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Depth-averaging effects on hydraulic head for media with stochastic hydraulic conductivity

R.L. Naff·A. V. Vecchia
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Abstract

Hydraulic conductivity of a porous medium frequently is considered to be a single realization of a three-dimensional spatial stochastic process. The most common observations of flow in porous media are hydraulic-head measurements obtained from wells which are screened over extensive sections of the medium. These measurements represent, approximately, a one-dimensional spatial average of the actual three-dimensional head distribution, the actual head distribution being a stochastic process resulting from flow through a random hydraulic-conductivity field. This paper examines, via ensemble averages, the effect of such spatial averages of groundwater flow on the spatial autocovariance function for a simple, yet viable, stochastic model of a bounded medium. The model is taken to be three-dimensional flow in a medium that is bounded above and below and in which the hydraulic conductivity is a second-order stationary stochastic process. Spatial averaging of the hydraulic heads is considered to take place over the entire thickness of the medium. Ensemble variances and autocorrelations for depth-averaged heads are computed for the resulting two-dimensional flow system and compared with those from a fully three-dimensional flow system.

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R.L. Naff, A. V. Vecchia. 2010-07-09. Depth-averaging effects on hydraulic head for media with stochastic hydraulic conductivity. https://doi.org/10.1029/wr023i004p00561

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