Abstract Persistent homology is a mathematical method to quantify topological features of shapes, such as connectivity. This study applied persistent homology to analyze fracture network patterns in rocks. We show that persistent homology can detect paths connecting from one boundary to the other boundary constituting fractures, which is useful for understanding relationships between fracture patterns and flow phenomena. In addition, complex fracture network patterns so-called mesh textures in serpentine were analyzed by persistent homology. In previous studies, fracture network patterns for different flow conditions were generated by a hydraulic–chemical–mechanical simulation and classified based on additional data and on expert's experience and knowledge. In this study, image analysis based on persistent homology alone was able to characterize fracture patterns. Similarities and differences of fracture network patterns between natural serpentinite and simulation were quantified and discussed. The data-driven approach combining with the persistent homology analysis helps to infer fracture forming processes in rocks. The results of persistent homology analysis provide critical topological information that cannot be obtained by geometric analysis of image data only.

中文翻译：

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通过表征具有持久同源性的裂缝网络模式来推断裂缝形成过程

摘要 持久同源性是一种量化形状拓扑特征（如连通性）的数学方法。本研究应用持久同源性分析岩石中的裂缝网络模式。我们表明，持久同源性可以检测从一个边界到另一边界构成裂缝的路径，这有助于理解裂缝模式和流动现象之间的关系。此外，通过持久同源性分析了蛇纹石中复杂的断裂网络模式，即所谓的网格纹理。在以前的研究中，不同流动条件的裂缝网络模式是通过水力-化学-机械模拟生成的，并根据额外的数据和专家的经验和知识进行分类。在这项研究中，仅基于持久同源性的图像分析能够表征骨折模式。量化并讨论了天然蛇纹岩和模拟之间裂缝网络模式的异同。结合持久同源性分析的数据驱动方法有助于推断岩石中的裂缝形成过程。持久同源性分析的结果提供了仅通过图像数据的几何分析无法获得的关键拓扑信息。