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JOEE JQSEPE QRZECK
1972

THESIS
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ABSTRACT
PROVENANCE PARTITIONING OF BEACH, RIVER, AND
CLIFF SANDS IN SAN DIEGO COUNTY, CALIFORNIA
USING FOURIER SHAPE ANALYSIS
BY

John Joseph Orzeck

Provenance determination is one of the primary
objectives in sedimentological studies. This study concerns
the provenance determination of a beach-fluvial system in
Southern California using the shape of quartz sand grains
as the distinguishing variable. Sand samples were collected
from three different environments: along the San Luis Rey
River, on the beach front at the river's mouth. and along
a cliff face parallel to the beach. From these environments
the exact shape of quartz grains were measured using a
technique employing a Fourier Series of closed forms.
Statistical analysis indicated that these environments
could be differentiated using the shape variable.

Chi-square tests indicated shape differences not
only between environments but also within each environment.
Shape differences were greater between environments as
compared to within environments. Sands from the cliff
environment were the most rounded, the beach intermediate.

and the river the least.

John Joseph Orzeck
2

River sand shape differences indicated many possible
sources along the river course. Beach sands indicated a
mixing of river and cliff sands with the beach sands
becoming less “river-like“ away from the river source
in the direction of longshore drift. Quantitatively.
the river sand contribution was about 10% greater than
the cliff contribution. Within all three environments
patterns of variation of grain shape were evident. These
patterns of variation along with significant differences
between environments suggest the shape of quartz grains
to be an ideal natural variable to indicate provenance
and its use is greatly encouraged for future provenance

studies.

PROVENANCE PARTITIONING OF BEACH, RIVER. AND
CLIFF SANDS IN SAN DIEGO COUNTY, CALIFORNIA
USING FOURIER SHAPE ANALYSIS

By
John Joseph Orzeck

A THESIS

Submitted to
Michigan State University
in requirement for the degree of
MASTER OF SCIENCE

Department of Geology
1972

TABLE OF CONTENTS
LIST OF FIGURES .............o..................o... 2???
LIST OF TABLES .......o......o.....o..o............. iv
INTRODUCTION .............a.........................
SAMPLING DESIGN ....................................
SAMPLE PREPARATION.....o............................
FOURIER TECHNIQUE ..................................

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RESULTS 0....O‘COOOOOOOOOOOOOOOOOCOICIOOOOOOOOOOOOOOO 11

CONCLUSIONS D0.0.00.00.00.00...OOOOOIOOOOOOOOOOOOOOO 19
BIBLIOGRAPHY 000......0.0.000......OOOOOOOOOOOOOOOOO 21

ii

Figure 1
Figure 2
Figure 3
Figure

Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11

LIST OF FIGURES

Location and Geologic Map

River, Beach. and Cliff
Mean Amplitude Spectra

Sample Histogram

Chi-Square/Degrees of Freedom Values
Between and Within Environments for
Each Harmonic

Mean Harmonic Values for River Samples
Percentage of River Grains in Maximum
and Minimum Cluster Intervals for Each
Harmonic

Percentage of Cliff Grains in Maximum
and Minimum Cluster Intervals for Each
Harmonic

Percentage of Beach Grains in Maximum and
Minimum Cluster Intervals for each
Harmonic

Proportion of Beach Grains Shaped like
River Grains‘

Skewness of Frequency Histograms for Beach
Samples

Mean Harmonic Values - Beach

iii

LIST OF TABLES

Table l .... Partitioning of Chi-Square Variation
Between and Within Environments for
Each Harmonic

iv

INTRODUCTION

Determination of sediment provenance is one of the
fundamental pursuits of sedimentology. In ancient sediments
provenance determination not only determines the source of
the sediments but. in addition. provides information concern-
ing the geomorphology of the source area. Provenance determi-
nation in recent sediments is of practical importance in
beach erosion. longshore transport of sediment around artifi-
cial and natural beach barriers. harbor fillings. and other
environmental problems. Provenance determination has been
hindered however because variables containing source informa-
tion within the sediment have.not been efficiently utilized.
Analyses of variables such as mineral composition or sediment
size and texture extract provenance information (Beal. 1956;
Komar. 19703 and Pittman. 1956.) but are generally only
applicable under special conditions. What is needed for
efficient provenance determination are variables in the sedi-
ment that are common, easily measured. and can be statisti-
cally supported.

Attempts have been made to trace the transport and
dispersal of recent sediments through the use of tracers.
Tracing sediments by treating the grains with dye or radio-
active material are quite common (Boon. 1969; Inman. 1955;

and Quickmore. 1967.). Tracer techniques are limited in
l

2
their use due to enormous dilution of treated grains in the
sediment mass. problems in dye application. and acquiring a
lasting dye that will not interfere with the characteristics
of the grains. Because of these limitations. artificial
application of characteristics upon the sediment are rela-
tively inadequate. Therefore. a natural variable. the shape
of the ubiquitous mineral quartz. served as the basis for
this provenance study. Ideally this variable could be used
to determine provenance in both recent and ancient sediments
as well.

The study involved the shape analyses of quartz
grains in a fluvial-beach system. The system studied was
located along the San Luis Rey River and a five mile coastal
strip at Oceanside in San Diego County, California (Figure 1).
The beach at Oceanside is bordered by a semi-consolidated
sand cliff which is presently undergoing active erosion.
River sediment is derived from igneous and metamorphic rocks.
Cenozoic non-marine sediments. in addition to near coastal
Pleistocene beach terraces.

River sediment, which is transported primarily during
the winter rains. is mixed with beach sediment at the river's
mouth at Oceanside. Longshore currents generally transport
the river-beach sediment southward (Wiegal. et al.. 195“).
Sand is also supplied to the river-beach sediment by the
eroding cliff which frequently lies within thirty meters of
beach swash zone.

The beach therefore has two main sources of sand,

the river and the cliff. The objectives of this study are

3
to differentiate between river. beach, and cliff sands. to
show beach source differences. and to evaluate the relative

contributions of these sources to the beach system.

 

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SAMPLING DESIGN

Prior to the winter rain and flood season. thirty-
five sand samples within the same size range were collected
for this study in December. 1971 (Figure l). The samples
were assigned to one of three groups based on location:
River. Beach. or Cliff. Thirteen of these samples were
collected in the river channel along fifty miles of the
San Luis Rey River. The river sampling interval progres-
sively decreased in the down river direction. This sampling
process was to insure a collection of samples which would
include a complete range of sediment sources for statistical
analyses. Thirteen beach samples were collected in the swash
zone on both sides of the river's mouth and southward along
the beach for approximately five miles. Nine cliff samples
were taken at approximately twelve foot heights along the
twenty-five foot high cliff faces. These cliff samples
were taken. whenever possible. directly shorewards of the

beach face samples.

SAMPLE PREPARATION

For each sample, sand grains were mounted in Duco
Cement on microscope slides. These grains were taken from
the collected sample after the samples were dried and pro-
cessed through a magnetic separator to eliminate many
accessory minerals.

Each slide was placed on a micrOprojector and the
outlines of approximately one hundred quartz grains were
traced. Using these outlines. the Cartesian coordinates
of forty-eight peripheral points were determined using an
automatic digitizer. The digitizer punches these points

into five Hollerith cards per sample for computer analysis.

FOURIER TECHNIQUE

Two dimensional grain shape can be measured
exactly using Fourier analysis according to Ehrlich and
Wineberg (1970). This method requires a closed shape
and that there exist no involutions in the shape outline.
The relatively equant shapes of detrital quartz grains are
ideal for Fourier analysis.

Grain shapes are measured from the center of gravity
using the digitized data in a computer technique. Precision
of fit is regulated by the limit set on the number of har-
monics in the Fourier program. The limit on the number of
harmonics is indicated by the number of points taken per
shape. The number of points should be at least twice the
desired number of harmonics as in this study where ten har-
monics were calculated using forty-eight points per grain.

Harmonic amplitude values provide the description of
the total shape. The zeroth harmonic is a circle with a
radius set at unity to eliminate any size dependence as a
source of variation. The first harmonicis shaped like an
offset circle. the second a figure eight. the third a trefoil.

th" harmonic which

the fourth a four leaf clover. on up the “n
has ”n” number of equidistant modes. The greater the harmonic
amplitude value the more closely the grain resembles that

harmonic shape. 6

ANALYTICAL TECHNIQUES

Mean Amplitude Spectra

For each environment (river, beach. and cliff) a
mean harmonic amplitude spectrum was determined (Figure 2).
This permits a visual subjective comparison of the shape of
grains from the three environments. Those sands with lowest
mean harmonic amplitudes more closely approach circularity.
Although the graphed amplitude spectra offer a means of
rapid visual comparison. the statistical significance of

any contrasts must be tested by some other means.

Chi-Square Analyses

Chi-square computations were used to examine for
shape differences between and within environments. Chi-
square contingency tables were compiled to statistically
examine the shape distributions. In this procedure each
harmonic was analyzed separately using three intervals
(i.e. high. intermediate and low) for each harmonicshape
family. The number of grains in each shape family consti-
tuted the data from which these tables were calculated.

Statistical differences can be obtained between and
within grouped samples using a chi-square computation
according to Maxwell (1961) and Kimball (1954). In this

technique the variations (measured as chi-square values) were

7

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computed in one large table. This calculationchtermines
total variation between all samples. Samples were then
pooled into various groups and variation was determined
between and within these groups. Table 1 shows chi-square
values for the groups constructed in this study. The com-
plete analysis concerns the evaluation of differences
between environments including an investigation of source
differences using an orthogonal breakdown of the total
between environment variation as well as a complete intra-

environment variation.

Histograms
Previous shape studies (Waltz. 19723 Ehrlich et al..

1972) have indicated that the frequency distribution for
each harmonic is distinctly polymodal. Polymodality of the
frequency distribution made it necessary to inspect each
frequency histogram. locate each mode. and thereby determine
the number of grains associated with each mode. This made
it necessary to visually examine the frequency distribution
for all harmonics in all of the samples. Although polymo-
dality was evident. no subjective method exists allowing a
visual location of modes and to assign grains to each mode
identified. In addition. relationship in grain membership
from harmonic to harmonic with the amplitude spectra of

each sample has to be considered.

ISODATA
ISODATA is an iterative program that describes
shape clusters by taking into account all harmonics

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9

simultaneously. It is used for locating clusters with "n”
dimensional space where 'n' is the number of variables.
ISODATA is structured to analyze polymodal distributionsgand
in order to facilitate pattern recognition. ISODATA shape
clusters were used to locate modes. Samples were analyzed
individually on the ISODATA program and each grain contribu-
ted to one of three shape families (i.e. clusters) for each
harmonic. Thus. ISODATA objectively determines clusters of
grains based on the occurrence of polymodality in one or
more of the frequency distributions within an amplitude
spectrum. The number of grains in each of these cluster
categories (i.e. high. intermediate. and low) constituted
the basis for the subsequent statistical analyses.

An example of the relationship between ISODATA and
the histogram distribution is shown in the sample. Beach 26.
ISODATA identified three clusters. Each cluster is defined
by its ”center” which in this case involves nine values. one
value for each harmonic. For example. location of the
cluster centers are specified on the frequency histogram
(Figure 3). It can be observed that whereas clusters one
and two are at distinct modes. cluster three is located at
an intermode position. However. inspection of the frequency
histogram for the third harmonic indicates cluster three
occupies an extreme position for that harmonic. Therefore
the cluster centers determined by ISODATA depend upon simul-
taneous evaluation of the nature and degree of polymodality

of the frequency histograms for all nine harmonics.

FIGURE 3

SAMPLE HISTOGRAM (Beach 26)

COMPARISON OF POLYNODAL DISTRIBUTIONS
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10

Discriminate Analysis

With dominant longshore drift. river sands should be
carried southward with concomitant mixing. The cliffs
approach the swash zone more closely south of the river's
month. In addition. the cliffs in the southern region are
undergoing greater erosion. With enhanced contribution from
the river in the north end of the beach and the cliff in the
south end. the functional relationship of grains along the
beach is not known a priori. The nature of the decrease in
river sands southward along the beach should provide an
estimate of the relative importance of the two sources. In
order to gain some insight into the relationship. discriminate
analysis was used; utilizing as training classes. an upriver
sample and a cliff sample. The cliff sample was selected
with a mean amplitude which most closely represented the
mean amplitude for all the samples. The discriminate function.
so utilized. classifies each grain and each sample as ”river-
like” or ”cliffélike”. Relative proportions of these groups
can be plotted against distance from the river's mouth

(Figure 9).

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RESULTS

Inspection of the mean amplitude spectra indicates
that for all harmonics. the mean of the River Group was
greatest. the Beach intermediate. and the Cliff Group was
least. Mean values for these three environments would
have random order from harmonic to harmonic if there was
no significant environmental relationship but since the
pattern of variation is preserved harmonic by harmonic,
it remains quite evident that this relationship is not
due to chance. Relative ranking of the spectra indicates
that the cliff sands approach circularity the most. the
beach intermediate. and the river the least.

In order to test the significance of these differ-
ences between environments as well as to study intra-
environmental variation, a series of chi-square contingency
tables were utilized to investigate variance for eabh har-
monic. Chi-square values in Table 1 indicate highly
significant differences between and within all sample
groups for all harmonics at the .001 confidence level. Chi-
square values are a function of degrees of freedom. Because
the values shown in Table l arise from contingency tables
with varying degrees of freedom. the values may not be
compared directly. In order to better appreciate the con-

trasts between chi-square values. the values were divided
ll

12

by the appropriate number of degrees of freedom for each
sample group. Figure 4 graphically displays this numerical
relationship for harmonics two through nine.

In the intermediate harmonics. five through eight.
Figure 4 demonstrates that the greatest variation arises
from differences between environments. To further investi-
gate these differences. variation between environments was
partitioned into two orthogonal sets: a River versus Beach
+ Cliff comparison and Beach versus Cliff comparison. Both
comparisons yielded significant differences with the River
versus Beach + Cliff set generating the largest chi-square
values indicating river sands differed more than beach and
cliff sands did from each other.

Chi-square values in Table 1 indicate that a large
portion of the total variation arises from differences
between samples in each environment for all harmonics.
Although intra-variation increases with increasing harmonic
number. variations within each environment remain generally
lower than between environments (Figure h). Because of
little a priori reason to expect significnat differences
for the intra-environmental samples. an orthogonal breakdown
of the Within Groups was not performed.

Variations within each of these environments may
arise from provenance factors involving their mutual inter-
action or contributions from other sources. For example,
intra-beach variations may arise from local contributions

of eroding cliff material in addition to river contributions.

 

Figure 4

Chl- Square
Degrees of Freedom

 

VALUES

BETWEEN AND WITHIN ENVIRONMENTS
FOR EACH HARMONIC

 

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Intra-cliff variation may arise from a different pattern of
fluvial systems which have deposited sediment on this
Pleistocene beach. And within river variations may be a
product of shape changes in transport in addition to shape
variation from source contributions from tributaries. The
importance of the significant Within Group variation leads
to the subsequent discussion on intra-environmental shape

differences.

Shape Variation Within the Rigs;

Shape variation within the river appears to be due
to progressive contributions of sand from various sources
along the river. Accumulation of sand from these sources
is reflected in greater shape variations as the river sand
approaches the beach. Inspection of the local geology
(Figure 1) along the river course indicates that upriver
there is a limited variety of potential source rocks. pre-
dominately granitic rocks and subsidiary amounts of
conglomerates. In the downriver direction. possible source
robks become even more varied. In addition to the upriver
lithologies. from location 66 to the river's mouth. the
river drains patches of Tertiary and Quaternary marine
sediments. With all of these possible sediment sources.
it is not surprising to obtain greater shape diversity in
the river sands closest to the beach (Figure 5).

Although there is generally greater diversity of
shape in sands downriver. shape relationships throughOut

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If any trend is present, it is an increase in angular
shapes in grains approaching the river's mouth. This
along with other irregularities indicates that there
probably is a general relationship between grains in a
river sample and the neighboring bedrock.

Realizing the data is polymodal. it should be
expected that mean harmonic amplitude in Figure 5 should
not give as clear an interpretation as the inspection of
the cluster data generated by ISODATA. In the cluster
data proportions of grains were assigned into three
cluster ranges: high. intermediate. and low. The high
and low cluster ranges are plotted against distance in
Figure 6. Comparison of Figure 6 with Figure 5 provides
direct evidence that the shift in the mean arises predomi-
nantly from changes in the shape of the frequency dis-
tribution rather than by simple changes with location.
That is, whereas for some harmonics the preportion of the
rounder grains are quite high (i.e. harmonics two and three).
the proportion of highly angular grains are greatest in

other harmonics (i.e. harmonics seven. eight. and nine).

Shape Variation Within the Cliff

Shape variations between cliff samples are quite
irregular upon examination of the chi-square values for
each harmonic (Table 1). Greatest shape variations arise
in the fourth. sixth. and eighth harmonics with lesser
variations in the third and ninth. These variations. harmonic

by harmonic with distance can be shown by the relative percentages

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of maximum and minimum cluster value intervals (Figure 7).
In general, differences between cliff samples are due to
greater percentages of the rounder grains eXpecially noted
in the higher harmonics.

Increasing circularity of the sand shapes of
samples within the cliff is generally manifested in sands
furtherest from the river month. These observations might
indicate that the present San Luis Rey River might occupy
a similar position to a river supplying sand to the
Pleistocene beach now eXposed in the cliff. It should
not be overlooked. however, that this pattern might arise
from accidentally sampling on progressively higher or
lower stratigraphic horizons on the cliff.

Shape Variation Within the Beach

Significant shape differences exist between beach
samples for all harmonics as indicated in the chi-square
contingency table (Table 1). Greater shape differences
arise in the higher harmonics. especially the fifth.
These differences could be the result of unequal mixing
of river and beach sands, natural abrasion due to wave
action. and nonuniform contributions of cliff sediment.
In order to consider these differences. mean harmonic
amplitudes and the percentage of grains within cluster
intervals were evaluated.

Examination of the relationship between mean
harmonic amplitude values and location along the beach

reveals no obvious trends (Figure 11). However. the

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frequency distribution of each sample for each harmonic
are distinctly polymodal and vary greatly in shape along
the beach front. With such distributions a measure of
central tendency such as the mean. loses much of its value.
An index which should reflect the change in shape of the
distribution is the ratio of grains within a sample that
belongs to shape families possessing either very high or
low harmonic amplitudes. These proportions then represent
examination of the tails of the distribution. For each
environment. high. intermediate. and low values were
determined such that the range of the variation was divided
intoequal thirds. In this way. each shape family identified
by ISODATA was categorized. The ratio between the total
number of grains in each shape category to the total number
of grains within the sample was used to investigate shape
variation along the beach.

In this calculation. trends were recognizable in
the higher harmonics but not in the lower harmonics. Again.
as with the variation with the mean. trends could not be
recognized in the second through fourth harmonics. However.
harmonics six through nine exhibit distinct differences
along the beach. For all these harmonics there is a surplus‘
of grains with low harmonic amplitudes. However. in the
northern portion of the beach front. the eighth and ninth
harmonics exhibit a relative surplus of grains with high
harmonic amplitudes. These results are also in harmony

with the chi-square contingency tables in which the maximum

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variance within the beach is reflected in harmonics five.
eight. and nine.

These results are also in agreement with the
variation of skewness along the beach (Figure 10). Beach
samples are much more positively skewed south of location
15. An obvious anomaly in all of these plots occurs in
the vicinity of location 7. adjacent to the pier. Location
of these values in the vicinity of the pier is probably not
coincidental. but quite likely reflects a local disruption
in longshore transport and concomitant accumulation of

said e

Qéscriminant Analysis of Beach Sands

The subsequent results support the concept of
relative proportion of grains of different shape along the
five mile stretch of beach examined in this study. The
discriminate function. in addition to classifying grains
in the beach samples. also classified grains of the two
training classes - river and cliff sands. 0f the 104
grains in River sample 64. 96 grains were calculated as
”river-like” and 8 grains as "cliff-like". However. of
the 102 grains in the cliff training class. only 35 were
classified as ”cliff-like”. Thus. if the cliff was the
only contributor to the beach without any river contribution
at all. about two-thirds of the grains on the beach would
be classified as ”river-like“. Therefore. evaluation of
the discriminate analysis of beach samples whose ”river-like"

preportion greatly exceed 67 per cent were considered to

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18

have significant addition from the San Luis Rey River.

The relative grain pr0portion with distance indicates
approximately ten percent increase in the vicinity of the
river mouth excepting the area around the pier. From the
pier southwards. the proportion lies on or near the base
line until Location 54 is encountered. The proportion in
Location 54 falls below the base lineaand further southward
Locations 51 and 44A are above the base line. These loca-
tions fall slightly south of the Buena Vista Lagoon. The
author considers it likely that these abnormalvalues are
due to sediments from the lagoon during periods of excep-

tionally high discharge.

CONCLUSIONS

Sand from three sources can be easily discriminated
using Fourier measurements of grain shape. River. beach.
and cliff sands from one general locality in California
were shown to possess distinct shape differences between
and within each environmental group. Grains from the cliff
approached circularity the most. the beach intermediate.
and the river the least. Shape differences within each
of these environments could arise from sedimentary process
factors or provenance. The beach system. the focal area
for the interaction of the three sediment typers. has two
major sediment sources. the cliff and the river. Samples
of beach sand contain more equant grains with distance
along the shore probably due to local contribution of
circular grains from the cliff or to natural abrasion by
wave action. Relative grain preportion with distance of
the beach sands indicated approximately a ten per cent
increase in “river-like” shape at the river's mouth and a
general decrease southward. Sediment derived from the
Buena Vista Lagoon may cause the disruption of this trend
and contribute "river-like” sands to the beach. Intra-cliff
variations might have arisen from either horizontal or

vertical changes that may have resulted from shore processes

19

20

since the cliff is a Pleistocene beach. Sediments from
local sources contribute significant differences in grain
shape between samples within the river system. In general.
results indicated that quartz shape. an ideal natural
variable. may be used as a precise provenance indicator

in recent sediments andgerhaps ancient sediments as well.

BIBLI OGRAPHY

BIBLIOGRAPHY

Beal. M. A. and Shepard. F. P.. 1956. A Use of Roundness
to Determine Depositional Environments. Jour.
Sed. Pet.. Vol. 26.PP. 49-60.

Boon. J. D.. 1969. Quantitative Analysis of Beach Sand
. Movement. Virginia Beach. Virginia. Sedime tolo .
Vol. 13.pp. 85-103.

Ehrlich. R.. Wineberg. B.. 1970. An Exact Method for
Characterization of Grain Shape. Jour. Sed. Pet..
Vol. 40. No. 1. pp. 205-212.

Ehrlich. R.. et aL. 1972. The Role of Textural Variations
in Petro enetic Analyses. Jour. G. S. A.. Vol. 83.

pp. 665- 76.

Inman. D. L. and Goldberg. E. D.. 1955. Neutron Irradiated
Quartz as a Tracer of Sand Movement. G. S. A. Bull..
V01. 66’ pp. 611-613e

Kimball. A. W.. 1954. Shortcut Formulas for the Exact
Positioning of Chi-square in Contingency Tables.
Biometrics. Vol. X. pp. 452-458.

Komar. P. D.. 1970. The Competence of Turbidity Current

Flow. Ge Se Ae 31.11%. VOle 81’ Pte 1’ 1313- 1555-
1562.

Komar. P. D. and Inman. D. L.. 1970. Lo shore Sand T ans art
on Beaches. Vol. 75. No. 30. pp. 39I4-3927.

Maxwell. A. E.. 1961. Anal zi ualitative Data. John
Wiley. & Sons. Inc.. pp. I65.

Pittman. E. D.. 1970. Plagioclase Feldspar as an Indicator

of Provenance in Sedimentary Rocks. Jour. Sed. Pet..
V01. 40. pp. 591-598e

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22

Quickmore. M. J. and Lean. G. H.. 1967. Measurement of
Sand Transport in Rivers with Special Reference
toaTracer Methods. Sedimentology. Vol. 8. pp. 175-
22 .

Waltz. S. R.. 1972. Evaluation of Shapes of Quartz Silt
Grains as Provenance Indicators—InICentraI Michi an.
Masters Thesis. MiChigan State University. East

Lansing. Michigan.

 

Wiegal. R. L.. et al.. 1954. Wave. Longshore Current. Beach
Profile Records for Santa Margarita Beach. Oceanside.
California. A. G. U. Trans.. Vol. 35. pp. 887-896.

MICHIGAN TATE UNIV

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