Markov Reversibility, Quasi-Symmetry, and Marginal Homogeneity in Cyclothymiacs Geological Successions

International Journal of Geoinformatics and Geological Science |

© 2021 by SSRG - IJGGS Journal |

Volume 8 Issue 2 |

Year of Publication : 2021 |

Authors : Zahid A. Khan, Ram Chandra Tewari |

##### How to Cite?

Zahid A. Khan, Ram Chandra Tewari, "Markov Reversibility, Quasi-Symmetry, and Marginal Homogeneity in Cyclothymiacs Geological Successions," *SSRG International Journal of Geoinformatics and Geological Science*, vol. 8, no. 2, pp. 9-25, 2021. *Crossref,* https://doi.org/10.14445/23939206/IJGGS-V8I2P102

##### Abstract:

Erodogic Markov chains have been popular technique to validate the presence of cyclic succession of facies, facies areas and corresponding environments. A review of published transition tally matrices of sedimentary sequences of different geological time reveals with a few exception the marginal homogeneity and symmetric implying that the underlying depositional processes is a reversible Markov process. Unlike the symmetry model the quasi-symmetry model, a rigorous method implying marginal homogeneity using different parameters for row and column categories and defined as a purely mathematical property of a matrix and can be written as a product of a diagonal and a symmetric matrix. It can then be shown that a Markov sequence is reversible if and only if it has a quasi-symmetric tally matrix. A simple Chi-square (χ2) test for symmetry on the tally matrix is sufficient to determine if an observed matrix is symmetrical and hence whether the Markov cyclicity is reversible or a non-reversible in a sedimentary succession. A new method Kolmogorov criterion is introduced for checking transition matrices of reversible Markov process without requiring knowledge of the stationary probabilities of observed transition probability matrix. The present contribution analyses classical examples with geological data (sedimentary and igneous) of different geological ages around the world to determine if the sequence confirms to a reversible or non-reversible erodogic Markov process and possess quasi-symmetry.

##### Keywords:

Erodogic Markov Chain, Markov reversibility, Quasi Symmetry, Marginal Homogeneity, Geological Application

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