Discerning connectivity features and scaling behaviour of spatial random fields through the Method of Anchored Distributions (MAD).

通过锚定分布方法 (MAD) 辨别空间随机场的连通性特征和缩放行为。

• 批准号: 245357759
• 负责人: Dr. Falk Hesse
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/245357759?language=en
• 关键词: Discerning; connectivity; features; scaling; behaviour

Hydrogeolocial quantities like conductivity or transmissivity are usually hard to represent in a precise manner due to having both a high degree of spatial variability as well as exhibiting a scarcity of information. As a result these quantities are commonly modeled as random fields, which, under the assumption of a Gaussian process, are defined by their expectation value and their covariance function respectively the variogram. This variogram is usually parametrized by fitting a model functions to an experimental variogram derived from measurements of the conductivity. Typical variogram model include the exponential, Gaussian and the spherical variogram. Despite their differences these different functions can often be fitted to the experimental variogram with similar accuracy. This observation is substantiated by the fact that the choice of the aforementioned model functions often has little impact on subsequently performed flow and transport simulations. In this study we will however, investigate the two scenarios, where such variogram models can be mistaken for structurally different variogram models therefore leading to very different results.The first scenario is a comparison of a Gaussian random field with a Gaussian variogram function vs. a non-Gaussian random field with a high degree of connectivity of the extreme values of the field. It has been shown that such fields can have very similar variogram functions making them nearly indistinguishable based on the experimental variogram alone. Due to the different connectivity features the resulting flow and transport behavior will however, differ strongly.The second scenario is a comparison of Gaussian random fields having either an exponential or a so called truncated power-law variogram function. In analogy to above scenario both these fields have a similar variogram function but strongly differ with respect to the scaling behavior. Falsely ignoring this fact will leads to errors if data from different scales are assimilated or the so found results are transferred to other spatial scales.These two presented scenarios both share the fact, that, based on characterization of mean and variogram alone, they are hard to discriminate yet can lead to very different results if used for further analyses of the properties they represent. As a result it is necessary to use additional data in order to discern the original structure of the random field.In this study we will use the Method of Anchored Distributions, which is a novel tool for the inverse characterization of spatial random fields. The method is very versatile with respect to the used data, has a modular structure and does not assume any formal relationship between the target variable (log hydraulic conductivity) and the data used for the inversion process.

水文地质量，如电导率或渗透率，通常很难以精确的方式表示，由于具有高度的空间变异性以及表现出的信息稀缺。因此，这些量通常被建模为随机场，在高斯过程的假设下，由它们的期望值和协方差函数分别定义为变差函数。该变差函数通常通过将模型函数拟合到从电导率的测量导出的实验变差函数来参数化。典型的变差函数模型包括指数变差函数、高斯变差函数和球面变差函数。尽管它们的差异，这些不同的功能往往可以拟合到实验变异函数具有类似的精度。上述模型函数的选择通常对随后进行的流动和运输模拟几乎没有影响，这一事实证实了这一观察结果。然而，在这项研究中，我们将研究两种情况，其中这种变差函数模型可能被误认为是结构不同的变差函数模型，因此导致非常不同的结果。第一种情况是比较高斯随机场与高斯变差函数与非高斯随机场的极端值具有高度的连通性。它已被证明，这些领域可以有非常相似的变差函数，使他们几乎无法区分的基础上的实验变差函数。由于不同的连通性特征，所得到的流动和运输行为将然而，强烈地不同。第二种情况是具有指数或所谓的截断幂律变差函数的高斯随机场的比较。与上述情况类似，这两个字段具有相似的变差函数，但在缩放行为方面存在很大差异。错误地忽略这一事实将导致错误，如果从不同尺度的数据被同化或发现的结果被转移到其他spatial scales.These两个场景都有一个共同的事实，即，基于单独的均值和变差函数的特性，它们很难区分，但如果用于进一步分析它们所代表的属性，可能会导致非常不同的结果。因此，有必要使用额外的数据，以辨别的原始结构的随机field.In这项研究中，我们将使用锚定分布的方法，这是一种新的工具，空间随机场的逆表征。该方法是非常通用的相对于所使用的数据，具有模块化结构，并不假设任何正式的目标变量（日志水力传导率）和用于反演过程的数据之间的关系。

项目成果

Characterizing the impact of roughness and connectivity features of aquifer conductivity using Bayesian inversion

使用贝叶斯反演表征含水层电导率的粗糙度和连通性特征的影响

• DOI: 10.1016/j.jhydrol.2015.09.067
• 发表时间: 2015
• 期刊: Journal of Hydrology
• 影响因子: 6.4
• 作者: Falk Heße;Heather Savoy;Carlos A. Osorio-Murillo;Jon Sege;Sabine Attinger;Yoram Rubin
• 通讯作者: Yoram Rubin