Groundwater contour mapping in Venice by stochastic interpolators: 1. Theory
Groundwater contour mapping in Venice by stochastic interpolators: 1. Theory
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使用随机插值器绘制威尼斯地下水等值线图：1. 理论
DOI：
10.1029/wr015i002p00281
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发表时间：
1979
影响因子：
5.4
通讯作者：
G. Volpi
中科院分区：
文献类型：
--
作者：
G. Gambolati;G. Volpi
克立格技术（Matheron，1969年，1970年）的适应开发和用于映射的三个主要含水层的威尼斯泻湖下的水头场z。现有的记录来自数量相当少的观测威尔斯井，这些井不均匀地分布在大陆、威尼斯和沿岸的。要重建的事件在概念上理想化为（1）给出z的主要趋势的确定性分量m和（2）给出z在m周围的自然分散的随机分量e的总和，具有零均值、恒定方差和高自相关。m和e都取决于观测尺度。选择基于物理的m表达式，包括考虑与一般水文地质背景相关的附加信息。为了降低选择的复杂性，在m中引入一些未知系数ak，并通过最佳拟合技术（例如，最小二乘法）“先验地”确定。m和ak之间的关系不一定是线性的。然后通过线性最优随机方差估计色散e，即，通过观测值的线性组合，要求插值误差E的方差最小。在没有仪器误差的情况下，观测器再现了观测点的测量量，而在场的其余部分，它提供了具有标准差σ的估计z*，其大小取决于给定z在m周围的色散以及测量的数量和分布。合理模型的先决条件是约化误差（z-z *）/σ具有零均值和单位方差，即，估计值不受系统误差的影响，并且（z-z *）与相应的σ一致。为三个威尼斯含水层中的每一个选择的解释模型的验证表明，本方法产生准确的结果，提供正确的评估趋势。
An adaptation of the kriging technique (Matheron, 1969, 1970) is developed and used to map the hydraulic head field z of three major aquifers underlying the Venetian lagoon. Available records come from a fairly small number of observation wells unevenly scattered across the mainland, Venice, and the littoral. The event to be reconstructed is conceptually idealized as the sum of (1) a deterministic component m giving the main trend of z and (2) a stochastic component e giving the natural dispersion of z around m with zero mean, constant variance, and high autocorrelation. Both m and e are dependent on the observation scale. A physically based expression for m is selected including the consideration of additional information related to the general hydrogeological context. To reduce the complexity of the choice, some unknown coefficients ak are introduced in m and determined ‘a priori’ by a best fit technique, for instance, the least squares method. The relationship between m and ak is not necessarily linear. The dispersion e is then assessed by a linear optimal stochastic interpolator, i.e., by a linear combination of the observed values with the requirement that the variance of the interpolation error E be minimal. In the absence of instrument errors the interpolator reproduces the measured quantity in the observation points, while in the remainder of the field it provides an estimate z* with a standard deviation σ whose magnitude depends on the dispersion of the given z around m as well as on the quantity and distribution of the measurements. A prerequisite for a plausible model is that the reduced errors (z−z*)/σ have zero mean and unit variance, i.e., the estimates are not affected by systematic errors and (z−z*) is consistent with the corresponding σ. Validation of the interpretation models selected for each of the three Venetian aquifers shows that the present approach yields accurate results provided the trend is correctly assessed.