. Skjeltorp, p. 133, Plenum, New York.