Abstract
This paper examines the issues of sedimentary cycles by means of reversible Markov chains. Two types of cyclic patterns in sedimentary processes are considered in terms of symmetric cycles (ABCDCBA) and asymmetric cycles (ABCDABCD). By introducing concepts of reversibility and unidirectionality, a general solution is given for decomposing all possible cyclic patterns of these two types existing in a sedimentary sequence. On the basis of two new measures fR and fU, the most probable trends in a sequence can be identified in an optimum way. Effective and reliable use of the technique proposed here is demonstrated by a case study.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Fudan University, 1981, Stochastic Process: Peoples Publishers, Beijing, 350 p.
Gingerich, W. D., 1969, Markov Analysis of Cyclic Alluvial Sediments: Sedman. Petro., v. 39, p. 330–332.
Hattori, Isamu, 1976, Entropy in Markov Chains and Discrimination of Cyclic Patterns in Lithologic Successions: Math. Geol. v. 8, p. 477–497.
Krumbein, W. C. and Dacey, M. F., 1969, Markov Chains and Embedded Markov Chains in Geology: Math. Geol., v. 1, p. 79–96.
Merriam, Daniel F., 1970, Comparision of British and American Carboniferous Cyclic Rock Sequence: Math. Geol., vol. 2, p. 241–264.
Pan, G. C., 1987, Decomposition of Unidirectionary Cyclic Patterns in Sedimentations: Geological Review (in Chinese), in press.
Qian, M. and Hou, Z., 1977, Inversible Markov Processes: Hunan Scientific Publishing House, Changsha, Hunan, China, 255p.
Schwarzacher, W., 1969, The Use of Markov Chains in the Study of Sedimentary Cycles: Math. Geol., vol. 1, p. 17–39.
Vistelius, Andrew B., 1976, A Degenerated Case of the Model of the Ideal Granite: Math. Geol., v. 8, p. 505–506.
Vistelius, Andrew B., 1981, Gravitational Stratification,in R. G. Graid, and M. L. Labovitz, (Eds.) Future Trends in Geomathematics, p. 154–158.
Vistelius, Andrew B. and Harbaugh, John W., 1980, Granite Rocks of Yosemite Valley and An Ideal Granite Model: Math. Geol. v. 12, p. 1–24.
Wang, B., et al, 1981, The Applications of Markov Chains to Sedimentary Cycles,in A Collection of Geomathematical Papers, Geological Publishing House, Beijing, China, p. 55–67.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pan, G. A stochastic approach to optimum decomposition of cyclic patterns in sedimentary processes. Math Geol 19, 503–521 (1987). https://doi.org/10.1007/BF00896917
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00896917