Sedimentary Geology 308 (2014) 53–62

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Sedimentary Geology

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Distinguishing different sedimentary facies in a deltaic system

Barendra Purkait a,⁎, Dipanjan Das Majumdar b

a Department of Geology, University of Calcutta, 35, Ballygunge Circular Road, Kolkata 700035, Indiab Department of Remote Sensing & GIS, Vidyasagar University, Midnapur, West Bengal 721102, India

⁎ Corresponding author.E-mail addresses: baren_purkait@yahoo.co.in, baren.p

dipddm@gmail.com (D.D. Majumdar).

http://dx.doi.org/10.1016/j.sedgeo.2014.05.0010037-0738/© 2014 Published by Elsevier B.V.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 February 2014Received in revised form 13 May 2014Accepted 14 May 2014Available online 22 May 2014

Editor: J. Knight

Keywords:Sedimentary faciesGrain-size distributionLog-normalLog-skew-LaplaceDiscriminant functions

An attempt has beenmade to differentiate sedimentary facies in a modern deltaic system bymeans of grain-sizecharacteristics of the Ganga alluvial plain ofWest Bengal, India. Threemain energy environments (marine,mixedand riverine) comprising the delta were considered. Sand samples were collected from rivers (both tidal andnon-tidal), coastal dunes, beaches and tidal flats of the deltaic plain. The grain-size distribution patterns werecompared with the two model distributions of log-normal and log-skew-Laplace. Different sedimentary facieswere identified by discriminant functions. The analytical results indicate that the energy gradient of the differentsedimentary facies of the deltaic system is well reflected by the grain-size characteristics of the individual facies.While critically analyzing the role of different textural parameters in discriminating the individual faciesassociations, it is observed that the mean size, alpha (slope of coarser fractions of Laplace model) and skewnesshave greater potential to distinguish different sedimentary facies of thedeltaic system. The results of discriminantanalysis might be applicable to paleo-environmental interpretation of a deltaic system by distinguishing theindividual facies associations.

© 2014 Published by Elsevier B.V.

1. Introduction

River deltas, the most significant coastal morphological and deposi-tional features, are sites of freshwater input into the sea and often causeprominent stratification in coastal waters, leading to stagnant bottomconditions and the accumulation and preservation of organic matterwithin thick sedimentary sequences. Deltas are among themost impor-tant sedimentary deposits because they record changes across marineand terrestrial environments (Edmonds et al., 2011). Heterogeneousenergy fields under different hydraulic processes (river, tide andwave) produce different landforms with different particle-size charac-teristics. Many landforms, such as distributary channels, mouth bars,sand sheets, distal bars and tidal flats are very important reservoirs inoil and gas fields. Therefore, deltas are favorable sedimentary settingsfor oil accumulation because the interbedded reservoirs there are closerto the potential source rock. Consequently, there is an urgent need tounderstand the sedimentary processes and the identification of differ-ent sedimentary sub-environments of a deltaic system.

A large amount of research has been carried out on the grain-sizecharacteristics of different sedimentary environments (e.g., Mason andFolk, 1958; Friedman, 1961, 1967, 1979; Shepard and Young, 1961;Folk, 1966, 1968; Hails and Hoyt, 1969; Purkait, 1972, 1991; Staporand Tanner, 1975; Taira and Scholle, 1979; Sahu, 1983). Passega(1957, 1964) presumed that the particular CM (C = one percentile

urkait@gmail.com (B. Purkait),

and M = mean size) pattern is indicative of the depositional agent orprocess. Sahu (1964), Moiola and Spencer (1979) and Kasper-Zubillaga and Carranza-Edwards (2005) used discriminant analysisand Klovan (1966) used factor analysis to describe variability amongobserved correlated variables, in terms of a potentially lowernumber of unobserved variable (factor), to differentiate depositionalsedimentary environments. As each environment is related to aparticular hydrodynamic condition of deposition, neither assumptionis wholly valid. The ideas of Bagnold (1937) and Krumbein (1938)highlighted the deficiency of conventional grain-size distributiondiagrams where the grain-size frequency is plotted against log particlesize (i.e., phi scale, Φ = − log2 d where d = particle diameter in mm).It is significant that grain-size distribution patterns have a differentappearance when both size and frequency are plotted on a log–logscale to differentiate different depositional environments (Bagnoldand Barndorf-Nielsen, 1980; Barndorff-Nielsen et al., 1982; Fielleret al., 1984; Vincent, 1986; Fieller and Flenley, 1992; Purkait, 2000,2002, 2003, 2006, 2010, 2011; Purkait and Mazumder, 2000).

Kasper-Zubillaga and Dickinson (2001) made an attempt to differ-entiate beach, dune and river environments in terms of theirmineralog-ical components by using simple bar charts. However, texturaldifferences of grain-size among different depositional environmentswith varying hydrodynamic settings like a deltaic system have notbeen studied in detail. In this studywe have followed a systematic anal-ysis to differentiate the different depositional sedimentary environ-ments of the Sunderban deltaic system (Fig. 1) from the analysis of a)textural parameters of sands and b) grain-size distribution patterns. Athree-tier methodology has been adopted for this research. In the first

Fig. 1. Location map of the study area showing the position of different sedimentary sub-environments of the deltaic system of the Ganga River. Studied river stretches are shown inoval shape.

54 B. Purkait, D.D. Majumdar / Sedimentary Geology 308 (2014) 53–62

tier, different sub-environments or sedimentary facies were separatedin the light of the best-fit statistical grain-size distribution model. Inthe second tier, multiple mean comparisons among the categorical var-iables (textural parameters) were analyzed, and in the last tier, with thehelp of a discriminantmodel, a final conclusion on distinguishing differ-ent sedimentary sub-environments in a deltaic system was reached.

2. Geomorphological set-up

A schematic diagram of the Sunderban deltaic system shows the dif-ferent sub-environments under study (Fig. 2a). A total of three differentsub-environments (marine, mixed and riverine) comprising the deltawere considered. The different sub-environments were selected in asystematic way from the deltaic system of the Sundarban Delta. Con-sidering the environmental gradient of the delta (Fig. 2b), the sub-environment classification was done on the basis of the dominanthydrodynamic operators in each environmental domain. A total of fivesub-environments were selected: from the marine environment —

beach and dune, from the mixed or transitional environment — thetidal flat, and finally from the riverine environment — both the tidaland non-tidal rivers (Fig. 2b). A description of the locations (Fig. 1) isgiven in the following section.

2.1. Coastal belt of Sagar Island and its adjoining coastal belts

Sagar Island, a part of the SunderbanDelta (Fig. 1) exhibits a high en-ergy, macro-tidal coast with a tidal range larger than 4 m (Pethick,1984; Paul, 2002; Purkait, 2008). A detailed description has beengiven elsewhere (Purkait, 2012). Fluvial, marine, tidal and aeolian pro-cesses are the chief agents actively shaping this coastal zone. Themacrotidal environment ofWest Bengal shores often provides extensiveareas of tidal flats. The relatively younger coastal foredunes, reachingabout 1 m in height, border the beach and consist of fine sands. Olderlongitudinal dunes up to about 5 m high occur farther inland.The Bakkhali–Freserganj coastal belt, extending for about 2 km in anortheast–southwest direction, is situated about 30 km south-east ofSagar Island (Fig. 1) and consists offine tomedium sandswith some ad-mixtures of silt and clay. The area forms a part of the Hooghly Delta andis only a few kmeast of theHooghly Estuary (Fig. 1). Themajor geomor-phic units consist of a flat, wide foreshore, a narrow backshore withdiscontinuous dunes, and saline back-water marshes fed by water ofthe high-tide entering along small creeks. The spring tidal height is~5.10 m. The beach is gently sloping (3–4°) with a dominance of finesands. The dunes form ridges and individual dunes attain heights of1–2 m. The Bakkhali dunes are prominent and numerous whereas thedunes of Freserganj are in decline as compared to the Bakkhali dunes.

Fig. 2. Schematic model showing the setting of a delta system: (a) distribution of thephysical processes operating in the deltaic set-up and the resulting facies zonation(adopted from Dalrymple et al., 1992), and (b) classified sub-environments in terms ofthe environmental gradient and their hydrodynamic conditions from the SundarbanDelta.

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The remarkable features of the Digha–Junput–Sankarpur beach(Fig. 1) are the straightness of the shoreline and smoothness of thebeach. The foreshore is at present experiencing active erosion. Thebackshore is bounded by scarps formed by the coastal dunes. Thebeach gradient varies from 1 cm = 50 cm near the high water line to1 cm=150 cmnear the lowwater limit. Tides are semi-diurnal varyingfrom 1.5 m (neap) to 5.25 m (spring). Waves (~63 m long and ~1.5 mhigh in the open sea) approach the shore normally at an angle of nearly70°.

On the coastal plain of the Digha–Junput–Sankarpur (Fig. 1) areathere are two persistent rows of dunes: one nearest to the sea — theDigha Dune (first row) and the other farthest from the sea— the ContaiDune (second row). The Junput beach is a gently sloping beach (3–4°)and is more stable (Purkait, 1972, 1991) than the Bakkhali andFreserganj beaches. In the Junput area, there are two prominent rowsof coastal dunes running almost parallel to the shoreline (Purkait,1981, Purkait, 2012, 2013).

2.2. The Bhagirathi–Hooghly River system

The Bhagirathi–Hooghly River is one of themost prominent rivers ofsouth Bengal (Fig. 1). This N–S elongated river forms the westernmostborder of the Ganga Delta. The Ganga–Bhagirathi–Hooghly and theirtributaries form the main deltaic river system of the Sunderban Deltalying partly in the state of West Bengal, eastern India. The lower reachof the Bhagirathi–Hooghly River system is known as the HooghlyRiver, while the upper reach is called the Bhagirathi (Purkait, 2011).The lower reach of the river is tidal in nature. One of themost significanttributaries to the Bhagirathi–Hooghly River system is the Ajay River(Fig. 1).

2.3. Ajay River and Damodar River

The Ajay River is about 288 km long with a catchment area of about6760 km2, of which less than 50% is hilly and the rest are flat plains. Theriver is characterized by seasonal flash floods during the monsoon. Thesoils in the Ajay River basin have been almost entirely derived from thegranite gneiss and schists and are mostly yellow and red at the surfaceexcept in lowlands where olive to olive gray soils may also be found.Most of these soils are sandy and loamy sand especially on uplands,and are, therefore, very light at the surface. However, in lowlands,medium-textured sandy loam to loam soils are encountered. The riverflows over recent alluvium in the lower part and is subject to spillingunder moderately high discharge. The river system lies to the north ofthe Damodar River system (Fig. 1).

The Damodar River is a small rain-fed river joining the HooghlyRiver. The catchment area of the river is about 22,000 km2 of whichabout 19,000 km2 is in uplands and 3000 km2is in plains which are ofa deltaic nature.

3. Methodology and data collection

The grain-size analysis was carried out for a total of 227 sedimentsamples by mechanical sieving of which 55 samples are from fourbeaches (Sagar Island, Junput, Bakkhali and Fraserganj), 64 from corre-sponding coastal dunes bordering the beaches, 24 from the correspond-ing tidal flats, and finally 84 samples from different rivers, both tidal(Hooghly, Bhagirathi) and non-tidal (Ajay and Damodar) of theSunderban deltaic plain and its adjoining area.

A mid-channel bar and a point bar of the Hooghly–Bhagirathi Riverwere studied. The natural levee deposits andfloodplainswere also sam-pled for grain-size analysis. Sediment samples were also collected fromthe stream bed. Details of the sample points were described elsewhere(Fig. 4.1of Purkait, 2011). In all, 26 samples were collected from theAjay River of which 19 samples are from the upper 2 cm of a left-lateral bar, from the foot of the valley wall to the waterline. Similarly,12 samples of the Damodar River were collected from the upper 2 cmof a right-lateral bar from the foot of the valley wall to the waterlineand one sample was collected from the streambed.

The beach sands were collected at an interval of ~30 m all along theprofile lines drawn across the trend of the beach between high and low-water lines i.e., covering the entire foreshore region. The sand samplesof the coastal dunes were collected along the extension of the samebeach profile lines. The beach and the dune sands were collected fromthe upper 2 cm of the beach face and the dune to confirm samplingfor one uniform layer only. Sampling from the beachwas done as rapid-ly as possible to represent the effect of one tidal cycle. Sediments werecollected: a) along the shore at regular spacing and b) also at regularspacing across the beach from the high-water line to the low-waterline. The sand samples of the tidal flats were collected at least 2 cmbelow the surface to avoid an aeolian influence.

Mechanical analyses of the sand samples were undertaken usingAmerican Standard Testing Materials (A.S.T.M.) sieves at 1/2 phi inter-vals. In each case, 30 g of sample was taken by mechanical splitting ofthe completely dried samples, and sieved in a Ro-Tap sieve shaker for15 min. The sieve materials were weighed by an electronic balance upto three decimal places. The frequency percentage (probability density)for each sieve fraction was calculated.

The textural parameters (mean, sorting, skewness and kurtosis)were calculated graphically after the Folk andWard (1957)method. De-scriptive terminologies of Folk and Ward (1957) and Krumbein (1934)were adopted. Grain-size distribution patterns were found to specifythe specific pattern pertaining to different depositional environmentsand compared with two model distributions — log-normal and log-skew-Laplace. Though the log-normal and log-skew-Laplace are thelimiting distributions of the log-hyperbolic family, in this study as

Table 1Textural parameters of beach, dune and tidal flat.

Location Mean size (MZ) (Φ) Sorting (σ) (Φ) Skewness Kurtosis

Platy to Mesokurtic Leptokurtic

−ve +ve N0 ≤ 1 N1 ≤ 2 N2 ≤ 3 N3

Beach(N = 55)

2.439 0.398 7(12.7%)

48(87.3%)

5(9.1%)

14(25.4%)

4(7.3%)

32(58.2%)

Dune(N = 65)

2.427 0.350 1(1.6%)

63(98.4%)

5(7.8%)

9(14.06%)

4(6.25%)

46(71.88%)

Tidal flat(N = 24)

6.105 1.604 8(33.3%)

16(66.7%)

20(83.33%)

3(12.5%)

0 1(4.17%)

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most of the distributions are skewed, we cannot use the hyperbolic dis-tribution (Barndorff-Nielsen, 1977; Christiansen and Hartmann, 1991).

In the present analysis the different sedimentary sub-environmentswere discriminated based mainly on i) statistical modeling, and ii)group discriminant functions of different sedimentary sub-environmentdomains.

3.1. Statistical modeling

3.1.1. Normal distributionThe density function for normal distribution can be calculated as:

g x; μ ;σð Þ ¼ 1=σ√ 2πð Þ exp −1=2 x−μð Þ2=σ2f g ð1Þ

where σ = standard deviation being N0, μ = mean size, and x =observed variable, π = 3.143 (constant). The log probability functionis a parabola.

3.1.2. Laplace distributionFollowing Fieller and Flenley (1992), the skew-Laplace distribution

can be written as:

G x;α;β; μð Þ ¼ αþ βð Þ−1expx−μα

n o:::: ::for x≤μ

¼ αþ βð Þ−1 exp x−μð Þ=βf g :::: ::for xNμð2Þ

where x indicates the observed variable, and α, β, μ are parameters:α = slope of the left asymptote, i.e., coarser fractions, β = slope ofthe right asymptote, i.e., finer fractions, and μ= point of intersectionof the two asymptotes. Graphically, the logarithm of the Laplace dis-tribution is a pair of intersecting lines. The difference between thevalues of the two slopes, i.e., (α ~ β) was taken as the symmetryindex (Purkait, 2010) and used as one of the parameters.

3.1.3. Test of significanceTo obtain a quantitative idea of the discrepancies, the weighted rel-

ative errors (E) between the computed and the observed values werecalculated by the following formula (Ghosh et al, 1986; Purkait, 2002)

E ¼ √X

Sc−Soð Þ 2=SoT½ � ð3Þ

where Sc = computed values i.e., wt.% of calculated amount in eachsieve fraction, So = observed values, i.e., wt.% of observed amount ineach sieve fraction, T = total value observed, here T = 100 as the wtfrequency is in %.

Table 2Characteristics of beach, dune and tidal flat in the light of Laplace distribution.

Location Average slope of left asymptote,i.e. coarser fraction (α)

Average slope of right asyi.e. finer fraction (β)

Beach (N = 55) 1.628 0.191Dune (N = 64) 1.573 0.090Tidal flat (N = 24) 2.813 0.405

3.2. Discriminant functions

3.2.1. Post hoc comparisonA total of six variables were used for a post hoc comparison and dis-

criminant analysis, where four parameters, viz. mean size, sorting,skewness and kurtosis, were from the textural parameters of grain-size and other two parameters, alpha (slope of the left asymptote, i.e.,coarser fraction) and beta (the slope of the right asymptote, i.e., finerfraction) were from the skew-Laplace distribution. Multiple post hoccomparisons lead to a problem in interpretation called “The Problemof Multiple Comparisons” which is concerned with identifying toomany random differences when many groups are taken. The post hoccomparisons are used in conjunction with an ANOVA (analysis of vari-ance) to find means that are significantly different from each other.The ANOVA test determined that at least one of the population meansis significantly different. The multiple mean comparison subsequentlycompares all possible pairs ofmeans to determinewhichmean is signif-icantly different from the other populationmean. In this study, Scheffe'smultiplemean comparison test (Scheffe, 1959)wasused as a preparato-ry step of discriminant analysis for analyzing the individual contributionof each parameter on the facies discrimination.

3.2.2. Discriminant analysisA linear discriminant analysis (MaLachlan, 2004) was used to judge

the results as predicted from the post hoc comparisons. Discriminantanalysis (DA) is a multivariate technique which can be used to deter-mine the relationships among a categorical variable and a group of inde-pendent variables. One primary purpose of the DA is to separate classes(populations) in a lower-dimensional discriminant space (canonicalspace). The most common application of discriminant function analysisis to include many measures in the study, in order to determine thosethat discriminate between groups. In the present study, a linear discrim-inant function (LDF) was used to determine the individual contributionof variables in group discrimination of different sedimentary sub-environments. Primarily a step-wise (forward) discriminant functionwas applied to identify at each step which variable will contributemost to the discrimination between groups. The linear discriminantfunction (LDF) is represented by

LDF ¼ b0þ b1xi1þ b2xi2þ � � � þ bkxik ¼ bX ð4Þ

where bj is the value of the jth coefficient, j = 1. . . k, and xi j is the valueof the ith case of the jth predictor.

mptote, Symmetry index (α ~ β) No. of scores

Lognormal Log-skew-Laplace

1.437 33 (60%) 22 (40%)1.483 28 (43.75%) 36 (56.25%)2.408 19 (79.2%) 5 (20.8%)

Table 3Textural parameters of river sands.

Location Mean size (Φ) Sorting (σ) (φ) (Φ) Skewness Kurtosis

Platy to Mesokurtic Leptokurtic

−ve +ve Zero N0 ≤ 1 N1 ≤ 2 N2 ≤ 3 N3

Hooghly(N = 22)

2.724 0.374 12(54.545%)

9(40.909%)

1(4.545%)

4(18.182%)

18(81.818%)

– –

Bhagirathi(N = 23)

2.919 0.528 15(65.217%)

8(34.783%)

– 1(4.348%)

22(95.652%)

– –

Ajay(N = 26)

1.296 0.605 16(61.538%)

10(38.462%)

– 7(26.923%)

19(73.077%)

– –

Damodar(N = 13)

1.790 0.474 5(38.462%)

8(61.538%)

– 5(38.462%)

8(61.538%)

– –

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For each of the groups, linear discriminant analysis assumes the ex-planatory variables to be normally distributed with equal covariancematrices. For each case, the estimated coefficient for an independent var-iable ismultiplied by the case's score on that variable. These products aresummed and added to the constant, and the result is a composite score,i.e., the discriminant score for that case. The rationality of this approachis that the independent and dependent variables are related in thesense that the between-group sum of squares is larger than the within-group sum of squares. Also the ratio of within-group divided by totalsum of squares (Wilks' lambda statistic or unexplained variability) wasused to test the relationship. Squared Mahalanobis distances (d2) be-tween the sub-environmentswere also calculated to identify the distinc-tiveness of different deltaic sub-environments (MaLachlan, 2004).Finally, the canonical discriminant function was applied to discriminatemultiple sedimentary sub-environments on the two-dimensional canon-ical space using the bi-plots of canonical root 1 vs canonical root 2.The first two canonical functions which contribute most to the sub-environmental group discrimination were calculated in the form of:

First canonical function

½−15:24988þ 3:660177 �mean sizeþ 0:42811 � sorting−0:43543� skewnessþ 0:12942 � kurtosisþ 3:16863 � alphaþ 1:82662� beta�: ð5Þ

Second canonical function

½−2:40259þ 0:67626 �mean size−5:78114 � sortingþ 4:92096� skewnessþ 0:24395 � kurtosisþ 1:43549 � alphaþ 0:59403� beta�: ð6Þ

4. Results

4.1. Textural characteristics of beach and dune sands

The results of the textural analysis of beach sands (Table 1) andthe grain-size distribution pattern in the light of the Laplace distributionmodel (Table 2) were critically analyzed. The mean size of beach sandsvaries from very fine to fine following the terminology of Krumbein

Table 4Characteristics of river sands in the light of Laplace distribution.

Rivers Slope of left asymptote(α)

Slope of right asympt(β)

Hooghly (tidal river)(N = 22)

0.716 0.159

Bhagirathi (tidal river)(N = 23)

0.485 0.413

Ajay (non-tidal)(N = 26)

0.754 0.375

Damodar (non-tidal)(N = 13)

0.544 0.338

(1934), and well to very well sorted after the terminology of Folk andWard (1957). Beach sands are positively skewed in 87.3% of cases andnegatively skewed in 12.7% of cases indicating preponderance of finesands. Beach sands are mostly leptokurtic (90.9%). The symmetryindex (α ~ β), i.e. difference between the slope of the left asymptote(coarser fraction), and the slope of the right asymptote (finer fraction)varies from 0.316 to 1.437, the average being 0.662. The log-normal dis-tribution fits best in most of the cases (60%) and the log-skew-LaplaceModel fits in 40% of the cases. The kurtosis value in 71.88% of the casesin coastal dunes is N3 i.e., highly leptokurtic. The symmetry index variesfrom 0.291 to 1.483 with an average of 1.483. No specific grain-size dis-tribution pattern is observed. Sometimes the distribution pattern is log-normal and sometimes it is log-skew-Laplace.

4.2. Textural characteristics of tidal flat sands

The tidal flat sediments are of silt size with poor sorting (Table 1). In66.7% of cases, the tidal flat sands are positively skewed. The low kurto-sis value (N0≤ 1) in 83.33% of cases exhibits a meso- to platykurtic dis-tribution. The symmetry index is 2.408, i.e. more asymmetric than thedune and beach sands. The log-normal distribution fits best in 79.2% ofcases (Table 2).

4.3. Textural characteristics of river sands

The Hooghly and Bhagirathi River sediments are mainly fine sands,well to moderately well sorted, mostly negatively skewed andplatykurtic to weakly leptokurtic in nature (Table 3). The Ajay Riversands are mostly negatively skewed and the Damodar River sands aremostly positively skewed (Table 3). The Ajay and Damodar Riversands are medium-grained, moderate to well sorted, platy- to weaklyleptokurtic. The Ajay River sands are mostly negatively skewed andthe Damodar River sands are mostly positively skewed (Table 3). Thesymmetry index for the river sands varies from 0.072 to 0.557, theaverage being 0.299, i.e. more symmetric than the beach and tidal flatsands (Table 4).

ote Symmetry index(α ~ β)

No. of scores

Log-Normal Log-skew-Laplace

0.557 11(50%)

11(50%)

0.072 6(26.087%)

17(73.913%)

0.379 17(65.385%)

9(34.615%)

0.206 9(69.231%)

4(30.769%)

Fig. 3.Results of Scheffe'smultiplemean comparison test for pairwise comparison of the significantmean difference aswell as to discriminate the deltaic facies in terms of the six responsevariables: mean size, sorting, skewness, kurtosis, alpha and beta. Red box indicates significant mean differences (α= 0.05) between the pairs while black box reveals insignificant meandifferences. (a) Mean size, (b) alpha (c) sorting, (d) skewness, (e) kurtosis and (f) beta. (For interpretation of the references to color in this figure legend, the reader is referred to thewebversion of this article.)

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Table 5Lamda test showing the arrangements of each independent variable according to theircontributions to group discrimination.

Parameters Wilks'lamda

Partiallamda

F-remove

p-Level

Tolerance 1-Tolerance

Mean size 0.022 0.089 368.368 0.00 0.421 0.579Alpha 0.009 0.217 129.573 0.317 0.683Sorting 0.005 0.394 55.093 0.542 0.458Skewness 0.004 0.471 40.170 0.579 0.421Beta 0.002 0.799 9.032 0.636 0.364Kurtosis 0.002 0.917 3.223 0.005 0.929 0.071

59B. Purkait, D.D. Majumdar / Sedimentary Geology 308 (2014) 53–62

4.4. Facies discrimination

The post hoc multiple comparison test reveals that out of six para-meters, mean size contributes most and beta contributes least to thesub-environmental discrimination (Fig. 3a–c). Scheffe's multiple meancomparison was tested for 21 pairs of facies. In Fig. 2, the red box andthe black box determine the significant and insignificant mean differ-ences (α = 0.05) respectively, between the pairs (Fig. 3). The highfrequency of red box or in other words, the low frequency of blackbox indicates a higher level of discrimination power of the variable.Table 5 presents the results of Lamda test showing the arrangementsof each independent variable according to their contributions to groupdiscrimination. Table 6 provides the output of the eigenvalues as wellas canonical correlation which indicates how well a variable differenti-ates the groups. The Mahalanobis distance (d2) for each of the groupcentroids reveals the neighborhood effects between the sedimentaryenvironments (Table 7). The rows in the Classification Count table(Table 8) are the observed groups of the observations and the columnsare the predicted groups. The values in the diagonal of the table reflectthe correct classification of observations into groups.

5. Discussion

5.1. Textural characteristics of beach and dune sands

The beach is composed of fine sands with good to very good sorting.The mostly leptokurtic (90.9%) nature of beach sands is indicative ofhigh-energy deposition. In general, dune sands are very fine and posi-tively skewed (98.4%) (cf., Friedman, 1967). Friedman observed thatthe distributions of present-day beach sands are negatively skewed orsymmetrical. From the present study it can be inferred that the kineticenergy plays an important role in the size-sorting of sands. Hence thedepositional processes as inferred from the study of textural parametersare more important than the environment of deposition. The highleptokurtic value (N3) indicates that relatively high energy conditionsprevailed in this coastal tract. Khalaf (1989) and Wang et al. (2003)also observed that dune sands are commonly leptokurtic.

5.2. Textural characteristics of tidal flat sands

The preponderance of fine fractions is indicative of the low energy ofdeposition as in general, we expect a much more winnowing effect ofthe high energy on the finer fractions. The low kurtosis values also

Table 6Canonical discriminant analysis showing the eigenvalue and percentages of variance shared by

Parameters Canonical root Eigenvalue Per

Mean size 1 42.867 86.Alpha 2 6.035 12.Sorting 3 0.539 1.Skewness 4 0.045 0.Beta 5 0.032 0.Kurtosis 6 0.009 0.

reflect the low energy of deposition. The tidal flat sands are moreasymmetric than the dune and beach sands indicating a wide variationof size classes with a low energy of deposition.

5.3. Textural characteristics of river sands

The statistical analysis of sediment samples indicates that the grain-size distribution pattern of the tidal stretch of the Hooghly–BhagirathiRiver system has a tendency of attaining a log-skew-Laplace distribu-tion model (Purkait, 2011), whereas for the other two non-tidal rivers(Ajay and Damodar) the log-normal distribution pattern is the best-fitstatistical model (Table 4).

5.4. Sub-environmental discrimination

The results of the post hoc multiple comparison indicate that thedissimilarity between the sub-environments can be best explained bythe mean size and alpha as in both cases the frequency of the red box(significant differences between the pairs) is high and the frequencyof the black box (insignificant differences between the pairs) is low(Fig. 3a). Apart from themean size, no other parameter can discriminatethe intra-river environments, i.e. non-tidal rivers from tidal rivers.Again, sorting should be considered more effective than skewness forsub-environmental discrimination because the red box position withinthe plot is highly dispersed for sorting although the frequency of thered box and the black box is almost equal in both cases (Fig. 3a, b). Inthese situations a decision should be taken on the basis of the level ofdispersion, i.e., whether the red boxes aremore dispersed from the stan-dard value or placed in close proximal to the standard (‘0’ value as setfor standard here), which in turn determines the power of discrimina-tion (Fig. 3a, b). On the other hand, skewness carries more dissimilarityamong the different environments than sorting and kurtosis.

When we simply compare the skewness values in respect of differ-ent environments, it is observed that beach, dune and tidal flat sandsare all positively skewed (Table 2). On the other hand, out of the fourrivers, grain-size distribution patterns of sands of the three rivers arenegatively skewed and of one river (Damodar) is positively skewedwhich in turn reflects the differential energy domains. The post hocanalysis results, however, are able to differentiate the beach and theriver, the dune and the river, the tidal flat and the river, beach andtidal flat, dune and the tidal flat (Fig. 3b). Thus the skewness is sensitiveto the energy domain vis-à-vis environments also. Based on linear dis-criminant analysis, Kasper-Zubillaga and Carranza-Edwards (2005)suggested that the variables that better discriminate the sands of differ-ent dunes (coastal and desert) are the mean size and skewness.

The maximum between-pair similarities in terms of beta exhibitsimilar kinds of sensitivities in the size distribution patterns towardthe finer fractions in the active delta plain (Fig. 3c). As a result, betacan only explain the differences between the sub-environments whichare very distinct in terms of their size distribution pattern, such as coast-al dunes and rivers. For the same reason alpha, on the other hand,explainsmuch of the difference between the sub-environments. Similarresults have also been found for sorting and kurtosis (Fig. 3b, c). Thesorting can distinguish the tidal flat environment from the rest of theenvironments under study whereas kurtosis is a good measure todiscriminate the marine and fluvial environments (Fig. 3b, c).

each parameter for group discrimination along with their canonical correlations.

centage of variance Cumulative Canonical correlation

55% 86.55% 0.98919% 98.74% 0.92609% 99.83% 0.59209% 99.92% 0.20806% 99.98% 0.17502% 100.00% 0.093

Table 7A squaredMahalanobis distance between the centroid of individual facies group signifies the similarities and dissimilarities between the facies. Smaller distance among the facies refers tohow homogeneous samples are in terms of their characteristic variables (mean size, alpha, sorting, skewness, kurtosis and beta), whereas a larger distance infers heterogeneity.

Sub-environments Hooghly Bhagirathi Ajay Damodar Beach Dune Tidal Flat

Hooghly 0.000Bhagirathi 2.162 0.000Ajay 32.986 33.510 0.000Damodar 16.668 19.170 4.059 0.000Beach 18.967 24.017 75.063 50.447 0.000Dune 22.043 28.471 79.771 54.011 0.564 0.000Tidal flat 402.922 381.706 609.286 559.143 342.559 352.810 0.000

60 B. Purkait, D.D. Majumdar / Sedimentary Geology 308 (2014) 53–62

The linear discriminant analysis (LDA) shows that the variableswhich better discriminate the sedimentary environments are meansize and alpha as is shown by the Wilks' Lamda test (Table 5, Fig. 3a).The more close to zero of the partial Lamda value means the morepower of discrimination. It is noteworthy to mention that LDA has itsown drawback in that it never predicts the contribution of any responsevariable to particular group discrimination like the post hoc analysis;rather it declares the total contribution of the variables in the totalgroup discrimination. Furthermore, canonical discriminate analysishas been applied to derive a linear combination of the selected sixvariables that has the highest possible multiple correlation with thesub-environmental groups. This maximal multiple correlation is calledthe first canonical correlation. The variable defined by the linear com-bination is the first canonical variable or canonical root. The secondcanonical correlation is obtained by finding the linear combination un-correlated with the first canonical variable that has the highest possiblemultiple correlation with the groups.

The larger the eigenvalue, the better the function differentiates thedifferent sedimentary environments. The test result shows that thefirst two canonical variables (mean size and alpha) jointly can explain97.60% of the variance, indicating that these two variables are usefulto discriminate the different sedimentary environments, as is shownby the results of post hoc comparisons (Fig. 3a). The high canonical cor-relation of these two variables (0.98 for mean size and 0.93 for alpha)also proves the same hypothesis regarding their efficiency in group dis-crimination. On the other hand, mean size and sorting explain 87.64% ofthe variance which is not good enough to discriminate the fluvial envi-ronment from themarine in the deltaic system. The rest of the variableshave no significant role in this respect as are depicted by their corre-sponding eigenvalue and canonical correlations.

A smaller Mahalanobis distance (d2) between two groups indicatesthat those are more identical in terms of their characteristic variables;on the contrary, a larger distance between two groups points to hetero-geneity. Classification results indicate that the tidal flat is totally distinctfrom the rest of the sub-environmental groups as a result of their larged2 values (Fig. 4a). The intra-facies d2 values are as follows: beach–duneis 0.564 (marine), Hooghly–Bhagirathi is 2.162 (tidal rivers) and Ajay–

Table 8Final results of the classification summary for training data along with the error rate percenfrequencies and column wise data represents the predicted frequencies for each sedimentary f

Tidal flat Hooghly Bhagirathi Ajay

Tidal flat 24 (100%)Hooghly 18 (81.82%) 3 (13.64%)Bhagirathi 9 (39.13%) 14 (60.87%)Ajay 25 (96.15Damodar 1 (7.69%) 3 (23.08%BeachDuneTotal (predicted) 24 28 17 28Percentage 10.57% 12.33% 7.49% 12.33%Prior error 0.10573 0.09692 0.10132 0.11454Rate 0.00% 18.18% 39.13% 3.85%

Damodar is 4.059 (non-tidal river) (Fig. 4a). On the other hand, theinter-facies d2 values are large enough to make a distinct classificationamong the tidal flat, marine and river environments (Fig. 4a). In thecase of fluvial facies, the character of the non-tidal Ajay River is distinctfrom the tidal Hooghly and Bhagirathi Rivers, whereas the boundary be-tween Damodar–Hooghly–Bhagirathi is closely spaced (d2 = 16.668,19.170) (Fig. 4a) due to the prevailing similarities being active tribu-taries of the Bhagirathi–Hooghly River system.

The classification summary of the training data reveals that the cor-rect group classification for the tidal flats is 100%, Hooghly is 81.82%,Bhagirathi is 60.87%, Ajay is 69.23%, Damodar is 76.92%, beach is43.64% and dunes is 78.13%. Out of a total of 227 samples, only 180have been correctly classified (Table 8, Fig. 4a). The canonical scoreplot reveals that the tidal flat is totally distinct from the other groupsas it is plotted at the very right side of the canonical space (Fig. 3b).The large Mahalanobis distance (d2) between the tidal flat and therest of the groups also confirms its distinctiveness in terms of hydro-dynamic conditions (Fig. 4a). The plot also highlights the separatespace for the marine environment, e.g. beach and dune, where a largeamount of sample sharing was observed from the beach to the duneenvironment as a result of the dynamicity of the beach–dune sandsharing processes. In the case of the tidal environment of theHooghly–Bhagirathi and the non-tidal environment of the Damodar, asmall amount of sharing was observed. Three samples of the Hooghlywere misclassified as the Bhagirathi and nine samples of the Bhagirathiwere misclassified as the Hooghly. These sharings are quite normal asboth rivers carry the same source sediments of the Ganga River. A fur-ther one sample of the Hooghly Riverwasmisclassified as theDamodar;on the contrary, one sample of the Damodar was shared with theHooghly (Fig. 4a, b). This may be due to the partial adjustment of theDamodar sediments with the compatibility of the Hooghly or it maybe statistics by chance. As concerns the classification results, 96.15% ofthe classification is correct for the Ajay River where only one sample(3.85%) was shared with the Damodar River. The total calculated errorfor the model is high (28.19%) due to the eventual high percentage ofthe intra-facies (beach–dune, Bhagirathi–Hooghly, and Damodar–Ajay) misclassification (Fig. 4b)

tage shared by each training component. Row wise distribution indicates the observedacies. See also Fig. 4.

Damodar Beach Dune Total (observed)

241 (4.55%) 22

23%) 1 (3.85%) 26) 9 (69.23%) 13

23 (41.82%) 32 (58.18%) 5514 (21.88%) 50 (78.3%) 64

11 37 82 227 (grand total)4.85% 16.30% 36.12% 100.00%0.05727 0.24229 0.2819430.77% 58.18% 21.88% 28.19%

Fig. 4. Results of canonical discriminant analysis: (a) the canonical score plot shows howthe first two canonical functions classify observation between groups by plotting the ob-servation score for each facies. The plot provides a succinct summary of the separationof the sedimentary facies. The clearer the observations are grouped, the better thediscrim-inant model is. (b) The Classification Summary Plot which shows the observed faciesgroups vs. predicted facies groups. The degree of sharing is reflected by the amount ofmixing of representing color of individual environments vis-à-vis the classificationstrategy.

61B. Purkait, D.D. Majumdar / Sedimentary Geology 308 (2014) 53–62

6. Conclusions

The overall performance of the different statistical distributionsshows that themarine sub-environments (beach and dune) have almostsimilar sensitivities toward the log-normal and the log-skew-Laplacedistribution models, whereas the tidal flat (mixed environment) sedi-ments follow the log-normal distribution. Similarly, on the other hand,for the tidal rivers the log-skew-Laplace is the best-fit and for the non-tidal rivers the log-normal is the best-fit statisticalmodel. So only the flu-vial environments can be well separated from the distribution models.

In terms of the symmetry index (α ~ β), a wide variation of thedegree of sorting among the sub-environments has been observed.The high symmetry index of the tidalflat (2.408) indicates its distinctivecharacter. The beach and dune sands can be well separated in terms ofthe symmetry index (0.662 and 0.290 respectively). On the contrary,the symmetry index varies from tidal rivers (0.314) to non-tidal rivers(0.293) the latter being best sorted. But there are several possibilitiesof intermixing between the symmetry indices of dune sands and non-tidal river sands.

On the other hand, the multiple mean comparisons provide goodoutput for sub-environmental discrimination. The three co-variates;

mean size, alpha and skewness are very effective for identifying the dis-similarities among the deltaic sub-environments. Moreover, it can alsobe said that for the first-hand discrimination of the sub-environmentsthe importance of mean size, alpha and skewness lies in the fact thatthese three variables are most sensitive to the hydrodynamic conditionpertaining to a particular environment. The discriminant analysis alsoproves that out of the six variables (co-variates), mean size and alphahave the highest potential to describe the inherent dissimilaritiesamong the sub-environments. Thus, the hypothetical model developedin this researchmight be applicable in distinguishing different sedimen-tary sub-environments in a deltaic system and also to decode the paleo-environments. Moreover, the textural parameters can be addressed asthe direct derivatives of the hydrodynamic responses and can be usedas proxies to differentiate different sedimentary environments or depo-sitional sub-environments with varying spatial and temporal scales.

Therefore, from the statistical point of view, it appears that it maynot be a coherent model. However, as regards the defined objective ofthis research concerning the inter-sub-environmental group discrimi-nation, the performance of the given model may be considered asgood enough as it clearly established the distinct fields for each sub-environment using the six characteristic variables: mean size, sorting,skewness, kurtosis, alpha and beta.

Acknowledgments

A part of the paper was presented at the 5th Joint Meeting of APN-Mega Deltas and IGCP-475 DeltaMAP project “International Conferenceon DELTAs”(Shangai–Quindao Venue, China) Shanghai, Oct. 26th–30th,2008. The 1st author is grateful to the project leaders Prof. Z. Chen, Prof.S. Goodbred and Dr. Yoshiki Saito for their invitation to presentthe paper. Thanks are also due to the Head, Department of Geology,University of Calcutta for providing infrastructural facilities during thepreparation of the manuscript. Editorial comments and suggestionsfrom Jasper Knight and Emmanuel Poizot were very helpful in themodification of the manuscript.

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