HR: 0800h
AN: H11B-0294    [Abstracts]
TI: Power averaging and inverse smoothing: implications for porous media flow
AU: * Krishnan, S
EM: sunderk@stanford.edu
AF: Stanford University, Department of Geological and Environmental Sciences,, Stanford, CA 94305 United States
AU: Journel, A
EM: journel@pangea.stanford.edu
AF: Stanford University, Department of Geological and Environmental Sciences,, Stanford, CA 94305 United States
AB: An extremely large data set of Venus elevation is used to study the behavior of spatial statistics (eg. variance) under power averaging (eg. geometric averaging over blocks). It is shown that a model of univariate and bivariate Gaussianity can be adopted for this data set. Multivariate Gaussianity, however, is clearly disproved by comparing the multiple point statistics of high and low indicator values with those from the multivariate Gaussian distribution. Power averaging is performed on the data set over increasing block sizes using a wide power parameter range going from -40 to +40. The spatial variance of each of these power averages is plotted against increasing averaging volume. Geostatistical theory predicts a decreasing trend for the variance of linear averages. This is the classical smoothing effect. However, for this elevation data set, the variance of power averages shows a significant non-decreasing trend for a range of power values from -4 to -0.5. The cause behind such ``inverse smoothing" is linked to the spatial clustering of extreme values. Note that the block-effective permeability of porous media lies, in general (but, not necessarily), within the two limiting power averages -1 (harmonic average) and +1 (linear average). Since the observed power range for inverse smoothing overlaps this interval, the consequences of inverse smoothing for permeability averaging are discussed. This inverse smoothing arises because of spatial clustering of extreme values in non-Gaussian and finite sized fields. Therefore, this bodes caution for techniques resorting to such assumptions which simplify the analytical and numerical computation of effective permeability, but, possibly, at some unexpected risk.
DE: 1829 Groundwater hydrology
DE: 1869 Stochastic processes
SC: Hydrology [H]
MN: 2004 AGU Fall Meeting