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.

The Kargali seam of Early Permian Barakar cyclothems of East Bokaro sub-basin of Jharkhand, India is 12–30 m thick, splits into two parts, and extends throughout the length of the basin. It is made up of interbedded sequences and variable proportions of Vitrain, Clarain, Durain and Fusain. Application of embedded Markov chain model rejects the phenomenon of randomness in the repetition of coal lithotypes. The preferential upward transition path for coal lithotypes that can be derived for the Kargali top coal seam is: Vitrain $\to$ Clarain $\to$ Durain $\leftrightarrow$ Fusain $\to$ Vitrain, and for the Kargali bottom coal seam is: Clarain $\leftrightarrow$ Vitrain $\to$ Fusain $\to$ Durain $\to$ Clarain. By and large, the cyclic repetition of coal lithotypes is similar in the Kargali bottom and top seams. Among the noteworthy features are two-way transitions between Durain and Fusian in Kargali top and between Clarain and Vitrain in the case of Kargali bottom coal seam. Entropy analysis corroborates Markov chain and indicates the presence of type A-4 asymmetrical cycles of coal lithotypes.

It is suggested that the banded structure of a coal seam is not a random feature and follows a definite cyclic pattern in the occurrence of coal lithotypes in vertical order and is similar to that described in Australian and European coal seams. Asymmetrical cyclic sequences are a normal, rather than an unusual condition, within coal seams. It is visualized that a gradual decline of toxic environment and ground water level resulted in the coal lithotype cycles in the Kargali seam of East Bokaro sub-basin. The close interbedding of Vitrain and Clarain is suggestive of seasonal fluctuation in anaerobic and aerobic conditions during peat formation.

The cross-association statistical technique is used to correlate major and minor lithofacies and the corresponding facies areas in the widely separated two borehole log profiles of Early Permian succession from the Kaghaznagar and Kothagudem sub-basins of Pranhita–Godavari Graben (PGG) of southeastern India. The one-to-one correspondence of the cross-association of major lithofacies and facies areas is strikingly similar and matches significantly more than expected. It indicates the continuity of single homogenous succession deposited under an identical depositional environment in the widely separated two sub-basins of PGG. However, the dissimilarity between the micro-lithofacies, on the other hand, suggests a different sub-environment through space and time. The significant correlation of major lithofacies and facies areas of the two sub-basins suggests meandering stream depositional facies model of the Early Permian Barakar succession in PGG. It may also provide information regarding the exploration of coal. The dissimilarities of cross-association at the micro-lithofacies level may reflect the differential subsidence through space and time.