HR: 08:35h
AN: H31F-03    [Abstracts]
TI: GEOSTATISTICAL CHARACTERIZATION OF MULTISCALE HYDRAULIC CONDUCTIVITIES AND TRANSMISSIVITIES
AU: * Neuman, S P
EM: neuman@hwr.arizona.edu
AF: University of Arizona, Department of Hydrology and Water Resources, Tucson, AZ 85750, United States
AU: Riva, M
EM: monica.riva@polimi.it
AF: Politecnico di Milano, Dipartimento di Ingegneria Idraulica Ambientale e del Rilevamento, Piazza L. Da Vinci 32, Milano, 20133, Italy
AU: Guadagnini, A
EM: alberto.guadagnini@polimi.it
AF: Politecnico di Milano, Dipartimento di Ingegneria Idraulica Ambientale e del Rilevamento, Piazza L. Da Vinci 32, Milano, 20133, Italy
AB: The subsurface consists of porous and fractured materials exhibiting systematic and random spatial and directional variations in hydraulic and transport properties on a multiplicity of scales. Traditional geostatistical moment analysis allows one to infer the spatial structure of a subsurface flow property, such as log hydraulic conductivity or transmissivity, on the basis of numerous values measured on a given support scale across a domain or "window" of a given length scale. There is growing evidence that geostatistical parameters one obtains in this manner vary systematically with support and window scales. This observed scale variation is captured quite faithfully upon considering log hydraulic conductivity or transmissivity to be a random fractal. Doing so allows representing measurements, having a common support scale and scattered across a given window, by a truncated power variogram having at most four parameters when the underlying fractal field is statistically isotropic and six parameters when it is anisotropic. One parameter is proportional to the length scale of the data support and another to that of the window. This allows predicting the truncated power variogram that one would obtain for similar data on other support and/or window scales within the same hydrogeologic unit. Such ability to bridge across support and window scales renders the fractal approach capable of (a) characterizing the spatial variability of multiscale hydraulic conductivities and transmissivities jointly by a single family of truncated power variograms, that is fully defined by at most four (in the isotropic case) or six (in the anisotropic case) parameters, and (b) conditioning this characterization on corresponding multiscale measurements via co-kriging. If the measurements represent support-scale mean field values, they can be used for this purpose directly. If (as is more commonly the case) they represent equivalent or effective support-scale values, it is first necessary to translate them into corresponding mean field data. A theoretical basis for doing so in the case of box-shaped support volumes, embedded in a mean uniform flow field parallel to a principal direction of statistical anisotropy, is available. Direct estimates of mean field values, as well as some key variogram parameters, can be obtained via stochastic interpretation of pumping tests in a manner proposed by Neuman et al. (2004) and illustrated by Blattstein et al. (2006). Mean field values obtained in this way represent a support scale proportional to the characteristic distance spanned by all participating wells and piezometers. Regardless of what variogram model one uses to interpret a pumping test, its parameters can always be translated into those of a corresponding truncated power variogram which (other than for support- and window-specific parameters) are representative of all scales. We illustrate some aspects of our ideas and proposed methodology on multiscale hydraulic data from an unconfined aquifer near Tubingen, Germany.
DE: 1829 Groundwater hydrology
DE: 1839 Hydrologic scaling
DE: 1869 Stochastic hydrology
DE: 1873 Uncertainty assessment (3275)
DE: 4440 Fractals and multifractals
SC: Hydrology [H]
MN: 2007 Joint Assembly