Chernyavskiy Mikhail, Timoshenko Vasilii, Morkovkin Andrey, Manukovskaya Diana, Zernyuk Andrey, Grishin Pavel, Kalashnikov Andrey, Grachev Eugene
Faculty of Physics, Lomonosov Moscow State University, 1-2 Leninskie Gory, Moscow, Russia, 119991.
Center for Petroleum Science and Engineering (CPSE), Skolkovo Institute of Science and Technology (Skoltech), 30, Bld. 1, Bolshoy Boulevard, Moscow, Russia, 121205.
Sci Rep. 2025 Jul 2;15(1):22582. doi: 10.1038/s41598-025-05692-9.
Description of the internal spatial structure and texture of geological objects is an important element in their study. A qualitative description of the internal morphology of samples, despite its clarity and wide applicability, does not have a sufficient degree of accuracy and detail. Quantitative description would provide the information in a compact form. This information can be used straightforwardly for classification and comparison with other samples and for evaluation of effective physical characteristics. Integral geometry and algebraic topology provide a set of powerful tools for the quantitative characterization of complex spatial structures regardless of their nature. An approach to quantitative characterization of the spatial structure and texture using the example of segmented rock sample has been developed in this paper. Segmentation in our paper means distinguishing X-ray density phases. The approach is based on integral geometry and algebraic topology. The example of a meimechite sample from the Kontozero complex demonstrates the applicability of this approach for the quantitative analysis of structures in geological sample. A classifier for objects of selected X-ray density phases of geological samples based on their integral-geometric characteristics has been developed, and the stability of its operation has been demonstrated. Detailed analysis of the algebraic-topological characteristics for the selected X-ray density phases and their combinations has been carried out. The obtained results have been meaningfully interpreted in geological-genetic terms. The developed approach will allow describing the volume distribution of more than two phases in any natural and synthesized substance or even space of properties. In this case, the phase can also be understood as the distribution of properties, which makes the approach widely applicable in many science sections.
描述地质对象的内部空间结构和纹理是其研究中的一个重要元素。对样品内部形态的定性描述，尽管清晰且适用性广泛，但准确性和细节程度不足。定量描述将以紧凑的形式提供信息。该信息可直接用于分类、与其他样品进行比较以及评估有效物理特性。积分几何和代数拓扑提供了一套强大的工具，用于对复杂空间结构进行定量表征，而不论其性质如何。本文以分段岩石样品为例，开发了一种对空间结构和纹理进行定量表征的方法。本文中的分段是指区分X射线密度相。该方法基于积分几何和代数拓扑。来自科托泽罗复合体的一块镁铁陨石样品的例子证明了该方法在地质样品结构定量分析中的适用性。基于地质样品选定X射线密度相的积分几何特征，开发了一种分类器，并证明了其运行的稳定性。对选定X射线密度相及其组合的代数拓扑特征进行了详细分析。所得结果已从地质成因角度进行了有意义的解释。所开发的方法将能够描述任何天然和合成物质甚至属性空间中两个以上相的体积分布。在这种情况下，相也可理解为属性的分布，这使得该方法在许多科学领域具有广泛的适用性。
