Hydraulic conductivity of a porous medium frequently is considered to be a single realization of a three-dimensional spatial stochastic process. The most common observation 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.
Additional publication details
DEPTH-AVERAGING EFFECTS ON HYDRAULIC HEAD FOR MEDIA WITH STOCHASTIC HYDRAULIC CONDUCTIVITY.