Abstract We rest on an Information Theory perspective and assess (i) the average information content and (i) the information shared between Darcy flux fields associated with fields of hydraulic conductivity (K) characterized by differing support (or measurement) scale. We treat hydraulic conductivity as a spatial random field, characterized by a given distribution and correlation structure. The latter is modeled through a truncated power law variogram (TPV), which explicitly takes into account a characteristic length scale of the support volume of K through a lower cutoff scale. We then frame our study in a numerical Monte Carlo context where groundwater flow is evaluated across a collection of realizations of hydraulic conductivity characterized by different values of the TPV parameters and subject to uniform in the mean flow. We quantify information through the Shannon entropy of the probability mass functions of the Darcy flux components as well as the mutual information and the multivariate mutual information respectively shared by pairs and triplets of Darcy flux components related to hydraulic conductivity fields evaluated at diverse scales and associated with various levels of heterogeneity. Partitioning of multivariate mutual information according to unique, redundant and synergetic contributions is also quantified. We found consistent trends (i) in the variation of the average information content with respect to the size of lower cutoff scale and (ii) in the way information is shared between pairs and triplets of Darcy flux components associated with diverse support scales of the underlying conductivities.

中文翻译：

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量化与不同尺度下评估的导水率场相关的达西通量的信息内容

摘要 我们基于信息理论的观点并评估 (i) 平均信息含量和 (i) 达西通量场之间共享的信息，这些场与以不同支撑（或测量）尺度为特征的水力传导率 (K) 场相关。我们将水力传导率视为一个空间随机场，以给定的分布和相关结构为特征。后者通过截断幂律变异函数 (TPV) 建模，该函数通过较低的截止尺度明确考虑了 K 的支持体积的特征长度尺度。然后，我们在数值蒙特卡罗环境中构建我们的研究，其中地下水流量通过一系列水力传导率的实现进行评估，这些实现的特征是 TPV 参数的不同值，并且受平均流量的影响。我们通过达西通量分量的概率质量函数的香农熵以及互信息和多元互信息来量化信息，这些互信息和多变量互信息分别由与在不同尺度评估并与水力传导率场相关的达西通量分量的对和三元组共享不同程度的异质性。根据独特的、冗余的和协同贡献的多元互信息的划分也被量化。我们发现了一致的趋势 (i) 平均信息内容相对于下截止尺度大小的变化，以及 (ii) 在与底层不同支持尺度相关的达西通量分量对和三元组之间共享信息的方式。电导率。