Generalized Sub‐Gaussian Processes: Theory and Application to Hydrogeological and Geochemical Data
Generalized Sub‐Gaussian Processes: Theory and Application to Hydrogeological and Geochemical Data
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广义亚高斯过程：水文地质和地球化学数据的理论与应用
DOI：
10.1029/2020wr027436
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发表时间：
2020
影响因子：
5.4
通讯作者：
M. Riva
中科院分区：
文献类型：
--
作者：
M. Siena;A. Guadagnini;Arnaud Bouissonnié;P. Ackerer;D. Daval;M. Riva
我们从各种水文地质和土壤科学变量及其空间或时间增量的概率分布和相关统计矩所显示的有据可查的尺度依赖性开始。这些特征可以通过广义次高斯（GSG）模型来捕获，根据该模型，给定变量Y通过从属变量U从属于（通常空间相关的）高斯随机场G。这项研究扩展了Riva等人最初提出的理论框架（2015，10.1002/2015 WR 016998），包括选择从属关系的一般形式的可能性，从而增强了GSG框架用于数据解释和建模的灵活性。分析表达式的GSG过程与对数正态分布，帕累托分布，伽玛从属分布。我们展示了GSG建模框架捕获与两个数据集跨尺度过渡相关的统计数据的关键特征的能力。后者对应于地球化学和水文地质环境的典型变量，即（i）在实验室规模环境中收集的表征方解石晶体微米级表面粗糙度的数据，由诱导矿物溶解产生，以及（ii）分米级孔隙度数据的垂直分布，在砂岩地层中沿沿着千米级深钻孔采集，通常用于含水层系统的水文地质和地球物理表征。我们提出的方法的理论发展和成功的应用提供了一个独特的框架，在这个框架内，人们可以解释各种地球和环境变量在各种情况下显示的广泛的尺度行为。
We start from the well‐documented scale dependence displayed by the probability distribution and associated statistical moments of a variety of hydrogeological and soil science variables and their spatial or temporal increments. These features can be captured by a Generalized Sub‐Gaussian (GSG) model, according to which a given variable, Y, is subordinated to a (typically spatially correlated) Gaussian random field, G, through a subordinator, U. This study extends the theoretical framework originally proposed by Riva et al. (2015, 10.1002/2015WR016998 ) to include the possibility of selecting a general form of the subordinator, thus enhancing the flexibility of the GSG framework for data interpretation and modeling. Analytical expressions for the GSG process associated with lognormal, Pareto, and Gamma subordinator distributions are then derived. We demonstrate the ability of the GSG modeling framework to capture the way key features of the statistics associated with two data sets transition across scales. The latter correspond to variables, which are typical of a geochemical and a hydrogeological setting, that is, (i) data characterizing the micrometer‐scale surface roughness of a crystal of calcite, collected within a laboratory‐scale setting, resulting from induced mineral dissolution, and (ii) a vertical distribution of decimeter‐scale porosity data, collected along a deep kilometer‐scale borehole within a sandstone formation and typically used in hydrogeological and geophysical characterization of aquifer systems. The theoretical developments and the successful applications of the approach we propose provide a unique framework within which one can interpret a broad range of scaling behaviors displayed by a variety of Earth and environmental variables in various scenarios.
影响因子：
5.4
作者：
Haslauer, C. P.;Guthke, P.;Sudicky, E. A.
通讯作者：
Sudicky, E. A.