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.

Late Cenozoic fresh water molasses sediments (+6000 m thick) deposited all along the length of the Himalayan fore deep, form the Siwalik Supergroup. This paper reports the results of the paleodrainage and paleohydrology of the Middle Siwalik subgroup of rocks, deposited in non-marine basins adjacent to a rising mountain chain during Pliocene. Well-exposed sections of these rocks have provided adequate paleodrainage data for the reconstruction of paleochannel morphology and paleohydrological attributes of the Pliocene fluvial system.

Cross-bedding data has been used as inputs to estimate bankfull channel depth and channel sinuosity of Pliocene rivers. Various empirical relationships of modern rivers were used to estimate other paleohydrological attributes such as channel width, sediment load parameter, annual discharge, and channel slope and flow velocity. Computed channel depth, channel slope and flow velocity are supported independently by recorded data of scour depth, cross-bedding variability and Chezy’s equation.

The estimates indicate that the Middle Siwalik sequence corresponds to a system of rivers, whose individual channels were about 400 m wide and 5.2–7.3 m deep; the river on an average had a low sinuous channel and flowed over a depositional surface sloping at the rate of 53 cm/km. The 700-km long Middle Siwalik (Pliocene) river drained an area of 42925 km² to the north–northeast, with a flow velocity of 164–284 cm/s, as it flowed generally south–southwest of the Himalayan Orogen. Bed-load was about 15% of the total load of this river, whose annual discharge was about 346–1170 m³/s normally and rose to approximately 1854 m³/s during periodic floods. The Froude number of 0.22 suggests that the water flows in the Pliocene river channels were tranquil, which in turn account for the profuse development of cross-bedded units in the sandstone. The estimated paleochannel parameters, bedding characteristics and the abundance of coarse clastics in the lithic fill are rather similar to the modern braided rivers of Canada and India such as South Saskatchewan and Gomti, respectively.