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Fourier grain-shape analysis of quartz sand from the Santa Monica Bay Littoral Cell, Southern California

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Fourier grain-shape analysis of quartz sand from the Santa Monica Bay Littoral Cell, Southern California

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FOURIER GRAIN-SHAPE ANALYSIS OF QUARTZ SAND
FROM THE SANTA MONICA BAY LITTORAL CELL,
SOUTHERN CALIFORNIA
By
Joshua Rafael Feffer
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment o f the
Requirments for the Degree
MASTER OF SCIENCE
(Geological Sciences)
May 1998
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UNIVERSITY O F S O U T H E R N CALIFORNIA
T H E G R A D U A T E S C H O O L
U N IV E R S IT Y P A R K
L O S A N G E L E S . C A L IF O R N IA 8 0 0 0 7
This thesis, written by
JOSHUA RAFAEL_FEFFER
under the direction of L S Thesis Committee,
and approved by all its members, has been pre
sented to and accepted by the Dean of The
Graduate School, in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE
D im a
T
\
/
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TABLE OF CONTENTS
FIGURES
TABLES
ACKNOWLEDGMENTS
ABSTRACT
INTRODUCTION
Purpose
LOCATION
REGIONAL SETTING
Regional Geography
PREVIOUS WORK
Borrow Pit
Regional Geology
Northwestern Block
Central Block
Southwestern Block
Offshore Area
METHODOLOGY
History
Fourier Grain-Shape Analysis
Sample Collection
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Bathymetric Study 24
Sample Preparation 27
Sample Processing 29
STATISTICAL METHODS 30
Introduction 30
Factor Analysis 31
One-Way Analysis of Variance 32
Duncan's New Multiple Range Test 33
Hotelling's T2 Test 35
Discriminant Function Analysis 36
RESULTS 38
General Statement 38
Beach Samples 38
Sample Relationships from Factor Analysis 38
End-member testing from Hotelling's T2 Test 41
Sample comparison from Duncan's New M ultiple Range Test 41
Beach and source samples using Fourier analysis 44
End-member Testing from Hotelling's T2 Test 44
Source sample comparison from Hotelling's T2 Test 48
Geological significance comparison from Hotelling's T2 Test 48
Comparison o f foreshore samples from Discriminant Function Analysis 50
iii
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Fourier Analysis o f Redondo Beach Samples 50
Sample comparison from Factor Analysis 50
End-member testing using Hotelling's T2 Test 54
Sample comparison using Duncan's New Multiple Range Test 54
DISCUSSION 59
Introduction 59
Sand Sources for the Santa Monica Bay 59
Sand grain composition north and south o f Redondo Canyon 60
Temporal affects on sand grain-shape 62
Infilling o f Redondo Beach Borrow Pit 63
Shape o f sand grains in Redondo Beach 67
Transport o f sand grains in Redondo Beach 67
Depth comparison 67
Transect comparison 68
CONCLUSIONS 70
FUTURE WORK 72
REFERENCES 73
APPENDICES 78
Appendix A: Latitude, longitude and depth of ocean floor
recorded during the 1993 bathymetric study. 78
iv
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FIGURES
Figure Page
1. Southern California littoral cells. Tick marks indicate the study
area (after United States Army Corps of Engineers, 1986). 2
2. Location map for the Redondo Beach area showing the approximate
location o f the nearshore borrow area. Hachured area shows the
approximate location o f thehydrographic survey by the U.S. Army
Corps o f Engineers in May, 1980 (from Osborne, 1994). 7
3. Bathymetry o f the 1972 hydrographic survey by the U.S. Arm y Corps
o f Engineers. 8
4. Bathymetry o f the 1980 hydrographic survey by the U.S. Arm y Corps
o f Engineers. 9
5. Map showing the bathymetry and physiography o f the study area. Tick
marks indicate the sample collection area (after Scheidemann, 1980). 11
6. Map showing the physiographic and major structural features o f the Los
Angeles Basin (after Yerkes et al., 1965). 12
7. Mathematical relationships for the classification o f grain sphericity
(from Carver, 1971). 18
8. Chart for visually estimation sphericity and roundness (from Krumbein
and Sloss, 1963, p. 111). 19
9. A classification o f shapes o f pebbles after Zingg (from Boggs, 1992,
p. 96). 20
10. Location map o f inner shelf samples used in the study. 26
11. Bathymetry o f the 1993 hydrographic survey by the author. 28
12. Factor plot o f Baywide sample set. 40
13. Factor plot o f Baywide and source sample sets. 46
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14. Location map o f samples collected during bathymetric survey. 52
15. Factor plot o f Redondo Beach sample set. 55
16. Contour map o f elevation difference between 1972 and 1980
bathymetric surveys. 64
17. Contour map o f elevation difference between 1972 and 1993
bathymetric surveys. 65
18. Contour map o f elevation difference between 1980 and 1993
bathymetric surveys. 66
19. Factor plot o f Redondo Beach sample set showing sample groupings. 69
vi
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TABLES
Table Page
1. Discharges o f streams (after Brownlie and Taylor, 1981). 3
2. Sample sets used for the study. Bolded samples are used for the
Baywide sample set. 25
3. The design for the one-way Analysis o f Variance as used in this study
(Davis, 1986). 34
4. Factor scores for Baywide sample set. 39
5. Hotelling's T2 Tests for end-member samples. 42
6 Results o f Duncan's New Multiple range Testing for the Baywide
sample set. Vertical lines indicate statistically similar groups. 43
7. Factor scores for Baywide and source sample sets. 45
8. Hotelling's T2 Tests for end-member samples. 47
9. Hotelling's T2 Tests for possible source samples. 49
10. Discriminant Function Analysis of Baywide sample set. 51
11. Factor scores for Redondo Beach sample set. 53
12. Hotelling's T2 Tests for end-member samples. 56
13. Results o f Duncan's Multiple range Testing for the Redondo Beach
sample set. Vertical lines indicate statistically similar groups. 57
vii
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ACKNOWLEDGMENTS
I would like to offer my sincerest and deepest regrets regarding the passing o f my
advisor Dr. Robert H. Osbome. He was a remarkable advisor, teacher, and friend.
Without his guidance, support, advice, and teaching I would never have had the ability
to complete this thesis. I would like to thank Dr. Donn S. Gorsline for taking over as
my advisor and pushing me to finish. Apologies and thanks go to Rory (Tony)
Robinson who gave hours o f his time, statistical expertise and needed guidance. My
family, specifically my parents and grandparents, have always encouraged and
facilitated my education, without them I would not have completed this degree.
Thanks go to my loving wife Jessica who never pushed during periods o f inactivity but
always supported me. Special thanks to my son, Jacob, and to the baby growing
within my wife, for giving me reason to hurry up and finish. Finally, thanks to
Marlene Wagner, close family friend, without her pushing and helping me, I would
never have entered graduate school.
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ABSTRACT
Fourier Grain Shape Analysis (FGSA) was conducted for the medium sand
fraction o f 86 samples collected within the Santa Monica Littoral Cell, Santa M onica
Bay, California. Samples were collected from the foreshore, shelf, rivers and dunes. A
bathymetric survey was also completed in the Redondo Beach area and was compared
to surveys taken by the Army Corps o f Engineers in 1972 and 1980.
Analysis shows that there are different transport mechanisms affecting the sand
grains during the different oceanographic seasons. Additionally, sand from North and
South o f Redondo Canyon is different, possibly indicating a different source terrane.
Furthermore, Redondo Canyon acts as a barrier to the southward transport o f sand
grains, although some leakage may occur during oceanographic winter due to large
waves.
It also appears that sand at 0 m below MLLW along the foreshore at Redondo
Beach is rougher and less equant than sand below 9 m MLLW. This indicates that
either rougher and less equant sand grains are selectively transported onshore or have
undergone abrasion in the surf zone during transport onshore or that deeper water
samples are not transported up onto the shore face during oceanographic summer
because effective fairweather wave base is shallower than 9 m MLLW.
Lastly, there possibly is a circulation pattern that inhibits mixing o f sand grains
at depths o f 12 m to 15 m below MLLW between southern Redondo Beach and areas to
the north.
ix
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INTRODUCTION
Purpose
Recent studies o f Santa Monica Bay using Fourier Grain Shape Analysis
(FGSA) have been completed in the Sedimentary Petrology Laboratory at the University
o f Southern California (Osbome, Ahlschwede, Broadhead, Cho, Compton, and Yeh,
1989; Lu, 1992; Lu and Osbome, 1993; Lee, 1993). These studies were completed
primarily to determine if FGSA is useful in preparing a sediment budget for a given
coastal reach. In addition, possible sources for sand along the foreshore in Santa
M onica Bay and the subsequent movement of the sand grains within the bay were also
analyzed.
The purpose of this study will be to build on the previous work described above
and to answer additional questions regarding movement of sand grains in Santa Monica
Bay. Using FGSA this study will attempt to determine 1) if geologically reasonable
source samples can be distinctly recognized by using FGSA, 2) if there is a dominance
o f Santa Monica Mountain-derived sand in northern Santa Monica Bay (indicating
southward longshore current), 3) if Redondo Canyon acts as a barrier to the transport of
Santa Monica Bay sand southward, 4) if samples collected along the Redondo Beach
foreshore from -18 m to 0 m below MLLW are sorted by shape, and 5) if there is a
difference in the shape of grains deposited during summer and winter seasons.
LOCATION
The study area lies within Santa Monica Bay, Los Angeles County, California.
Santa Monica Bay is part of the Santa Monica Littoral Cell (Figure 1). This cell extends
from Point Dume in the north to the Palos Verdes Hills in the south and is
approximately 70 kilometers long. The cell has three submarine canyons; Santa
1
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Santa Maria Cell
Santa Uarbara Cell
STUDY AREA
Santa Monica Cell
1 lucncmc Canyon
Mugu Canyon
San Pedro Cell
Oceanside Cell
Mission
Pencil Cell
\ Silver
\ Strand
\ Cell
La Julia Canyon
50 Km
11/°
121-
Figure 1. Southern California littoral cells. Tick marks indicate the study area (after
United States Army Corps of Engineers, 1986).
to
Monica, Dume and Redondo, although both the Dume and Santa Monica canyons are
presently inactive (Ingle, 1966; Scheidemann, 1980). Redondo Canyon acts as a barrier
to sediment transport according to studies by Handin (1951), Gorsline and others
(1968), and Rice and others (1976).
Creeks and rivers that actively contribute varying amounts of sand and gravel to
the Santa Monica Bay include Malibu, Las Flores, Topanga, and Ballona Creek.
Historically, the Los Angeles River has contributed large amounts of sediment to the
Bay but most likely not since the early Holocene.
Table I illustrates the differences in sediment discharge between major rivers to
the north in Ventura (Santa Clara River), in the Santa Monica Mountains, and to the
south (Los Angeles River) (Brownlie and Taylor, 1981).
STREAM DRAINAGE AREA KM2 ANNUAL SEDIMENT
DISCHARGE
Santa Monica Mountains
Group
1490 Km2 330,000 Tons
Santa Clara River 4220 Km2 3,720,000 Tons
Los Angeles River 2155 Km2 600,000 Tons
Table 1. Discharges of streams (after Brownlie and Taylor, 1981).
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REGIONAL SETTING
Regional Geography
Sediments deposited in the study area were derived from the San Gabriel and
Santa Monica Mountains. The beaches along central and southern Santa Monica Bay
were supplied mainly by the Los Angeles River carrying detritus shed by the San
Gabriel Mountains. The northern section of Santa Monica Bay was and is supplied by
the Malibu and Ballona Creek watersheds which carry detritus from the Santa Monica
Mountains.
These two terranes were not tributary to the Santa M onica Bay during the same
time periods. As explained by Osbome (1994), central and southern Santa M onica Bay
detritus was principally supplied by the Los Angeles River during late Pleistocene and
early Holocene time. The absence of significant channeling in the Ballona Gap area
during middle and late Holocene time led Poland and others (1959) to conclude that the
Los Angeles River drained southward into San Pedro Bay during much of the
Holocene. Historical evidence discussed by Josselyn and Chamberlain (1993) indicate
that the Los Angeles River changed course again and flowed through the Ballona Gap
until it diverted again into San Pedro Bay in 1825. This evidence indicates that San
Gabriel sediments have not been actively deposited in Santa M onica Bay during recent
times.
Malibu Creek (282 km2) and Ballona Creek (239 km2) watersheds in the Santa
Monica Mountains became the principal sediment sources for Santa Monica Bay when
the Los Angeles River flowed into San Pedro Bay in 1825 (Lu, 1992). These creeks
produced coarse-grained deltaic deposits following major runoff events (Shepard and
MacDonald, 1938).
4
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With the introduction of engineered structures within Santa Monica Bay
watersheds, however, the average rate of shoreline retreat was 0.27 m/year between
1876 and 1933 (Page, 1950). From 1925 to 1941, Dockweiler and El Segundo beaches
receded to the base of the Hyperion coastal dune field.
Osbome states that the most important reason for the loss of coarse-grained
terrigenous sediment dates back to middle-to-Iate Holocene time, when the Los Angeles
River first diverted to San Pedro Bay. Erosional rates must have increased even more
following the development o f flood control structures in the Ballona and M alibu Creek
watersheds which caused a decrease in the amount of sediment carried.
Woodell and Hollar (1991), Coastal Frontiers (1992), Flick (1993) and Wiegel
(1994), all pointed out that the widths of the present beaches in the Dockweiler-El
Segundo area are largely due to artificial nourishment and remained relatively unchanged
since 1935.
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PREVIOUS W ORK
Borrow Pit
Between October 1967 and October 1971, two dredging operations were
contracted to Shellmaker by the U.S. Army Corps, of Engineers (Figure 2). The first
dredging operation, conducted between October 1967 to October 1968, resulted in the
dredging of 1.07 x 10^ cubic meters of sand from an area offshore o f Redondo Beach
(Osbome, 1994). Sediment was removed from the seafloor at depths ranging from 9 to
20 meters below mean lower low water level (MLLW). The dredge spoil was deposited
from Topaz Street to Malaga Cove using a 36-inch cutter head and hydraulic pipeline to
remove sediment from the seafloor.
A second dredging operation was conducted during 1971 and resulted in the
removal of an additional 7.65 x 10^ cubic meters o f sediment from offshore of Redondo
Beach at depths ranging from 9 to 25 meters below mean lower low water level (Shaw,
1980). Therefore, a total of 1.835 x 10^ cubic meters of sediment was mined from the
inner continental shelf from 1967 to 1971 (Osbome, 1994).
In 1969, 1972 and again in 1980, hydrographic surveys were completed by the
U.S. Army Corps, o f Engineers between Redondo Canyon and Palos Verdes Peninsula
to determine to what extent the dredged area was being filled by sediment. The 1969
survey (scale 1 inch = 500 feet) and 1972 survey (scale 1 inch = 300 feet) covered the
complete area o f the borrow pit. The 1980 survey (scale 1 inch = 200 feet) covered the
southern 40% o f the mined area. The 1972 and 1980 surveys are shown in Figures 3
and 4. Analysis o f these surveys plus additional survey work by the author is discussed
in a later section.
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TORRANCE
j BLVD
KM
TORRANCE
Figure 2. Location map for the Redondo Beach area showing the approximate location
of the nearshore borrow area. Hachured area shows the approximate location of the
hydrographic survey by the U.S. Army Corps of Engineers in May, 1980 (from
Osbome, 1994).
7
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o
*33 * 48 ' 43 '
0 3
Figure 3. Bathymetry of the 1972 hydrographic survey by the U.S. Army Corps of
Engineers.
8
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33 * 49 *52 *
o
u
1km
Figure 4. Bathymetry of the 1980 hydrographic survey by the U.S. Army Corps of
Engineers. J
9
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Regional Geology
The following description of the regional geology is taken from Lu (1992).
The study area is part of the Santa Monica Embayment (Figure 5)
which extends from Point Dume to the Palos Verdes Hills (Shepard and
MacDonald, 1938; Emery, 1952; Terry et al, 1956; Osbome et al., 1980;
Scheidemann, 1980). The Santa Monica Embayment is bounded by the
Santa M onica Mountains to the north, Palos Verdes Hills to the south,
and the Los Angeles Basin to the east. Geology of the Santa Monica
Embayment is characterized by a basement complex and overlying
Cretaceous, Tertiary and Quaternary strata. The present setting of the
Santa Monica Bay is believed to be the result o f Late Quaternary geologic
evolution o f the Santa Monica Embayment, which involved sea level
fluctuations, sedimentation o f marine deposits, and development of
coastal eolian dunes.
Major structural features o f the Santa Monica Embayment and the
adjacent Los Angeles Basin are the Santa Monica Fault and Newport-
Inglewood fault zones, which separate the area into a Northwestern
Block, a Southwestern Block, and a Central Block as shown in Figure 6
(Yerkes et al., 1965). Geologic history of these three blocks are
significantly different across the two fault zones.
Northwestern Block
Basement rocks of the northwestern block include the Santa
Monica Slate (Hoots, 1931), which is composed of argillaceous rock
that locally has been altered by contact metamorphism to mica schist,
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p - = SAN
SAN
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VALLEY /
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LC:
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Figure 5. Map showing the bathymetry and physiography of the study area. Tic
marks indicate the sample collection area (after Scheicemann, 19S0).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
( ;t*w r
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I SA N F C ftN A N O O s v S l m ,
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Fault or fault » n Anudinc Syactee Boundary of rtniettiml 6iu cfc
0uA«d « U n fv rw M M v Im u i, fa«A « u wUn t f r u i M M i twuiM fluU < s u m tffn au u M v I muiM
Figure 6. Map showing physiographic and m ajor structural features o f the Los Axueles
Basin (after Yerkes et al., 1965).
12
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phyilite and spotted cordierite slate (Yerkes et al., 1965) and the diorite
and granodiaorite that intruded the Santa Monica Slate in the eastern part
o f the northwestern block (Yerkes et al., 1965).
The Upper Cretaceous Chico Formation, which is composed of
sandstone, conglemerate, shale, and limestone, overlies the basement
rocks (Bailey and Jahns, 1954; Yerkes et al., 1965). In turn, these strata
are unconformably overlain by nonmarine sandstone and conglomerate
o f the Sespe Formation. The uppermost Sespe Formation interfingers
with the overlying marine sandstone and siltstone o f the Vaqueros
Formation. Deposition during the middle Miocene resulted in the
accumulation o f marine sandstone and minor siltstone of the Topanga
and Modelo Formations (Yerkes et al., 1965).
Along the southern flank o f the Santa M onica Mountains, upper
Pleistocene deposits are preserved as uplifted marine wave-cut platforms
and related sedimentary deposits filling up fluvial channels (Birkeland,
1972). Holocene sediment is limited to stream deposits at the base of the
canyons (Scheidemann, 1980).
Central Block
The basement rocks of the central block are questionably inferred
to be granitoid intrusives and the associated metamorphic rocks that are
Jurassic to late Cretaceous in age (Yerkes et al., 1965).
Upper Cretaceous and Paleocene strata o f the central block occur
locally within this block, but are not well studied. Eocene through
Miocene strata occur in most of the central block, but are buried by
13
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younger strata. These strata generally are referred to as undivided
marine clastic sedimentary and extrusive igneous rocks (Yerkes et al.,
1965). These strata, in turn, are conformably overlain by the Pliocene
Repetto Formation. Unlike the Repetto Formation in the southwestern
block, the formation in the central block consists of marine fine- to
coarse-grained sandstone with minor interbedded siltstone. The Repetto
Formation grades upward into the Pico Formation, which is composed
o f marine siltstone and sandstone.
The Quaternary strata of the central block consist of the lower
Pleistocene San Pedro Formation, the upper Pleistocene Lakewood
Formation, and recent deposits. The San Pedro Formation is composed
o f stratified sand with some beds of fine gravel, silty sand and silt.
Marine muds and fragments o f shells are common in this formation. The
Lakewood Formation consists o f marine sand and gravel beds. The
formation grades upward to finer sediment (mostly fine sand, silt and
clay) of fluvial origin. The recent deposits include modem alluvial,
beach and active sand dune deposits.
Southwestern Block
Basement rocks of the southwestern block consist of the Catalina
Schist, which is exposed in a small area on the north slope of the Palos
Verdes Hills, and was described as "chiefly fine-grained chlorite-quartz
schist and blue glaucophane- or crossite-bearing schist" (Yerkes et al.,
1965).
14
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The Monterey Formation unconformably overlies the basement
rocks, and consists o f massive shale, diatomites, mudstone, and
siltstone. Ar/K and fission-track dating indicate that the Monterey
Formation extends from middle Miocene to early Pliocene in age
(Boellstorff and Steineck, 1975). The Monterey Formation is overlain
by the lower Pliocene Repetto Formation, and the upper Pliocene Pico
Formation. The Repetto Formation consists of massive, glauconitic
foraminiferal siltstone, and minor sandstone. The Pico Formation is
composed of marine siltstone, claystone and sandstone (Yerkes et al.,
1965). Recent work by Bandy and Wilcoxon (1970), Bandy (1972) and
Boellstorff and Steineck (1975) indicates that the Pico Formation ranges
in age from late Pliocene to early Pleistocene. The Pleistocene strata of
the southwestern block include the lower Pleistocene San Pedro
Formation and the upper Pleistocene Palos Verdes Sand. The former
consists of predominantly sand and gravel, intercalated with minor beds
o f marine gravel and sand. The Palos Verdes Sand fines upward into
silt, clay and fine-grained sand o f flood plain origin (Poland et al.,
1959).
Recent deposits of the southwestern block include the flood
plain, fluvial, lagoonal, eolian, and littoral deposits (Poland, et al., 1959;
Yerkes, et al., 1965).
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Offshore Area
The offshore area of this study is the Santa Monica Shelf and it is believed to be
the offshore continuation of the southwestern block (Scheidemann, 1980). As
explained by Gorsline and others (in press) the shelf is typical o f active continental
margins; narrow, high-gradient, and characterized by high wave energy. The width of
the Santa Monica Shelf is variable though, and the relatively broad shelf is bordered and
compartmentalized by narrow shelves to the north at Point Mugu and to the south at the
Palos Verdes Hills.
Gorsline and others (in press) indicate that the Santa Monica Shelf is a starved
shelf with 35% of its area rocky or with less than 2 m of sedim ent cover. Ludwig and
others (1992) determined that of the remaining area, sediments were up to 60 m thick
and date to the Holocene.
16
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METHODOLOGY
H istory
Sedimentologists have attempted to develop techniques for quantifying particle
grain-shape, mainly by measuring their sphericity and roundness (Wentworth, 1919,
1922; W adell, 1932; Zingg, 1935; Powers, 1953; Sneed and Folk, 1958; Krumbein and
Sloss, 1963; Dobkins and Folk, 1970). Sphericity can be defined as the degree to
which a sedimentary particle approaches a sphere in shape, and roundness can be
defined as the measure of the sharpness of grain edges or comers. Wadell (1932),
Krumbein (1941) and Sneed and Folk (1958) developed mathematical relationships to
classify the sphericity of grains by the ratio of the length of grain axes (Figure 7).
Rittenhouse (1943) Powers (1953), Krumbein and Sloss (1963) and Dobkins and Folk
(1970) developed classifications for the measurement of sphericity and roundness of
grains by the use of visual estimation charts and by the radius of an inscribed circle
(Figure 8). Alternative classifications of particle form are provided by Zingg (1935),
who plotted the ratios of grain axes on a bi-variate plot (Figure 9).
It is important to point out that by adopting and accepting the use of visual
estimation charts, sedimentologists have accepted the concept that geologically useful
information can be obtained from the two-dimensional maximum projection outline of
sedimentary particles (Osborne and Yeh, 1992.) When sphericity is measured using
visual charts, sedimentologists are actually estimating the degree to which the two-
dimensional maximum projection outline of a grain approaches a circle. The problem
with visual estimation charts for sphericity and roundness measurements and the use of
alternative classifications of form is that they do not relate easily to the study of sand
grains and do not completely describe the complete grain form (i.e. roughness,
roundness, and sphericity). Barrett (1980) suggested that even the best of the
17
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\\/w = W adell’s W orking S p h ericity (W adell, 1 9 3 5 )
W 4 -t t
< v -
where Ap = projected area of grain,
dp = diameter of smallest circumscribed circle aroun
projection.
i//j- = Krumbein’s Intercept Sphericity (Krumbein, 1941)
3 L- I - S
where L = longest axis,
I = intermediate axis,
S ~ short axis.
= Maximum Projection Sphericity (Sneed and Folk. 1958]
i L-1
"'here L = longest axis,
I - intermediate axis,
S = short axis.
Carver^ l ^iemat* ca^ relationships for the classification of grain sphericity (from
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sphericity
o
o
O
o 0
o o o
. C 3 o
o
o
O
o
< 2 r ?o » c ?
0-3 0 .5 0.7
R oundnes
Figure 8. Chart for visually estimating sphericity and roundness (from Krumbein and
Sloss, 1963, p .l 11).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A
Ot»ate
Ecuont
©»»)
- V x
0 6
2
-
-
z
0 6 - ‘
Slated
Pfoiofe
(Roller)
0 4
# -J r
i
5 1 02
-
* *
D s
D,
1.0
0.6 \ 0.7 .0.5
0.8
0.4'
0.8
0.6
0.4
7 T 0 -2
0.8
0.4
0.2
D,
Figure 9. A classification of shapes of pebbles after Zingg (from Boggs, 1992, p. 96).
20
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commonly used procedures for determining sphericity and roundness are limited by
observational subjectivity and low discriminatory power. Measurement of the axes of a
particle does not provide a unique characterization of particle form and the
reproducibility of roundness measurements can be quite low (Boggs, 1992).
Fourier Grain-Shape Analysis
Fourier grain-shape analysis (FGSA) is based on the maximum projection
outline of a grain and improves on visual estimation charts by quantitatively measuring
the shape components of the outline by means o f a closed-form Fourier series. FGSA,
since its introduction by Schwarz and Shane (1969) and Ehrlich and W einberg (1970),
has been used for numerous sedimentological studies. The following description of
FGSA was taken from Osborne and Yeh (1991).
Ehrlich and W einberg (1970) described a closed-form Fourier
method to analyze the observed variation of two-dimensional, maximum-
projection, grain-shape area. Grain shape may be estimated by an
expansion of the periphery radius as a function of angle about the grain's
center of gravity by a Fourier series (Boggs, 1992). In Fourier analysis,
a series of sine and cosine curves with periods equal to fundamental
harmonics are fit to the observed data by a least squares technique.
Fundamental harmonics are the prime fractions (1/2, 1/3, 1/4.......1/N),
where N equals half the number of digitized points used to define the
periphery of a grain. As the number of fundamental harmonics is
increased, the computed curve converges with the observed data. The
highest frequency that can be estimated is known as the Nyquist
frequency, which is equal to twice the distance between successive
21
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observations (Davis, 1986). If the nyquist frequency is exceeded, error
may be introduced by the incorporation of irresolvable high frequencies
into lower frequencies (aliasing). The radius of the grain is given by:
oo
R ( 6 ) = Ro + ^ Rn cos (n 9 - 0n).
n = !
where 9 is the polar angle measured from an arbitrary reference line.
The first term in the series Ro is equivalent to the average radius of the
grain in the maximum projection orientation. For the remainder o f the
terms, n is the harmonic order, Rn is the harmonic amplitude, and 0n is
the phase angle. The phase angle appears to provide little additional
grain-shape information, and therefore is not considered further. It is
important to note that the n'th harmonic contributes to the explanation of
the observed shape variation as a figure with n "bumps", for example,
the "zeroth" harmonic is a centered circle with an area equal to that of the
maximum projection; the first harmonic is an off-centered circle; the
second is a figure eight; the third is a trefoil, and so forth. The amplitude
of each harmonic represents the contribution of each basic shape
component to the overall shape o f the maximum projection outline for
each grain. The phase angle represents the orientation of each
component. With given combination of amplitudes and phase angles, a
regularly shaped two-dimensional maximum projection outline can be
partitioned into its fundamental shape components. The center of gravity
of the maximum projection shape is used as the origin of the radius
expansion to simplify interpretation of the Fourier series (Full et al.,
1984). Coordinates of points along the periphery of the maximum
projection outline are required for the Fourier expansion. At least twice
22
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the number of such points must be known as the number o f the highest
desired harmonic. The initial origin of the periphery points may be
arbitrary, because a later transformation placers the origin at the center of
gravity of the maximum grain-projection area. If a harmonic or periodic
function exists within the data, the amplitude of the sine and cosine
curves with periods close to the natural harmonic will be considerably
larger than the amplitudes of other harmonics in the sequence.
Shape information is contained in both amplitude and phase angle
values. Amplitude is invariant with respect to grain orientation, whereas
phase angle is not. As the orientation procedure is time consuming and
spectra of harmonic amplitude values normally serve to distinguish
between and/or among constituent grain-shape populations,
consideration of the phase angle is usually not considered in Fourier
grain-shape analysis.
Although conceptually similar to the closed form methodology described by
Ehrlich and Weinberg (1970), the methodology used in this study is the newer and more
widely used Fast Fourier Transform (FFT) (Brigham, 1974; Bloomfield, 1976; Bendat
and Piersol, 1971). This procedure involves the calculation of many values of the line
spectrum using the Fast Fourier Transform computer algorithm to produce a smoothed
estimate of the continuous spectrum. The FFT is extremely rapid and requires only
n*log2n arithmetic operations rather than the n^ operations as do alternative methods.
23
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Sample Collection
The 56 sand samples used for this study were collected from beaches, rivers,
dunes and inner shelf areas associated with the Santa Monica Bay and Santa Monica
Littoral Cell. Sample location numbers, Beach names, collection dates and sample
names used in this study are shown in Table 2. Samples were collected from October
1990 to November 1993. Note that the sample names are used on all figures and charts.
The locations each of the 52 beach and inner shelf samples are shown on figure 10.
Thirty-eight samples were collected from the beach-foreshore at 0 m MLLW
elevation by placing approximately 500 cm3 of sand into a container. The fourteen
samples analyzed in this study from - 5 m MLLW to -18 m MLLW were taken by
dredge collection from the U.S.C. research vessel SEA WATCH.
The four possible fluvial and dune source samples were taken from the San
Gabriel Mountains, Santa Monica Mountains and from the Hyperion and Parkfield
Dunes.
Bathym etric Study
A cruise in Santa Monica Bay was conducted aboard the U.S.C. research vessel
SEA W ATCH on November 9 and 10, 1993 to examine the bathymetry of the dredged
area o f Redondo Beach by the U.S. Army Corps in 1967 and 1971 and to collect
sediment samples. A total of 60 Van Veen grab samples were collected at water depths
ranging from 5 to 21.5 m below the water surface. The bathymetric study of an
approximately 15 km^ area in water depths ranging from 5.5 to 15 m was performed
using a single channel 248E Transceiver with an EPC 3200 Recorder. The fathometer,
a 12 Khz transducer, was mounted 1.4 m below the hull of the SEA WATCH. A
Magnavox M X -100 Global Position Satellite receiver was used to record positions
24
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Table 2. Sample sets used for the study. Bohled samples are used for the Baywide sam ple set.
• • • -
„ ___ _ _ _______
October
1990
November
1991
April
1992
November
1993
Location
number
BEACH LOCATIONS
SAMPLE
NAMES
SAMPLE
NAMES
SAMPLE
NAMES
SAMPLE
NAMES
1 0.5 N. of Trancas Cny.
la lb
2 Zuma Beach
2a 2b
3 Dan Blocker State Beach
3a 3b
4 Keller’ s Shelter
4a
5 Las Tunas State Beach
5a 5b
6
Will Rogers State Beach
6a
7
Santa Monica Beach (Entrada)
7a 7b
8
Santa Monica Pier (North Side)
8a 8b
9
Venice Pier (North Side)
9a 9b
10
Marina del Rey (North of Channel)
10a 10b
11
Dockweiler Foreshore
11a lib
12
Dockweiler Foreshore
12a 12b
13
Dockweiler Foreshore
13a 13b
14
Dockweiler Foreshore
14a 14b
15
Manhattan Beach (Longfellow)
15a 15b
16
Redondo Pier (South Side)
16a 16b
17
Redondo Beach (Topaz Street)
17a 17b
18
Redondo Beach Transect #1 (0 m)
Red 10
18
Redondo Beach Transect #1 (9 m)
Red 19
18
Keoondo Beach t ransect #1 (12 m)
Red 112
18
Redondo Beach Transect #1 (15 m)
Red 115
18
Keoondo Beach t ransect #1 (18 m)
Red 118
19
Redondo Beach Transect #2 (0 m)
Red 20
19
Redondo Beach Transect #2 (9 m)
Red 29
19
Redondo Beach Transect #2 (12 m)
Red 212
19
Keoondo Beach t ransect #2 (15 m)
Red 215
19
Kedondo Beach Transect #2 (18 m)
Red 218
20
Redondo Beach Transect #3 (0 m)
Red 30
20
Redondo Beach Transect #3 (9 m)
Red 39
20
Redondo Beach Transect #3 (1-2 m)
Red 312
20
Keoondo Beach t ransect #3 (15 m)
Red 315
20
Keoondo Beach Transect #3(18 m)
Red 318
21
Redondo Beach (I Street)
21a
22
North Malaga Cove Beach
22a 22b
23
Hyperion Dune Field
H-138
24
Big Tujunga Canyon
BTUJ
25
Parkfield Sand Dune
PARK
26
Santa Monica Shelf sample
SLF-4
27
Dockweiler Beach Shelf sample
SLF-6
28 Mandeville Canyon
MAND
25
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iiuU Y ftuair^
TORRAHCt i
Figure 10. Location map of inner shelf samples used in the study.
26
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during the survey. Depths and locations were recorded at predetermined intervals and
are shown in Appendix A. Eighteen distinct transects were run perpendicular to
Redondo Beach and were tied together with three transects that were run parallel to the
beach. The bathymetric survey is shown in Figure 11.
Sample Preparation
Samples were prepared for FGSA in the Sedimentary Petrology Laboratory. All
chemical treatments of the samples were carried out in a fume hood.
Quartz grains in the 0.25 to 0.50 mm (1 to 2 phi) size fraction are used in this
study for FGSA. By using only quartz in a restricted size range the affects on selective
transport by differences in size and specific gravity are removed. Also, only using
quartz eliminates shape effects of differences in cleavage or fracture of different
minerals. Therefore, shape is the only variable that will be measured.
Approximately 50 to 100 grams o f sediment are placed on top of a 0.50 and
0.25 mm sieve stack (1.0-2.0 phi). Sediment samples are then gently wet sieved to
minimize grain abrasion and to separate the 0.25 to 0.50 mm, medium sand-size fraction
used for FGSA analyses. The 0.25 to 0.50 mm size fraction is then transferred to a
labeled beaker and dried in a convection-oven at 100 degrees Fahrenheit. After the
samples are dried they are treated in a solution of 10% hydrochloric acid with stannous
chloride crystals to remove any iron-oxide and carbonate coating that might alter the two
dimensional shape outline o f the grains. Samples are then rinsed with de ionized water
and dried again in the convection oven. The samples are then treated with a 50%
solution of HF1 in order to clean the quartz grains, corrode the feldspars, and remove
organic material. Finally, the samples are treated with a saturated solution o f Sodium
Cobaltinitrite to stain the feldspars for ease in distinguishing the quartz.
27
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3 S .C Z .0 t t
1 k m
M
W
c i
c
Figure 11. Bathymetry of the 1993 hydrographic sur/ev by the author.
28
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Two-hundred quartz grains were then randomly separated from the samples by
using a small brush to pick the grains under a petrographic microscope. The grains are
then dry mounted on a glass slide.
Sam ple Processing
Digitizing of sand grains for FGSA was done in the Sedimentary Petrology
Laboratory. The hardware consists o f a Video-Microscope connected to a Digital
Corporation Vax-Station 3200. The Video-Microscope consists of a standard binocular
petrographic microscope connected via an ordinary camera attachment to a black-and-
white video camera. The imaging software was written by Tim Fogarty.
The camera projects the maximum two-dimensional image of the quartz grain
from the microscope to the video screen. A maximum contrast appears between the
grain (dark) and the surrounding background (light) allowing the computer to record the
boundary points of the grain as Cartesian coordinates. The computer also calculates the
centroid of the projected grain. This data is transferred into amplitude files which
contains the averaged values for each o f the first 24 harmonics for each sample.
29
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STATISTICAL METHODS
Introduction
The statistical tests used in this study include Factor Analysis, One-way
Analysis of Variance, Hotelling's T^ Test, Duncan's New Multiple Range Test and
Discriminant Function Analysis (DFA).
All tests results except for Discriminant Function Analysis were obtained using
the commercially available statistical software package called "Bio-Medical Data
Processing" (BMDP), developed by BMDP statistical Software for VAX/VMS
operating systems (Dixon, 1990). Discriminant Function Analysis results were
obtained by using a subroutine included within the EDGE digitizing program written by
Tim Fogarty.
As described by Robinson (1993) data processing can be divided into three
broad phases, significance testing, composition determination, and single harmonic
analysis.
In significance testing, the equivalency in shape composition of two or more
samples is tested. Significance testing for this project consists of a one-way ANOVA
design which are employed to determine whether there are significant differences
between samples collected at the same time from different locations, samples collected at
different times from the same location, and the amplitude values for a single harmonic
for several samples. The Duncan's New Multiple Range Test is employed to specify
which samples are causing the significant differences found from the ANOVA and
Student's t Tests.
In composition determination, the Hotelling's T^ Test, factor analysis, and
Discriminate Function analysis, are used to describe the shape composition of the beach
samples in terms of percentages o f associated source samples. Source samples are
30
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defined by a combination of geologic observation and data analysis using the above
named tests. Specifically, factor analysis is used to identify end-member samples,
which are the most diverse with respect to each factor. Once the operator has selected
the probable source samples based on geological information, the Hotelling's Test
may be used to formally test whether the shape composition of the source samples differ
by a statistically significant amount. Discriminant Function analysis is then used to
partition beach samples into percentage o f composition from the previously defined
source samples.
B rief descriptions of the previously discussed statistical analysis are found
below.
Factor Analysis
As discussed by Lu (1992) and Lee (1993) Factor analysis was originally
developed by experimental psychologists in the 1930's. It is an algebraic method of
measuring multiple correlation’ s in a matrix of variables or samples in an attempt to
simplify relationships (Davis, 1986). The "factor" is an attempt to arrange data in such
a way that explains most of the variance in the data system. Contacts between biologists
and paleontologists resulted in the introduction of factor analysis to geologists (Joreskog
and others, 1976).
Although many types of factor analysis exist, this study used the "Q-mode,
maximum variance, principle component analysis determined from a variance-
covariance or correlation matrix" (Davis, 1986). The variance associated with a
multivariate data matrix can be analyzed by projecting the data onto axes. To
accomplish this, eigenvalues and eigenvectors are derived from a variance-covariance
matrix which are obtained from the original data matrix of interest, multiplied by its
31
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transpose (Davis, 1986). The Q-mode factor-analysis method was used to identify
relationships between and among sample means by processing the mean harmonic
amplitude value o f 200 measurements per sample for each o f harmonics 2 through 24.
The amplitude value for the first harmonic was not used in the factor analysis since its
average is typically one order o f magnitude greater than the other amplitude values and
thus would bias the resulting factors.
Factor analysis is used to retain as much of the variance associated with the
original data matrix as possible, and to reduce the amount o f variables or factor axes
necessary for analyzing the variance associated with the original data matrix. The factor
axes are Cartesian coordinates fit by linear regression to the array of multivariate sample
means. Such factor axes thus represent fundamental and independent relationships
among these means. End mem ber samples along the factor axes represent the most
dissimilar samples and are therefore useful in determining important harmonics and
possibly in identifying source samples. Harmonic by harmonic significance test are
then used to identify which harmonics contribute to each axes.
One-W ay Analysis of V ariance
As discussed by Lee (1993) one-way analysis of variance (ANOVA) is an
algebraic process for partitioning the sum o f squares into components or sources to test.
These components are evaluated to determine their relative contributions to the total
variability in the observations. The basic assumptions o f this test (Davis, 1986) are that
the error terms of the variates in each sample are independent, each parent population is
normally distributed, and each population has equal intrasample variance.
In One-Way ANOVA the total variance of the tested data sets are separated into
among sample variance, within sample variance, and an error term (Alder and Roessler,
32
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1977). If the variances are similar it is assumed that the sample populations are likely to
be from the same parent population. An f-value is obtained by dividing the variance
among samples by the variance within samples. The obtained f-values were then
compared to critical f-values at the five percent (alpha=0.05) significance level to
determine if the null hypotheses of equal means should be rejected. If the null
hypothesis is rejected than at least one sample of the sample set is statistically different.
The standard One-way ANOVA table calculated by using the BMDP software
program is shown in Table 3.
One way analysis o f variance was used in this study to determine the
equivalency of mean harmonics, from 2 to 24, for factor 1 and 2 end-members samples.
If end member samples are statistically different then the factor analysis is yielding
significant data.
D uncan's New M ultiple Range Test
While ANOVA can discern when there is a significant difference between or
among samples or sample sets, it cannot identity which o f the samples are the cause of
the observed difference. Duncan's New Multiple Range Test was performed to identify
which samples or sample sets were significantly different. The Duncan's test provides a
series of shortest significant ranges with which to compare difference between means
(Alder and Roessler, 1977). Samples which are not significantly different are grouped
together, whereas dissimilar samples are grouped separately. Assumptions for the
Duncan's Test are identical to those of ANOVA (Alder and Roessler, 1977).
As described by Robinson (1993), in the Duncan's Test, the mean for each of
the samples to be tested is determined and then placed in a table listed from highest to
lowest. Based on the number of sample means, the significance level, the number of
33
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Table 3. The design for the one-way Analysis of Variance as used in this study.
(Davis, 1986).
Source Sum of Squares
Degrees
of
Freedom
Mean
Square
F Ratio
Main Effect
(between)
y r f ( E > 2
; = 1 ", "
C - 1
S S UB
DFM e
MSme
m s S0
Sample
Deviations
(within)
I - y x , ; - E |
N - C
SSso
DFS0
Total
N - 1
Where: J = treatments; I = variates; T = treatment totals; n = observations;
N= total number of observations; C = total number of treatments: x = data:
SS = sum of squares; DF = degrees of freedom; M S = mean square.
34
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degrees of freedom, and the standard error of the mean, the shortest significant ranges
are computed. The standard error o f the mean is the square root o f the within sample
mean square from the analysis of variance table, divided by the square root of the
number of observations on which each of the means is based (Alder and Roessler,
1977) The difference between any two sample means is then compared to the shortest
significant ranges, and if it is lower is not considered significantly different.
The present study used a five percent significance level (alpha = 0.05) for the
Duncan's Test to identify which samples were different within the samples sets
identified to be significantly different by Student t-Test.
H otelling's Test
The Hotelling’ s T ^ Test is used to compare the multivariate means between two
sample populations. It is used to determine if end-member samples as determined by
factor analysis or potential source samples as chosen by geologic reasoning are
statistically different with respect to mean values. The Hotelling's T^ Test consist of
determining the multidimensional mean vector for each sample, as well as the associated
variance-covariance matrices (Alder and Roessler, 1977). Then, using matrix algebra,
the variance-covariance matrix, the inverse of the variance-covariance matrix, and the
difference from each o f the mean vectors is multiplied. Lastly, the resultant matrix is
multiplied by the number of observations to obtain the T^ value. The associated F value
is the T^ value multiplied by the resultant of the difference of the number of
observations and the number of measurements divided by the degrees of freedom (Alder
and Roessler, 1977). The Hotelling's T^ Test requires that data consist of random
samples from normally-distributed parent populations that have no interaction effects
(Alder and Roessler, 1977).
35
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The present study used a five percent significance level (alpha = 0.05) for the
Hotelling’ s Test and input data consisted of normalized amplitude values for the
second through 24th harmonic for each grain in every sample tested.
D iscrim inant Function Analysis
As described by Robinson (1993) Discriminant function analyses (DFA) is
employed as the most appropriate multivariate statistical technique for estimating the
percentage o f beach sand derived from each local source. DFA is one of the most
powerful statistical tools for assigning or partitioning samples into previously-defined
populations. Each of the 200 quartz grains in each sample used is assigned to identified
and predetermined sand sources on the basis of grain-shape as determined by harmonic
values. This allows the percentage of sand grains derived from each sand source to be
determined.
Mathematically, DFA consists of computing a transform which gives the
minimum ratio o f difference between or among a set of multivariate means to the
multivariate dispersion (variance) of the set of previously-defined groups (e.g.. sand
sources for this study). If one were to consider only two groups as consisting of points
within multivariate space, DFA computes the equation of one orientation along the two
clusters where spatial separation is maximized and each cluster has smallest possible
dispersion. Therefore, the spatial separation between clusters is maximized. Once, the
transform is computed, new samples may be extended to two or more classificatory
groups (Davis, 1986).
The International Mathematical Subroutine Library DFA subroutine is used to
compute the required transform for the harmonic amplitude values o f samples selected to
be partitioned to each source Once the discriminatory equations are computed, the
36
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harmonic amplitude values for each of the 200 grains per beach sample are analyzed and
assigned to one of the previously identified sources. These numbers are then expressed
as the percentage of sand derived from each source.
DFA assumes that each potential source is 100 percent unique with respect to
grain-shape when assigning percentages for selected samples. Because each potential
source is a mixture of grain-shape components, the initial assignment is recast when
applicable, to reflect the unique grain-shape components of that particular source.
37
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RESULTS
General Statem ent
Presentation of results is separated into two sections based on the geographical
location of the samples: 1) samples taken throughout Santa Monica Bay (Baywide),
2) samples taken south of Redondo Canyon during the bathymetric survey cruise.
Thirty five beach samples, 2 shelf samples, 2 river samples, and 2 dune samples
were analyzed by Fourier methodology. Results are given separately for the beach
samples and possible source (shelf, river, dune) sample sets.
Beach Samples
The 35 beach samples were selected from 19 approximately equally spaced
locations. All locations have samples that were collected in summer (October and
November) and winter (April) seasons except locations 4 (summer only), 6 (summer
only), and 21 (winter only).
Sample Relationships from Factor Analysis
A Q-mode, maximum variance, principle component analysis was performed on
the averaged amplitude values for the second through the 24th harmonic for all 35 beach
samples. The resulting two-factor solution, as calculated from the factor scores,
describes 79 percent of the total variance in the system (Table 4). Factor 1 describes 71
percent of the variance and factor 2 describes 8 percent of the variance. The resulting
factor score plot has four end-member samples, two end-members for each factor axes
(Figure 12). End-member samples for factor one are 13a and 22a and end-member
samples for factor two are 2a and 16b.
38
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Sample Name FACTOR1 FACTOR 2
1a -0.39 1.793
1b -0.227 1.305
2a -0.085 2.809
2b 1.164 0.059
3a -0.083 -1.331
3b 0.018 0.958
4a 1.422 -1.27
5a 1.315 0.95
5b 1.838 0.869
6a 0.203 -1.446
7a -0.215 -1.412
7b -1.032 0.3
8a 0.397 -0.626
8b -0.597 1.481
9a -0.341 0.2
9b -0.851 0.618
10a -0.413 -0.781
10b -0.915 -0.89
11a -0.168 -0.368
11b -0.907 0.566
12a -0.935 -0.464
12b -0.174 0.675
13a -1.327 0.346
13b -0.489 -0.081
14a -1.108 -0.24
14b -0.596 -0.766
15b -0.491 -0.006
15a -0.652 -0.675
16a 1.238 -1.027
16b -0.884 -1.721
17a -0.769 -0.107
17b 0.79 0.18
21b 0.342 0.177
22a 2.586 -0.35
22b 2.335 0.276
Table 4. Factor scores for Baywide sample set.
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< ■ — uo!ie6uo|3 Buiseajoui
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Figure 12. Factor plot of Baywide sample set.
End-member testing from Hotelling’s Test
Individual harmonic Hotelling’s T - Tests were run for harmonics 2 through 24
for the four end-member samples (Table 5). Results o f the tests show that significant
differences occur in harmonics 6 through 24 for Factor 1 and only harmonic 2 for
Factor 2. The higher order harmonics (6-24) represent grain roughness and the lower
order harmonics (2-5) represent overall grain shape, in this case, harmonic 2 represents
elongation. Average amplitude values for the statistically significant harmonics of these
end-members increase from 13a to 22a (left to right) for Factor 1 end-member samples,
and from 2a to 16b (bottom to top) for Factor 2 end-members. Thus, samples increase
in roughness from left to right along Factor 1 and samples become more elongate with
an increase in the Factor 2 score.
Sample comparison from Duncan's New Multiple Range Test
Duncan’s New Multiple Range Test was run for the 35 foreshore samples to
determine if significant differences could be found among the samples. Results are
shown in Table 6. Statistically significant differences were not found separating most
samples collected during winter and summer. Samples collected south of Redondo
Canyon though with the exception of sample 16b, are significantly different than those
collected north of the canyon.
41
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harmonic 1x2 1x3 1x4 2x3 2x4 3x4
2
0 0 .0 0 6 2 , 0.0002
0 .0 3 3 5 0.3134 0.2368
3
0.0555 0.0475 0.2181
0.9744 0.467 0.4595
4 0.1604 0.3327 0.7441 0.5865 0.3465 0.6029
5
0.1984 0.2277 0.8766 0.8738 0.2929 0.3352
6 0.2721 0.0898 0.5301
0.5984 0.0985 0.0267
7 0.1484 0.0378 0.2786
0.5974 0 .0172 0.0031
8 0.1428 0.1271 0.0652
0.9023 0.002 0
9
0.115 0.0066 0.0523
0.2788 0.0013 0.0002
10 0.2164 0.0291 0.0547
0.3865 0.0029 0
11
0.0719 0.0084 0 .0455
0.4449 0.0004 0
12 0.2046
0.0549 0 .0137 0.5009 0.0003 0.0001
13 0.221 0.0646 0.0227 0.5361 0.0008 0
14 0.2495 0.0188 0 .0 1 5 2 0.1696 0.0005 0.0001
15 0.2871 0.0351 0 .64$$ 0.206 0.0025 0
16 0.0423 0.0066 0.0706
0.3983 0.0003 0.0001
17 0.119
0.0191 0.0579
0.3839 0.0008 0.0001
18 0.093 0.63 0.0476
0.6549 0.0004 0
19 0.3055 0.0371 0 .0 3 4 0.2392 0.0017 0
20 0.4161 0.0223 0 .0 3 6 6
0.0914 0.0031 0
21
0.4594 0.0249 0 .0239
0.1283 0.003 0
22 0.6526 0.0444 0.0153
0.112 0.0041 0
23 0.6896 0.0463 0 .0161
0.1197 0.0058 0
24 0.7739
0.0966 0.0077
0.1737 0.0034 0
0.0259 0.0038 0.2882
0.5294 0.0008 0
l)2a 2) 16b Represent
3) 13a 4)22a Represent
Numbers in bold statistic!
Numbers bold and italics
-actor 2 end-members
-actor 1 end-members
illy different at the 0.5 signifigance level.
are statistically diffemet at the 0.01 S.L.
Table 5. Hotelling's T2 Tests for end-member samples.
4 2
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T able 6. Results of Duncan’ s Multiple Range Testing for the Baywide
sample set. Vertical lines indicate statistic ally similar groups.______
Sample Name
10a
7b
14b
15a
12a
7a
10b
lib
13b
14a
la
9a
9b
3a
11a
13a
6a
lb
16b
15b
8a
12b
8b
3b
4a
5b
2a
2b
5a
16a
17a
17b
21b
22a
22b
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Beach and source samples using Fourier analysis
A Q-mode, maximum variance, principle component analysis was performed on
the averaged amplitude values for the second through the 24th harmonic for all 35 beach
samples and for 6 possible source samples. These potential source samples include
samples taken from dunes (Hyperion & Parkfield), Santa M onica Mountains
(Mandeville Canyon), San Gabriel Mountains (Big Tujunga Canyon), and the inner
continental shelf (Slf-4, Slf-6). The resulting two-factor solution, as calculated from the
factor scores, describes 74 percent of the total variance in the system (Table 7). Factor
1 describes 63 percent of the variance and factor 2 describes 11 percent of the variance.
The resulting factor score plot has four end-member samples, two end-members for
each factor axes (Figure 13).
End-m em ber Testing from Hotelling’s Test
End-member samples for factor one are 13a and 22a and end-member samples
for factor two are 2a and H-138. Individual harmonic T-tests were run for harmonics 2
through 24 for all end-member samples (Table 8). Results o f the T-tests show that
significant differences occur in harmonics 7 through 24 for Factor 1 and harmonics 2,
3, and 17 for Factor 2. The higher order harmonics (6-24) represent grain roughness
and the lower order harmonics (2-5) represent overall grain shape. In this case it looks
as though Factor 2 represents some form of elongation and triangularity. The difference
in harmonic 17 is considered noise. Average amplitude values for the statistically
significant harmonics of these end-members increase from 13a to 22a (left to right) for
Factor 1 end-member samples and from H-138 to 2a (bottom to top) for Factor 2 end-
members. Thus, samples increase in roughness from left to right along Factor 1 and
samples become more elongate and triangular with an increase in the Factor 2 score.
44
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SAM PLE N A ME FACTOR ONE FACTOR TW O
1a -0.476 2.043
1b -0.228 1.517
2a -0.03 2.972
2b 1.42 0.209
3a 0.017 -1.113
3b 0.112 1.195
4a 1.621 -1.128
5a 1.542 1.039
5b 2.044 1
6a 0.327 -1.233
7a -0.209 -1.201
7b -1.149 0.514
8a 0.501 -0.41
8b -0.542 1.682
9a -0.364 0.396
9b -0.837 0.865
10a -0.49 -0.555
10b -0.888 -0.631
11a -0.141 -0.219
11b -0.968 0.759
12a -0.962 -0.255
12b -0.071 0.882
13a -1.336 0.558
13b -0.459 0.174
14a -1.059 0.013
14b -0.667 | -0.576
15a -0.687 -0.473
1 5b -0.428 0.176
16a 1.459 -0.816
16b -0.714 -1.496
17a -0.544 0.1 16
17b 1.089 0.344
21b 0.501 0.375
22a 2.792 -0.298
22b 2.581 0.274
BTUJ -0.593 -0.234
H-138 -0.048 -1.986
M AND 0.624 -0.21
PARK -0.21 -1.425
SLF-4 -0.938 -0.793
SLF-6
Table 7. Factor scores for Baywide and source sample sets.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Figure 13. Factor plot of Baywide a n d source sample sets.
harmonic 1 x 2 3 x 4
2 0 0.0027
3 0.475 0 .0 4 7 2
4 0.1604 0.7028
5 0.1984 0.2664
6 0.2721 0.1572
7 0.015 0.2435
8 0.006 0.0913
9 0.0003 0.2386
1 0 0 .00 02 0.5639
1 1 0 0.3684
1 2 0 .00 16 0.283
1 3 0.0002 0.2673
1 4 0.0001 0.1674
1 5 0.0001 0.269
1 6 0.0001 0.1452
1 7 0 0.048
1 8 0 0.754
1 9 0 0.3256
20 0 0.4586
21 0 0.4983
22 0 0.9328
23 0 0.780
24 0 0.4575
l)13a 2)22a Represent Factor 1 end-members
3)2a 4)H-138 Represent Factor 2 end-members
Numbers in bold statistically different at the 0.5 signifigance level.
Numbers bold and italics are statistically diffemet at the 0.01 S.L.
Table 8. Hotelling's T: Tests for end-member samples.
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Source Sample Comparison from Hotelling’s Test
As discussed previously, possible sources for Santa Monica Bay detritus are
represented by samples taken from dunes (Hyperion & Park), Santa M onica Mountains
(Mandeville Canyon), San Gabriel Mountains (BTUJ), and the inner continental shelf
near Santa Monica Beach (SLF-4) and Dockweiler Beach (SLF-6). Hotelling’s T~ Tests
were run on these possible source samples to determine if they were significantly
different from each other; a necessary prerequisite before attempting to run discriminant
function analysis. Determined values are shown in Table 9. H-138, which represents
Pre-Flandrian dune sand, does not differ significantly from any other source sample.
Interestingly the Mandeville Canyon sample (MAND), which represents the Santa
M onica Mountain terrane, and the Big Tujunga Canyon sample (BTUJ) which
represents the San Gabriel Mountain terrane, do not differ significantly from each other.
Since none of the potential source samples are significantly distinct from all
other source samples there is an insufficient number o f distinct sample sets to run a
meaningful discriminant function analysis using these sources.
Geological significance comparison from Hotelling’s Test
Testing of potential source samples by Hotelling’s T^ Test indicated that they
are not significantly different enough to run a Discriminant Function Analysis.
Therefore, Hotelling’s T^ Test was performed on various selected samples to find
samples which are significantly different and therefore can be used for discriminant
function testing. The following samples were found to be significantly different:
sample la, which is the northernmost sample of Santa M onica Bay, 22a, which is the
southernmost sample in Santa Monica Bay and is south of Redondo Canyon, and
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Table 9. Hotelling's T: Test for possible source samples.
49
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BTUJ, the sample from the San Gabriel Mountains. These three samples were therefore
chosen as sources to be used for the Discriminant Function Analysis.
Comparison of foreshore samples from Discriminant Function Analysis
To further investigate if differences exist between foreshore samples collected
north and south of the Redondo Canyon, Discriminant Function Analysis was
performed using the northernmost and southernmost samples collected for this study.
Results of the DFA are shown in Table 10.
Fourier Analysis of Redondo Beach Samples
Fifteen samples were collected along three offshore transects within the beach
south of Redondo canyon and north of Palos Verdes Peninsula in conjunction with the
previously discussed bathymetric study of the area (Figure 14). The bathymetric study
was conducted in order to compare present topography to topography shown on
previously published maps. Sand samples collected onshore of, within, and offshore of
a borrow pit were studied to determine whether relative influx of shelf, beach, and
upcoast sand sources could be determined.
Sample comparison from Factor Analysis
A Q-mode, maximum variance, principle component analysis was performed on
the averaged amplitude values for the second through the 24th harmonic for 15 samples.
The resulting two-factor solution, as calculated from the factor scores, describes 83
percent of the total variance in the system (Table 11). Factor 1 explains 74 percent of
the variance and Factor 2 explains 9% of the total variance. The factor score plot has
50
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Sample Name
Percentage of
Sample la
Percentage of
Sample 22a
Percentage of
Sample BTUJ
la 54 16 30
lb 38.5 21.5 40
2a 39 25 50.5
2b 34.5 27 38.5
3a 35.5 28.5 36
3b 40.5 24 35.5
4a 40 24.5 35.5
5a 34 30.5 35.5
5b 38 30.5 31.5
6a 33 28 39
7a 37.8 28.8 33.4
7b 46.5 22.5 31
8a 33.5 28 38.5
8b 43 20.5 36.5
9a 42.5 21.5 36
9b 44.5 22 33.5
10a 41 29 30
I Ob 40.5 24.5 35
11a 38 24 38
11b 44.5 18 37.5
12a 43.5 23 33.5
12b 46 20.5 33.5
13a 38 26 36
13b 40.5 20.5 39
14a 43.5 21 35.5
14b 42 26 32
15a 42.5 26.5 31
15b 44.5 20.5 35
16a 32 45 23
16b 37.3 35.8 26.9
17a 34 44 22
17b 22 48 30
21a 30 44 26
22a 33 37.5 29.5
22b 27 43 30
Table 10. Discriminant Function Analysis o f Baywide sample set.
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Fisure 14. Location map of samples collectec during bathymetric study.
52
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Sample Name Factor 1 Factor 2
1 0 1.767 0.874
130 -0.632 -0.971
140 -1.636 0.944
150 0.241 -0.812
160 -0.0019 -1.561
20 0.441 1.958
230 -0.275 -0.086
240 -0.835 0.77
250 0.437 -0.993
260 -0.923 0.1
30 1.9 -0.514
330 0.639 1.231
340 0.381 -0.913
350 -0.261 0.348
360 -1.225 -0.378
Table 11. Factor scores Redondo Beach sample set.
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four end-member samples, two end-members for each factor axes (Figure 15). End-
member samples for factor one are Red 112 and Red 30 and end-member samples for
factor two are Red 118 and Red 20.
End-m em ber testing using Hotelling's Test
Individual harmonic tests were run for harmonics 2 through 24 for the end-
member samples (Table 12). Results of the tests show that statistically significant
differences occur in harmonics 2 through 20 for Factor 1 and in harmonics 3 and 4 for
Factor 2. Factor 1 therefore represents some form o f gross overall shape and asperity
or roughness and Factor 2 represents only the gross shape o f the grains. Average
amplitude values for the statistically significant harmonics of these end-members
increase from Red 112 to Red 30 (left to right) for Factor 1 end-member samples and
from Red 118 to Red 20 (bottom to top) for Factor 2 end-members.
Sample Com parison using D uncan’s New M ultiple Range Test
Duncan’s New Multiple Range Test was performed in an attempt to determine if
there are any statistically significant differences within the transects and among sample
depths. Table 13 summarizes the results. Results of the Duncan's Test for same
sample depth show that statistically significant differences were found for the 12 meter
and 15 meter samples. The transect three 12 and 15 m eter samples are different than the
transect one 12 and 15 meter samples. Results of the Duncan’ s Test for same transect
sample sets indicate that in transect 1 the 0 meter depth (Red 10) sample is different
from the 9, 12 and 18 meter samples but not the 15 m eter sample. In transect 2 the 0
meter (Red 20) sample is different from all other samples. In transect #3 the 0 meter
54
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■ R e d 20
i n o w T ^ •
o ' ? ' ' "7
OM-L UOiOVd
55
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Figure 15. Factor plot of Redondo Beach sample set.
Harmonic 1 x 2 3 x 4
2 0.0302 0.0813
3 0.0329 0.0175
4 0.0659 0.0003
5 0.0181 0.0513
6 0.0177 0.1018
7 0.0251 0.0898
8 0.0017 0.0859
9 0 0.0754
10 0.001 0.094
11 0.0058 0.1138
12 0.0001 0.936
13 0.0078 0.2194
14 0.0109 0.3583
15 0.0074 0.124
16 0.0201 0.1426
17 0.0094 0.0896
18 0.0109 0.0867
19 0.0237 0.35
20 0.0043 0.31
all 0.0001 0.0732
1)Red 112 2)Red 30 3)Red 118 4)Red 20
Factor one end-members Factor two end-members
Table 12. Hotteling's T2Test for end-member samples.
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Table 13. Results of Duncan's M ultiple Range Testing for the Redondo Beach
sample set. Vertical lines indicate statistically similar groups.
Red 10
Red 115
Red 19
Red 112
Red 118
Red 20
Red 29
Red 218
Red 215
Red 212
Red 30
Red 39
Red 312
Red 315
Red 318
Red 10
Red 20
Red 30
Red 19
Red 29
Red 39
Red 112
Red 212
Red 312
Red 315
Red 215
Red 115
Red 118
Red 318
Red 218
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(Red 30) sample is different from all the other samples and the 9 meter sample
different from the 12, 15, and 18 meter samples.
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D ISC U SSIO N
Introduction
Analysis of the Baywide samples was performed to determine if the beach
samples can be differentiated with respect to shape and source input (San Gabriel or
Santa Monica Mountain detritus). Additionally, analyis was performed to see if there
are differences between summer and winter grain-shape along the foreshore and if the
Redondo Canyon is an efficient barrier to southward longshore drift.
Sand Sources for the Santa Monica Bay
Analysis of geologically reasonable sources for sand grains in Santa Monica Bay
using FGS A found that there is no statistical distinction among samples taken from
dunes, rivers, and the inner shelf. The factor analysis plot (Figure 13) o f possible
source samples and beach samples shows that the source samples all group in the same
area. This seems to indicate that the source samples are not different with regard to
shape. Results from the Hotelling’ s T^ Test (Table 9) further indicates that most of
these samples, with regard to shape, are not statistically distinct.
These results indicate that FGSA is either:
1) Not sensitive enough to differentiate differences in the shape of the sand
grains from these sources;
2) The shape o f the sand grains from these sources are not very different, which
is not very likely;
3) The shape o f the sand grains from these sources are distinctly different but
that the samples collected and tested are not from a large enough sample set to identify
the differences.
59
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A further analysis of the Factor plot (Figure 13) shows that there is wide
separation of samples la, 22a, and BTUJ. These samples are geologically distinct from
one another. Sample la is from northern Santa Monica Bay, 22a is from the southern
portion of the Bay, and BTUJ is from the San Gabriel Mountains and, as discussed
above, this terrane has not been actively deposited in Santa Monica Bay since 1825.
Analysis of these samples by Hotelling T^ Test found them to be statistically significant
from each other. If the assumption is made that these three geographically and
statistically distinct samples represent possible source samples for Santa Monica Bay
then sources for the Bay are distinctly different with regard to shape.
Sand G rain Composition North and South of Redondo Canyon
Analysis o f the Duncan's New Multiple Range Test performed on the Baywide
samples indicates that samples taken south of Redondo Canyon are statistically different
from samples taken north of Redondo Canyon. A close look at Table 6 shows that most
samples are not statistically different from one another but that samples 16a, 17a, 17b,
21b, 22a, and 22b are statistically similar to themselves but to no other samples. These
samples were all collected south of the Redondo Canyon. Sample 16b, also collected
south of the canyon is not statistically similar to the other samples from south of the
canyon.
A possible explanation for the grouping of the samples taken south of canyon
(with the exception of 16b) are that the sand north and south of Redondo Canyon have
sources that are statistically different with regard to grain shape and that no mixing
occurs between the sample sets. This means that the canyon is a barrier to southward
longshore transport.
60
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It is possible that the separation o f sample 16b from the other samples taken
south o f the canyon is not an anomaly and is distincly different with regard to shape.
Sample 16b is the southern sample collected closest to the canyon and was collected
during oceanographic winter. If this sample is most closely associated with samples
collected north o f the Redondo Canyon it might indicate that some leakage o f sand
grains occurs southward during winter storms.
Discriminant function analysis performed on the Baywide sample set suggests
that sand grains north and south of Redondo Canyon are also statistically different.
Table 10, which shows the percentage o f sand grains derived for geographically
distinct and statistically differenct samples, indicates that the most abundant sand grain
source north o f redondo Canyon is from sample la, which most likely represents the
Santa Monica Mountain Terrane. The large percentage o f sand grains attributed to the
BTUJ sample, suggests that much of the sand north o f the Redondo Canyon is
comprised o f San Gabriel Mountain Terrance as well. This indicates that although the
San Gabriel Mountains do not currently shed debris into Santa M onica Bay, the
remnant detritus still remains along the shoreface.
South o f Redondo Canyon, the sand takes on a different makeup. Review o f
Table 10 shows that the samples analyzed south o f Redondo Canyon (16a, 17a, 17b,
21a, 22a, 22b) have a higher percentage o f sand grains derived from the southern
sample. The samples analyzed north o f the Redondo Canyon, have a relatively smaller
percentage o f sand grains derived from the southern sample. This means that the
sands north o f Redondo Canyon are different from the sand grains south o f the canyon.
Redondo Canyon is indicated to be a barrier to the transport o f grains southward.
One exception to this is sample 16b. This sample, which was found to be
different from other samples collected south o f the canyon by the Duncan's Test is also
61
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found to be different by the DFA. 16b is the sample taken south of the Redondo
Canyon that has the highest percentage sand derived from sample la This again might
mean that there is some leakage across the canyon during winter storms.
Further analysis of Table 10, shows that the sand south of the Redondo Canyon
is predominantly made up o f the sample found in the Palos Verdes Hills, inc icating that
this is the likely source of much o f the sand in the Redondo Beach area. Samples south
o f the Redondo Canyon however, do have a large percentage of their makeup comprised
o f sand derived from sample la and BTUJ. This indicates that sand derived from the
sources represented by samples la and BTUJ, although not currently deposited south of
Redondo Canyon, are still remnant.
Tem poral affects on sand grain-shape
Results o f the Duncan's New Range Multiple Test performed on the Baywide
sample set does not indicate that the samples collected in oceanographic winter (April)
are statistically differ from samples collected in oceanographic summer (October and
November) (Table 6). The "a" (summer) samples are not grouped differently from the
"b" (winter) samples. This means either that the nearshore movement o f sand due to
winter storms and the summer ridge and runnel system do not selectively sort the grains
on the foreshore by shape or that FGSA is not sensitive enough to pick up a difference.
Contrary indications though, are seen in the results from the Discriminant
Function Analysis performed on the Baywide sample set (Table 10). Comparison of
samples collected at the same station but from different time periods show that samples
collected in oceanographic winter (b samples) almost consistently have higher
percentages of sand derived from sample la. This indicates that the different
62
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oceanographic processes that occur during winter and summer affect the composition
and possible the transport of different shapes of sand grains throughout the Bay.
It is unclear however, as to what shape differences occur in these samples. The
Factor plots show no distinct separation between “a” and “b” samples.
Infilling of Redondo Beach Borrow Pit
Analysis of the 1972, 1980, and 1993 bathymetric surveys discussed previously
was performed at the Civil Engineering Department at U.S.C. with the help o f Desmond
Andrews. The program TECHBASE 2.11 was used to input and generate the survey
maps and to analyze the differences between the surveys. The surveys were digitized
into the Civil Engineering computer and a kriging program was used to develop
contours of the data points (Figure 3 ,4 , 11). Then plots were generated showing the
elevational differences between the various maps.
The 1972 bathymetric survey indicates that there are several areas that look like
"holes"; possible where large amounts o f material was removed (Figure 3). Analysis
indicates that a net aggradation of the borrow pit area has taken place and that it has been
completely filled in. The maps showing the differences between the 1972 and 1980
surveys (Figure 16) and the 1972 and 1993 surveys (Figure 17) show a net aggradation
of the borrow area and that the "holes" have filled in. Maximum aggradation in the
1972 vs. 1993 and the 1980 vs. 1993 maps is 10 feet. Analysis of the difference
between the 1980 and 1993 surveys indicate that the net change between these two dates
is minimal (Figure 18). This indicates that the filling of the borrow area occurred
between 1972 and 1980.
63
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o
< o
s
M
U
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0 1
1km
f O
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o
Figure 16. Contour map of elevation difference between 1972 and 1980 bathymetric
surveys.
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
O-
\
s
ro
w
M
a
1km
Figure 17. Contour map of elevation difference between 1972 and 1993 bathymetric
surveys.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
/jti/n
i n i '
33*48* 43*
0 9
N J
a t
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1km
fu rv ey s8' C° nt0Ur map of eIevation difference between 1980 and 1993 bathymetric
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Shape of Sand G rains in Redondo Beach
Results of the Factor Analysis for samples collected along the three sampling
transects are shown in Figure 15. Testing o f the end-member samples by Hotelling's
T - Test (Table 12) yields strange shape differences. Factor one represents harmonics 2
through 20 and factor two represents harmonics 3 and 4. The fact that harmonics 3 and
4 are represented in factors one and two indicates that the factors don’t effectively
separate the grains by a meaningful shape difference. Factor two however has higher
average amplitude values for harmonics three and four. This means that grains that have
higher factor two scores are probably more equant and that grains with higher factor one
scores are rougher.
T ransport of Sand G rains in Redondo Beach
Depth comparison
Although the shape difference between the factors is difficult to understand, the
factor analysis plot does separate the samples by some form o f shape difference. Figure
19 shows that the most shallow of the collected samples and the deepest samples
collected plot at different ends. This indicates that these groups of samples are different
with regard to shape. The 0 m samples are distinctly rougher and probably less equant
than the samples collected in deeper water.
The results of the Duncan’s Test also show that, with the exception of sample
Red 115, the 0 m samples, Red 10,20, and 30, are all significantly different than
samples collected in deeper depths (Table 13). The deeper water samples, with some
exceptions, are statistically homogenous with respect to grain shape.
The results of both of these tests may mean that the deeper samples are lag
deposits and the rougher less equant grains are selectively transported onshore because
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
they are easier to move by wave action. A different explanation is that the 0 m grains
are rougher because they have undergone abrasion in the surf zone during transport
onshore. Another possible explanation is that there is little mixing between the 0 m
samples and those collected deeper than 9 m MLLW. This suggests that the deeper
water samples are not transported up onto the shore face during oceanographic summer
when the samples were collected. Effective fair-weather wave base, the mechanism that
would transport sand onto the shoreface, might be shallower than 9 m MLLW.
Transect Comparison
Further analysis of Factor plot for Redondo Beach shows that there is some
separation o f samples collected along the same depth but in different transects (Figure
19). The 12 m samples of transect one and two are grouped separately from the 12 m
sample of transect three. Additionally, the 15 m samples o f transect one and two are
grouped separately from the 15 m sample of transect 3. Review of the results from the
Duncan’s test of Redondo Beach also show that the 12 m and 15 m samples for
transects one and two are different than the 12 m and 15 m samples of transect three.
These results indicate that there might be a circulation or flow pattern that does
not allow for the mixing of sand at these depths between the area represented by
transects one and two and transect three.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
R eproduced with permission of the copyright owner. Further reproduction prohibited without perm issio n .
1.5
0.5
o
<
u.
-0.5
-1
- 1.5
-2
-2
■Red 20
■Red 112
■Redt
■Red 212
■Red 315
■Red 21
■Red 29
■Rod 318
■Red 30
JiRed 15
■Red 118
■1.5 -1
-0.5 0 0.5
FACTOR ONE
1.5
^ Figure 19. Factor plot o f Redondo Beach sample set showing sample groupings.
V O
CONCLUSIONS
Fourier grain-shape analysis o f quartz in the m edium sand sized fraction of 86
samples collected within Santa M onica Bay and the statistical results from Q-mode
factor analysis, D uncan's New M ultiple Range T ests, H otelling's Test, and
Discriminant Function Analysis of these samples indicate that:
1) There is a difference in samples collected along the foreshore in summer and winter
indicating that there are different transport mechanisms affecting the sand grains during
the different oceanographic seasons.
2) Sand samples in northern Santa Monica Bay are statistically different from samples
south o f the Redondo Canyon possible indicating a different source terrane and little
mixing.
3) Redondo Canyon acts as a barrier to the southward transport o f Santa Monica
M ountain derived sand grains, although some leakage o f sand grains southward may
occur during oceanographic winter due to large waves.
4) The borrow pit dredged between 1967 to 1971 has been completely filled in.
5) Samples collected at 0 m below MLLW along the foreshore at Redondo Beach are
different from samples collected from below 9 m MLLW indicating that either rougher
and less equant sand grains are selectively transported onshore or have undergone
abrasion in the surf zone during transport onshore, or that deeper w ater samples are not
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
transported up onto the shore face during oceanographic summer because effective fair
weather wave base is shallower than 9 m MLLW.
6) There is possibly a circulation pattern that inhibits mixing o f sand grains at depths of
12 m to 15 m below MLLW between southern Redondo Beach and areas to the north.
7) FGSA is not able to effectively distinguish among potential sources from samples
collected from dunes, rivers, and the shelf.
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FUTURE W ORK
The U.S. Army Corps o f engineers recovered 29 vibracores in the area o f the
borrow site during November 1965 and January 1966. The samples are no longer
available but the core logs (scale 1 inch = 5 feet) are filed in the Sedimentary Petrology
Laboratory. The logs might contain enough information to determine possible different
sediment populations within the borrow area. If this analysis were combined with new
vibracores and samples obtained with Senckenberg boxes to preserve the detail of
stratigraphic and sedimentologic structures it might help to determine the depositional
processes associated with the filling of the borrow area.
The utilization of Fourier grain-shape analysis on the obtained samples could
help elucidate differences in grain shape populations and possibly determine sources
(offshore or onshore) and movement of grains as they filled the borrow pit.
72
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77
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Appendix A: Latitude, longitude and depth o f ocean floor
recorded during the 1993 bathymetric study.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNE DEPTH LATITUDE LO NGITUDE
1 41.4 33°48.751 118°23.891
35.7 33°48.744 118*23.854
32.9 33°48.745 118*23.800
29.5 33°48.750 118°23.750
25.6 33°48.746 118°23.703
21 33°48.745 118°23.698
UNE DEPTH LATITUDE ; LONGITUDE
2 20.8 33°48.830 118*23.641
26 33°48.817 118*23.690
31.5 33°48.809 118°23.726
34.9 33°48.805 118°23.776
37.6 33°48.808 118°23.828
40.2 33°48.818 ' 118°23.866
41.8 33°48.831 ! 118°23.906
UNE DEPTH LATITUDE ! LONGITUDE
3 42.7 33°48.877 : 118°23.869
41.7 33°48.881 118°23.836
38.3 33°48.873 118°23.790
37.2 33°48.873 118°23.757
32.8 33°48.877 118°23.717
27.4 33°48.879 118°23.672
21.1 33°48.880 118°23.634
UNE DEPTH LATITUDE LO NG ITUDE
4 20.5 33°48.957 118°23.611
24.1 33°48.962 118°23.627
29.6 33°48.965 118°23.658
33.2 33°48.962 118°23.686
37.9 33°48.957 118*23.747
40.5 33°48.955 118°23.795
41.6 33°48.950 118*23.836
42.8 33°48.947 118*23.889
43.3 33°48.950 118°23.910
UNE DEPTH LATITUDE LO NG ITUDE
5 43 33°49.013 118°23.878
42.2 33°49.014 118*23.834
40.9 33*49.011 118°23.789
39 33°49.012 118*23.744
35.3 33°49.01 5 118°23.692
31.7 33°49.01 6 118°23.649
24 33*49.013 1 18*23.597
UNE DEPTH LATITUDE LO NG ITUDE
6 24.1 33*49.089 118°23.585
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29.4 33°49.095 118°23.610
34.6 33°49.089 118°23.645
38.1 33°49.087 118°23.697
40 33°49.087 118°23.739
44.9 33°49.098 118°23.777
45.6 33=49.129 118°23.814
46.6 33°49.1 51 118°23.843
UNE DEPTH LATITUDE LO NG ITUDE
7 45.4 33°49.115 118°23.871
45.2 33°49.118 118°23.838
42.8 33°49.121 118°23.790
40.2 33°49.126 118°23.744
38 33°49.132 118°23.696
33.2 33°49.138 118°23.648
28.5 33°49.140 118°23.606
23.9 33°49.147 118°23.572
UNE DEPTH LATITUDE L O N G ITU D E
8 22.4 33°49.217 118°23.563
29.4 33°49.226 118°23.610
33.4 33c49.221 1 118°23.647
39.1 33°49.218 118=23.696
42.5 33°49.219 118°23.735
46 33°49.221 118°23.781
46.8 33°49.216 I 118°23.816
47.6 33°49.216 ' 118°23.854
UNE DEPTH LATITUDE LO N G ITU D E
9 49.3 33°49.277 118°23.820
48.1 33°49.279 118°23.783
47.9 33°49.274 118°23.740
45.3 33°49.274 118°23.703
42.5 33°49.277 118=23.668
35.4 33=49.278 118°23.638
29.9 33°49.276 118°23.603
23.4 33°49.284 118°23.567
UNE DEPTH LATITUDE LO N G ITU D E
9 A 48.6 33=49.311 118°23.821
47.8 33°49.303 118°23.788
47.9 33°49.312 1 18=23.757
46.2 33°49.313 1 18=23.727
39.3 33°49.309 1 18=23.676
33 33°49.308 1 18=23.635
27.4 33°49.314 1 18=23.596
23.7 33°49.320 1 18=23.572
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNE D EPTH : LATITUDE LONGITUDE
1 0 23.5 i 33°49.340 118°23.595
32.4 , 33°49.345 : 118°23.648
39.5 33°49.340 118°23.687
46.2 33°49.337 118°23.751
48.4 33°49.326 ! 118°23.771
,
48.2 ; 33°49.330 I 118°23.814
48.6 : 33°49.347 I 118°23.851
UNE D EPTH ; LATITUDE ! LONGITUDE
1 1 47.1 i 33°49.409 | 118°23.835
46.7 33°49.414 ; 118°23.800
46.2 33°49.407 118°23.754
42.4 33°49.407 118°23.712
36.1 33°49.408 : 118°23.665
28.3 ' 33°49.414 | 118°23.622
23 ! 33°49.417 i
C O
00
in
C O
CM
o
UNE D EPTH LATITUDE ' LONGITUDE
1 2 17.4 33°49.480 i 118°23.564
25.2 33°49.494 j 118°23.600
32.1 33°49.492 ! 118°23.641
37.2 33°49.489 i 118°23.686
42.7 33°49.485 | 118°23.725
45.7 33°49.480 ! 118°23.770
46.7 33°49.474 I 118°23.818
47.5 33°49.479 i 118°23.850
UNE i D EPTH LATITUDE I LONGITUDE
1 3 47.6 33°49.522 : 118°23.810
44.4 33°49.538 , 118°23.747
38.3 33°49.529 i 118°23.700
32.7 33°49.536 , 118°23.658
28.2 33°49.546 ' 118°23.614
22.7 33°49.552 , 118°23.590
UNE D EPTH LATITUDE LONGITUDE
1 4 18.2 33°49.620 118°23.560
27.4 33°49.633 118°23.611
32.7 33°49.634 118°23.653
37.5 33°49.632 : 118°23.695
44 33°49.630 I 118°23.740
46.7 33°49.627 ! 118°23.782
46.9 ;
48.1 33°49.602 1 118°23.875
UNE D EPTH LATITUDE LONGITUDE
1 5 33°49.684 : 118°23.880
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47 33°49.680 | 118°23.769
41.3 33°49.676 118°23.729
34.4 33°49.682 118°23.686
29.9 33°49.682 118°23.645
23.1 33°49.677 118°23.601
UNE DEPTH LATITUDE LONGITUDE
1 6 21 33°49.722 1T8°23.590
31.5 33°49.746 118°23.658
36.4 33°49.741 118°23.700
43 33°49.745 118°23.739
45 33°49.747 118°23.780
50.9 33°49.747 118°23.821
47.1 i 33°49.749 11 8°23.852
UNE DEPTH i LATITUDE LONGITUDE
17 45.3 i 33°49.816 118°23.837
43.7 j
41.6 33°49.830 118°23.779
43.7 33°49.821 118°23.736
38.9 33°49.816 118°23.693
32 33°49.821 118°23.650
25.5 i 33°49.817 118°23.605
UNE DEPTH i LATITUDE LONGITUDE
18 21.6 i 33°49.866 118°23.584
: 22.8 I |
29.4 33°49.882 118°23.627
34.5 33°49.877 118°23.670
38.2 33°49.864 118°23.725
40.2 33°49.860 118°23.754
42.6 33°49.860 ' 118°23.805
47.9 33°49.866 118°23.851
TIE UNE DEPTH LATITUDE LONGITUDE
1 39.6 i 33°49.872 118°23.735
40.4 33°49.836 118°23.732
42.4 ; 33°49.815 I 118°23.735
41.6 ! 33°49.772 ! 118°23.738
39.6 33°49.713 j 118°23.739
38.5 33°49.677 | 118°23.736
37.1 33°49.647 ! 118°23.735
37 33°49.619 ; 118°23.732
37.1 33°49.586 i 118°23.727
37.4 33°49.551 118°23.723
38.2 33°49.518 118°23.718
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39.6 ' 33°49.483 118°23.714
40.3 ' 33°49.449 ! 118 °2 3 .7 1 2
41 .7 33°49.417 118 °2 3 .7 1 2
42.7 33°49.389 ! 118 °2 3 .7 1 3
43.5 33°49.360 118°23.714
44.7 33°49.330 i 118°23.713
44.6 33°49.302 I 118 °2 3 .7 1 1
44.1 33°49.273 118°23.708
41.7 33°49.233 118°23.701
40 33°49.177 118°23.696
39.4 33°49.122 118°23.700
39 33°49.055 118 °2 3 .7 1 5
39 33°48.995 118°23.720
35.8 33°48.922 118°23.735
33.5 33°48.846 | 118°23.742
! 31.1 33°48.776 118°23.751
28.7 33°48.751 118°23.750
TIE UNE: DEPTH LATITUDE LONGITUDE
2 j 20.9 33°48.751 118°23.662
j 21.9 33°48.792 118°23.655
i 22.8 33°48.821 118°23.654
! 24.3 33°48.849 118°23.656
i 25.3 I 33°48.876 118°23.660
27.5 33°48.906 118°23.665
28.9 33°48.932 118°23.666
29.5 33°48.962 118°23.667
31.9 33°48.995 118°23.667
: 33.3 , 33°49.029 118°23.664
33.1 33°49.061 118°23.661
i 33.7 33°49.091 118°23.659
34.9 ; 33°49.123 118°23.658
35.7 ! 33°49.152 118°23.659
37.5 | 33°49.185 118°23.659
i 38.1 i 33°49.21 118°23.661
i 39.1 i 33°49.234 118°23.665
39.1 33°49.265 118°23.670
38.2 ; 33°49.294 118°23.671
i 38.1 i 33°49.330 118°23.668
3 8 .8 ! 33°49.360 118°23.668
: 37.8 j 33°49.386 118°23.668
: 37.2 I 33°49.426 118°23.666
35.8 i 33°49.458 118°23.664
; 34.6 ! 33°49.486 118°23.667
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34.4 ■ 33°49.515 ! 118°23.669
33.5 33°49.544 ! 118°23.671
! 33.2 i 33°49.572 118°23.671
33.2 ! 33°49.605 118°23.670
33 I 33°49.635 118°23.666
; 32.6 i 33°49.671 118°23.662
32.6 ! 33°49.700 118°23.660
33.6 ! 33°49.739 1 i 8°23.659
35 i 33°49.773 118°23.663
36.2 33°49.805 118°23.668
35.8 ; 33°49.834 118°23.676
36.3 I 33°49.868 118°23.693
36.5 33°49.885 118°23.693
TIE LINE DEPTH ! LATITUDE LONGITUDE
3 ' ; 33°49.868 118°23.595
1 20.3 I 33°49.859 118°23.592
! 19.5 ! 33°49.835 118°23.588
1 8 ! 33°49.805 118°23.583
; 17.1 i 33°49.766 118°23.577
! 16.4 C O
C O
o
C O
Li
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118°23.572
16.6 33°49.712 118°23.568
! 17.5 33°49.677 j 118°23.571
18.7 33°49.641 118°23.574
: 19.8 33°49.609 | 118°23.578
I 22.6 33°49.576 ! 118°23.578
; 2 2 .4 33°49.537 j
in
C O
in
C O
CM
0
0 0
T —
! 23.6 33°49.503 j 118°23.590
2 5 .2 33°49.476 ! 118°23.593
: 2 6 .4 33°49.444 I 118°23.600
i 26.6 33°49.108 ! 118°23.605
, 27.2 33°49.364 118°23.607
; 27.4 33°49.336 118°23.607
|
0 0
CM
33°49.307 I 118°23.604
: 28.1 33°49.274 j 118°23.596
28 .4 33°49.243 I 118°23.592
: 29.2 33°49.213 I 118°23.588
, 2 9 .4 33°49.171 i 118°23.590
28.9 33°49.140 ' 118°23.591
28.6 33°49.115 ! 118°23.594
28.4 33°49.083 i 118°23.598
28.3 33°49.054 118°23.608
26.1 33°49.010 118 °2 3 .6 1 1
24.9 33°48.979 i 118°23.621
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
23.9 33°48.940 I 118°23.626
22.4 33°48.912 ! 118°23.632
21.7 33°48.881 I 118°23.632
19.9 33°48.852 ! 118°23.630
17.7 33°48.767 : 118°23.632
17.7 33°48.745 i 118°23.634
TIE UNE DEPTH LATITUDE i LONGITUDE
4 46.7 33°49.855 ! 118°23.852
46.4 33°49.844 118°23.846
33°49.823 118°23.839
45 33°49.798 118°23.833
33°49.779 118°23.831
50.6 33°49.750 118°23.827
49.6 33°49.706 118°23.830
46.1 i 33°49.682 118°23.831
46.5 j 33°49.650 1 18°23.833
47.5 I 33°49.614 1 18°23.837
47.7 i 33°49.579 118°23.834
47.9 ’ 33°49.545 1 18°23.834
i 47.1 i 33°49.512 118°23.833
i 46.9 33°49.478 1 18°23.834
!
47.3 : 33°49.442 1 18°23.837
i
47.7 ! 33°49.406 1 18°23.839
i 48.3 j 33°49.369 118°23.841
i 48 : 33°49.331 118°23.840
•
48.4 i 33°49.296 118°23.841
48 33°49.262 118°23.841
47.4 , 33°49.227 1 18°23.849
48 ! 33°49.190 1 18°23.854
47 33°49.161 1 18°23.857
46 33°49.128 118°23.860
45.6 33°49.099 : 1 18°23.862
44.4 33°49.068 1 18°23.860
43.6 33°49.036 j 118°23.860
42.8 33°49.005 I 1 18°23.858
42.2 33°48.970 I 118°23.858
41.8 33°48.937 I 118°23.857
42 33°48.905 I 1 18°23.854
41.3 33°48.874 i 118°23.853
40.9 33°48.838 j 118°23.852
40.1 33°48.800 ! 118°23.852
38.3 33°48.770 i 1 18°23.854
36.5 33°48.752 I 118°23.855
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TIE LINE DEPTH LATITUDE LONGITUDE
5 40.5 33°48.748 118°23.916
41 ; 33°48.755 118°23.916
41.3 i 33°48.778 118°23.912
42.1 33°48.815 118°23.923
42.5 33°48.847 118°23.926
43.4 33°48.879 118°23.928
43.7 ; 33°48.907 118°23.928
43.7 33°48.927 118°23.925
43.7 33°48.953 118°23.917
43.5 33°48.982 118°23.909
43.8 33°49.011 118°23.902
44.5 33°49.042 i 1 18°23.895
45.-3 33°49.073 ! 118°23.892
46.4 : 3 3 °4 9 .105 | 118°23.891
t
47.3 ' 33°49.131 ! 118°23.891
47.8 : 33°49.155 i 1 18°23.891
I
48.8 ! 33°49.186 ! 118°23.892
49.1 33°49.218 i 118°23.892
49.4 : 33°49.251 I 118°23.894
. 49.7 : 33°49.283 I 118°23.894
49.6 1 33°49.315 1 18°23.891
49.6 1 33°49.346 | 1 18°23.889
49.4 ! 33°49.376 | 118°23.889
;
49.6 i 33°49.410 | 1 18°23.888
49.6 ! 33°49.444 i 118°23.890
49.6 ! 33°49.478 ! 118°23.890
49.7 I 33°49.509 118°23.892
49.7 : 33°49.541 i 118°23.895
50 ' 33°49.570 118°23.897
50.2 j 33°49.600 118°23.895
48.6 1 33°49.630 ! 118°23.893
48.3 33°49.660 ! 118°23.891
48.2 i 33°49.681 i 1 18°23.893
48.4 i 33°49.706 i 118°23.895
48.9 33°49.733 1 18°23.895
48.6 ! 33°49.761 ; 118°23.895
49.2 33°49.792 118°23.900
49.6 i 33°49.829 ! 1 18°23.899
50.4 ; 33°49.866 i 1 18°23.898
51.8 33°49.88 1 18°23.901
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Asset Metadata

Creator Feffer, Joshua Rafael (author)

Core Title Fourier grain-shape analysis of quartz sand from the Santa Monica Bay Littoral Cell, Southern California

School Graduate School

Degree Master of Science

Degree Program Geological Sciences

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Geology,mineralogy,OAI-PMH Harvest,physical oceanography

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Gorsline, Donn (committee chair), [illegible] (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-21335

Unique identifier UC11341188

Identifier 1391082.pdf (filename),usctheses-c16-21335 (legacy record id)

Legacy Identifier 1391082.pdf

Dmrecord 21335

Document Type Thesis

Rights Feffer, Joshua Rafael

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA