Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one‐ and three‐dimensional flows

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Abstract
The complex variation of hydraulic conductivity in natural aquifer materials is represented in a continuum sense as a spatial stochastic process which is characterized by a covariance function. Assuming statistical homogeneity, the theory of spectral analysis is used to solve perturbed forms of the stochastic differential equation describing flow through porous media with randomly varying hydraulic conductivity. From analyses of unidirectional mean flows which are perturbed by one‐and three‐dimensional variations of the logarithm of the hydraulic conductivity, local relationships between the head variance and the log conductivity variance are obtained. The results show that the head variance produced by three‐dimensional statistical isotropic conductivity perturbations is only 5% of that in the corresponding one‐dimensional case. The head variance is also strongly dependent on the correlation distance of the log conductivity covariance function. These results emphasize the importance of including spatial correlation structure and multidimensional effects in stochastic simulation of groundwater flow.