Отправлено: 14.12.11 09:37. Заголовок: Application of Markov chain and entropy analysis to lithologic succession

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 Tewari1,∗, D P Singh2,∗∗ and Z A Khan3,†
1Department of Geology, Sri J.N.P.G. College, Lucknow 226 001, India.
2SMEC India Pvt. Ltd., 5th Floor, Tower C, DLF Building 8, Cyber City, Phase II,
Gurgaon 122 002, Haryana, India.


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 coalfield 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 → interbedded fine-grained sandstone/shale →
shale → 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.


http://www.ias.ac.in/jess/oct2009/d8j-79.pdf