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2024 | OriginalPaper | Buchkapitel

10. Markov Random Fields and Random Walks

verfasst von : Gabor Korvin

Erschienen in: Statistical Rock Physics

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Chapter Highlights

Markov Random Fields, which are spatial generalizations of Markov Chains in time, are mainly used in geophysical inverse problems and geologic image processing (Table 10.1). Discrete-time and continuous-time Random Walk models (Sect. 10.2, and Table 10.2) are among the most popular petrophysical simulation tools. Three important applications are discussed in details: anomalous diffusion, the NMR response of fluids in porous rocks, and an attempt (of Ioannidis et al. 1997) to derive the formation factor F in Archie’s equation. Mathematical details (such as: Derivation of the Gibbs Distribution; Proof of the Hammersley-Clifford Theorem; Polya’s Theorem and its proof; and Partial Differential Equations governing Continuous Time Random Walks) are discussed in appendices.

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Titel: Markov Random Fields and Random Walks
verfasst von: Gabor Korvin
Verlag: Springer Nature Switzerland
Buch: Statistical Rock Physics
Print ISBN: 978-3-031-46699-1

Electronic ISBN: 978-3-031-46700-4

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-46700-4_10