Integrating multiple scales of hydraulic conductivity measurements in training image‐based stochastic models
Integrating multiple scales of hydraulic conductivity measurements in training image‐based stochastic models
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DOI：
10.1002/2014wr016150
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发表时间：
2013-12
影响因子：
5.4
通讯作者：
K. Mahmud;G. Mariéthoz;Andy Baker;Ashish Sharma
中科院分区：
文献类型：
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作者：
K. Mahmud;G. Mariéthoz;Andy Baker;Ashish Sharma
渗透系数是许多地下水模型中最关键的参数之一，同时也是最不确定的参数之一。一个普遍面临的问题是，数据通常不收集在同一规模的离散元素中使用的数值模型。此外，它是常见的，不同类型的水力传导系数测量，对应于不同的空间尺度，共存于一个研究领域，必须同时集成。在这里，我们解决这个问题的背景下，图像绗缝，最近开发的多点地质统计学方法之一。基于代表细尺度空间变异性的训练图像，我们使用简化的重整化升尺度方法来获得一系列升尺度训练图像，这些图像对应于测量可用的不同尺度。然后，我们应用图像绗缝与这样的多尺度训练图像，能够同时将调节数据在几个空间尺度的异质性。所获得的实现满足条件数据完全跨越所有尺度，但它可以在一个小的近似的物理尺度关系的表示的代价。为了减轻这种近似，我们迭代地将基于克里金的校正应用于最细尺度，以确保在粗尺度上的局部调节。该方法进行了测试，在一系列的合成的例子，它给出了良好的结果，并显示出不同的测量方法在真实的情况下的水文地质模型的集成的潜力。
Hydraulic conductivity is one of the most critical and at the same time one of the most uncertain parameters in many groundwater models. One problem commonly faced is that the data are usually not collected at the same scale as the discretized elements used in a numerical model. Moreover, it is common that different types of hydraulic conductivity measurements, corresponding to different spatial scales, coexist in a studied domain, which have to be integrated simultaneously. Here we address this issue in the context of Image Quilting, one of the recently developed multiple‐point geostatistics methods. Based on a training image that represents fine‐scale spatial variability, we use the simplified renormalization upscaling method to obtain a series of upscaled training images that correspond to the different scales at which measurements are available. We then apply Image Quilting with such a multiscale training image to be able to incorporate simultaneously conditioning data at several spatial scales of heterogeneity. The realizations obtained satisfy the conditioning data exactly across all scales, but it can come at the expense of a small approximation in the representation of the physical scale relationships. In order to mitigate this approximation, we iteratively apply a kriging‐based correction to the finest scale that ensures local conditioning at the coarsest scales. The method is tested on a series of synthetic examples where it gives good results and shows potential for the integration of different measurement methods in real‐case hydrogeological models.