Much of the stochastic analysis of flow fields in heterogeneous formations in the literature treats the random input parameters that appear in the stochastic differential equation for the groundwater flow perturbations can be characterized by a covariance function. However, it may be that the covariance functions of the input parameters cannot be identified with the limited field data or that the covariance functions of the parameters do not exist at the regional scale. It is therefore necessary to generalize the existing stochastic theories for the quantification of groundwater flow variability to the case of nonstationarity of input parameter processes, which is the goal of the present work. This work deals with the problem of steady-state flow in heterogeneous confined aquifers with variable thickness, where the spatial variability of hydraulic conductivity and aquifer thickness are considered as intrinsic (nonstationary) random input processes. The introduction of the intrinsic spectral representations for the log conductivity and log aquifer thickness leads to an intrinsic process for the perturbation of the depth-averaged head, and therefore nonstationary semivariograms of the depth-averaged hydraulic head and the integrated specific discharge are developed to quantify the variability of the flow fields. The stochastic theories developed here improve the quantification of the variability of flow fields in natural confined aquifers. The analysis clearly demonstrates that the unbounded increase of the semivariograms of depth-averaged head and integrated discharge with separation distance indicates that quantifying the variability of depth-averaged head and integrated discharge using the assumption of second-order stationarity for the input parameters may lead to a significant underestimation of the variability of head and discharge for the case of variation of random input parameters characterized by a linear semivariogram model. The parameters that appear in the linear semivariograms of the logarithmic conductivity and the logarithmic thickness of the aquifer play a role in increasing the variability of the depth-averaged hydraulic head and thus the variability of the integrated discharge.

中文翻译：

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非平稳随机输入参数过程引起的地下水流场空间变化


文献中对非均质地层中流场的大部分随机分析都涉及地下水流扰动的随机微分方程中出现的随机输入参数，可以用协方差函数来表征。但是，可能无法用有限的字段数据识别输入参数的协方差函数，或者参数的协方差函数在区域尺度上不存在。因此，有必要将现有的地下水流变率量化随机理论推广到输入参数过程不平稳的情况下，这就是本研究的目标。这项工作涉及可变厚度的非均质承压含水层中的稳态流动问题，其中水力传导率和含水层厚度的空间变化被认为是内在的（非平稳的）随机输入过程。对数电导率和对数含水层厚度的内禀光谱表示的引入导致了深度平均水头扰动的内禀过程，因此开发了深度平均水头的非平稳半变异函数和综合特定流量来量化流场的变化性。这里开发的随机理论改进了天然承压含水层中流场变化性的量化。 分析清楚地表明，深度平均水头和综合流量的半变异函数与分离距离的无限增加表明，使用输入参数的二阶平稳性假设量化深度平均水头和综合流量的变异性可能会导致在以线性半变异函数为特征的随机输入参数变化的情况下，严重低估水头和流量的变异性型。含水层的对数电导率和对数厚度的线性半变异函数中出现的参数在增加深度平均水力水头的可变性方面发挥作用，从而增加综合流量的可变性。