**4.1 Bedform height and channel depth (Hm) & (Dc)**

To calculate original bedform heights from average cross-set measurement, the empirical relationship [14] was used. These equations determined relationships between the mean value of the exponential tail of the probability density function

*Analyzing Sedimentary Rocks to Evaluate Paleo Dimensions and Flow Dynamics of Permian… DOI: http://dx.doi.org/10.5772/intechopen.106994*

(PDF) for cross-set thicknesses and dune heights [14, 15]. The work [14, 16] has shown that the dune height (*H*m) can be estimated from mean cross–set thickness (*S*m) using a regression equation:

$$H\_{\mathfrak{m}} = \mathfrak{5}.\mathfrak{3}\ \mathfrak{\beta} + \mathfrak{0}.001\ \mathfrak{\beta}^2$$

Where β = *S* m/1.8. This can be simplified as:

$$H\_{\rm m} = 2.90 \left( \pm 0.70 \right)^{\*} \text{ S}\_{\rm m} \tag{1}$$

Where 2.90 are the mean and 0.70 is the standard deviation. *H* <sup>m</sup> is the mean dune height; *S* <sup>m</sup> is the mean cross-set thickness, β is the mean value of the exponential tail of the probability density function (PDF) for topographic height relative datum. While Eq. (1) relating formative dune heights to preserved cross bedding sets perhaps unusual in a wide variety of natural forces and random events accompanying the formation of such cross-sets. Nevertheless' the above equation is valid for a wide range of flume and river experiments [1, 2] to suggest that abnormally thick, isolated cross bedding sets formed by unit bars should be excluded from the data. The formative dune height is calculated from the preserved cross-sets and erosional surfaces at the top and bottom of cross bedding sets are almost horizontal so it is unlikely that aggradations and degradations played any role in the expression of cross-sets within the Barakar sandstone.

Equations for relating dune height to channel depth were developed [14] (Eq. (2)) show that flow depth is typically 8 to 10 times mean dune height. Alternatively, ref. [17] empirical relationship (Eq. (3)) based on the relation between bankfull depth and dune height referred to as *Dc* = 11.6 *H*<sup>m</sup> 0.84 can be used as a measure of maximum channel bankfull flow depth (*D*c)

$$8 < Dc/H\_m < 10\tag{2}$$

$$Dc = \mathbf{11.6} \, H\_{\text{m}} \, ^{0.84}, 0.1 \, \text{m} < Dc < \text{100 } \text{m} \tag{3}$$

Where *D*c is river channel depth and *H* <sup>m</sup> is mean dune height.

The method of using cross-beds to determine channel flow depth has been tested in several modern and ancient rivers [14, 15, 18]. Based on measured sections thickness of dune scale cross-strata sets are on average 47 � 31 cm (Brahmini sub-basin); 43 � 28 cm (Pachwara sub-basin); 37 � 20 cm (Chuperbhita sub-basin); and <sup>31</sup> � 14 cm (Hurra sub-basin)' respectively. Setting (*S*m) = 47─30 cm, the above Eq. (1) yields a mean dune height (*H*m), varying from 0.928–1.363 m for the above four Gondwana sub- basins from south to north. These reconstructed mean dune heights agree closely with those reported by ref. [2] of 0.90–1.52 m and ref. [1] of 1.07–1.42 m from ancient fluvial channel bars. According to ref. [14] bankfull flow depth is typically 8 to 10 times mean dune height. This suggests bankfull flow depths (*Dc*) of between 7.25–13.63 m. Using ref. [17] relationship, average bankfull channel depth of Barakar sandstone is varying between 10.87–14.96 m. We thus determine maximum (i.e. bankfull) flow depths to be about 13.0 m.

The paleochannel flow depth was estimated from the thickness of lateral macroform using the equation [19]; a 10% reduction in thickness for the conversion of sand to sandstone as a result of compaction appears conservative following Ingles and Grant suggestion, therefore, divided by 0.9 to convert these measures to original bankfull depth.

$$D\mathfrak{c} = D^\* / \mathfrak{0}.\mathfrak{9} \tag{4}$$

Where *D*\* is the maximum channel bankfull flow depth, which is represented by the thickness of the sandstone macroform, 0.9 compensates for the compaction factor.

The average thickness of the fining-upward facies sequence of the Barakar sandstone varies from 15 m in Brahmini sub-basin in the north through Pachwara subbasin and Chuperbhita sub-basin to 10 m in Hurra sub-basin in south. The bankfull depth so calculated yield a value in between 11.12–16.67 m which is similar to those calculated from Eqs. (2) and (3) calculated above.
