SHAPE RESPONSE OF PLEiSTOCEN-E
-_ AND RECENT SEDIMENT--CHUKCH| SEA:
A FOURIER ANALYSIS

Thesis for the Degree of M. S.
MICHIGAN. STATE UNIVERSITY
JAMES WATON KENNEDY

1972 .

LIBRA. Y

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University

 

 
  
 

  
 
      

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LIBRARY BINDEBS

ABSTRACT

SHAPE RESPONSE OF PLEISTOCENE AND RECENT
SEDIMENT--CHUKCHI SEA: A FOURIER ANALYSIS

BY

James Waton Kennedy

A Fourier analysis of grain shape was performed to determine
if sand grain shape is a variable which will display some general
utility in making inference about provenance, transport and deposi-
tional environment of Holocene sediments in the Chukchi Sea.

The shape, expressed as amplitudes of a Fourier series, was
analyzed using both a pattern recognition-clustering program, ISODATA,
and a complex analysis of chi-square contingency tables.

The results indicate that the shape variable is extremely
sensitive to changes in provenance, transport and depositional envir-

onment o

SHAPE RESPONSE OF PLEISTOCENE AND RECENT SEDIMENT--

CHUKCHI SEA: A FOURIER ANALYSIS

BY

James waton Kennedy

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Geology

1972

ACKNOWLEDGMENTS

I gratefully acknowledge Dr. Joe S. Creager, of the University
of'Washington Department of Oceanography, and National Science Found-
ation Grant GA 28002, for providing me with the samples on which this
research was based. Dr. Creager's comments, criticisms and suggestions
were invaluable to the success of this project.

I also extend grateful appreciation to Dr. Robert Ehrlich, my
thesis advisor, for his tireless effort and enthusiasm throughout the
entire project. Without his constant encouragement and helpful discus-
sions this project would have taken considerably more time.

Dr. Bernhard Weinberg, of the Computer Science Department at
Michigan State was extremely helpful in working out and assisting in
many of the computer programs used.

Thanks also go to Drs. Sam Upchurch and Robert Anstey, my
committee members, whose criticisms were quite helpful.

Last, but not least, I wish to express my sincere gratitude to
my wife, Sharon, for her patience and understanding throughout the
entire period, during which the project often took precedence over the

family.

ii

TABLE OF CONTENTS

Contingency Tables

LIST OF TABLES . . . . . . .
LIST OF FIGURES . . . . .
Chapter

I. INTRODUCTION . . . . .

II . GENERAL STATEPENT OF THE PROBIEM

III. METHODS . . . . . . .

IV. RESULTS . . . . . . .
Hierarchy I . .
Hierarchy II .

V . CONCLUSIONS . . . . .
LIST OF REFERENCES . . . . .
.APPENDICES

A. ISODATA Cluster Center Analyses

B. Numerical Values for Chi-Square

C. Locality Maps . . . .

iii

Page

iv

11
18
18
21
24

26

27
32

34

LIST OF TABLES

Page
Results of contingency tables for hierarchy I. . . 15
Results of contingency tables for hierarchy II . . 16

Sample designations as related to contingency table
hierarchies and sample locations . . . . . . 17

Numerical values for chi-square contingency table
(hierarchy I). . . . . . . . . . . . . 32

Results of contingency tables (hierarchy II). . . . 33

iv

LIST OF FIGURES

Figure Page
1. General location map of Chukchi Sea region . . . . 2
2. Modern bathymetry of Chukchi Sea . . . . . . . 6
3. Pre-B sand bathymetry of Chukchi Sea . . . . . . 7
4. Schematic current pattern with south wind . . . . 9
5. Schematic current pattern with north wind . . . . 10
6. Map showing core locations . . . . . . . . . 14

7. ISODATA cluster center analysis (harmonic 2;
all locations except location 1). . . . . . 27

8. ISODATA cluster center analysis (harmonic 10;
all locations except location 1). . . . . . 28

9. ISODATA cluster center analysis (harmonic 14;
all locations except location 1). . . . . . 29

10. ISODATA cluster center analysis (harmonic 18;
all locations except location 1). . . . . . 30

11. ISODATA cluster center analysis for harmonics
2, 10, 14 and 18 at location 1 . . . . . . . 31

12. Map showing locations of most rounded (x) and
most angular (o) B sands . . . , , , , , , 34

13. Map showing locations of most rounded (A) and
most angular (*) B sands. . . . . . . . . 35

CHAPTER I

INTRODUCTION

The Chukchi Sea is located to the north of the Bering Strait,
between Alaska and Siberia (Figure 1). As shown by Creager and
McManus et al. (1969), the surface dispersal mechanisms and charact-
eristics are markedly influenced by the strong northward flowing
Bering Strait Current, which introduces silts and sands from a Yukon
River source to the south into the Chukchi Sea. During the last
glacial maximum, sea level was lowered sufficiently to expose all of
the Chukchi Sea south of wrangel Island permitting a subaerial erosion
surface to deveIOp. As sea-level rose, a transgressive sedimentary
sequence was deposited over this surface. Initially the sediment
available for dispersal and inclusion in the transgressive sequence
was the reworked surface sediment and detrital sediment from the sur-
rounding land mass. The main sediment source was the Kobuk and Noatak
rivers and their drainage basins (Creager and MeManus, 1965). This
sedimentary regime must have changed dramatically after the sill at
Bering Strait was breached by rising sea level, permitting establish-
ment of the Bering Strait Current and the introduction of its sediment
load.

The significant change in sediment source should produce a

marked change in sediment character within the transgressive sediment

.Auowmouu noummv seamen mum “noxaeo no use nowuuooH Managua.-.a mmpuHm

 

3

sequence north of Bering Strait that identifies the time of intro-
duction of first Yukon River sediment.

Ehrlich and Weinberg (1970), have shown that grain shape, if
characterized exactly, can carry important information concerning both
the provenance of sediments and their response to various processes.

Assuming this method is effective, then a powerful tool exists
for objectively interpreting the sedimentary record in this area. It

was toward this end then, that the Chukchi Sea samples were evaluated.

CHAPTER II

GENERAL STATEMENT OF PROBLEM

As part of a more comprehensiVe study of the Holocene history
of the Chukchi Sea, a detailed stratigraphy of the last transgressive
sedimentary sequence has been formulated (Creager et al., in prepar-
ation). 0n the basis of texture, mineralogy, microfauna, subbottom
profiles, and radiocarbon dates, the type stratigraphy of the trans-
gressive sequence north of the Bering Strait and west of Point Hape
consists from the base upwards of a) z-clay--a barren, compacted pre-
Holocene sediment separated unconformably from an overlying; b) B-sand--
a basal sand presumably deposited near sea-level along the shores of
a large Kobuk-Noatak estuary; c) A' c1ay--an upward fining sediment
deposited in gradually deepening water; d) A" silt overlain by A'
silt-~upward coarsening sediments postulated as resulting from intro-
duction of silt from the south; e) A sand--a sand deposited under
fairly stable sea-level conditions. Immediately north of Bering Strait
the A sand is interpreted as part of a northward moving depositional
front associated with Bering Strait Current. Elsewhere the A sand is
believed to be reworked basal sand or of local derivation.

Clearly, sediment in the Chukchi Sea has been affected by a
variety of provenance, transport and depositional effects. The sedi-

ment emanating from the Kobuk-Noatak and Yukon drainages have different

S
provenances. In addition these sediments have undergone differing
degrees of ice action (perms-frost, sea or glacial ice). During
transport much of these sediments suffered transportation abrasion
on beaches and in rivers. Sediments affected by some or all of these
factors, some of which involve the Opening of the Bering Strait, are
now present in the Chukchi Sea.

Thus, if Fourier shape analysis results indicate a lack of
significant difference between samples, this will tend to reflect
more upon the adequacy of the method, rather than a high degree of
homogeneity in the provenance and history of the samples.

Alternatively, the presence of significant differences between
samples would permit useful interpretations relative to the deposi-
tional history postulated in the stratigraphic sequence presented
above.

Significant differences do, in fact, exist. However, because
of the small number of samples, a detailed explanation for these
differences cannot now be undertaken.

Samples were collected to test hypotheses concerning past and

present sedimentary provenance and transport hypotheses.

Bathymetry, Paleobathymetry and Currents
Comparison of the present bathymetry (Figure 2) with the
paleobathymetry of the pre-Holocene transgression surface (Figure 3)
clearly indicates the significance of the Bering Strait Current
derived sediment in changing the bathymetry of the Chukchi Sea conti-
nental shelf surface north of Bering Strait. The paleobathymetric

sill had depths of 50-52 meters but the modern sill is at depths of

.Auowmmuo nouns «mucous a“ mu30ucoov mom wsoxsnu mo muuuahnuwn vase nuoumuu.m umDUHm

 

46-48 meters. The filled valley south of Cape Thompson (Figures 2,
3) is related to a previous lower sea level--Kobuk-Noatak delta
(Creager and McManus, 1967).

In deciphering the transgressive history of the Chukchi Sea
sediments it is of permanent importance to: (1) specifically identi-
by, if possible, each sand unit as either a wave reworked shallow-
water transgressive sand or a deeper-water current transported advancing
depositional front sand; and (2) identify characteristics of a sedi-
ment which can place its source and hence identify the onset of sedi-
ment contribution by the Bering Strait Current (Figures 4 and 5). It
is of interest, then, to examine two separate analytical hierarchies
in the contingency tables, in order that both an overall A-B contrast
and overall between A and between B comparisons can be made. Addition-

ally, individual A-B comparisons and between-core contrasts are use-

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CHAPTER III

METHODS

In evaluating the grain shape of the Chukchi Sea samples,
quartz was chosen as the mineral to be analyzed. The reason for
choosing quartz, vis-a-vis some other mineral was two-fold. First
of all, quartz is ubiquitous. Secondly, quartz shape, because of
its presumed lack of cleavage control, was thought to carry a more
uniform response history to the processes at work in eroding, trans-
porting and ultimately depositing the sediment. The size of the grains
analyzed ranged from medium silt to medium sand.

In preparing samples for analysis, they were first thoroughly
washed, in order to remove most of the fine, organic rich muds holding
the grains together. After filtering and drying, the grains were
mounted on petrographic slides using a mounting oil. The grains,
when strewn on the slide, would then theoretically position themselves
in their area of maximum projection.

In order that the shape would be characterized as exactly as
possible, a camera lucida was used which projected the image of the
grain onto a starburst pattern, consisting of 48 radial lines of equal
angular spacing, upon which the outline of the grain was traced. An
automatic digitizer was then employed which would assign a four digit

X, and a four digit Y co-ordinate to each point at which the grain

11

12

boundary crossed one of the 48 radial lines, and punch these co-
ordinates in a counterclockwise pattern onto Hollerith cards.

It has been shown empirically (Redmond, 1969; Waltz, 1972;
Orzeck, 1972), that a sample size of 100 grains is sufficient to
overcome any bias due to incorrect digitization of a small number of
grains.

Once digitized, the first twenty harmonics of a Fourier series
were calculated for each grain using a computer program developed by

Dr. Bernhard Weinberg (see Ehrlich and Weinberg, 1970, for a discussion
A of Fourier analysis of grain shapes).

Each sample, consisting of 100 grains, the shape of each des-
cribed by values of 19 harmonic amplitudes, was evaluated by a pattern
recognition procedure, ISODATA. ISODATA is an acronym for Iterative
Self Organizing Data Analysis Technique (A) (Ball and Hall, 1967).
ISODATA is a clustering technique for multi-variate data which uses
an average response pattern to represent a group of patterns. The
endpoint of this technique is to minimize the sum of the squared
distances of each data point from the nearest cluster center (Ball
and Hall, 1967). The resulting output then, has distributed the
grains in each sample into clusters, the mean shape of which can be
inferred from an analysis of the harmonic amplitudes of the cluster
centers.

In addition, a complex analysis of chi-square contingency tables
was performed, harmonic by harmonic, using samples as rows, as the
harmonic amplitude variation divided into six categories and the

columns. The chi-square analyses were performed to identify those

l3

harmonics that carried significant shape information and to locate the
origin of significant variation within each such harmonic. The degrees
of freedom of the total chi-square was partitioned in a manner equi-
valent to Kimball's method for partitioning degrees of freedom in chi-
square (Kimball, 1954).

The chi-square analyses were hierarchical in character. How-
ever, two different hierarchies were evaluated; one for harmonics 2-
10, and another for harmonics 11-20.

The hierarchy employed for harmonics 2-10 included an overall
test for A sands versus B sands, as well as breakdowns to show selected
within and between A sand variations. For harmonics 11-20, the hier-
archy was selected so as to test for significant variation between A
and B sands within single cores, as well as to test for significant
between-core variation.

Admittedly this procedure injects some ambiguity into data inter-
pretation. However, all comparisons must, by definition, be estab-
lished before data are inspected. In the case of the Chukchi Sea sam-
ples, two hierarchies were of equal interest. Both, however, could
not be performed on the same set of data. Therefore, separate hier-
archical analysis of harmonics 2-10, and 11-20 were performed.

This procedure depends on redundancy between the two sets of
data, an assumption warranted by previous studies (Redmond, 1969;
Waltz, 1972; Orzeck, 1972). Tables 1 and 2 show the hierarchies
employed in the contingency tables. Table 3 shows how the members
of the hierarchies are related to the core locations that are dis-

played on Figure 6.

 

 

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FIGURE 6.--Map showing core locations (see TABUE 3 for sample designations).

15

TABLE 1.--Results of contingency tables for hierarchy I.

 

 

 

Harmonic

Source of
ygriapility g,f, Z 3 4 5 6 7 8 _9 10
Total 85 X X
A vs B* 5
Within
A.vs B 80 X X X
Between A 35 X
.A

2+3+4+5+

9+12 vs ArhAa 5 X
Al vs A2
vs vs4vs5
vs9vs12 30 X
A1 V8 A8 5 X
Between
A2 3,4,5,

9,12 25 x x
A12 vs A2+
3+4+5+9 5
Between
A2,3,5,9 20 x x x
A. vs A2+3
+3+5 5 x
Between
A2,3,4,5 15 X X
Between B 45

X indicates significance at 5% level

* See TABLE 3 for explanation of A and B sand subscripts.

16

TABLE 2.--Resu1ts of contingency tables for hierarchy II.

 

 

Harmonic

Source of
variability d.f. 11 12 13 14 15 16 17 18 19 20
Total 80 X. X X X X
Between
cores 25 . X
Bet. A vs B
W/cores 30 X
A1 V8 B]. 5
A2 vs B2 5 X X X X X X X
A3 V8 33 5 X
Ag vs B4 5
A5 vs B5 5
A9 vs 39 5
Tot. bet.
unpaired
A and B 20 X X X X
A8 vs A12 5 X
B vs B

7 10

B 10

vs 11 X X
A8+A12 V8
B7+B16+B11 5 X X X X X

X indicates significance at 5% level

* See TABLE 3 for explanation of A and B sand subscripts.

17

 

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CHAPTER IV

RESULTS

The first hierarchy, evaluating harmonics 2-10, was designed
to evaluate the Chukchi Sea samples from a stratigraphic point of
view. This hierarchy tested for differences within and between strati-
graphic units.

The second hierarchy, involving harmonics 11-20, was designed

primarily to evaluate the differences between cores and within cores.

Hierarchy I

In the first hierarchy, the overall contrast between A and B
sands was evaluated. If the A.and B sands do, in fact, represent
separate transport histories and depositional environments with no
mixing of sediment, it would be expected that the results of this con-
trast should be statistically significant.

The results do, however, indicate no significant difference
between A and B sands for any of the harmonics thus evaluated.

These results indicate either that the A and B sands are, in
fact, everywhere homogeneous, or that they change in character from
core to core in an irregular manner. For reasons which will become
clearer upon looking at the second hierarchy, the latter explanation
is favored.

Orthogonal comparisons at lower levels of hierarchy I evaluate

18

19

the significance of differences between samples of A sand that differ
in location

Because there was little "a priori" reason, such a breakdown
was not performed between samples of B sand.

The results of these comparisons (TABLE 1), indicate that
significant differences occur predominantly at the higher order har-
monics, 8, 9 and 10, with harmonic 10 displaying the greatest number of
significant differences.

Two core locations, (1 and 8), are the farthest west in the
sample array and are both almost due north of Bering Strait. The first
orthogonal comparison compares these samples with the more landward
samples, those at locations 2, 3, 4, 5, 9 and 12 (TABLE 3 and FIGURE 6).
This comparison generated a significant difference at the second har-
monic only, indicating that the seaward samples, 1 and 8, contained
significantly greater numbers of more highly elongate grains. This
suggests that Kobuk-Noatak sediment is present in significant amounts
in the more shoreward samples, and that such sediment is significantly
less highly elongate. This in turn suggests that the sum total of the
diverse bottom current directions (FIGURES 4 and 5), have a strong north-
ward component directly north of the Bering Strait, with a north west-
ward component near shore.

All other significant differences in this hierarchy occur at
the higher level harmonics, especially harmonic 10.

0f the two seaward locations, the northernmost, location 1,
contains significantly less grains with a high tenth harmonic. There

are two possible explanations for this.

20

First, as the A sand started its migration northward upon the
opening of the Bering Strait, the current patterns were such as to
allow for a higher degree of mixing in of Kobuk-Noatak type sediment
with the more northerly of the Yukon sediment. This resulted in the
northernmost location receiving a greater contribution of Kobuk-
Noatak type sediment than did the more southerly sample. By the time
the sediments were deposited at the southernmost location, the Kobuk-
Noatak contribution was significantly diluted by the preponderance of
Yukon sediments.

'Secondly, the northernmost A sample, sample 1, must have passed
through the strait considerably earlier than did the southernmost --
as much as several thousand years. A result of this time lag might
be sediment of a significantly different character being transported
at the leading edge of the wave front than that later derived sediment
which followed.

The remaining orthogonal comparisons involve tests of hypotheses
between the more shoreward samples. These samples display significant
differences at harmonics 9 and 10. This variation was orthogonally
partitioned in order to gain some insight into the pattern of diffusion.

The sample at location 12 is nearest the present Kobuk-Noatak
delta, and was compared with the more northerly shoreward samples, 2,
3, 4, 5 and 9. No significant differences could be detected for har-
monics 2-10, indicating either large scale homogeneity of shoreward
samples, or that the more northern samples are different, but when
summed resemble sample 12. Examination of the more northern samples
indicates that differences do, in fact, exist between them (harmonics

8, 9 and 10).

21

Thus, location 12, although areally closest to the Kobuk-
Noatak source, in terms of current pattern, (FIGURES 4 and 5), contains
appreciably more Bering Strait sediment. That is, Kobuk-Noatak sedi-
ment may be transported predominantly north-westwardly along the coast,
rather than due west through Kotzebue Sound.

This is supported by the results of comparisons between the
remaining five shoreward samples (2, 3, 4, 5 and 9, excluding 12),
which exhibits significant differences at harmonics 8, 9 and 10. This
result, however, as can be seen in the next breakdown (A9 versus A2,

3, 4 and 5), is generated solely by differences between the samples at
locations 2, 3, 4 and 5, with location 9 not differing significantly
from these except at the eighth harmonic. As with the comparison eval-
uating A12 versus A2, 3’ 4’ 5, and 9 the shape frequency distribution

of the more southerly sample resembles that of the sum of the more north-

erly samples.

Hierarchy II

The second hierarchy, as previously discussed, involved har-
monics 11 through 20, and was designed to evaluate variation within and
between cores (TABLE 2).

The most striking result of this hierarchy was, even though the
overall A vs. B contrast, as evaluated in hierarchy one, was non-signi-
ficant, that there were significant differences between A and B sands
in two cores. The A and B sands for PC090, location 2, differed signi-
ficantly at harmonics 11 through 15, 17 and 18. Sample P0137, location
3, displayed a significant difference at harmonic 14.

This result supports the previous argument that the sands are

22

constantly changing character, and that the non-significant overall A
vs. B contrast was not a result of the sands being everywhere homo-
geneous.

Qualitatively, the remaining cores for which there was both an
A and B sand range from A sands whose shape frequency distribution is
essentially the same as B sands from other locations, to B sands whose
shape frequency distribution is more Arlike. (FIGURES 7, 8, 9, 10,

11, APPENDIX A).

This indicates that the processes involved in the sedimentation
of the Chukchi Sea are not as simple as the tentative model prOposed
earlier, although in general, these results bear out the hypothesis.

The remainder of the second hierarchy concerned, primarily,
differences between cores that had an A, but no B, and those that had
a B, but no A. The results of these comparisons indicated a significant
difference between the A sand at location 8 and that at location 12.
This is, however, not to say that A8 and A12 necessarily stem from a
different source, but that there is a greater degree of mixing in of
Kobuk-Noatak type material with the A sand at location 8 than with that
at location 12, due to the pattern of current circulation.

This result amplifies the previous argument that location 12,
although closest to the Kobuk-Noatak source, receives little contri-
bution from that source, while an observable amount of mixing is taking
place in the more seaward samples.

The comparison between unpaired B sands showed significant differ-
ences to exist between the B sands at locations 7, 10, and 11. It can

be shown qualitatively, by inspection of the frequency distributions

23

of these three samples, FIGURES 7, 8, 9, 10 and 11, that the difference
is generated by a significant deficiency of grains having harmonic am-
plitude values in the higher ranges in sample 7.

These results indicate that the B sands, as the A, are changing
character from location to location. This means that there must have
been a significant amount of differential fluctuation in the provenance
or the transport processes during the time of deposition of the B sands.

These fluctuations might be dependent upon a) particle size;

b) environment of deposition, particularly whether the sediment was

markedly wave reworked; c) distance of provenance.

CHAPTER.V

CONCLUSIONS

The preceding analyses indicated that shape differences occur
between sand samples from the Chukchi Sea. These differences are the
manifestation of both stratigraphic and areal effects. That is, dif-
ferences exist between some pairs of Recent A sands and the early
Holocene B sands. Likewise, significant differences exist between A
sands from location to location in the sample array, as well as between
B sands.

In a technical sense, such results indicate presence of a loca-
tion by strata interaction. This effect is undoubtedly the result of
the complex transport and depositional history of the area.

The significant chi-square differences arise from changes in the
polymodal shape frequency distributions from sample to sample (APPENDIX
A). That significant differences are manifest principally at the higher
order harmonics (e.g. 10-20), indicates that shape differences reside
in the finer scaled shape characteristics. This suggests that grains
in those samples characterized by low amplitudes for these harmonics
may have been smoothed by abrasion or chemical etching. In that light
such samples might represent grains that have passed through beach or
littoral environments, whereas the grains with rougher surfaces may

have been subjected to glacial-fluvial processes without subsequent

24

25

beach abrasion.

Examination of the shape frequency data (APPENDIX.A), indicates
that most sands are represented by a dominant mode accompanied by
lower valued peripheral modes. For the tenth harmonic, for instance,
the amplitude frequency distribution generally displays a strong mode
in the region .007 to .009. Samples.A2, A8, B3, and By, however, lack
a dominant mode in this interval and in addition contain grains which
are assigned to modes of considerably higher amplitude (to .014).

The graphs for harmonics l4 and 18 exhibit shifts of the dominant mode
to relatively higher values, or addition of higher valued modes.

Samples A4, A5, B2, B7, and B10 exhibit consistently lower
values for harmonics 10, 14, and 18.

The rougher (those with high harmonic amplitudes) Bsands occur
in samples 3 and 4, northwest of Point Hape. The smoother samples may
represent sands associated with estuarine beaches, whereas the loca-
tions containing the more angular material may represent fluvial sands
that have bypassed this environment.

Smoother A sands occur west of Cape Dyer, whereas the rougher
occur at location 8, directly north of the Bering Strait, and west of
Cape Dyer. These latter samples contain a higher proportion of Yukon
sediment, and the smoother, more Kobuk-Noatak.

These conclusions are at best tentative, due to the fact that
they are based on such a small sample array.

At the least, however, the shape results indicate the presence

of a complex pattern of shape variation in these sediments. Further

resolution of that pattern should help delineate the sedimentary history

of the region.

LIST OF REFERENCES

LIST OF REFERENCES

Ball, G. H., and Hall, D. J., 1967, A clustering technique for
summarizing multivariate data: Behavioral Science, v.12,
no. 2, pp. 153-155.

Creager, J. S., and MoManus, D. A., 1965, Pleistocene drainage
patterns on the floor of the Chukchi Sea: Marine Geology,
v. 3, pp. 279-290.

, , 1967, Geology of the floor of Bering and
Chukchi Seas--American Studies. The Bering Land Bridge
(Symposium at the VII INQUA Congress) Stanford University
Press, pp. 7-31.

Ehrlich, R., and Weinberg, B., 1970, An exact method for charact-

erization of grain shape: Journal of Sedimentary Petrology,
v. 40, no. 1, pp. 205-212.

Kimball, A. W., 1954, Short-cut formulas for the exact partition
of X2 in contingency tables: Biometrics, v. X, pp. 452-458.

McManus, D. A., Echols, R. J., Creager, J. S., and Holmes, M. L.,
1969, Holocene Oceanography of Chukchi Sea: American Assoc.
Petroleum Geologists--Soc. Economic Paleontol. and Mineral.
Annual Meeting, Dallas. (Abstract).

Orzeck, J., 1972, Fourier shape analysis of some beach, river and
cliff sands from California [M.S. Thesis]: East Lansing,
Michigan, Michigan State University.

Redmond, B., 1969, The utility of Fourier estimates of grain shape
in sedimentological studies [M.S. Thesis]: East Lansing,
Michigan, Michigan State University.

Waltz, S. R., 1972, Evaluation of shapes of quartz silt grains as

provenance indicators in central Michigan [M.S. Thesis]:
East Lansing, Michigan, Michigan State University.

26

APPENDICES

APPENDIX A

ISODATA CLUSTER CENTER ANALYSES

27

grains / cluster

I7 " 40
l J ' L'li ‘ J r :- 2°
.08 12 .18 .20 .24 .28 .32
human“: amplitude

01
2.

FIGURE 7.--ISODATA cluster center analysis (harmonic 2; all locations
except location 1).

28

>
I”
IIIII

m > m > 0
I a a o o n
I I I I I I I I I I I I I I I I I l I I

’
o
;L__
III

D II > a

3 o In on
IIIIIIIIIIIIIIIIIIII
Quins I cluster

—.0
" 80

or - «I
‘. Lilly. . . . . f 39
.o'oT ooo .oos .010 .012 .014 on ma
hstmonlc smplltudo

FIGURE 8.--ISODATA cluster center analysis (harmonic 10; all locations
except location 1).

29

.. l
I
.. I
A3 I
as I
I
.. I
I .
.. I
.5 l
I

grains/clans:

.. I
I
so I
A12 I
I

sIo I
I I

, l
.. I

" I I

'__A

o oh oh: oh: .064 .060 .060 .607 .600
hstmonlc autumn.

8338

FIGURE 9.--ISODATA cluster center analysis (harmonic 14; all locations
except location 1).

30

.. I

.. I
—- I

.3 I

s: l

.._ I i

.. |
A5 I

A0 I

grains/cluster

m I
I I

s10 I

III I
I

.. I

- so
37 - so
L L -..
.IF .74 .I'. .s'c .is .s'o .54 .s's 3:
human“: smpIImdo IIIOO

FIGURE 10.--ISODATA cluster center analysis (harmonic 18; all locations
except location 1).

31

81s I
I

DID

 

 

.I...I...I....

Is II J. an .is is .us is

.. I
_._ I I

II. I

010

 

 

§JIII|IIIIIIII

V ' T V V V V
.0“ one .003 .004 .0“ .000 .007 .000

males [cluster

34
8
O
3.
e.
O
2
O
9
O
§JIIIIIIIIIIII

__4. .1 I I 7 '°

r v 1’ v V Y ‘
00‘ .0. .‘2 s'. .20 .2‘ 02. '32 '3.
harmonic amplltudo

FIGURE ll.--ISODATA cluster center analysis for harmonics 2, 10, 14
and 18 at location 1.

APPENDIX B

NUMERICAL VALUES FOR CHI-SQUARE CONTINGENCY TABLES

32

TABLE 4.--Numerica1 values for chi-square contingency table

(hierarchy I.)

 

 

 

 

Harmonic

Source of
variability d.f. 2 3 4 5 6 7 8 9 10
Total 85 109.9 80.7 101.3 72.7 102.4 67.7 94.2 112.4 116.
A vs B 5 .9 6.9 9.5 10.0 10.0 3.0 5.6 9.2 5.
Within
A vs B 80 107.0 73.8 91.8 62.7 92.4 64.6 88.5 103.2 110.
Between A 35 47.7 37.4 42.4 26.4 39.7 20.3 44.4 46.5 60.
A+34%?»-

9+12 vs
AI+A8 5 19.7 .7 7.4 4.9 5.4 3.9 5.1 3.5 5.
ALI-8V8 A2

vsts4vs5
vs9vs12 30 28.0 36.7 35.3 21.4 34.4 16.4 39.3 43.0 54.
A1 vs A8 5 2.5 1.5 4.9 1.7 4.3 2.0 3.0 5.2 12.
Between
A2.3.4.5.

9,12 25 25.6 35.2 30.4 19.7 30.1 14.5 36.3 37.8 42.
A12 V8 A2+

3H4k5+9 5 1.2 5.5 3.1 4.3 8.3 4.4 2.3 5.8 7.
Between
A

2.3.4.5.9 20 24.4 30.0 27.3 15.4 21.7 10.1 34.0 32.0 34.
A9 vs A2+3
+4+5 5 7.6 7.0 8.3 2.2 2.4 1.8 14.7 4.4 2.
Between
42’3’4’5 15 16.8 23.0 19.0 13.2 19.3 8.3 19.3 27.5 32.
Between B 45 59.3 36.3 49.1 36.3 52.7 44.3 44.1 56.7 50.
* For significant harmonics, see TABLE 1.

33

TABLE 5.--Resu1ts of contingency tables (hierarchy II.)

 

 

 

Harmonic
Source of
variability d.f. 11 12 13 14 15 16 17 18 19 20
Total 80 85.3 93.3 111.7 114.9 101.9 107.6 107.0 107.5 89.8 101.3
Between
cores 25 23.3 29.8 20.6 30.4 27.4 32.7 32.9 27.6 31.7 39.5
Bet.AvsB 5
W/cores 30 38.2 43.0 55.2 42.7 36.0 35.9 32.5 36.9 32.5 17.2
A1 vs B1 5 4.3 3.4 1.9 8.7 1.4 7.0 3.5 4.2 2.0 3.5
A2vs B2 5 18.5 17.2 32.8 11.5 14.5 9.2 17.3 14.7 3.3 4.4
A3 vs 33 5 2.8 4.7 5.3. 12.1 7.3 3.6 1.9 1.8 9.7 2.3
An vs 84 5 5.3 6.9 2.0 6.6 7.5 9.6 1.9 5.6 5.7 .5
A5 vs 35 5 4.7 6.4 4.3 .8 2.8 2.0 6.5 1.7 4.4 3.9
A9 vs 89 5 2.5 4.4 8.9 3.1 2.5 4.5 1.4 8.8 7.3 2.5
Tot. bet
unpaired
A and s 20 13.6 25.4 21.3 25.9 28.5 25.4 33.4 36.9 24.4 33.0
A8 vs A12 5 3.2 5.6 3.7 9.0 9.4 14.1 9.3 9.4 9.3 8.6
B7 vs B10
V8 311 10 7.0 19.1 12.5 10.7 14.3 13.9 14.0 24.4 12.9 16.5
Aé+A12 vs
B+B +B

7 10 11 5 3.3 .7 5.1 6.2 4.8 7.4 10.1 3.2 2.1 7.9

 

* For significant harmonics, see TABLE 2.

APPENDIX C

LOCALITY MAPS

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