Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one‐ and three‐dimensional flows
Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one‐ and three‐dimensional flows
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DOI：
10.1029/wr014i002p00263
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发表时间：
1978-04
影响因子：
5.4
通讯作者：
A. A. Bakr-A.;L. Gelhar;A. Gutjahr;J. R. Macmillan
中科院分区：
文献类型：
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作者：
A. A. Bakr-A.;L. Gelhar;A. Gutjahr;J. R. Macmillan
在连续介质意义下，天然含水层材料导水率的复杂变化被表示为一个空间随机过程，其特征在于一个协方差函数。假设统计均匀性，谱分析理论被用来解决扰动形式的随机微分方程描述通过随机变化的水力传导系数的多孔介质中的流动。通过对受水力传导系数对数的一维和三维变化扰动的单向平均流量的分析，获得了水头方差和对数传导系数方差之间的局部关系。结果表明，三维统计各向同性电导率扰动所产生的水头方差仅为相应一维情形的5%。水头方差也强烈依赖于对数电导率协方差函数的相关距离。这些结果强调了在地下水流随机模拟中考虑空间相关结构和多维效应的重要性。
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.