Field Measurement and Theoretical Study of the Fractal Properties of Hydraulic Conductivity

在过去的十年中，人们对使用分形概念来描述包括地下水文在内的地球科学中的各种现象越来越感兴趣。很明显，许多（如果不是大多数的话）多孔介质具有层次结构。目前尚不清楚基于代表性基本体积概念的经典输运理论如何应用于这些自然介质中不同尺度的兴趣。虽然尚不清楚“层次结构”一词应该如何定义，但有实验证据表明，三维水力传导函数的层次结构表现出某些自仿射的空间结构，称为高斯噪声（fGn）和分数布朗运动（fBm）的随机分形。这项工作将开发一种基于分形的方法，用于从有限数量的测量中构建现场测量K的三维分布。使用新的电磁（EM）钻孔流量计将在各种现场获得三维水平K分布。然后将使用重新缩放的范围分析来分析数据集是否存在fGn/fBm。接下来是随机K插值的生成和使用现代计算机图形学研究分布特性。最后，将尝试将天然多孔介质的潜在分形特性与决定沉积物性质分布的可能混沌过程的物理特性联系起来。从含水层输运的观点来看，K是唯一最重要的性质函数。对于任何特定的含水层，K在一个或多个数量级上变化，并且是高度不均匀的。然而，理解K分布通常是理解污染含水层中污染物迁移模式的先决条件。人们花费了大量的资金，试图用不适合这项任务的工具来描述含水层的特征。拟议的工作有可能导致新的理论工具和实践见解的发展，这可能对地下污染问题的长期解决方案做出重大贡献。它将有可能为天然多孔介质中各种尺度的输运现象建立一个新的实用框架。

19405075 Molz During the past decade, interest in the use of fractal concepts to describe various phenomena in the Earth Sciences, including subsurface hydrology, has been increasing. It has become apparent that many, if not most, porous media posses a hierarchical structure. It is not clear how classical transport theory based on the concept of a representative elementary volume should be applied at the vastly different scales of interest in such natural media. While it is not known how the term "hierarchical structure" should be defined, there is experimental evidence that the hierarchical structure of the three-dimensional hydraulic conductivity function exhibits the spatial structure of certain self-affine, stochastic fractals called Gaussian noise (fGn) and fractional Brownian motion (fBm). This work would develop a fractal-based method for constructing three-dimensional distributions of field-measured K from a limited number of measurements. Three dimensional horizontal K distributions will be obtained at a variety of field sites using the new electromagnetic (EM) borehole flowmeter. Data sets will then be analyzed for the presence of fGn/fBm using rescaled range analysis. This will be followed by the generation of stochastic K interpolations and a study of the distribution properties using modern computer graphics. Finally, an attempt will be made to relate the potential fractal properties of natural porous media to the physics of the probably chaotic processes that determine the property distributions of sediments. From an aquifer transport viewpoint, K is the single most important property function. For any particular aquifer, K varies over one or more orders of magnitude and is highly heterogeneous. Yet making sense of the K distribution is often a prerequisite to understanding the pattern of contaminant migration in polluted aquifers. A tremendous amount of money is spent attempting to characterize aquifers using tools that are not adequate to the task. The proposed work has the potential to lead to the development of new theoretical tools and practical insights that could contribute significantly to the long-term solution of subsurface contamination problems. It will have the potential to establish a new practical framework for transport phenomena at a variety of scales in natural porous media.