We address the problem of characterizing spatially variable Natural Background Levels (NBLs) of concentrations of chemical species of environmental concern in a large-scale groundwater body. Assessment of NBLs is critical to identify significant trends of (possibly hazardous) chemical concentrations in aquifer systems, the latter being typically associated with spatially heterogeneous hydrogeochemical characteristics. Our study considers the entire probability density function (PDF) of the concentration of the chemical species of interest as atom of the statistical analysis. These PDFs are estimated across a network of observation boreholes in the investigated spatial domain, and modeled as random points in a Bayes Hilbert space, in the context of Object Oriented Data Analysis. This approach enables one to take advantage of the entire information content provided by these objects for the purpose of spatial prediction and uncertainty quantification. As a key element of innovation, we investigate the use of depth measures for distributional data with the distinctive aims of $\left(i\right)$ detecting central and outlying NBL distributions in the dataset, and $\left(ii\right)$ building prediction regions for NBL distribution at unsampled locations. We illustrate the results of the proposed approach to the analysis of NBLs of a selected chemical species detected at an environmental monitoring network within a large-scale alluvial aquifer in Northern Italy.

我们解决了在大型地下水体中表征环境相关化学物种浓度的空间可变自然本底水平（NBLs）的问题。NBL的评估对于确定含水层系统中（可能是危险的）化学物质浓度的显着趋势至关重要，后者通常与空间异质水文地球化学特征有关。我们的研究将目标化学物质浓度的整个概率密度函数（PDF）视为统计分析的原子。这些PDF是在研究的空间域中的整个观测井眼网络中估算的，并在面向对象数据分析的背景下建模为Bayes Hilbert空间中的随机点。这种方法使人们能够利用这些对象提供的全部信息内容，以进行空间预测和不确定性量化。作为创新的关键要素，我们调查深度数据在分布数据中的使用，其独特目标是$（\mathrm{一世}）$ 检测数据集中的中央和外围NBL分布，以及 $（\mathrm{一世}\mathrm{一世}）$在非采样位置建立NBL分布的预测区域。我们说明了拟议方法的分析结果，该方法用于分析在意大利北部大型冲积含水层内的环境监测网络中检测到的选定化学物种的NBL。