Tuesday, April 1, 2008 : 10:20 a.m.

Geostatistical Characterization of Multiscale Hydraulic Conductivities and Transmissivities

Shlomo P. Neuman1, Monica Riva2 and Alberto Guadagnini2, (1)University of Arizona, (2)Politecnico di Milan

The subsurface often exhibits a hierarchical geologic structure which gives rise to hydraulic and transport property variations on a multiplicity of scales. Traditional geostatistical moment analysis allows one to infer the spatial covariance structure of such materials on the basis of numerous measurements on a given support scale across a domain or “window” of a given length scale. The resultant sample variogram often appears to fit a stationary variogram model with constant variance (sill) and integral (spatial correlation) scale. We propose that (a) the apparent ability of stationary spatial statistics to characterize the covariance structure of nonstationary hierarchical media is an artifact stemming from the finite size of the windows within which geologic and hydrologic variables are ubiquitously sampled, and (b) the artifact is eliminated upon characterizing the covariance structure of such media with the aid of truncated power variograms, which represent stationary random fields obtained upon sampling a nonstationary fractal over finite windows. We demonstrate the ability of truncated power models to capture these variations in terms of a few scaling parameters; show that exponential and truncated power variograms are often difficult to distinguish from each other, which helps explain why hierarchical data may appear to fit the former; note that truncated power models are unique in their ability to represent multiscale random fields having either Gaussian or heavy-tailed symmetric Levy stable probability distributions; detail the way in which these models allow conditioning the spatial statistics of such fields on multiscale measurements via co-kriging; and illustrate these capabilities on multiscale hydraulic data from an unconfined aquifer near Tübingen, Germany.

Shlomo P. Neuman, University of Arizona Regents' Professor of Hydrology, B.Sc. (1963) Geology Hebrew University Jerusalem, M.S. (1966) and Ph.D. (1968) Engineering Science UC Berkeley, Member U.S. National Academy of Engineering, Fellow American Geophysical Union and Geological Society of America.

Monica Riva, Politecnico di Milan Monica Riva received the laurea and doctoral degrees in hydraulic engineering from the Politecnico di Milano, Milano, Italy, in 1996 and 2000, respectively. She is currently Assistant Professor of Hydraulics at the Politecnico di Milano. Research activity focuses mainly on subsurface flow dynamics, solution of stochastic groundwater flow equations, characterization of multiscale hydraulic properties of aquifer systems, inverse problems, geostatistics, Monte Carlo analyses of flow and transport in the subsurface, probabilistic estimation of well catchments and distribution of solute travel times. She is Associate Editor of the AGU journal Reviews of Geophysics.

Alberto Guadagnini, Politecnico di Milan Alberto Guadagnini received the laurea and doctoral degrees in hydraulic engineering from the Politecnico di Milano, Milano, Italy, in 1989 and 1992, respectively. He is currently Professor of Hydraulics and head of the doctoral program in Water Engineering of the Politecnico di Milano. His research focuses on subsurface flow dynamics of (variably) saturated soils, parameter estimation, geostatistics, characterization of multiscale hydraulic properties of aquifer systems, stochastic analyses of flow and transport in heterogeneous aquifers, geochemical processes in heterogeneous systems, pumping and tracer tests. He is Associate Editor of Water Resources Research and Vadose Zone Journal.


2008 Ground Water Summit