Mathematical Geology, I/ol. 2, No. 2, 1970

Ordination of Sediments from the Cape Hatteras Continental Margin 1 Peter H . Feldhausen 2

Ordination is a multivariate technique developed by plant ecologists which has proven effective in the interpretation of paleoenvironments. It allows gradational relationships among samples to be depicted h~ contrast to other quantitative techniques which classify samples into discrete groups, bT this study, ordination is used to interpret textural data for 62 bottom samples taken from the Cape Hatteras, North Carolina, continental margin. The ordination suggests the existence of six sedimentary facies that are similar to those obtained by cluster analysis using a dendrograph display. The facies represented are: littoral sands and outer-shelf shelly sands," inner-shelf sands; outer-shelf sands and silts; outer-shelf slope silts; and two highly biogenic, deep-water silt and clayey silt facies with similar characteristics. The facies are related in a qualitative manner to the environmental processes operating off Cape Hatteras.

INTRODUCTION Ordination, a multivariate technique developed by plant ecologists Bray and Curtis in 1957, has proven effective in interpreting paleoenvironments (Park, 1968) and recent marine environments (Park and Feldhausen, 1969). Ordination is proposed here as an alternative to the use of grain-size parameters in characterizing sedimentary environments. This study is intended (1) to emphasize the advantages realized by the use of the ordination technique applied to environmental analysis, and (2) to demonstrate this by an ordination of sediment samples taken from the Cape Hatteras continental margin. The facies suggested by the ordination will be related to the environmental processes operating off Cape Hatteras. The term ordination ("Ordnung") probably was proposed first by Ramensky in 1930, and following Goodall (1954), it may be defined as an arrangement of objects in a uni- or multidimensional continuum as opposed to a classification in which the objects are arranged in discrete classes. The objects ordinated by either R- or Q-mode techniques are arranged within the continuum so that the proximity of any two objects is a measure of their dissimilarity. The ordination method of analysis is useful because it indicates the gradational relationships among samples. The same relationships may be obscured in a standard cluster analysis.

xManuscript received 6 January 1970. ChicagoBridgeTechnical Paper No. 5139. 2 ChicagoBridge and Iron Co. (USA). 113

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Peter H. Feldhausen

Factor analysis as an analytical technique is most useful in the absence of a hypothesis to account for the observed variations in measured sediment properties. A large number of phenomena within the sample domain are determined by a small number of environmental factors. In ordination we are concerned with the elements used to describe a sediment's composition. Sample structure and composition are regarded as the key to the interpretation of the environment. Although the factor axes obtained by factor analysis may be orthogonal, they are not necessarily independent geologically. The subsequent results may be difficult to interpret. Ordination, on the other hand, depicts with some degree of quantitative exactness the composition of sedimentary facies responding to a set of physical, chemical, and biotic environmental factors and their interaction. Ordination has been employed as a method of analysis in a variety of ecologic and environmental studies (of vegetation by Loucks, 1962, Ream, 1963, and Knight, 1964; of bird communities by Beals, 1960; of soils by Hole and Hironaka, 1960; of paleo- and paraecology by Park, 1968, and Park and Feldhausen, 1969; and of numerical taxonomy by Kaesler, 1969, and Rowell, 1969). The 62 bottom samples used in this study were collected in 1963 by the U.S.

Figure 1A. Chart of Cape Hatteras continental margin with sediment sampling stations occupied by USC&GS Explorer during July 1963. Limits of Gulf Stream and position of Virginia and Carolina Coastal Currents are shown. DS and WS stand for Diamond Shoals lightship station and Wimble Shoals, respectively.

Ordination of Sediments from the Cape Hatteras Continental Margin

115

Figure lB. Chart of Cape Hatteras and vicinity. Sediment sampling stations occupied by USC&GSExplorerduring July 1963are shown.

Coast and Geodetic Survey (now a part of Environmental Science Services Administration) from the Cape Hatteras continental shelf, slope, and rise. The sampling localities are aligned along two traverses (Fig. 1), one southeasterly from Diamond Shoals lightship station (marked DS) and the other easterly from Wimble Shoals (marked WS). Core subcuts have larger "sample" numbers than their corresponding surface sample. For example, samples 2, 3, and 4 are core subcuts from sample station 1, whereas 5 is the next shoreward surface sample on the Wimble Shoals traverse. The sedimentation, paraecology, and physical oceanography of the study area have been discussed by Feldhausen (1967), Milliman, Pilkey, and Blackwelder (1968), Rowe

116

Peter H. Feldhausen

and Menzies (1968), Field (1969), Park and Feldhausen (1969), and Pilkey and Milliman (1969), among others. ORDINATION METHOD Similarity Index

The choice of a suitable index of similarity between two objects depends mainly on the type of data compared. Product-moment correlations may be unsatisfactory in studies of this type because they require that the objects' attributes be related linearly and that the paired objects hold the same attributes in common (Johnson, 1962). Distance and associative coefficients examine the correspondence of each attribute separately and, therefore, are more useful for comparison. The associative similarity index C = 2w/(a+b), Sorenson's coefficient (Sokal and Sneath, 1963), has been used for many published ordinations and will be used in this study. Iterative Method

The choice of reference sample pairs is crucial to success of an ordination because positioning of the samples within the continuum depends on their relationships to the reference samples. Samples which are dissimilar will be more useful for judging intersample relationships than will samples which are similar. Several criteria may be used to select reference samples; lowest similarity (Bray and Curtis, 1957), most dissimilar (Beals, 1960), and standard deviation criteria (devised by F. G. Goff while at the University of Wisconsin Plant Ecology Laboratory) are among the most common. Principal eigenvectors (Goff and Cottam, 1967) and principal components (Rowell, 1969) also have been used for ordination axes construction. Although these methods produce ordination diagrams with similar sample distributions, the position of a given sample may change 20 percent or more from one diagram to another. An ordination technique has been developed by Goff and Cottam (1967) which assigns a unique position to each sample, being based on dissimilarity to all other samples rather than to the reference sample pair only. For unidimensional ordination, their algorithm may be described as follows: (1) Similarity index values are generated and subtracted from unity to create dissimilarity indices. (2) The reference sample pair is selected. The lowest similarity criterion of Bray and Curtis (1957) is a satisfactory method for this purpose. Index values of 1 and 10 are given to the reference samples. (3) The weighted mean index values of all samples are computed by summing the product of the dissimilarity of each sample to the initial reference samples times the index value of the corresponding reference samples, and dividing by the sum of the dissimilarities. Thus, if a sample had 30-percent dissimilarity with one reference sample and 50 percent with the other, its uncorrected index value would be (30 • 1)+(50 x 10)/(30+ 50) = 6.63

Ordination of Sediments from the Cape Hatteras Continental Margin

117

After all samples, including the two reference samples, have been given index values, the highest and lowest values are found and all values transformed to the original t-10 index scale. (4) A new weighted mean index is computed for each sample by using all samples rather than the reference samples only, that is, the new unsealed index for the kth sample is given by

i=1

i=1

where S~k is the dissimilarity between sample k and sample i, and Vi is the previous index of the ith sample. (5) The calculated values of Ik then are transformed on the 1-10 scale. Step 2 is re-entered with these values and the process repeated until the system of index values becomes stable. Final sample ordering is independent of the initial choice of reference samples because this choice serves only to determine the number of cycles necessary to stabilize the system. With each iteration the position of all samples is free to change and new samples may be chosen as axis endpoints. Usually 8-15 iterations are required to achieve system stability. To display the ordination, the final reference samples are made x-axis endpoints and the axis length is set equal to their original dissimilarity. Final index values for the remaining samples are rescaled and arrayed along the axis. In this manner an x-ordinate is assigned to every sample. Ordering the samples along an x-axis with the above algorithm does not account for all the dissimilarity between samples. The remaining dissimilarity is calculated by subtracting the statistical distances of the ordered samples from their original dissimilarity values. The residual dissimilarity matrix formed in this manner serves as the basis for the selection of a y-axis reference sample pair. Theoretically, the process of axis extraction could be repeated as long as the elements of the final residual dissimilarity matrix are predominately nonnegative. However, axes which reduce the dissimilarity by less than 10 percent are of little analytical value. Within a multidimensional ordination the distance between two samples is proportional to their dissimilarity only if sufficient axes have been extracted to account for most of the dissimilarity expressed in the original matrix.

ORDINATION OF CAPE HATTERAS SEDIMENTS R - M o d e Ordination

The bottom samples were compared against each other with Sorenson's coefficient C = 2 w / ( a + b ) computed for the sediment weight percent contained in each phi-size class. C is the similarity index, a is the sum of the weight percents in one sample and b is the sum for the second sample, and w is the sum of the lesser weight percents held in common by the paired phi classes in samples a and b. If two samples have exactly the same weight percents in all their paired phi classes, C is unity. Conversely, if they hold

Peter H. Feldhausen

118

Table I. Statistical Data on Variables Used in Q-Mode Analysis

Phi-size class

Max. presence (in percent)

Mean presence (in percent)

Max. weight (in percent)

Mean weight (in percent)

18 31 77 95 100 100 95 85 81 77 81 84 86

3.6 1.6 1.7 4.2 13.1 27.1 16.4 9.9 9.2 15.9 5.7 3.3 3.8

16 6 19 71 90 71 37 26 21 58 20 14 11

0.6 0.5 1.3 3.9 13.1 27.1 15.6 8.5 7.4 12.3 4.6 2.8 3.3

< --1 0 1 2 3 4 5 6 7 8 9 10 > 10

R-Mode

Ordination

Phi Unit VQriobles 9 5

0 o_ 1

>1 O9 6 7~ 2

10. 9

1

9

8o

Figure 2. Two-dimensional R-mode ordination of phi-size classes used as variables in Q-mode ordination and cluster analysis (rrERAX computer program for IBM System 3601Model 50 supplied by R. A. Park, Department of Geology, Rensselaer Polytechnic Institute). Reference variables are < - 1 and 7 phi, and 4 and 8 phi. Total dissimilarity reduction by two axes is 70.2 percent.

Ordination of Sediments from the Cape Hatteras Continental Margin

119

Table 2. R-Mode Ordination Axes Statistics Axis First endpoint Second endpoint Axis length Dissimilarity reduction (percent) Total dissimilarity reduction (percent)

First < - 1 phi 7 phi 97.3

Second 4 phi 8 phi 63.0

Third 3 phi < - 1 phi 24.3

54.6

15.6

2.3

54.6

70.2

72.5

no classes in common, C is zero. Statistical data for the 13 variables are listed in Table 1. An iterative program written by R. A. Park (Department of Geology, Rensselaer Polytechnic Institute) was used to obtain a unique R-mode ordination of the phi-size class variables (Fig. 2). Initial reference variables were selected by the lowest similarity criterion and 15 iterations were programmed per axis. Pertinent axis data are provided in Table 2. Figure 2 indicates that most of the phi-size classes are relatively independent of each other in distribution. However, some of the variables are redundant because those of 6 phi and greater group together at high levels of similarity. All variables were used in Q-mode analysis. Q-Mode Ordination A unique Q-mode ordination was constructed with Park's iterative program using the same dissimilarity matrix and reference sample selection criterion as in the R-mode ordination. Axis data are given in Table 3. Reference sample composition summary data are given in Table 4. The z axis has been omitted from the ordination diagram shown in Figure 3 because it contributes little to the dissimilarity reduction. Table 3. Q-Mode Ordination Axes Statistics Axis First endpoint Second endpoint Axis length Dissimilarity reduction (percent) Total dissimilarity reduction (percent) Iterations to stabilize endpoints Iterations to stabilize samples

First (x)

Second(y)

Third (z)

59 53 66.7

26 4 37.8

52.9

12.8

7.5

52.9

65.7

73.3

2

3

9

7

12

16

37 5 96.7

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Peter H. Feldhausen

T a b l e 4. Composition of Reference Samples ~

C~

Sample 37 5 59 53 26 4

X~p

- 1.00 1.55 - 1.00 2.30 3.05 1.70

S~

1.32 7.24 2.33 3.88 6.28 6.78

0.96 2.18 2.43 0.96 2.14 1.71

SK~ 1.20 -0.28 0.41 1.30 0.18 -0.61

Shepard class.

P/B

MO no.

Biotope

Sand Clayey sift Sand Sand Clayey silt Silt

0.13 5.17 1.40 0.86 2.11 6.05

43 14,273 2,698 1,302 21,703 16,846

Shelf Rise Slope Shelf Rise Rise

C is the first percentile, .~ is the mean diameter, S is the sorting (standard deviation), the skewness, P/B is the planktonic-to-benthonic foraminifer ratio, and MO is the microorganism number (Biotope from Park and Feldhausen, 1969).

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• Figure 3. Two-dimensional Q-mode ordination of Cape Hatteras sediments (ITERAX computer program for IBM System 3601Model 50 supplied by R. A. Park, Department of Geology, Rensselaer Polytechnic Institute). x-axis endpoints are samples 37 and 5, and y-axis endpoints are 59 and 53. Total dissimilarity reduction by two axes is 65.7 percent. Six sedimentary facies are suggested by ordination; they are labeled I through VI.

Ordination of Sediments from the Cape Hatteras Continental Margin

121

G R A D I E N T ANALYSIS Textural Gradients

I f sample attributes are plotted at their corresponding coordinates, patterns will be produced within the ordination. Areas of high value commonly are surrounded by areas o f progressively lower values. Environmental significance may be assigned to the gradients and the ordination axes by isolating the causal interaction of the attributes with environmental phenomena. In this manner environmental significance will be attached to the sedimentary facies found within the study area. Preliminary environmental inferences may be drawn from Table 4. Sample 37 has the lowest phi-mean diameter and sample 5 the highest. Even though three of the reference samples are classified as sands, they are separated within the ordination because their phi weight percents are different. Thirty-five percent of 37 is coarser than one phi, whereas less than 12 percent of 59 and less than 2 percent of 53 are coarser than one phi. The clay content o f the six reference samples, in order of ascending x ordinate, is trace, 4, 2, 9, 23, and 37 percent. A marked decrease in environmental energy from sample 37 to 5 is suggested. A similar gradient occurs between 53 and 59. However, the x axis accounts for more than four times as much dissimilarity reduction as does the y axis.

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122

Peter H. Feldhausen

A more precise picture of the sediment textural changes within the ordination may be obtained from Figure 4. In this figure sample mean phi diameter X, sorting (standard deviation) S, and skewness SK are plotted against their x and y ordinates. The straight lines fit to the data by a least-squares technique have the following equations: Xx Sx

= 0.06X+1.034, = 0.01X+0.93~b SK:, = -0.02X+l.65~b

Xy = -0.04Y+6.564~ Sy = -0.01Y+2.19~b SKr = 0.02Y-0.19q~

The gradients inferred from Table 4 are substantiated. Mean diameter, sorting, and skewness decrease with increasing x and decreasing y. A slight improvement in sorting occurs in some of the finer samples, reflecting a decrease in microorganism number (the number of microorganisms per gram of dry, unwashed sediment) without any noticeable change in planktonic-to-benthonic foraminifer ratio. The ordination continuum (Fig. 3) reflects a wide range of rapidly changing environments as revealed by the steep linear gradients and the extreme values of the textural parameters.

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Ordination of Sediments from the Cape Hatteras Continental Margin

123

Faunal Gradients

Sample microorganism number (MO no.) and planktonic-to-benthonic foraminifer ratio (P/B), if plotted vs their x and y ordinates in Figure 5, indicate an increase in water depth from shallow in the vicinity of sample 37 to deep in the vicinity of sample 5; the same depth trend exists between samples 53 and 59. The trends are represented by MO= -- 428.61X-13383.9 PBx = 0.06X-2.18

MOy = -478.08Y+35340 PBy -- -0.08Y+5.62

The curvature of the lines in Figure 5 is a product of the semilogarithmic plot. Scatter of the indices in the region of coarse sediments suggests a relict history for many samples or their transport into deeper-water. Scatter among the very fine samples suggests down-the-slope transport or differential winnowing related to geostrophic bottom currents and topographic anomalies. A Q-mode ordination of the 62 samples was made by Park and Feldhausen (1969) using Beals' method (1960) and 21 nonspecific bionomic type numbers (Park, 1968).

0.5

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Figure 6. Q-mode cluster analysis dendrograph display of Cape Hatteras sediments (dendrograph program for IBM System360/Model 50 supplied by R. B. McCammon,Department of Geological Sciences, University of Illinois at Chicago Circle). Relationship to six sedimentaryfacies is shown.

124

Peter H. Feldhausen

Three basic biotopes were delimited on the basis of the various bionomic types and sediment textural gradients through the ordination. They are a shelf, a slope, and a rise biotope (also see Table 4). In the sediment and biotic ordinations, the samples from the continental slope and rise are more closely related to each other than to the continental shelf samples. The distinct separation between the shelf and the deepwater biotopes was found to occur at a depth of 60 m, which roughly coincides with the limit of attached plants, and with the beginning of the bathymetric break in slope and the approximate inner margin of the Gulf Stream at Cape Hatteras. SEDIMENTARY FACIES ANALYSIS The major sample groupings within the sediment ordination (Fig. 3) are composed of samples with high intersample similarity. Their response to physical, chemical, and biotic environmental processes was similar. Consequently, the major sample groupings are considered to represent sedimentary facies. Although the facies boundaries are not quantitatively defined, the relative distance between neighboring samples gives approximate boundaries. The ordination suggests that five sedimentary facies are present in the study area. They are not significantly different from the sample clusters of the dendrograph (McCammon, 1968) displayed in Figure 6. The dendrograph

0.5 Q-Mode Dendrograph

0.6

0.7

+ o"

0,8

0.9

1,0

Figure 7A. Q-mode cluster analysis dendrograph display of Cape Hatteras sedimentswith patterns found in Figure 7B.

Ordination of Sediments from the Cape I-][atteras Continental Margin

125

Figure 7B. Two-dimensional Q-mode ordination of Cape Hatteras sediments. Concentriccontours reflect pyramidalstructure of dendrograph. Patterns correspond to those in Figure7A.

indicates that six facies are present and these have been labelled I-VI on the ordination diagram. The gradational aspect of the ordination display shows that facies V and VI are closely related, a fact not established by the dendrograph. The sample groupings of the two diagrams compare at the 92-percent level. The dendrograph and ordination have a similar structure, even though one depicts discrete relationships and the other gradational relationships. The pyramidal structure of the dendrograph is projected onto the ordination diagram in Figure 7. The concentric contours enclose samples as dictated by the cluster branches and demonstrate the pyramidal structure of the ordination facies. Ordination facies I is related to Passega's (1957) beach pattern VII and facies II and III to his tractive transport patterns I, IV, and V. Samples from the three facies may be classified as beach sands, surf-zone sands, offshore and shelf sands, and shell sands according to the scatter diagram presented by Inman and Chamberlain (1955). Probably only samples 37, 38, 44, and 57 represent relict beach-type deposits, because the coarse fractions of 59 and 60 are composed almost entirely of broken shell fragments, and that of 58 of small clinkers. According to Pilkey and Milliman (1969), discrete relict beach sediments are quantitatively unimportant within the study area despite the lowering of sea level up to 123 m during Wisconsin Stage glaciation (Donn, Farrand, and Ewing, 1962).

126

Peter H. Feldhausen

These writers also suggest that Cape Hatteras and vicinity is one of the few areas along the Carolina coast where sediments now are being deposited. Deposition is enhanced where the Virginia and Carolina Coastal Currents meet off Cape Hatteras (see V.C.C. and C.C.C. in Fig. 1). Both northeast and southwest prevailing winds blow onshore on one side of the Cape and offshore on the other. Thus, the combination of winds, Cape geography, and circulation pattern retards and deflects offshore one of the opposing current gyres. Sedimentation takes place as the gyres slow or as they interact with the Gulf Stream. Samples 10 through 14 are biogenic turbidites. These and other samples from facies IV have low planktonic-to-benthonic foraminifer ratios, even though their micro-organism numbers are moderate to high. Faunal displacement also is indicated by Carter's method (1951). These facts suggest down-slope transport, processing by geostrophic bottom currents, or both. The sediment source may have been the outer shelf because sample 42 is included in this facies. Sample 42 is from the same geographic locality as samples 41, 43, 45, and 46, which have a much greater sand content and lower planktonic-to-benthonic ratio and micro-organism number. Heezen, Hollister, and Ruddiman (1966) postulate that the Gulf Stream deposits its bedload after its inner reaches pass from the shelf into deeper water near the Cape. Ordination facies IV lying off Wimble Shoals may represent the terrigenous and biogenie sediment load that has been deposited by the Gulf Stream and the Virginia Coastal Current. Some sediments may have been carried into deeper water through the Hatteras Canyon system as suggested by the bathymetric contours in Figure 1. Some may have been transported south b y t h e Western Boundary Undercurrent, which is known to reach velocities as high as 21 cm/sec in the study area (Barrett, 1965). Samples from facies V have a fine texture, high standard deviation, and low skewness. This suggests markedly lower environmental energy than was associated with previously described facies. Samples in facies V are almost identical with those in VI, the latter having negative skewness and generally larger microorganism numbers. The usually high first percentile values can be attributed to the coarseness of the Orbulina, Globigerina, and other planktonic foraminifers which comprise the sand fraction of the samples; some quartz sand grains also are present. Samples from facies V and VI are Globigerina silts and clayey silts. Petrographic evidence has been used by Feld (1969) to show that the source of the quartz sands found on the lower slope and rise (ordination facies V and VI) was the continental shelf north of Cape Hatteras. Presumably the sands were carried southward by the Western Boundary Undercurrent and by the Virginia Coastal Current and funneled into deeper water through the Hatteras Canyon system.

Facies Environmental Significance

The environmental information derived from the sediment textural and biotic gradients is used to attach environmental significance to the ordination facies as follows:

Ordination of Sediments from the Cape Hatteras Continental Margin

127

(1) Facies I represents littoral sands and outer-shelf shelly sands. (2) Facies II represents an inner-shelf environment with some relict sandy sediments. (3) Facies III represents an outer-shelf sand and silty sand environment. (4) Facies IV includes outer-shelf and upper-slope organically rich sandy silts which have experienced down-slope transport, transport by geostrophic bottom currents, or both. (5) Facies V and VI represent Globigerinasilts and clayey silts which accumulated in quiescent, deep, and organically productive water.

CONCLUSION Ordination is a powerful tool for the analysis of modern depositional sedimentary environments and should be applicable particularly to the study of ancient environments. A previous knowledge of sample environmental and geographic position is not a prerequisite to the analysis. The ordination is constructed from an objective consideration of the entire grain-size distribution. Samples are arranged in a continuum so that their proximity to neighboring samples is a measure of their dissimilarity. Consequently, gradational intersample relationships are displayed instead of discrete classifications. Its axes are not single grain-size parameters, and they do not represent single environmental factors. Instead they are compositional gradients related to the interaction of the sediment and its environment. This facilitates the classification of sediments into mappable facies, and the isolation of the causal relationship between the facies and their environment through gradient analysis. The advantages of the ordination technique were demonstrated during the interpretation of textural data from 62 samples collected from the Cape Hatteras continental margin. Six sedimentary facies were suggested by the ordination which are almost identical to those obtained by cluster analysis. The facies possess a pyramidal structure similar to that of the dendrograph display. Through gradient analysis the facies were related qualitatively to the environmental processes operating in the vicinity of Cape Hatteras.

ACKNOWLEDGMENTS This paper is based on data presented in a thesis submitted as partial fulfillment of the masters degree at the University of Wisconsin. Bottom samples were collected on Explorer Operation-438 and loaned to the writer by R. B. Starr, U.S. Coast and Geodetic Survey (now under ESSA), and the thesis research was supervised by L. M. Cline. Results of corroborative research were made available by R. A. Park, who furnished the ITERAXordination computer program. The study and manuscript were improved by the suggestions of R. B. McCammon, who also furnished the dendrograph program. This paper has been approved and released for publication by Chicago Bridge and Iron Company.

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Peter H. Feldhausen

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