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Estimation of spatial covariance of log conductivity from particle size data
Author(s) -
Riva Monica,
SanchezVila Xavier,
Guadagnini Alberto
Publication year - 2014
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2014wr015566
Subject(s) - hydraulic conductivity , covariance , soil science , logarithm , spatial variability , covariance function , aquifer , borehole , mathematics , groundwater , geology , hydrology (agriculture) , statistics , geotechnical engineering , soil water , mathematical analysis
We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity ( K ) and that of representative soil particle sizes and porosity. The latter quantities can be directly measured during routine sedimentological analyses of soil samples and provide a way of incorporating K estimates into groundwater flow models at a relatively modest experimental cost. Here we rely on widely used empirical formulations requiring measurements of representative particle diameters and, in some cases, of medium porosity. We derive exact formulations relating the spatial covariance of these quantities and K and present workable approximations on the basis of perturbation methods. Our formulations provide a direct link between key geostatistical descriptors of sedimentological and hydraulic parameters of heterogeneous aquifers which can be employed in classical estimation and simulation procedures. The approach and theoretical results are tested on an extensive data set comprising 411 particle size curves collected at 12 boreholes in a small‐scale alluvial aquifer.