Abstract We use Approximate Bayesian Computation and the Kullback-Leibler divergence measure to quantify to what extent horizontal and vertical equivalent electrical conductivity time-series observed during tracer tests constrain the 2-D geostatistical parameters of multivariate Gaussian log-hydraulic conductivity fields. Considering a perfect and known relationship between salinity and electrical conductivity at the point scale, we find that the horizontal equivalent electrical conductivity time-series best constrain the geostatistical properties. The variance, controlling the spreading rate of the solute, is the best constrained geostatistical parameter, followed by the integral scales in the vertical direction. We find that horizontally layered models with moderate to high variance have the best resolved parameters. Since the salinity field at the averaging scale (e.g., the model resolution in tomograms) is typically non-ergodic, our results serve as a starting point for quantifying uncertainty due to small-scale heterogeneity in laboratory-experiments, tomographic results and hydrogeophysical inversions involving DC data.

中文翻译：

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从盐水示踪剂测试和等效电导率时间序列推断水力传导场的地质统计特性

摘要 我们使用近似贝叶斯计算和 Kullback-Leibler 散度度量来量化在示踪剂测试期间观察到的水平和垂直等效电导率时间序列限制多变量高斯对数水力电导率场的二维地质统计参数的程度。考虑到盐度和电导率在点尺度上的完美和已知的关系，我们发现水平等效电导率时间序列最好地限制了地质统计特性。控制溶质扩散速率的方差是最好的约束地质统计参数，其次是垂直方向的积分尺度。我们发现具有中高方差的水平分层模型具有最佳解析参数。