Depth-averaging effects on hydraulic head for media with stochastic hydraulic conductivity
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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.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Depth-averaging effects on hydraulic head for media with stochastic hydraulic conductivity |
| Series title | Water Resources Research |
| DOI | 10.1029/WR023i004p00561 |
| Volume | 23 |
| Issue | 4 |
| Year Published | 1987 |
| Language | English |
| Publisher | American Geophysical Union |
| Description | 10 p. |
| First page | 561 |
| Last page | 570 |
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