D P Singh
Articles written in Journal of Earth System Science
Volume 118 Issue 5 October 2009 pp 583-596
Application of Markov chain and entropy analysis to lithologic succession – an example from the early Permian Barakar Formation, Bellampalli coalfield, Andhra Pradesh, India
Ram Chandra Tewari D P Singh Z A Khan
A statistical approach by a modiﬁed Markov process model and entropy function is used to prove that the early Permian Barakar Formation of the Bellampalli coal ﬁeld developed distinct cyclicities during deposition.From results,the transition path of lithological states typical for the Bellampalli basin is as:coarse to medium-grained sandstone $\longrightarrow $ interbedded ﬁne-grained sandstone/shale $\longrightarrow $ shale $\longrightarrow $ coal and again shale.The majority of cycles are symmetrical but asymmetrical cycles are present as well.The chi-square stationarity test implies that these cycles are stationary in space and time.The cycles are interpreted in terms of in-channel,point bar and overbank facies association in a ﬂuvial system.The randomness in the occurrence of facies within a cycle is evaluated in terms of entropy,which can be calculated from the Markov matrices.Two types of entropies are calculated for every facies state;entropy after deposition 𝐸 (post)and entropy before deposition 𝐸(pre),which together form entropy set;the entropy for the whole system is also calculated.These values are plotted and compared with Hattori ’s idealized plots,which indicate that the sequence is essentially a symmetrical cycle (type-B of Hattroi).
The symmetrical cyclical deposition of early Permian Barakar Formation is explained by the lateral migration of stream channels in response to varying discharge and rate of deposition across the alluvial plain.In addition,the ﬁning upward cycles in the upper part enclosing thick beds of ﬁne clastics,as well as coal may represent differential subsidence of depositional basin.
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