Natural porous media are generally heterogeneous and anisotropic. The structure of porous media plays a vital role and is often the source of their heterogeneity and anisotropy. In physical processes such as fluid flow in porous media, a small number of dominant features, here referred to as wide channels, are responsible for the majority of the flow. The thickness and orientation of these channels often determine the permeability characteristics of the media. Typically, identifying such dominant features requires extensive and costly simulations. Here, we propose a prompt approach based on geometric properties derived from three-dimensional (3D) images. The size or radius of the dominant features is obtained via distance maps, and their orientations are determined using Principal Component Analysis. Subsequently, we visualize these dominant features with color and color brightness according to their orientation and size, together with their location and distribution in 3D space. The combined visualization of anisotropy (orientation) and heterogeneity (size) in a single plot provides a straightforward way to enhance our understanding of pore structure characteristics. Besides, we propose a refined stereographic projection method to statistically illustrate both heterogeneity and anisotropy. Based on these insights, we further present a potential approach to reduce model size in numerical simulations, significantly reducing computational costs while preserving essential characteristics.

中文翻译：

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基于三维图像的几何特性了解异质性和各向异性多孔介质


天然多孔介质通常是异质和各向异性的。多孔介质的结构起着至关重要的作用，通常是其非均质性和各向异性的来源。在物理过程中，例如多孔介质中的流体流动，少数主要特征（此处称为宽通道）负责大部分流动。这些通道的厚度和方向通常决定了介质的渗透特性。通常，识别这些主要特征需要广泛且昂贵的模拟。在这里，我们提出了一种基于三维 （3D） 图像衍生的几何属性的提示方法。主要特征的大小或半径是通过距离图获得的，它们的方向是使用主成分分析确定的。随后，我们根据它们的方向和大小，以及它们在 3D 空间中的位置和分布，用颜色和颜色亮度来可视化这些主要特征。在单个图中将各向异性（取向）和异质性（大小）相结合，为增强我们对孔隙结构特征的理解提供了一种直接的方法。此外，我们提出了一种改进的立体投影方法来统计说明异质性和各向异性。基于这些见解，我们进一步提出了一种在数值模拟中减小模型大小的潜在方法，在保留基本特性的同时显著降低计算成本。