Abstract
The Banff Formation (Mississippian) is a sequence of limestone and shale exposed in the southern Canadian Rocky Mountains and underlying the adjacent plains. It was chosen as a vehicle to evaluate Markov-inspired techniques in sedimentary sequences where repetition of rock types is typical but a pattern of cyclicity is not obvious. Distributions of rock-unit thickness in two outcrop sections of the Banff Formation are not all exponential, therefore a one-step Markov model using an equal observational interval is not valid. Memory is indicated by the embedded-chain model. The most likely pattern of recurrence is delineated; shale is the most independent lithologic type and therefore the initial lithology in any ideal pattern. Neither factoring nor powering a probability matrix for the Banff Formation revealed geological cyclicity as defined by W. Schwarzacher. Several problems limit the application of Markov models to sedimentary sequences. Statistical validity requires a minimum number of observations, and in the attainment of a sound statistical basis, geological pertinence may be seriously reduced. Treatment of the probability matrix, by principal components analysis or by powering, yields an exacting criterion for cyclicity.
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Ethier, V.G. Application of Markov analysis to the Banff Formation (Mississippian), Alberta. Mathematical Geology 7, 47–61 (1975). https://doi.org/10.1007/BF02080633
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DOI: https://doi.org/10.1007/BF02080633