The Internal Topology of Rocks

We discuss the modern mathematical tools for studying the topology of pore space. In Sect. 3.1. Minkowski functionals are introduced through the paradigm of[aut]Kac, M. Mark Kac (Kac, Am Math Monthly 73:1–24, 1966) ‘Can one hear the shape of a drumCan one hear the shape of a drum?’. Euler characteristicsEuler characteristic, a powerful tool to study connectivityConnectivity is treated in 3.2. The elegant and sophisticated research tool, Persistent HomologyPersistent homology, is built up in a series of easy-to-follow steps in 3.3. The abstract constructions are illustrated with practical examples, and there are copious references in the text and in Tables (3.1, 3.4, 3.11) for their use in Petrophysics.