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Stochastic analysis of the concentration variability in a three‐dimensional heterogeneous aquifer
Author(s) -
Vomvoris Efstratios G.,
Gelhar Lynn W.
Publication year - 1990
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 - 10.1029/wr026i010p02591
Subject(s) - covariance function , covariance , anisotropy , hydraulic conductivity , aquifer , mathematics , exponential function , correlation function (quantum field theory) , soil science , perturbation (astronomy) , statistics , mathematical analysis , physics , geology , spectral density , geotechnical engineering , groundwater , optics , soil water , quantum mechanics
A spectrally based perturbation approach is used to evaluate the concentration variability for a steady concentration field in a three‐dimensional statistically homogeneous and anisotropic aquifer. The analysis assumes small, locally stationary concentration perturbations, and consequently, is valid only after mean displacements that are large compared to the scale of aquifer heterogeneity. It is shown that the concentration variance is proportional to the square of the local mean concentration gradient and the variance and the correlation scales of log‐hydraulic conductivity (ln K ) and is inversely proportional to the local dispersivity. The concentration covariance function is highly anisotropic, with the largest correlation length aligned to the mean flow direction. Another important finding is the sensitivity of the longitudinal persistence of the concentration field to the high wave number behavior of the input ln K spectrum. The commonly employed exponential‐type covariance function, which corresponds to a nondifferentiable random field, results in extremely large concentration correlation lengths along the flow direction. Input spectra corresponding to differentiable fields with more rapid high wave number cutoffs produce a significant reduction of the longitudinal correlation length.