The result data from sieve analysis indicates that the study samples are dominated by sand-size sediments (Table 1). The sand content of the samples varies from 57.97% to 96.57%. Sample D7 has the lowest sand concentration (57.97%) whereas Sample A2 has the highest percentage of sand (96.57%). The silt content in the samples ranges from 1.47% to 30.01%. The lowest silt percentage is observed in sample E6 (1.47%) and the highest content is seen in samples D7 (30.01%). The clay content varies from 1.42% to 12.25%. The clay content is lowest at sample A2 (1.42%) and highest at B5 (12.25%). A2 has the lowest clay content and the highest sand content, while D7 has the lowest sand content and the highest silt content. The overall percentage composition of grain size distribution showed that the studied samples are sand dominated. The distribution of higher percentage of sand-size sediments in the studied samples from Ngrayong Sandstone is probably due to the prevailing high-energy environment during deposition of these clastic sediments.

Figure 3(a) [23] and Figure 3(b) [24] show the textural classification of sediments based on sand/silt/clay ratios. The Ngrayong sediments are classified as sands (except one sample which falls in the clayey sand) (Figure 3(a)), whereas the majority of the Ngrayong samples are classified as muddy sands (Figure 3(b)).

Statistical parameters deduced from grain size data for the sandstone samples and interpretation for classes of class, sorting, roundness and skewness are shown in Table 2.

Graphic Mean (Mz)

The mean value of the graph is the average grain size of the overall data. Graphic means corresponds very closely to the mean as computed by the method of moments, yet it is much easier to find. It is calculated based on three points and gives a better overall picture. Graphically, the calculation of mean value is calculated by the following formula [2] [22]:

Mz = ∅ 16 + ∅ 50 + ∅ 84 3

Classification scheme of [22] was used in order to classify the sand size grain from the mean value. Graphic mean values of the sandstones range between 1.67 and 3.35 and fall in the size class very fine to medium (Table 2). The average mean value (2.7) of the studied samples indicates the dominance of fine-grained sand. The size of the sand can be used as to infer the medium of transportation and average kinetic energy that prevailed during deposition of sediments. Coarse sands are transported as bed loads, medium sand are carried by saltation and finer grains are transported via suspension. The variation in grain size in the studied samples indicates the variable kinetic energy at the time of deposition. However, the dominance of fine-grained sediments in the Ngrayong sandstone samples implies low energy condition during the deposition of these sediments.

Inclusive Graphic Standard Deviation (σ₁)

It is a measure and mathematical expression of sorting. Sorting value indicates the level of uniformity of grain sorting. In other words, the sorting of a given population is a measure of the range of grain-size present and the magnitude of these sizes around the mean sizes. The graphic standard deviation (δG) is a good measure of sorting and is computed as δ G = ( ∅ 84 − ∅ 16 ) / 2 . It takes in only the central two-thirds of the curve. Inclusive graphic standard deviation (σ₁) formula includes 90% of the distribution and is the best overall measure of sorting. Standard deviation values also represent changes in the kinetic energy or the velocity of depositional agent during deposition [11]. It is defined from the standard deviation and mathematically expressed as follows [2]:

σ 1 = ∅ 84 − ∅ 16 4 + ∅ 95 − ∅ 5 6.6

The classification of the sorting class from the standard deviation values follows the scheme of [25]. Standard deviation values of the sandstone samples from the study area range from 0.19 to 0.57 (Table 2). These standard deviation values indicate that the sandstones are moderately to very-well sorted. These values also imply that perhaps the energy level of depositing medium fluctuated from time to time during the deposition of these sediments.

Inclusive Graphic Skewness (SK₁)

It is an analysis of grain distribution of sediments as fine or coarse. It indicates the degree of asymmetry of the population or entire sediment distribution. The graphic skewness only covers the central 68% of the curve, mostly in the “tails” of the curve. Therefore, this is not sensitive enough measure. However, the Inclusive Graphic Skewness (SK₁) is a better statistic one that includes 90% of the curve and skewness value is computed by the following equation [2]:

SK 1 = ∅ 84 + ∅ 16 − 2 ∅ 50 2 ( ∅ 84 − ∅ 16 ) + ∅ 95 + ∅ 5 − 2 ∅ 50 2 ( ∅ 95 − ∅ 5 )

It is mathematically expresses as positive or negative. Positive skewness means symmetry curve peaked to the left of mean and sediment is dominated by coarser grain size. In contrast, negative skewness indicates symmetry curve peaked to the right of mean and sediment is dominated by finer grain size.

Sorting skewness values is in the range of −5.97 and 4.82 (Table 2). In case of skewness, only one sample is fine-skewed, seven samples are very fine-skewed and seven samples are coarse-skewed. Variation in the sorting skewness values of the sandstone samples indicate that these sandstones may have been deposited under fluctuated (low and high) energy conditions.

Graphic Kurtosis (K_G)

The graphic kurtosis represents a measure of the peakedness of curves and a valuable test normality of a distribution. According to Folk and Ward [2], it is mathematically expressed as:

K G = ∅ 95 − ∅ 5 2.44 ( ∅ 75 − ∅ 25 )

Kurtosis values range from 0.36 (very platykurtic) to 2.43 (very leptokurtic) (Table 2). The lowest value is seen at sample E6 where the sediments are very plakykurtic and highest at D7 where the sediments are very leptokurtic. Variation in kurtosis values of the sandstone samples indicates that variation in the flow characteristics of the depositional medium occurs at the time of deposition.

The relationship between different grain size parameters help to understand, the nature of sediments, transportation processes, energy level of depositing agents and depositional environments of siliciclastic sediments ( [2] [3] [4] [9] [12] [26] [27] [28] [29] [30] ).

The bivariate plot between mean and standard deviation (Figure 4(a)) [30] indicates that sandstones are moderately- to very well-sorted. Moderately to very-well sorting are likely due to winnowing action of depositing agent under moderately to high energy level conditions.

The plot between mean and skewness also shows a wide range of plot from strongly fine skewed to strongly coarse skewed zones (Figure 4(b)) [30]. Sandstones having very fine-skewed and coarse-skewed natures indicate that these sandstones were deposited under low to high energy conditions. Mean versus kurtosis scatter diagram shows variation in kurtosis from very leptokurtic to very platykurtic (Figure 4(c)) [30].

Variation in these values expresses the reflection of the flow characteristic of the depositing medium [31] [32]. Platykurtic show low energy and mesokurtic show moderate energy flow whereas leptokurtic show high energy flow. This fact indicates that Ngrayong sediments were deposited under extreme environments characterized by low to high energy flow environment.

Modal distribution of the sediments is described by the frequency diagrams whereas the description of the transportation medium is generally given by the curves.

Histograms: The histogram distribution of different grain size for some selected samples given in Figure 5. All samples show uni-modal distribution (except sample Sp-D7 which shows bimodal distribution). Bimodal distribution is likely to be the sub-populations. In most cases, modal class lies in the range of phi value 2 to 3.

Cumulative curves: and cumulative weight percent versus phi (ϕ) value of all studied samples were shown in Figure 6(a) and Figure 6(b). Cumulative curves

plotted on the probability ordinate scale do not form continuous straight line except few samples curves which show two, three or more straight line segments. Each segment carries different slopes which indicate the presence of more than one population of grains. Different population is likely to be related with different modes of transportation—traction, saltation and suspension [13] [33] [34]. Cumulative curves indicated that the processes such as saltation, traction and suspension have played an important role during deposition of sandstones.

The statistical parameters (mean, inclusive graphic standard deviation, skewnessand graphic kurtosis) are also used to decipher the depositional environment following discriminant function analysis (Table 3) [10]. The following equations are applied in order to distinguish the different depositional environments:

Y 1 = − 3.5688   M z + 3.7016   σ 1 2 − 2.0766   S K + 3.1135   K G (1)

Y 2 = 16.6534   M z + 65.7091   σ 1 2 + 18.1071   S K + 18.5043   K G (2)

Y 3 = 0.2852   M z − 8.7604   σ 1 2 − 4.8932   S K + 0.0482   K G (3)

where Mz, σ₁, SK and KG represents mean grain size, standard deviation, skewness and kurtosis respectively. Equation (1) is applied to distinguish between shallow agitated water and beach environment of sediment deposition. In order to differentiate between beach and shallow marine environment, Equation (2) is used. Equation (3) is for the discrimination of fluvial and shallow marine environment of depositon.

The following parameters are used to distinguish the different depositional environments:

Y1 > −2.7411 beach; Y1 < −2.7411 shallow agitated

Y2 < 65.365 beach; Y2 > 65.365 shallow marine

Y3 < −7.419 fluvial; Y3 > −7.419 shallow marine

In this research, the value of Y1 ranges from −17.78 to 8.0, (Table 3) suggesting most sandstones were laid down in shallow agitated water, whilst the remaining samples show deposition in beach environment. Y2 values in the samples range from −3.90 to 135.91 (Table 3), thus, suggesting the deposition of sandstones in shallow marine and beach environments. The result of Y3 equation for the samples ranges between −1.90 and 27.79 (Table 3) indicating the deposition of these sediments under shallow marine and lacustrine conditions. Therefore, these sediments were mainly deposited in shallow marine environment by beach and wave processes.

Figure 7 and Figure 8 are cross plots of linear discriminants of the Ngrayong sediments of Rembang area. These plots indicate that Ngrayong sandstones were deposited under diverse conditions. Large numbers of samples show combine effect of Lacustrine, beach, shallow marine, and turbidity environment. However shallow marine is regarded as the most influential environment.

The Passega diagram (C-M Pattern) (Figure 9) is commonly applied to determine the environmental conditions of sediment deposition. Passega diagram is based on parameter C (one percentile value) and M (the Median: 50 percentile value). The relationship between C and M helps to understand the nature of sediment types and energy of transporting medium [4] [9]. The diagram involves several fields, pelagic suspension (T field), uniform suspension (SR field), graded

suspension (QR field), suspension and rolling (QP field), rolling and suspension-(PO field), rolling (ON field) corresponding to the various transports and sedimentation conditions in the marine, littoral or fluvial regimes.

On the Passega diagram (Figure 9), eight samples plotted in the suspension and rolling zone (QP zone). Two samples plotted near the graded suspension (QR) zone, a sample plotted around the uniform suspension (SR) zone, and other three samples plotted outside the featured fields. The C-M diagram reveals that the sediments from Rembang area were deposited under diverse conditions and transportation. However, transportation by suspension and rolling is the dominant process.