University of Southern California Dissertations and Theses

Grain-size and Fourier grain-shape sorting of ooids from the Lee Stocking Island area, Exuma Cays, Bahamas

(USC Thesis Other)

Grain-size and Fourier grain-shape sorting of ooids from the Lee Stocking Island area, Exuma Cays, Bahamas

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content INFORMATION T O USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may
be from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedtfarough, substandard margins,
and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g^ maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand comer and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in
reduced form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9" black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly
to order.
A Bell & Howell information Company
300 North Zeeb Road. Ann Arbor. M l 48106-1346 USA
313/761-4700 800/521-0600
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.
GRAIN-SIZE AND FOURIER GRAEN-SHAPE SORTING OF OOIDS FROM
THE LEE STOCKING ISLAND AREA, EXUMA CAYS, BAHAMAS.
by
Malcolm Stephen Webster
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(Geological Sciences)
May 1997
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI Number: 1384929
UMI Microform 1384929
Copyright 1997, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNIVERSITY O F SOUTHERN CALIFORNIA
THE GRADUATE SCHOOL.
UNIVERSITY PARK
LOS ANGELES. CALIFORNIA 9 0 0 0 7
T his thesis, 'written by
Malcolm Stephen Webster
under the direction o f h.%s Thesis C om m ittee,
and approved by all its members, has been pre
sented to and accepted by the D ean o f The
Graduate School, in partial fu lfillm e n t o f the
requirements fo r the degree of
Master's of Geological Sciences
T)att> February 20, 1997
TfJESIS COMMITTEE
Chai
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CONTENTS
FIGURES iv
TABLES v
ACKNOWLEDGEMENTS v i
ABSTRACT vii
INTRODUCTION 1
STUDY AREA 8
General Geologic Conditions 8
General Oceanographic Conditions 1 5
METHODS 17
Sample Collection 1 7
Sample Preparation 2 3
Grain-Size Analysis Procedures 24
Grain Types 2 5
Exuma Ooids Classification 2 6
Fourier Grain-Shape Analysis 4 0
Analytical Equipment and Procedures 4 4
Statistical Methods 4 7
RESULTS AND DISCUSSION 5 1
Grain-Size Analysis 5 1
Results 5 1
Discussion 5 8
Fourier Grain-Shape Analysis 6 2
Shape Distribution Relative to Sample Location 6 2
ii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Factor Analysis 6 2
Significance Testing Between Sampling 7 0
Discussion 7 0
Shape Distribution Relative to Sample Location 8 0
Factor Analysis 8 0
Discussion 8 5
Ooid Maturity 8 8
Discussion 9 1
CONCLUSIONS 9 8
REFERENCES 102
APPENDICES 107
Appendix A: Grain-Size Data 1 0 8
Appendix B: Digitizing Procedures 138
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FIGURES
Figure Page
1. Aerial photograph of study area 3
2. Map of Bahama Banks 9
3. Site location map for Lee Stocking Island area 1 1
4. Sample location map 18
5. Photographs of grains thin-sections of different 31
grain types taken using a binocular
microscope and transmitted light
6. Photograph of a grain thin-section of a heavily 3 5
micritized and heavily bored grain taken using a
binocular microscope and transmitted light
7. Photographs of a grain thin-section of a heavily 3 8
micritized grain stained with Alurzian red stain
8. Mean grain size for each sample 5 2
9. Standard deviation for each sample 5 4
10. Skew values for each sample 5 6
11. Factor 1 v Factor 2 for all samples 6 5
12. Factor 1 v Factor 2 for Shoal 1 7 4
13. Factor 1 v Factor 2 for Shoal 2 7 7
14. Factor 1 v Factor 2 for 18 ooid types 8 2
15. Factor score trends between thin and thick ooid types 8 9
16. Percentage of grains with two layers for all 23 samples 9 3
i v
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i v
TABLES
Table Page
1. Sample location summary 20
2. Exuma ooid classification system. 2 8
3. Factor 1 and Factor 2 values for all samples 6 3
4. Comparison of Factor 1 and Factor 2 endmembers 6 8
for all 23 samples
5. Comparison of shape characteristics of all 23 samples 7 2
to one another using Hotellings test.
6. Factor 1 and Factor 2 values for each grain type 8 1
7. Comparison of Factor 1 and Factor 2 endmembers 8 6
for grain types
8. Percentage of Grains with 0, 1, 2, and 3 concentric 9 2
layers by sample
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
v
ACKNOWLEDGEMENTS
This thesis would not have been completed had it not been for the
help of many people. Without the guidance of my advisor,Dr.
Robert Osborne, I wouldn’t have learned a fraction of what he
taught me. I will always remember him and how he helped and
inspired me and countless other people during his life. The Osborne
family (Sally, Todd, and Mark) also were extremely helpful.
My parents Robert and Beverlee Webster were supportive and
provided critical review of a very rough draft. Thanks for always
being there and spending Christmas patiently laboring over the
breakfast table with me.
Dr. Robert Dill not only provided his field expertise but also
tirelessly reviewed this document checking my results against his
knowledge of the Bahamas. My current committee chairman Dr.
Don Gorsline and my third comittee member Dr. David Bottjer were
very helpful and patient.
The list of people who helped push me along starts with Semele
Yuan, Kathy Campbell, Rory 'your data looks funky-Mal' Robinson,
Rahul 'your wrong-Mal' Bahadur, the rest of Ozzy’s lab, Sue
Pittenger, Whiteford P. Hagadorn, Rene 'calm down' Kirby, the rest
of the geology office, Sanford Britt, Peter Bentham, Andrew Miegs,
and numerous others. Spike Casey, Adam Woods, and Matt Kelliher
were a great help. Finally, I would like to thank the man who
prepared my thin-sections following all of my crazy criteria, Brian
Burnham. If there are others that I should have acknowledged and
did not, please accept my apologies.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ABSTRACT
The eastern margin of the Great Bahama Bank, adjacent to Exuma
Sound, is bounded by a chain of islands and cays. These islands and
high-energy inter-island currents are a strong influence on the
Holocene sediment that blankets Pleistocene bedrock. This study
focuses on the inter-island channels between Lee Stocking Island
and associated cays where strong tidal and wind driven currents
(averaging between 60 and 100 cm/s) have developed flood tidal
deltas from a variety of carbonate sediments produced in this
region. One of the main components of these features is ooids. Two
discreet ooid sand bodies were studied with regard to grain size,
grain shape, and internal structure.
Results indicate that sand characteristics have similar distributions
across the two shoals. Similar shapes and grain sizes were
observed in areas where depositional conditions (primarily water
depth and related relative current energy) were similar. This
sorting is most pronounced in the areas of the shoal under less than
2 meters of water.
Grain size from collected samples indicates that ooids are unimodal,
and size and shape data show that there is sorting which is relative
to depositional environment. Surface roughness, due to the degree
of boring observed on the laminae of the ooid, is the controlling
factor in shape.
Number of concentric layers is also related to location on
sedimentary bodies. The most common ooid type (representing
over 80% of grains throughout both shoals) is the immature ooid
containing one accreted layer around a central nuclei. Over 90% of
these nucleii were peloids. The number of grains per sample with
more than one layer varies with water depth and distance from the
bank margin. This differs from the trends in ooid maturity
observed in other areas of the Bahamas. Possible explanations for
this is that no active ooid generation is occuring in this area, or that
the environmental conditions (ie. availability of nuclei, current and
wave energy, and water chemistry) only allow young ooids (low
number of concentric layers) to develop.
vii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
INTRODUCTION
Aerial photographs, shuttle flights, and satalite imagery vividly
show that the margins of the Great Bahama Bank are vast areas of
present and past ooid generation (Figure 1). Studies of this ooid-
generating environment and general facies have provided models
which explain the ooid sand settings and their origin (Newell and
others, 1960; Imbrie and others, 1965; Ball, 1967; Harris, 1977;
Hine, 1977; and Hine and others, 1981 and 1981a).
Hine and others (1981) divided the shallow carbonate bank
margins where Bahamian carbonate sands are found into five
classes: (1) windward-open; (2) windward-protected; (3)
leeward-open; (4) leeward-protected; and (5) tide-dominated.
Ball (1967) in a similar study classified the sand bodies into four
types: (1) marine sand belts; (2) belts of tidal bars; (3) eolian ridges;
and (4) platform interior sand blankets. Each of these
environm ents have d ifferen t sedim entary stru ctu res and
morphology associated with them. Imbrie and Buchanan (1965)
describe the different structures found in sand bodies from beach
and shoal-water bottoms in the Florida Keys and Bahamas. Newell
and others (1960), in an extensive survey of the ooid-bearing
environment near Bimini, showed that ooids decrease in maturity
with distance from the crest of oolitic ridges, which are usually
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
areas of water depth less than 2 m. The crest areas are reportedly
where ooids form because of current agitation. It also was noted
that grains seaward of this ridge had larger nuclei and fewer
concentric laminations. Sands which were fine, thinly coated, and
intensely bored were identified in the low-turbulent restricted
waters of Bimini lagoon (Bathurst, 1975). The above studies
indicate that the hydraulic setting (i.e. type, strength and duration
of current, and water depth) affects the maturity of ooid grains,
internal grain structure, and sand-body geometry.
One such ooid sand-body is found in the migrating sand shoals of
the Joulters Cay area. The ooids are believed to be actively forming
along the sand ridges which parallel the bank margin (Harris, 1977;
Carney, 1990). Bankward of these sand shoal complexes are large
sheets of ooids and associated hardgrounds which are believed to
be spill-over lobes from the sand shoals (Newell and others, 1960;
Kendall and others, 1990). Sand-starved spill-over lobes are found
oceanward of the shoals, evidence of the dominant tidal flow forces.
Various general trends have been observed across the ooid
generating environment of Joulters Cay; Harris (1977) and Carney
(1990) observed an increase in ooid maturity (number of outer
layers) in the inner bank area on traverses across the bank margin.
Harris (1977) observed a similar increase in micritization.
Internal characteristics and descriptions of ooid petrology have
been published by Bathurst (1975), Simone (1981), Peryt (1983),
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 1. Aerial photograph of Lee Stocking Island area; the
eastern margin of the Great Bahama Bank at the southern end of
the Exuma chain of island and cays. Note the extensive light
colored sand bodies in the areas surrounding the islands and cays.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and Richter (1983). These studies provide summaries of the
formation conditions and characteristics of the two main types of
ooids, tangentially-oriented and radially-oriented crystal laminae.
Illing (1954) first distinguished between superficial ooids (having
one layer) and true ooids (well developed concentric structure).
Carozzi (1960) defined a pseudo-ooid as a mineral or organic
nucleus surrounded by one concentric layer. A normal ooid is
defined as a mineral or organic nucleus surrounded by at least two
concentric layers (Carozzi, 1960). Carrozzi (1960) also provides a
model of "the oolitization process" (the way in which ooids grow).
The system describes how the size of nuclei and the current energy
dictate the size and maturity (number of layers) of the ooid. The
ooids found in the study area are predominantly tangentialiy
oriented aragonite crystal laminae formed around predominantly
pelloid nuclei. The ooids also are predominantly superficial or
pseudo ooids, with most containing only one well developed
laminae. Thus, they are classic superficial Bahamian-type ooids.
The above described studies have delineated general facies zones
and ooid types for many of the ooid environments observed in the
western and northern margins of the Bahamas. However, prior to
this study, it was unknown whether these descriptions adequately
describe the distribution within the little studied Exuma Island
chain where actively migrating ooid sand shoals, which develop
within inter-island channels and associated spill-over lobes, are
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
located. Areas of ooid sand generation occurs along the outer edge
of the Bahama bank. However, environmental conditions must be
different because the sand bodies within the Exuma Island chain
contain growing stromatolites which have not been found in other
studied regions of the northern and western Bahamas. Marine
cem entation is intense in the Exumas, causing strom atolitic
preservation, hard grounds, and dense calcification of marine plants
and organisms (Dill, 1991). However, the ooid sands are less
mature, smaller in size, and exhibit less biodegredation than their
counterparts found in Joulter's Cay. Prior to this study, no
published studies have dealt specifically with the Exuma Island
sand shoals or have considered the size ranges, ooid type and
internal micro-structures of the sands found within the shoals in
areas where they are associated with stromatolites (Kendall and
others, 1990; Dill, 1991; Boardman and Carney, 1991).
The objective of this study was to determine the characteristics and
variations of ooids within the reported ooid-generating zone of sand
shoals and closely associated spill-over lobes within the Exuma
Island complex, Bahamas. In order to relate ooid development
within this environment, 23 sand samples were obtained from two
sand shoals that characterize the region. Sediments collected were
analyzed for their shape characteristics, internal petrography, and
their size characteristics. In particular, the study set out to address
the following three issues: 1) are there relationships between
internal and external shape characteristics of contemporary ooids;
6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2) do external shape characteristics play a role in the sorting of
ooids across a shoal; and 3) do these shape characteristics correlate
with differences in grain-size characteristics across a shoal.
These issues were addressed by 1) performing a grain-size analysis
on each of the samples; 2) performing a grain shape analysis on
each of the samples; and 3) developing a classification scheme
dependent on the dominant internal ooid m icro-structures and
comparing them to the overall shape characteristics o f each grain
type. The results from these three studies were then compared to
determine whether there were trends and comparisons to be made
between grain shape sorting and grain size sorting across an ooid
environm ent.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
STUDY AREA
G eneral G eologic C onditions
The Exuma Islands and Cays, located on the eastern margin of the
great Bahama Bank carbonate platform, have been flooded and
exposed several times during past periods of glaciation driven sea
level fluctuations over the past million years (Figure 2). During
periods of low sea level, dune systems composed of ooids,
pelletoids, and shell matter formed topographic highs along the
bank margin (Kendall and others, 1990). These Pleistocene aged
dunes became cemented by calcite cementation through fresh
water percolation (Hailey and others, 1979). These cemented dunes
form the nucleus of the islands and cays along the bank margin. In
the southern Exumas, islands and cays act as barriers, restricting
tidally induced water flow on and off the bank, thus causing high
current velocities of up to three knots (Kendall and others, 1990).
The channels between these islands range in depth from 2-10 m
and have widths of up to 1 km (Figure 3).
Most of the islands and channel bottoms are capped by a well
developed paleosol which is used to mark the boundary between
Holocene and Pleistocene sediments (Aalto and Dill, 1996). The
inter-island sediment shoals, composed primarily of ooids, have
Holocene isotope ages and blanket the densely cemented paleosol.
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 2. Map of Bahama Banks in relation to Florida. Note the
outline of the study area in the south eastern area of the Bahamas
at the bank margin with the Exuma Sound.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Little Bahama
Bank
o Km 100
I 1 D epth less than 20 m
West Pfllm
Beach
Atlantic
Ocean
Providence Chennei
Florida
New Providence
Channel
Joulters
Cays
Eleuthera
Florida
Straits
Cat
Island
Exuma
Sound
Cay Sal
Bank
Webster
Study Area Tongue
otthe
Island:
Columbus
Basin
CUBA
Old Bahama
Channel
i o
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 3. Loction map showing sediment distribution patterns in
the study area near Lee Stocking Island, Southern Exumas,
Bahamas. This map was constructed by scanning navigational
charts and plotting surveyed sand bodies located by Global
Positioning System (GPS) and air photos. Base map was provided
by R.F. Dill, 1989.
1 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
to
76°11
i White Horse
Cay SHOAL2
Adderiy
C
Normans
Pond Cay
Lee Stocking
Island
SHOAL 1
v
Tug Boat Shark Rock
Children's
Cay
SCALE IN METER8
LEGEND
Flood Spill-Over Lobes
I ' '' I Tidal Channels
1 B I lnter-lsland Sand Bars
i - I Sub-Aerially Exposed Sand
■ H Land
[//A Deep Water
I I Shallow Bank
Thin lenticular deposits of lime mud (up to 1 m thick) are
periodically exposed within the troughs of the migrating mega
dunes of the sand shoals. These muds, believed to be deposited on
the bank by "Whitings", are resuspended by high energy storms
(hurricanes) and subsequently deposited along the bank margin by
ebb (Shinn and others, 1988; Robbins and Blaskwelder, 1990; and
Steinen and others, 1988). These muds blanket the bank after a
storm (Dill and Steinen, 1988). Most of the muds are subsequently
eroded but the current shadows created by trough areas of the
mega dunes prevent erosion.
Within these sand dune fields, stromatolites are anchored to
hardgrounds and are periodically covered by the dunes (Kendall
and others, 1990). Gross morphology of these areas changes little
although the shoals are continually being reworked by tides.
Laterally adjacent to these dunes are scoured hard grounds of
exposed lithified Pleistocene sediments. Corraline algae, sponges,
and gorgonian corals anchor on these Pleistocene hardgrounds.
These inter island sand shoals terminate as sediment starved ebb
tidal spill-over lobes towards the bank margin (in approximately
10 m of water). Water depth of the inter-island sand shoals range
from 10 m to 2 m. The most significant chage in water depth
occurs as the channels shallow and enter into the unrestricted
leeward side of the islands. A natural sand levee exists, marking
the point at which the sand shoal becomes a series of spill-over
1 3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
lobes which coaless and spread over the bank forming sand sheets
on the leeward side of the islands (Figure 3).
The natural levee formed by spill-over lobes often build up to a
point where they become subareally exposed sand dunes during
low tide. The lower tidal energy areas, found in the deeper waters
adjacent to the inter-island sand shoals, are areas populated by sea
grass beds, predominantly Thalassia. These act as a sediment trap.
These areas are continually reworked by organisms such as conch,
shrimp, and fish (Kendall and others, 1990). Further bankward are
finer grained sediments, pelloids, and lime muds.
On the leeward side of the larger islands and cays are shallow lime
mud flats usually associated with mangrove forests (Kendall and
others, 1990; Dill and others, 1989; Shinn and others, 1989). Mixed
with these muds is skeletal material from the biological activity in
the area.
Aerial photography shows that the islands have prograding beaches
on both their leeward and seaward sides. Low energy wave-action
and higher wave-energies generated by storms move coarser
sediment onto the beaches of the islands. Wind action further
pushes this sedim ent into low elongated dunes immediately
landward of the beaches. Aerial photography shows parallel
elongated dunes on the leeward and seaward sides of the cays.
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Skeletal sands caused by extensive bioerosion of coral reefs
seaward of the cays are found in greatest abundance on the
oceanward pocket beaches and in entrances to the tidal channels
(Kendall and others, 1990). These skeletal sands continually add to
the seaward pocket beaches causing them to prograde.
G eneral O ceanographic C onditions
The Exuma chain of north-south trending islands and cays form a
ridge or lip along the eastern margin of the Great Bahama Bank.
The average depth of the Bank is about 10 m. At the margin, a
terraced slope, formed during sea level lows, rapidly drops off into
very deep water, forming an almost vertical wall in depths below
50 m. Within 2 km east of the margin islands, water depths exceed
100 m (Dill and others, 1989). The tides run perpendicular to the
margin, making a radial flow pattern when the Bank is viewed as a
whole. Tides have a maximum range of about 1 m. The restriction
of water to inter-island channels increases tidal velocities up to a
maximum peak flow of 150 cm/s with a usual peak flow averaging
between 60 and 100 cm/s. Tidal velocities decrease when not
restricted between islands and cays. The strength and levels of
normal tides are subject to variation depending on bank margin
topography, wind direction, velocity and duration.
Both tidal and wind-current regimes are capable of transporting
sand-sized materials near the platform margin. This is observed as
current developed ripples of the sands as well as shoal morphology.
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
On flood tide, relatively cool Exuma Sound waters flood the bank for
a distance of up to 15 km. Sound water is clear (up to 50 m
visibility) and has a salinity of between 37 and 38 parts per
thousand (ppt). Ebb-tidal waters are not as clear, have a greenish
color and tend to be more saline, up 40 ppt in the summer months.
Water temperature ranges for this area vary with season from the
highest temperature of 31 degrees Celsius recorded in August to 22
degrees Celsius recorded in February (Kendall, Wicklund and
others, 1990). This low temperature is due to upwelling of deep
Exuma Sound water (Lang and others, 1988).
Storms (hurricanes) significantly alter the conditions described
above. Extreme storm driven currents rework the sand shoals and
suspend fine-grained sediment, turning the water a milky white.
During the waning stages of the storms, this suspended load is
deposited, blanketing the Bank with fines (Dill, 1991; Shinn and
others, 1993).
1 6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
METHODS
Sam ple C ollection
A total of 23 samples was obtained from two separate sand shoals
and associated spill-over lobes in the area of Lee Stocking Island,
Exuma Cays, Bahamas (Figure 4). Samples were collected in July
and August, 1991 by the author. Samples were of the upper 5 cm
of sediment surface. In the regions where tidal energy was great
enough to form large scale ripples, the sample was obtained from
the tops of actively forming dune crests. Ripples were most
dominant in the elongate portions of the shoal; the spill-over lobes
had only small scale ripples.
Sample location was initially marked on a map and a written
description of the location was made. Samples were collected using
either SCUBA or free diving, depending on the conditions of the
sample location (in deep, high-energy current locations SCUBA was
used). The upper 5 cm of sediment over approximately 10 cm by
10 cm was scraped into ziploc bags which were labeled with the
sample number, date sampled, and approximate location. Table 1
provides a summary of the conditions and dates in which each
sample was obtained.
Samples S38 through S48 were obtained from the inter-island sand
shoal which begins at Adderly Channel north of Lee Stocking Island
(LSI) and wraps around its northwestern portion and ends as an
1 7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4. Location map showing sample sites on the two shoals
studied. Patterns depict different subaqueous features associated
with the ooid sand shoals. (Base map obtained from Robert Dill).
1 8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
' V
> White Horse
Cay
SHQAL2
Adderiy
Norman's
Pond Cay
Lee Stocking
Island
SHOAL 1
v
Tug Boat
Shark Rock
Children's
Cay
SCALE IN METERS
LEGEND
v o
Flood Spill-Over Lobes
I 1 '-'"-! Tidal Channels
H H lnter-lsland Sand Shoal
I . ' - ■ . 1 Sub-Aerially Exposed Sand
1 ^ 1 Land
U W 1 Deep Water
I 1 Shallow Bank
TABLE 1: SAMPLE LOCATION SUMMARY
Sampla Shoal
Approximate
Water Depth
(in Meters) Setting
Current
How (at
Time of
Sampling)
Relative
Current
Velocity
Tidal Drift Number
(same number
indicates sampled
during same tidal
drift)
S38 1 9.1
inter-island flood
tidal sand body flood low 1
S39 1 7.6
inter-island flood
tidal sand body flood medium 1
S40 1 6.1
inter-island flood
tidal sand body flood medium 1
S41 1 7
inter-island flood
tidal sand body flood medium 1
S42 1 5.5
inter-island flood
tidal sand body flood medium 1
S43 1 4.6
inter-island flood
tidal sand body flood medium 1
S44 1 3
inter-island flood
tidal sand body flood medium 1
S45 1 2.4 natural levee flood high 1
S46 1 2.1
flood spill-over
lobe flood high 1
S47 1 1
flood spill-over
lobe flood high 1
S48 1 0.8 natural levee flood very high 1
S50 2 1.2
channel within
flood spill over
lobe ebb very high 2
S51 2 1.5 natural levee ebb high 3
S52 2 1.2 natural levee ebb high 3
S53 2 0.6
subaerial intertidal
sand bar ebb none 4
S54 2 1.8
flood spill-over
lobe ebb medium 4
S55 2 1 natural levee ebb medium 4
S56 2 1
flood spill-over
lobe ebb high 5
S57 2 0.5
flood spill-over
lobe ebb high 5
S58 2 1.8 natural levee ebb medium 5
S59 2 6.1
inter-island flood
tidal sand body flood medium 6
S60 2 1.8
inter-island flood
tidal sand body flood high 6
S61 2 7.6
inter-island flood
tidal sand body flood low 6
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
elongate sand bar that forms a natural levee on the eastern and
southern side of the channel between Norman's Pond Cay (NPC) and
LSI. This shoal was designated Shoal 1. The samples from this
shoal were obtained during a drift-dive during a flood tide across
the area.
The deepest sample (S38) was obtained in approximately 10 m of
water from an ebb flow spill-over lobe on the eastern edge of the
sand shoal west of the entrance to Adderly Channel (Table 1).
Samples S39 through S43 were obtained from flood tidal
megadunes of the gradually-shallowing, inter-island sand shoal
within the channel between Normans Pond Cay and Lee Stocking
Island. Depths in this area ranged from 8 m to 5 m. The channel is
approximately 2 km long and terminates south of NPC and west of
LSI. Bedforms characteristic in this area include small sand ripples
superimposed over the larger (up to 2 ra) megadunes.
Continuing south in this channel, the water depth decreases until it
reaches a natural levee along the eastern and southern end of the
inter-island channel (Figure 4). Sample S44 was obtained from the
end of the channel/base of the levee in approximately 3 m of
water. Sample S48 was taken along the natural levee in
approximately 0.8 m of water. The natural levee is an elongated
sand bar which occurs between the deeper inter-island channel and
the shallow spill-over lobes. This bar is located at the point where
the inter-island channel enters the unrestricted shallow bank west
2 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of LSI. South of the natural levee are coalessing spill-over lobes
which grade into a broad shallow sand sheet. Samples S45 (2.4 m
of water) and S48 were obtained from along the natural levee and
samples S46 (2.1 m of water) and S47 (1 m of water) were obtained
southeast and south of the levee (respectively) within the spill-over
lobe area. Samples S45 and S46 are from a greater depth than S47
and S48 because they were sampled from a minor channel which
extends south into the sand sheet. Bedforms characteristic of the
spill-over lobes immediately east and south of the natural levee are
small ripples up to approximately 0.25 m in height.
Samples 50 (1.2 m of water) through 61 (7.6 m of water) were
obtained from a separate sand system which extends from the
channel northeast of NPC westward and wraps around the northern
tip of NPC (Figure 4). The channel is the main conduit for waters
which flow onto and off of an extensive shallow sand bar which
extends east-west to the west of NPC (designated Shoal 2). The
sand bar is made up of a series of flood tidal spill-over lobes which
extend south from the channel. Samples 50 through 58 were
obtained during a series of four ebb tidal skin diving drifts (from
south to north) over the sand bar (Table 1). All sand bar and spill
over lobe samples were obtained from water depths of less than
2 m. Sample S50 was obtained from a very high current energy
spill-over lobe distributary channel located immediately west of
the northern tip of NPC. Planar bedforms indicate this is a zone of
turbulent, high velocity currents. Sand bar bedforms were
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
characterized by ripples up to approximately 0.25 m in height.
Sample S53 was obtained from the subaerially exposed portion of
the sand bar (known as Shell island).
Samples S59 through S61 were obtained using SCUBA during a
flood tidal drift dive in the east-west trending channel north of LSI.
The depths and conditions in the channel were much more varied
than those in LSI channel (Shoal 1). Sample S59 was obtained from
the eastern portion of the inter-island sand shoal in approximately
6.1 m of water (Figure 4). Asymetrical dunes in this area indicate a
higher energy flood tide (slip faces to the west). Sample S61 was
obtained from the western portion of the channel where Thalassia
had stabilized the bottom sediments at a water depth of
approximately 7.6 m. Asymetrical dunes in this area indicate a
higher energy ebb flow tide (slip faces to the east). Sample 60 was
obtained in approximately 1.8 m of water from the highest
megaripple located in the central portion of the shoal. This highest
central dune form was not asymetrical in form, sloping at similar
angles on either side of its apex. This is an indication that both
tides influence the gross morphology of this area. The central
portion of this sand shoal was built up due to the continual
reworking caused by both tidal currents.
Sample Preparation
Once the samples were brought out of the water, the excess sea
water was drained off. Each sample was then double bagged to
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
insure against rupture during transport. To minimize movement of
samples, they were firmly packed into boxes for shipment to
University of Southern California (USC).
At USC, samples were rinsed with tap water and dried at low
temperature (40-60 °C) in a convection oven. Drying takes from
two to four hours, depending on the volume of sample. Plastic
stirrers were used to mix the sediment during drying to reduce
drying time and prevent any crust from forming on the surface of
grains.. Plastic was used to minimize alteration of the grain shape
and size.
After drying the samples were split in two equal amounts and
stored in quart cardboard containers labeled with sample number,
sample year, and sampler. One set of each sample were used for
analyses in this thesis and the other set was placed in storage.
Grain*Size Analysis Procedures
Samples were mechanically sieved at 0.25 < ] ) intervals from 0.0 < |)
(1 mm) to 4.0 < t > (0.063 mm). Sieving procedures from Ingram
(1971) were followed for grain-size analysis. One-hundred grams
of sample were placed into the stacked sieves. The sieves were
then placed on a Fisher Wheeler Sieve Shaker and vibrated for ten
minutes. The sieve stack was then dismantled and the grains from
each sieve weighed to the nearest 0.01 g. A Mettler P-1000 scale
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
was used to weigh the samples. The scale was calibrated using an
one-hundred gram weight.
Resulting weight data were then put into a Microsoft Excel v.3.0
spread sheet.. Using this program the first three moment measures
(mean, standard deviation, skewness) were calculated for each
sample using the procedure described by Boggs, 1992. A size
distribution histogram was also generated for each size category
(Appendix A).
Grain Types
The shape of particles was examined to determine if grain shape
characterisitics could be correlated to the pattern of deposition at
the various sites. Ooids exhibit different internal structures, giving
rise to a number of different ooid classifications. Previous
classification of carbonate grains were based prim arily on
concentric laminae characteristics (number of layers, tangential
versus radial crystal structures) and the environmental settings in
which they formed (caves, lakes, marine) (Richter, 1983; and Peryt,
1983).
These classifications are too general, and all of the ooids in this
study would fall into one category in each scheme. In Richter's
proposed schem e they would all be Structural Type 1
(concentrically layered) with Primary Aragonite; Peryt would
classify them as micro-ooid. Further descriptors were used to
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
distinguish between similar grains (such as degree of micritization,
degree of algal boring, overall grain size, and nuclear grain size)
(Ball, 1960, Carozzi, 1960; Harris, 1977). These classifications and
descriptors, while providing good ooid petrography characteristics,
are inadequate for this study because none relate these to overall
grain shape. For this study, a more comprehensive classification
scheme was created based on internal grain characteristics affecting
overall grain shape. The scheme was based on analyzing thin
sections for internal characteristics which appeared to have
controlling factors in overall grain shape. When this classification
scheme is combined with Fourier grain shape analysis (FGSA), it is
possible to determine correlations between internal characteristics
and overall grain shape.
Exuma Ooid Classification
My Exuma Ooid Classification System (ECS) was derived based on
observation of the key factors which determined overall grain
shape. Twenty three samples from the two shoals were wet sieved
and the medium sand size (dominant mode) of 0.25 to 0.35 mm
(1.5 < t > to 2.0 < J > ) was obtained. Sand grains were mounted and
sectioned through the approximate center of the grain. Given that
ooids are roughly spherical in shape, this allowed for the maximum
projection of the grains. Thin-section grain mounts were made by
Burnham Petrographies of Monrovia, CA. Half of the slide was
stained with alizarin red. The characteristics of the nucleus (size,
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
shape, and type) and cortex (thickness and layering) were
examined under transmitted and reflected light.
Basic ooid types are distinguishable by nucleus shape and type,
cortex thickness and the degree of algal boring and subsequent
micritization (Table 2). There are 18 different categories of grains.
Rows represent the different shapes and types of nuclei observed,
and columns distinguish between thin/thick cortex and the
presence/absence of borings within the structure. Distinguishing
features used in the classification are described below.
Nucleus
Three types of nuclei can be identified; namely (1) fossil fragments,
(2) grapestone and (3) peloid. Fossil fragments (predominantly
foraminiferia, mollusk shell fragments, halimeda, coral and algae
fragments) tend to be highly angular and irregular in shape;
grapestones are generally agglomerates of two or more peloid
and/or smaller ooid grains.
Peloids are the dominant nuclear type and account for more than
80 percent of the grains examined. Observed shapes were divided
into five categories: (1) kidney, (2) circular, (3) elongate oval, (4)
quadrate, and (5) triangular. Figure 3 shows pictures of each type
of nucleus. The distinction between circular and oval is a length-to-
width ratio of 1.5:1.0; any ratio less than this is considered circular.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2. Exuma Ooid Classification System. Each grain types is
assigned an identification number from 1 to 18 depending on the
grain's characteristics. For example, a triangular grain with a thin
cortex and no surface borings would be identified as grain type 10.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SUMMARY OF EXUMA OOID CLASSIFICATION SYSTEM
Nuclear
Shape Thin C ortex * Thick Cortex B ored **
Oval 1 2 3
Circular 4 5 6
Q uadrate 7 8 9
Triangular 10 11 12
Kidney 1 3 14 1 5
Fossil 16 17 18
The difference between thin and thick cortex is 0.02 mm.
Outer cortex considered bored when over 20% exhibited signs of boring.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Since the shapes of the grapestones are similar to the five basic
shapes used to describe the peloid nuclei, they were identified by
their shape. The observed shape of fossil nuclei ooids had highly
unusual shapes which could not always be classified as one of the
five basic shapes and therefore was included as its own category.
Cortex Thickness
Growth of laminae around the nucleus is not regular; laminae does
not grow always at constant rates around the whole grain. When
the core of an oolite consists of an elongate grain, there is a common
tendency for more rapid growth on the sides than on the ends, and
sphericity of the grain becomes more and more marked (Carozzi,
1960). Sim ilar observations have been made (but never
quantitatively tested) by Ginsburg (1957), Newell and others
(1960), and Bathurst (1975). An example of this is shown by the
grains in Figure 5 with thick corteces. Thickness of the cortex was
used as one of the distinguishing characteristics in this study.
Thickness refers to the maximum thickness of laminae around the
grain. A thickness of 0.02 mm is defined herein as the boundary
between thin and thick laminae. This seems to be a medial value
where laminae thickness appears to significantly change the shape
from that of the nucleus.
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 5. Photographs are of the six nucleus types (circular, oval,
triangular, quadrate, kidney, and fossil). Indicated on the circular
nucleus grain photograph (Photo A) are the thick cortex and
micridc area within the cortex. Indicated on the oval grain
photograph (Photo B) is the thin cortex. The dark grainy areas
surrounding the grains are the glue used to mount the grains on the
slide. Photographs of grain thin-sections taken using a binocular
microsope and transmitted light.
3 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
B. Oval nucleus
Circular nucleus
'. .thick cortex
thin cortex
micrite filled
m icroborings
Triangular nucleus
D. Quadrate nucleus
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F. Fossil nucleus Kidney nucleus
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Algal. Boring
Borings are found in all classes of ooids. Endolithic algal boring
creates intraparticle pore space (Choquette and Pray, 1970) in the
corteces of the grains. Given the diameter of an individual boring,
one algal boring alone would not be enough to significantly effect
the outer surface grain shape. However, if the borings are
numerous and concentrated in one area, they could undermine and
weaken grain surfaces and cause collapse of the weakened area due
to impact with other grains (Gaffey, 1983). These collapsed and
heavily bored areas could alter the overall shape of a grain by
adding either roughness to its surface or, if the extent of boring and
collapse is sufficient, changing the overall shape of the grain.
Heavily bored and collapsed areas often become filled with micrite,
partially erasing the internal structure. Zones of micrite are shown
in Figure 5. This process has been observed in samples from
Joulters Cay (Gaffey, 1983). If an ooid grain had over 20% boring
on its outer grain surface it was identified as a bored grain (Table 2,
grain types 3, 6, 9, 12, 15, 18). An example of a grain with a
heavily bored outer layer is shown in Figure 6.
Micritized Ooids
The final stage of endolitihic algal boring in an active ooid
generating zone is the infilling of borings with debris and carbonate
cement. This process is described as micritization (Ginsburg, 1957;
Bathhurst, 1966; Monty, 1967; Newell and others, 1960; and Harris,
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 6. Photograph is of a highly micritized grain with a
heavily bored surface. Note the high asperity created by the
boring. The dark grainy area surrounding the grain is the glue used
to mount the grains on the slide. Photograph of grain thin-section
taken using a binocular microsope and transmitted light.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1977). However, since micritization did not appear to significantly
alter the shape of the grains, it is not included in this classification
scheme. A description of micritized ooids is included herein in
order to explain how the internal structures of these ooids were
identified since micritization often obscures the internal structures
of the ooid.
Many of the ooids have undergone extensive micritization; causing
their internal structures to become obscured; the most extreme
cases of m icritization erase the internal structure. Heavily
micritized grains have a translucent mud-grey appearance under
both transmitted and/or reflected light (Figure 7). Similar grain
characteristics have been made by Harris (1977).
In some cases, the outermost laminae are visible. This could be due
to the grain being isolated from the ooid generating system, while
becoming micritized, and re-exposed. The re-exposure would cause
new layers to accrete around the micritized grain. Harris (pers.
comm.) observed an increase in micritization associated with a drop
in transport energy associated with shoal fringes and lagoonal
areas. The highest percentage of micritized grains at Joulters Cay
was in the low-energy lagoonal areas. It is unknown whether the
micritization occurs from burial of grains in the higher energy sand
shoal areas, temporary deposition in the lower-energy lagoonal
areas, or both.
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 7. Photographs of grain thin-section taken using a
binocular microsope. Photograph A is of a heavily micritized grain
stained with Alurzian red stain under transmitted light. Note how
the internal structure has been erased. Photograph B is the same
grain under reflected light. Note how the outline of the nucleus is
highlighted by the stain. The dark grainy area surrounding the
grain is the glue used to mount the grains on the slide.
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A. Alurzian red-stained micritized ooid
under transmitted light
0.1 0.2 0.3 mm
utline of
nucleus
B. Alurzian red-stained micritized ooid
under reflected light
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The nucleus outline can be seen in many grains by reflecting light
off grain sections stained by alizurin red stain (Figure 7). The red
stain roughly outlines the former nucleus shape. This could be do
to an increased concentration of fine crystals, increasing surface
area. A second possibility could be that the old nucleus surface is a
zone of increased pore space, allowing stain to concentrate. The
cortex of these micritized grains are whiter than the nuclei under
reflected light. Laminae of these ooids tend to be thicker than non-
micritized ooids.
This classification is an attempt to incorporate all major grain types
which appear to effect the shape of the ooid grain. The result was
the 18 different grain types in Table 2. Each grain exmined during
the FGSA analysis was classified based on these 18 grain types;
enabling a comparison of ooid shape versus internal characteristics
to be made.
The results of FGSA in concert with the classification was designed
to show: 1) any shape difference and thus sorting between samples,
2) any shape differences between ooids with different internal
structures and 3) a possible ooid shape evolution from immature to
m ature.
Fourier G rain-Shape Analysis
Schwarcz and Shane (1969) and Ehrlich and Weinberg (1970) were
the first to introduce Fourier Grain Shape Analysis (FGSA) as an
4 0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
analytical tool for sediment shape analysis. The technique has been
applied to sediment containing detrital quartz grains to study
sediment source and petrofacies problems (Osborne and Yeh, 1991).
The same methodology used to analyze the two-dim ensional,
maximum-projection, grain shape area of quartz was employed to
study ooid grains in this study. Osborne and Yeh (1991) provided
the following description of the FGSA technique:
Ehrlich and Weinberg (1970) describe a closed-form
Fourier method to analyze the observed variation of
two-dim ensional, m axim um -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. In Fourier
analysis, a series of sine and cosine curves with periods
equal to fundamental harmonics is fit to the observed
data by a least-square technique. Fundam ental
harm onics are the prim e 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 observed data. The
highest frequency that can be estimated is the Nyquist
Frequency, which is equal to twice the distance between
the successive observations. If the Nyquist frequency
is exceeded, error may be introduced by the
4 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
incorporation of irresolvable high frequencies into lower
frequencies (aliasing). The radius is given by:
R(d) = Ro + 1 L R » C 0S(6n-<&n) ( 1)
n=l
Where theta is the polar angle measures from an
arbitrary reference line. The first term in the series R o
is equivalent to the average radius of the grain in the
maximum projection orientation. For the remainder of
the terms, n is the harmonic order, Rn is the harmonic
amplitude, and 3>n if 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; etc. The center of gravity of the maximum-
projection shape is used as the origin of the radius
expansion to sim plify interpretation of the Fourier
series. Coordinates of points along the periphery of the
m axim um -projection outline are required for the
Fourier expansion. At least twice the number of such
points must be known as the number of the highest
4 2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
desired harmonic. The initial origin of the periphery
points may be arbitrary, because a later transformation
places the origin at the center of gravity of the
maximum grain-projection area. If a harmonic of
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.
Although conceptually sim ilar to the closed-form
methodology described by Erlich and Weinberg (1970),
the methodology employed in this study makes use of
the newer and more widely used Fast Fourier
Transform (FFT). This procedure involves the
calculation of many values of the line spectrum using
the FFT computer algorithm to produce a smoothed
estim ate of the continuous spectrum. The FFT
algorithm, as its name implies, is extremely rapid and
requires only nlog2n arithmetic operations rather than
the n2 operations as do alternative methods. The reader
is referred to Brigham (1974), Bloomfield (1976), and
Bendat and Piersol (1971) for extensive treatments of
the mathematically complex FFT.
Therefore, this process results in a m athm atical shape
representation of the overall grain projection.
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Analytical Equipment and Procedure
The digitizing station consists of a binocular petrographic
microscope and a black and white video camera connected via an
ordinary camera microscope coupling. This setup is connected to a
32-bit VMS/VAX workstation with a 650 megabyte internal hard
drive and an external hard drive for storage grain shape
information and statistical software.
Each grain-mount thin section was placed on the stage of the
petrographic microscope. The grain was visually examined through
the microscope oculars to determine its internal structures. This
allowed the grain to be classified on the basis of the internal
structures (cortex thickness, nuclear grain type, and degree of
boring). Each grain was assigned a "grain type number" which
coincided with the category of grain structure it best fitted
(Table 2).
The grain image was then transferred to the video camera
connected to the microscope. The image digitized by the
videocamera provides a dark image against a light background.
The backlit maximum-projection outline of the grain is transmitted
to both the VMS/VAX and the black and white video screen. The
operator then tells the computer to mathmatically determine the
outline of the grain. The computer performs this using a grain
shape analysis (GSA) program written in FORTRAN by Tim Fogarty
for the USC Sedimentary Petrology Laboratory. The computer
4 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
determines the outline of the grain from a standard multi-pixel
single frame image transm itted by the video camera. The
boundary algorithm determines the grain outline, by assuming that
the maximum contrast in the image occurs along the grain
boundary, or the transition from the dark grain (high-tone pixels)
to the lighter background (low-tone pixels). These areas of
maximum contrast, high tone pixels which adjoin a low tone pixel,
are recorded in an arbitrary Cartesian coordinate (X-Y) system as
the boundary points. Further, the center of gravity (centroid) of
the grain outline also is computed. The boundary points and "grain
type number" are then written to a storage device as a binary data
(BPT) file. Grains of a single sample are written in series, one after
another, into the same BPT data file. A total of 200 grain outlines
from each grain mount thin section were recorded. Appendix B
provides the sequence used to image and record the shape data for
each grain.
The BPT file is recalled and prepared for the Fast Fourier Transform
using the Fortran program written by Tim Fogarty. At this point,
the boundary point data can be recalled in two ways: 1) by sample
ID (i.e. all 200 grains from each sample) or 2) by grain classification
(i.e. the number the grain was assigned according to its "grain type
number"). This allows grains to be grouped by each grain type as
well as by sample ID. Two different sets of statistical analyses
were run then to: 1) compare each of the 23 samples to one
another, and 2) compare each of the classification categories.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The Fast Fourier Transform is the same for both of these groupings.
This preparation includes conversion of the X-Y Cartesian
coordinate boundary points into polar coordinates of radius versus
angle. The radius is the distance from any one boundary point to
the centroid of the grain outline with the angle being measured
from a horizontal line which bisects the centroid. Next, because the
mathematics behind the FFT require data to be equally spaced and
centered about the zero, the irregular polar boundary points are
first linearly interpolated to 128 evenly-spaced data points with
the mean radius then being subtracted from each of the 128 points.
This radius is later placed in the final amplitude spectrum.
The FFT may now be calculated using the 128 evenly-spaced data
points. The amplitudes for each wave number are then considered
to equal the square root of the summation of the square of the real
and imaginary FFT values. However, because the imput data is real,
half of the wave numbers represent reflections, and are therefore
omitted. This entire process results in amplitude values for each
of 64 different wave numbers for each grain. The amplitude values
and their respective wave numbers embody a m athem atical
representation of the grain, which is later used for statistical
analysis. After the amplitudes are determined, they are written to
a binary data file with an '.AMP' file type identifier extension.
Values for a single grain are written into the same AMP file in
series, from the lowest to highest wave number. This is followed
by the wave numbers from the next grain from that grouping.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The GSA program can calculate the Fourier amplitude values using
one of two methods. The first method, the standard method, is
described in the preceding paragraph. For the second method, the
normalized method, the GSA program initially calculates the Fourier
amplitude values as in the standard method, but then divides all
values by the amplitude value of the zeroth harmonic. This
procedure to "normalize" the amplitude values, reduces any effect
due to variations in grain size. This method also decreases the total
variance of the sample set.
After creating the AMP files for a given project, the Fourier data
contained in those files is prepared for the statistical analyses
described in the next section. The files for these analyses need to
be in ASCII format in order for the statistical package to read it.
Three different software programs, written by Rory Robinson of the
USC Sedimentary Petrology Laboratory, were needed to convert
binary AMP files to ASCII files. These programs (BYWAVEIT,
CONVRTIT, or STATSIT) also allowed multiple AMP files to be
combined into one ASCII file for analysis.
Statistical Methods
Converted ASCII data files were entered into the statistical
programs package Bio-Medical Data Processing (BMDP) which is
commercially available software created by BMDP Statistical
Software, Inc. All grain-shape statistical analyses were performed
on this software.
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Two different sets of statistical analyses were performed: 1) Factor
analysis and Hotelling T2 test were used in the comparison of
shapes between samples; and 2) Factor analysis and Hotelling T2
test were used in the comparison of the different grain types as
specified in the Exuma grain classification scheme (ECS) described
earlier in this chapter. The Bio-Medical Data Processing (BMDP)
statistical software package for VAX was used for all statistical
calculations.
Factor Analysis
Factor analysis was developed by experimental psychologists in the
1930's, to identify patterns in multivariate data matrices (Davis,
1973). In this test, a hypothetical set of axes (factors) is created in
multivariate space. These axes explain as much of the total
variance of the data set as possible. Eigenvalues and eigenvectors
are used to determine the factors from a square matrix produced
by multiplying a data matrix by its transpose (Davis, 1973). These
m ultivariate data points are projected onto a two-dimentional
plane. The X and Y axes are the two factors which describe the
maximum possible variance in the data set.
Initially, the use of factor analysis in this study was to identify the
end-member samples from the factor plot. These samples exhibit
the most variance in shape. The end-members allowed for the
determination of the shape characteristics controlling the maximum
plot variation. This was done by comparing the values of the 2nc*
4 8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
through 24lh harmonic values; the harmonics used to perform the
factor analysis. The relative locations of the 23 samples on this
factor plot were used to determine the shape similarities and
differences between samples. In the same manner as above, factor
analysis also was used to determine the variations in shape
between 18 ooid types as defined in the Exuma Ooid Classification
schem e.
Hotelling's T2. Test
The multivariate means between two sample populations are
compared by the H otelling's T^ test. This test was used to
determine which of the samples mean values were statistically
similar and different; allowing samples to be grouped on the factor
plot. This test determines the multidimensional mean vector for
each sample and the related variance and covariance matrices
(Alder and Roessler, 1977). The variance and covariance matrix,
the inverse of the variance and covariance matrix, and the
difference from each of the mean vectors is multiplied using matrix
algebra. The resultant matrix is multiplied by the number of
observations. This provides the T2 value. The associated F value
equals the T2 value m ultiplied by the difference between the
number of observations and the number of measurements divided
by the degrees of freedom (Alder and Roessler, 1977). The
requirements for the Hotelling's T2 Test is: (1) that data consists of
random samples; (2) the data has normally-distributed parent
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
populations; and (3) the data do not effect one another. A
significance level of five percent (alpha = 0.05) was used in this
study to determine similarity between data.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
RESULTS AND DISCUSSION
G rain-Size Analysis
Results
Mean grain-diameter sizes (in millimeters) of all samples are shown
in Figure 8. The samples from Shoal 1 (S38 through S48) have very
similar means. The size analysis showed that most samples, with
the exception of samples S47, S54, S58, S60, and S61, appear to be
unimodal. With the exception of sample S48 which has a mean of
0.42 mm, the size range for Shoal 1 was from 0.35 mm to 0.28 mm.
Shoal 2 has the greatest range in grain size (0.92 mm to 0.22 mm),
although most of the Shoal 2 samples have larger mean size values
than Shoal 1.
The standard deviations for all samples are presented in Figure 9.
Note again the similarities in the standard deviations for Shoal 1;
samples S46, S47, and S48 have noticeably larger standard
deviations. Shoal 2 has a much greater range in standard deviation
values (0.291 to 0.613); with the exception of S46, S47, and S48 the
standard deviations are all greater than Shoal 1. Sample S39
(Shoal 1) has the smallest overall standard deviation and S58
(Shoal 2) has the largest overall standard deviation.
Skewness values are presented in Figure 10 and are highly variable
throughout both shoals. Seventeen of the twenty-three samples
5 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 8. Mean grain-diameter size (in millimeters) for all 23
samples. Samples obtained from Shoal 1 are identified by square
data points and Shoal 2 samples are identified by circular data
points.
5 2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UJ
_J
0.
2
<
c n
X
o
X
s
1 1 1
N
C O
z
<
X
C D
z
<
UJ
I.9S
09S
6SS
CM
8SS
9SS
SSS
OSS
I P S
60S
80S
C D O O t ^ C O i n - M - C O C M T - o
a
CL
CO
o o o o o o o o o
(ININ Nl) 3 Z IS NIVUO NV3IN
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 9. Standard deviation for all 23 samples. Samples
obtained from Shoal 1 are identified by square data points and
Shoal 2 sam ples are identified by circular data points.
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UJ
C L
s
5
5
<
U J
C C
2
o
§
5
U J
Q
Q
D C
<
Q
Z
09
6S
93
S3
- S3
- O S
- 86
CD ID CO CM O
a
Q .
C O
o o o o o
N0I.LVIA3Q QUVQNV1S
5 5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 10. Skewness for all 23 samples. Samples obtained from
Shoal 1 are identified by square data points and Shoal 2 samples
are identified by circular data points.
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UJ
_l
CL
S
s
5
2
IT
O
U L
(f)
U J
o
%
6
£
09
6S
8S
LS
c\j
9S
SS
es
os
l p
St-
IP
6£
86
in CM CM o
0 l
(0
A A 3M S
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
were negatively skewed (an excess of coarse particles). For Shoal 1,
samples S40 and S41 had the most positively skewed values and
samples S42, S38 and S48 had the most negatively skewed values.
There is an overall decrease in skewness from samples S38 to S48.
For Shoal 2, samples S50, S53, and S59 had the most positively
skewed values and samples S51, S52, and S54 had the most
negatively skewed values.
Discussion
The initial assessment of the size analysis indicates that Shoal 1
samples have a much more uniform and unimodal size distribution
(Figures 8, 9, and 10) than Shoal 2. Samples S38 through S44 were
obtained from the inter-island channel sands which extends from
north of LSI to between NPC and LSI (Figure 4). Within this area
similar physical conditions exist along the elongated inter-island
sand shoal as indicated by the similar sedimentary features (small
ripples superimposed on larger megadunes); there is a gradual
shallowing of water depth to the west (from approximately 10 m to
5 m over approximately 1.5 Km lateral length) but the greatest
change occurs as the channel extends south of NPC and LSI. At this
point the sand shoal slopes steeply upwards toward the point at
which the channel terminates into the spill-over lobes at an
approximate depth range of 2 m to 0.75 m of water. Samples S45
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
through S48 were obtained from the natural levee and spill-over
lobe to the south and southeast of the channel.
The greatest variation in size related parameters occurs in samples
S47 and S48 (Figures 8, 9, and 10). These samples were obtained
(along with samples S45 and S46) from the most shallow areas, the
natural levee and coalessing spill-over lobes (Figure 4). Samples
S45 and S46, having been obtained from a smaller distributary
channel extending further south into the spill-over lobe area, have
similar size characteristics to the other samples which were all
obtained from the main inter-island channel. Skewness decreases
overall with decrease in depth. The most shallow sample area
(samples 45 through S48) are the most negatively skewed.
The results from Shoal 2 were far more varied. The samples from
the inner spill-over lobe area (S51, S54, S56, and S57) had the most
similar size parameters. The depositional conditions are similar
between these samples; all samples are from a depth of less than
2m, are distant from the main feeder channel, and are reworked by
similar current energies. The samples S52, S55, and S58 have
coarser mean grain-size values. All of these samples are from or
near the east-west elongated natural levee area of the spill-over
lobes. This area is under continuous reworking by greater tidal
currents than those experienced in the inner sand sheet area. This
would prevent fines from being deposited in this area.
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
For Shoal 2, S53 receives the lowest amount of tidal energy, being
submerged only during the apex of high tide. Since this sample
location is the only one exposed to both water and wind transport,
it would be expected to differ from the other samples. This area is
where the finest grained, best sorted, and positively skewed sands
are located.
Samples S50 and S60 were sampled in areas of high prevailing tidal
currents. Sample S50 was located in a very high energy tidal
channel (planar bedforms) and thus should be a location of coarse
deposits; the bulk of the fines having never developed here or been
allowed to be deposited by the high current energy. This sample is
coarser, better sorted, and more positively skewed than other
locations. Sample S60 was obtained from the highest point of the
inter-island sand shoal (in approximately 1.8 m of water). Relative
to samples S59 and S61, which were sampled from the relatively
lower energy deeper (6.1 m and 7.6 m respectively) portions on
either side of this high point, S60 is undergoing more reworking at
higher energy levels due to restriction of water flow over the
elevated megadune. Sample S60 has a mean grain size between
that of S59 and S61 (Figure 8) and a greater standard deviation
(Figure 9) than both sample locations. This is an indication that the
elevated area is being influenced by both sides, as is evident by
ebb current sand dunes on the bankward side and flow current
sand dunes on the oceanward side of the sample S60 high point
location (refer to sample collection description). The skew of S60 is
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
more negative than S59 and S61, likely due to lack of finer grain
sizes resulting from the continual reworking of sediments at higher
current energy levels.
In conclusion, the greatest variation in grain-size characteristics
seem to be due to variations in depositional environment, which are
closely related to the depth of the sampling locations. The depth
depends on the location of the sample on the sand shoals, which
tend to shallow with distance from the open Exuma Sound. Ball
(1967) noted a correlation of water depth, tidal current, and wave
action with sedimentary structures and bedforms. My data
indicates grain-size characteristics within these two shoals are
correctable with water depth, current, and wave action. The
following summarizes the findings from each shoal:
• Shoal 1: The similarities between the samples in Shoal 1 are
due to their sample locations being predominantly from within the
inter-island channel which did not have any drastic variations in
sand dune elevation or sedimentary structures. Where elevation
does change (approaching the natural levee and spill-over lobes)
the size characteristics become more variable as evidenced by
increases in mean grain size and standard deviation. Skewness also
becomes more negative in this area.
• Shoal 2: Much more variation occurs in samples from Shoal 2.
This is due to greater variation in depositional environments. The
coarsest most positively skewed sample (S50) was obtained from a
6 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
relatively shallow sm all-channel deposit which exhibited the
highest energy bedforras (planar bedding). Samples from similar
environmental conditions, such as samples S51, S54, S56, and S57
obtained from the interior of the spill-over lobe area, have similar
grain-size characteristics. Sample S60 had size characteristics
which were between the characteristics of the samples (S59 and
S61) which had sedimantary structures which indicated that they
both influenced the area in which sample S60 was obtained. The
finest, best sorted, positively skewed sample (S53) was obtained
from a relatively low-energy, sub-subaerially exposed high point
on a spill-over lobe. This is the only location influenced by both
wind and water energies.
Fourier Grain-Shape Analysis
Shape Distributions Relative to Sample Locations
Factor Analysis
The factor analysis, which examines the maximum variance of the
principal shape components, was perform ed using the mean
harmonic values for the 2nd through the 24th harmonic of the 23
samples analyzed. Table 3 lists the factor scores for each of the 23
samples. The resultant two-factor solution plot (Figure 11)
describes 94.7 percent of the total variance in shape between the
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3. Factor 1 and Factor 2 values for each of the
samples analyzed.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FACTOR 1 AND FACTOR 2 VALUES FOR ALL SAMPLES
SAMPLE FACTOR 1 FACTOR 2
s38 -0.491 -1 .0 3 3
s39 0.287 0 .2 6 8
s40 0.136 -0 .2 2 6
s41 -0.464 0 .9 7 6
s42 0.614 -0 .6 4
s43 -1.087 0 .8 8 3
s44 0.756 -0 .1 2 4
s45 -0.489 -0 .0 1 8
s46 -0.881 0 .0 4 9
s47 -0.22 1 .1 6 2
s48 0.839 -0 .6 2 8
s50 0 .214 -1 .3 8 8
s51 -0.472 -0 .6 2 2
s52 -1.478 0 .0 0 3
s53 -0.549 -2 .3 2 6
s54 -0.324 -0 .4 5 6
s55 -1.641 0 .6 7
s56 1.08 1 .9 7 4
s57 1.297 0 .1 9
s58 0.488 -1.31
s59 0.104 0 .8 3 8
s60 2 .914 0 .3 1 9
s61 -0.633 1.44
6 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 11. Factor plot of Factor 1 versus Factor 2 for all 23
samples. Factor 1 (X-axis) represents grain asperity, with
roughness increasing to the right. Factor 2 (Y-axis) represents grain
elongation, with elongation increasing to the top of the graph. Shoal
1 samples are represented by black dots; Shoal 2 samples are
represented by outlined squares. Note how samples from Shoal 1
plot in the central portion of the graph. The end-members for both
Factor 1 and Factor 2 are from the more varied environments of
Shoal 2.
6 5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FACTOR 1 v FACTOR 2 F O R A L L SAMPLES
C N
00
00
On
O
m
in
< n
•n
r s i
cs in — » in
©
m
©
~ in c n in
< N
UOpcSuotO StHSBOJOUl 1 J O p e j
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Factor 1 in c re a sin g asperity
23 samples as represented by harmonics 2 through 24. Factor 1
describes 59.8 percent and Factor 2 describes 34.9 percent of the
total variation.
The distinguishing shape characteristics of the variations
represented by the two factors was determined by comparing the
mean values of the wavelengths 2 through 24 from the end
members as depicted on the factor plot (Figure 11). The end
members for Factor 1 are samples S55 and S60 and the end
members for Factor 2 are samples S53 and S56. Statistical
significance testing (Hotelling T2) indicates each of wavelengths 2
through 24 have highly significant differences between end-
member samples (alpha < 0.01). This is an indication that all of the
23 harmonics are factors in controlling shape. Thus, in order to
determine the harmonics which are most heavily weighted in the
factor plot, the mean numeric values of harmonics 2 through 24
were examined. The factor end member set with the highest and
lowest numeric mean values for a given harmonic or set of
harmonics are the most weighted determinants for the factor.
Table 4 shows this by subtracting the values of Factor 1 wavelength
differences (the n-value) from Factor 2 wavelength differences
(the m-value). A positive value indicates that a particular
wavelength is more significant in describing Factor 2; a negative
values indicates that a particular wavelength is more significant in
describing Factor 1. For Factor 1, harmonics 12 through 24 (which
represent grain asperity) had the highest differences in values. For
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4. E nd-m em ber w av elen g th co m p a riso n to
determine controlling shape characteristics for Factor 1 and Factor
2. The difference between the wavelength values of Factor 1 end-
members were subtracted from the difference between wavelength
values of Factor 2 end-members. This difference indicated which
wavelength controlled which factor; a positive value indicated that
the wavelength controlled Factor 2 and a negative value indicated
that the wavelength controlled Factor 1.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
COMPARISON OF FACTOR 1 AND FACTOR 2 ENDMEMBERS FOR ALL 23 SAMPLES
W avelegth
FACTOR 1
Sample
5 5
Endmembers
Sample
6 0
Difference
between
Factor 1
endm em bers
(n)
FACTOR 2 E
Sample
5 3
ndmembers
Sample
5 6
Difference
betw een
Factor 2
endm em bers
(m)
m - n
2 0 .0 2 5 6 0 .0 2 9 7 0 .0 0 4 1 0 .0 1 7 8 0 .0 3 0 2 0 .0 1 2 4 0.0083
3 0.0 1 7 1 0.021 0 .0 0 3 9 0 .0 0 9 3 0 .0 2 1 7 0 .0 1 2 4 0.0085
4 0 .0 0 8 0 .0 1 1 9 0 .0 0 3 9 0 .0 0 5 0 .0 1 3 1 0 .0 0 8 1 0.0042
5 0 .0 0 5 0 .0 0 9 5 0 .0 0 4 5 0 .0 0 2 8 0 .0 0 9 8 0 .0 0 7 0.0025
6 0 .0 0 3 6 0 .0 0 6 7 0 .0 0 3 1 0 .0 0 1 9 0 .0 0 6 7 0 .0 0 4 8 0.0017
7 0 .0 0 2 7 0 .0 0 5 1 0 .0 0 2 4 0 .0 0 1 6 0 .0 0 5 4 0 .0 0 3 8 0.0014
8 0 .0 0 2 0 .0 0 4 5 0 .0 0 2 5 0 .0 0 1 2 0 .0 0 4 5 0 .0 0 3 3 0.0008
9 0 .0 0 1 6 0 .0 0 3 8 0 .0 0 2 2 0.001 0 .0 0 3 8 0 .0 0 2 8 0.0006
10 0 .0 0 1 4 0 .0 0 3 3 0 .0 0 1 9 0 .0 0 0 9 0 .0 0 3 0 .0 0 2 1 0.0002
1 1 0 .0 0 1 2 0 .0 0 3 1 0 .0 0 1 9 0 .0 0 0 8 0 .0 0 2 8 0 .0 0 2 0.0001
12 0 .0 0 1 1 0 .0 0 2 6 0 .0 0 1 5 0 .0 0 0 8 0 .0 0 2 2 0 .0 0 1 4 -IE -0 4
13 0.001 0 .0 0 2 5 0 .0 0 1 5 0 .0 0 0 7 0 .0 0 2 0 .0 0 1 3 -0 .0 0 0 2
14 0 .0 0 0 9 0 .0 0 2 2 0 .0 0 1 3 0 .0 0 0 7 0 .0 0 1 9 0 .0 0 1 2 -0 .0 0 0 1
15 0 .0 0 0 9 0 .0 0 2 0 .0 0 1 1 0 .0 0 0 7 0 .0 0 1 8 0 .0 0 1 1 -2 .1 6 8 E -1 9
16 0 .0 0 0 8 0 .0 0 1 9 0 .0 0 1 1 0 .0 0 0 6 0 .0 0 1 9 0 .0 0 1 3 0.0002
17 0 .0 0 0 8 0 .0 0 1 7 0 .0 0 0 9 0 .0 0 0 6 0 .0 0 1 7 0 .0 0 1 1 0.0002
18 0 .0 0 0 7 0 .0 0 1 8 0 .0 0 1 1 0 .0 0 0 6 0 .0 0 1 7 0 .0 0 1 1 0
19 0 .0 0 0 7 0 .0 0 1 7 0 .001 0 .0 0 0 6 0 .0 0 1 6 0 .0 0 1 0
2 0 0 .0 0 0 7 0 .0 0 1 6 0 .0 0 0 9 0 .0 0 0 6 0 .0 0 1 5 0 .0 0 0 9 0
21 0 .0 0 0 7 0 .0 0 1 6 0 .0 0 0 9 0 .0 0 0 6 0 .0 0 1 4 0 .0 0 0 8 -0 .0 0 0 1
2 2 0 .0 0 0 6 0 .0 0 1 6 0 .001 0 .0 0 0 6 0 .0 0 1 3 0 .0 0 0 7 -0 .0 0 0 3
2 3 0 .0 0 0 6 0 .0 0 1 6 0.001 0 .0 0 0 5 0 .0 0 1 1 0 .0 0 0 6 -0 .0 0 0 4
2 4 0 .0 0 0 6 0 .0 0 1 5 0 .0 0 0 9 0 .0 0 0 5 0.001 0 .0 0 0 5 -0 .0 0 0 4
Factor 2, the lower harmonics especially the even harmonics
between harmonics 2 and 8 (which represent grain elongation) had
the highest values.
Significance Testing Between Samples
H otelling's T2 test was used to compare all 23 samples to one
another. This comparison shows which samples are significantly
different in shape from each other, allowing samples which are not
significantly different in shape characteristics to be grouped into
fields within the factor plot. A summary of these results is
provided in Table 5. With the exception of samples S38 and S46
through S48, the samples from Shoal 1 were all similar in shape;
where as Shoal 2 exhibited significant variation in shape. Samples
S51, S53, S56, and S60 (all from Shoal 2) had the most unique
shape characteristics, having significant differences with most other
samples. These shape charactreristics are discussed below.
Discussion
Factor analysis and Hotelling's T2 tests indicate that there are
differences in shape characteristics between Shoals 1 and 2. Based
on their shape characteristics, samples can be divided up as to their
specific locations along the two shoals. There appear to be three
different zones on Shoal 1: (1) the most seaward deepest flood tidal
sand dunes; (2) the central inter-island sand shoal, and (3) the
natural levee and spill-over lobe area.
70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Shoal 1 has very similar shape characteristics as indicated by there
not being significant differences for samples S39 through S45
(Table 5 and Figure 12). The samples which are significantly
different (S38, S46, S47, and S48) are from either end of the shoal.
Sample S38 is from the most oceanward side of the shoal and is the
sample obtained from the greatest water depth. It contains the
least elongate (most rounded) characteristics and relatively low
asperity. The current energy at this depth is relatively low. The
coarser, more rounded grains could have been preferentially
removed. Rougher, elongate grains are more easily moved and/or
entrained. Thus, they are preferentially moved on the surface of
the sand body (saltation) or remain entrained in the water column.
Samples S46, S47, and S48 were obtained from the natural levee
(shallowest portion) of the shoal. The sample from the flood tidal
sand sheet spill-over lobe (S47) was the most elongate sample from
Shoal 1. This sample has medium asperity; the sample with the
highest asperity (S48) is found on the natural levee of the spill
over lobes. Sample S46, obtained from the small distributary
channel which extends directly from the main inter-island channel,
appears to have low asperity and medium elongation. Given that
this sample is from a relativley higher current energy, the high
level of smoothness of the grains can be explained by the coarser
grains remaining entrained in the water column to be deposited in
a lower energy environment.
7 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5. Comparison of shape characteristics of all 23
samples to one another using Hotellings T2 test. Most of the
samples from Shoal 1 had shapes which were not significantly
different from one another. The greatest shape variation occurs in
Shoal 2, especially samples S51, S53, S56, and S60 which are all
from different hydraulic environments. Sample S53 is the only
sample also influenced by wind since it is intermittantly subaerially
exposed. A significance level of five percent (alpha = 0.05) was
used.
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SIGNIFICANCE TEST OF ALL 23 SAMPLES TO EACH OTHER
Shoal 1 Shoal 2
S39|S40|S41 S42 S43 S44 S45 S46 S47 S48 S50 S51 S52 S53 S54 S55 S56 S57 S58 S59 S60 S61
S38
* * * * * * * * * * * * * * *
S38
S39
* * * * * * *
S39
S40
* * * * * * * * *
S40
S41
* * * * * * *
S41
S42
* * ♦ * * * * * ♦
S42
S43
* * * * * *
S43 Shoal 1
Shoal 1 S44
*
* * * * *
S44
S45
* * * * * * * *
S45
S46
* * * * * * * * * r" * *
S46
S47
* * * * * *
S47
S48
* * * * * *
S48
S50
* * * *
S50
S51
* * * * * * * * *
S51
S52
* * *
S52
S53
* * * * * * * *
S53
S54
* * * * *
S54
Shoal 2 S55
* * *
S55 Shoal 2
S56
* *
S56
S57
* *
S57
S58
* * *
S58
S59
*
S59
S60
*
S60
S61
* - indicates a significant difference (alpha < 0.05) in shape characteristics between the samples.
Figure 12. Factor plot of Shoal 1 samples only. The samples
within the bordered area were found to have sim ilar shape
characteristics. These similarly shaped samples are from the inter
island sand shoal area. The samples with significantly different
shape characteristics are from the most bankward area of the shoal
(S38) of the flood tidal spill-over lobe lip area (S46, S47, and S48).
These areas have the greatest current variations.
7 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FA C T O R 1 v F A C T O R 2 F O R S H O A L 1
C M
0 0
CO
in in
o
in C M O
Z U 010V J
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-0.5 0 0.5 1 1.5 2 2 .5
FACTOR 1 Jncreaslng_aspsdty_^.
Much like Shoal 1, Shoal 2 appears to be divided into four different
portions: (1) the central inter-island sand shoal; (2) the natural
levee area; (3) the coalessing flood tidal spill-over lobe area; and
(4) the subaerially-exposed portion of the spill-over lobe area.
Samples S50, S52, S55, and S58 are from the natural levee area. As
Table 5 indicates, these samples have similar shapes to one another.
A plot of Factor 1 versus Factor 2 of these samples shows that they
occur in the central portion of the graph (Figure 13). Sample S54
has similar shape characteristics to these samples and is located in
a small channel which diverts water around the subaerially
exposed area of the sand dune. This environment is similar to that
of the natural levee, not the relatively flat spill-over lobe sand
sheet environment.
With the exception of the five samples mentioned above, Shoal 2
samples had much more shape variation. Sample S53 was
significantly different in shape to all other samples (Table 5). This
sample had the most spherical characteristics of any of the samples
analyzed. Size analysis indicated that it was the finest grained
deposit. This was the only subaerially exposed sample obtained;
comparison is not possible since none of the other samples were
obtained from a subaerially-exposed sand dune.
The samples obtained from the greatest distance from the channel
(S51, S56, and S57) indicate that there are significant variations in
shape within this area characterized by similar, relatively low
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 13. Factor plot of Shoal 2 samples only. The samples
w ithin the bordered area were found to have similar shape
characteristics. These similarly shaped samples are from the
natural levee. The samples with significantly different shape
characteristics are from the other portions of the lobe where water
depths (and thus depositional conditions) vary.
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FACTOR 1 v FACTOR 2 F O R SH O A L 2
CM
00
to
©□
to
CM
CM
CM to
O
UOJ)BSu O[3 SuiSB3J3Ut
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Factor 1 in c re a sin g asperity
energy depositional conditions. Samples S56 and S57 both exhibit
high levels of asperity; sample S56 also exhibits a very elevated
level of elongation. The reason for the asperity could be due to two
reasons: 1) the area is a location where rougher grains are allowed
to settle; and 2) the area provides for increased amounts of algal
boring. Both of these reasons are due to the relatively lower
current energies found in the interior of this sand sheet area.
Sample S51 is also from the interior of the sand sheet but was
obtained from a higher energy, deeper small distributary channel.
Its shape is more similar to the higher-energy natural levee
samples for this reason.
Sample S60 has a higher asperity than and similar elongation
values to samples S59 and S61; samples which are from either end
of the inter-island sand shoal (Figure 13). The high central portion
of Shoal 2, where sample S61 was obtained, is the area where
buildup has occured due to deposition of sediment obtained from
either side of the inter-island portion of the shoal. The amount of
elongation is similar for all three samples, although samples S59
and S61 appear slightly more elongate.
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Shape Distributions Relative to Ooid Classification
Factor Analysis
The factor analysis, which examines the maximum variance of the
principal shape com ponents, was performed using the mean
harmonic values for the second through the 24th harmonic of the
18 grain types examined. Table 6 lists the factor scores for each of
the 18 grain types. The resultant two-factor solution plot (Figure
14) describes 95.9 percent of the total variance in shape. Factor 1
describes 90 percent and Factor 2 describes 5.9 percent of the total
variation. The distinguishing shape characteristics of the variations
represented by the two factors was determined by comparing the
mean values of the wavelengths 2 through 24 from the end
members as depicted on the factor plot (Figure 14). The end
members for Factor 1 are the quadrate thin shape and the kidney
with voids shape and the end members for Factor 2 are the
triangular thick shape and the fossil with voids shape. Statistical
significance testing (Hotelling T2) indicates each of wavelengths 2
through 24 have highly significant differences between end-
member samples (alpha < 0.01). This is an indication that all of the
23 harmonics are factors in controlling shape. Thus, in order to
determine the harmonics which are most heavily weighted in the
factor plot, the mean numeric values of harmonics 2 through 24
were examined. The factor end member set with the highest and
lowest numeric mean values for a given harmonic or set of
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 6. Factor 1 and Factor 2 values for each of the
grain types analyzed.
8 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FACTOR 1 AND FACTOR 2 VALUES FOR EACH GRAIN TYPE
NUCLEUS CORTEX FACTOR 1 FACTOR 2
Oval Thick -0.258 -0 .7 1 5
Thin -1.006 -0 .5 7 5
Bored 0.913 -0 .3 0 8
Circular Thick -0.748 -0 .4 1 4
Thin -0.377 -0 .5 6 3
Bored 1.347 -0 .6 2 4
Quadrate Thick -1.004 -0 .2 6 2
Thin -1.369 0 .3 6 2
Bored -0.363 1.157
Triangular Thick -1.029 -0 .9 6 3
Thin -0.826 -0 .4 3 5
Bored 1.081 -0 .2 5 7
Kidney Thick -0.732 -0.248
Thin 0.944 -0 .2 4 9
Bored 1.979 -0 .5 3 7
Fossil Thick 0.801 0 .3 7 3
Thin 0.8 0 .9 3 6
Bored -0.155 3 .3 2 2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 14. Factor plot of Factor 1 versus Factor 2 for all 18
grain types as defined in the ECS. Factor 1 (X-axis) represents grain
asperity, with roughness increasing to the right. Factor 2 (Y-axis)
represents grain elongation, with elongation increasing to the top of
the graph. Note how the grains which exhibited boring on their
outer corteces and the grains with fossil nucleii have increased
asp erity .
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
FACTOR 1 v FACTOR 2 FOR 18 OOID TYPES
C D
o 3
0 )
052.5
’w
c o 2
0 )
h_
o
ot .E1.5
0
-0.5
-1
-1.5 -H -
-2
-------------1 ----------------- 1 ------------
-1.5 -1
------1 ------
-0.5
----------- 1 -------------
0
F actor 1
— I ----------------- 1 -------------
0 .5 1
increasing asperity^
L e g e n d
oo
• circ u lar nucleus ♦ oval nucleus ■ q uadrate nucleus
4^ A train g u lar n u cleu s X kidney nucleus X fossil nucleus
th - denotes thin cortex tk - thick cortex
non filled-in symbols are grains with greater than 20% boring on surface
harmonics are the most weighted determinants for the factor.
Table 7 shows this by subtracting the values of Factor 1 wavelength
differences (the n-value) from Factor 2 wavelength differences
(the m-value). A positive value indicates that a particular
wavelength is more significant in describing Factor 2; a negative
values indicates that a particular wavelength is more significant in
describing Factor 1. For Factor 1, harmonics 14 through 24 (which
represent grain asperity) had the highest differences in values. For
Factor 2, the lower harmonics (which represent grain elongation)
had the highest values.
Discussion
The significant differences in shape occur between the non-bored
and bored grains. As Figure 14 indicates, there is a significant
increase in asperity with grains which contain endolithic algal
borings in their outer corteces. The amount of boring does not
appear to cause any significant increase or decrease in overall grain
shape. According to Gaffey (1983), areas of intense algal boring
often decreases the integrity of that area of the grain, causing it to
collapse or disintigrate. One would expect this to significantly alter
the gross shape of the grain; these results indicate that these areas
of intense boring merely add to the grains roughness. Roughness
related to boring, not gross shape, is the determining factor in
shape differentiation.
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 7. E nd-m em ber w av elen g th co m p ariso n to
determine controlling shape characteristics for Factor 1 and Factor
2. The difference between the wavelength values of Factor 1 end
members were subtracted from the difference between wavelength
values of Factor 2 end-members. This difference indicated which
wavelength controlled which factor; a positive value indicated that
the wavelength controlled Factor 2 and a negative value indicated
that the wavelength controlled Factor 1.
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
COMPARISON OF FACTOR 1 AND FACTOR 2 ENDMEMBERS FOR GRAIN TYPES
FACTOR 1 Endmembers FACTOR 2 Endmembers
Difference Difference
between between
W avelegth Factor 1 Factor 2 m - n
Q uadrate Kidney endm em bers Triangular Fossil endm em bers
Thin Bored (n) Thick Bored (m)
2 0 .0 2 8 3 0 .0 4 8 9 0 .0 2 0 6 0 .0 3 3 2 0 .0 3 7 9 0 .0 0 4 7 - 0 .0 1 5 9
3 0 .0 2 2 6 0 .0 2 6 4 0 .0 0 3 8 0 .0 1 1 2 0 .0 1 8 8 0 .0 0 7 6 0.0038
4 0 .0 1 1 6 0 .0 1 6 8 0 .0 0 5 2 0 .0 0 6 9 0 .0 1 6 0 .0 0 9 1 0.0039
5 0 .0 0 8 0 .0 1 1 2 0 .0 0 3 2 0 .0 0 4 3 0 .0 1 2 0 .0 0 7 7 0.0045
6 0 .0 0 5 4 0 .0 0 7 1 0 .0 0 1 7 0 .0 0 2 7 0 .0 0 6 8 0 .0 0 4 1 0.0024
7 0 .0 0 4 0 .0 0 5 5 0 .0 0 1 5 0 .0 0 1 9 0 .0 0 5 6 0 .0 0 3 7 0.0022
8 0 .0 0 2 7 0 .0 0 4 8 0 .0 0 2 1 0 .0 0 1 5 0 .0 0 5 6 0 .0 0 4 1 0.002
9 0 .0 0 2 3 0 .0 0 4 1 0 .0 0 1 8 0 .0 0 1 2 0 .0 0 4 2 0 .0 0 3 0.0012
10 0 .0 0 1 9 0 .0 0 3 3 0 .0 0 1 4 0.001 0.0 0 4 1 0 .0 0 3 1 0.0017
1 1 0 .0 0 1 7 0 .0 0 3 2 0 .0 0 1 5 0.0 0 1 1 0 .0 0 2 7 0 .0 0 1 6 1E-04
12 0 .0 0 1 4 0 .0 0 2 8 0 .0 0 1 4 0 .001 0 .0 0 2 6 0 .0 0 1 6 0.0002
13 0 .0 0 1 2 0 .0 0 2 5 0 .0 0 1 3 0 .0 0 0 8 0 .0 0 2 2 0 .0 0 1 4 0.0001
14 0 .0 0 1 1 0 .0 0 2 5 0 .0 0 1 4 0 .0 0 0 8 0 .0 0 2 0 .0 0 1 2 - 0 .0 0 0 2
1 5 0.001 0 .0 0 2 2 0 .0 0 1 2 0 .0 0 0 7 0 .0 0 2 0 .0 0 1 3 1E-04
1 6 0 .0 0 0 9 0 .0 0 2 2 0 .0 0 1 3 0 .0 0 0 7 0 .0 0 1 6 0 .0 0 0 9 - 0 .0 0 0 4
17 0 .0 0 0 9 0 .0 0 2 0 .0 0 1 1 0 .0 0 0 7 0 .0 0 2 0 .0 0 1 3 0.0002
1 8 0 .0 0 0 9 0 .0 0 1 9 0.001 I 0 .0 0 0 7 0 .0 0 1 5 0 .0 0 0 8 - 0 .0 0 0 2
1 9 0 .0 0 0 9 0 .0 0 1 9 0 .001 0 .0 0 0 6 0 .0 0 1 3 0 .0 0 0 7 - 0 .0 0 0 3
2 0 0 .0 0 0 8 0 .0 0 1 6 0 .0 0 0 8 0 .0 0 0 6 0 .0 0 1 4 0 .0 0 0 8 0
21 0 .0 0 0 8 0 .0 0 1 6 0 .0 0 0 8 0 .0 0 0 6 0.001 0 .0 0 0 4 - 0 .0 0 0 4
2 2 0 .0 0 0 7 0 .0 0 1 5 0 .0 0 0 8 0 .0 0 0 6 0.0 0 1 1 0 .0 0 0 5 - 0 .0 0 0 3
2 3 0 .0 0 0 7 0 .0 0 1 4 0 .0 0 0 7 0 .0 0 0 5 0 .0 0 0 9 0 .0 0 0 4 - 0 .0 0 0 3
2 4 0 .0 0 0 7 0 .0 0 1 3 0 .0 0 0 6 0 .0 0 0 6 0 .0011 0 .0 0 0 5 -1E -04
The difference between the thin- and thick-layered grains do not
appear to play a significant role in determining the overall grain
shape. With the exception of the fossil nuclei grains and the thin
layered kidney nuclei grains, all non-bored thin and thick grains
plot in the area of low asperity and elongation (Figure 14). The
reason for the high level of asperity exhibited by the kidney nuclei
with thin cortex grains is unknown. All the fossil nuclei grain types
have high levels of asperity and elongation. The asperity can be
explained by the highly irregular shape of the fossil fragments; the
elongation can be explained by the elongated characteristics of
many of the fossils (Hailmeda, mollusk, etc.). All other nuclear
types are composed of micritic peloids of similar composition with
relatively smooth regular outer surfaces.
There does appear to be a slight decrease in grain elongation with
an increase in cortex thickness for all nuclear types except circular
nuclear grain types (Figure 15). This seems logical, since an
increase in thickness of layers would move a grain toward
sphericity. The trend towards sphericity is very slight in this
instance.
Ooid Maturity
In addition to the grain types examined as part of the Exuma
Clasification System, a point count was performed to determine the
number of concentric cortex layers for 200 grains in each of the 23
samples. The Galgolov-Chayes method for point counting as
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 15. Factor plot showing trends from thin-cortex grain
types to thick-cortex grain types. The arrows point from thin to
thick for each nuclear type. With the exception of circular nuclei,
there is a slight reduction in elongation with thicker corteces.
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
FACTOR SCORE TRENDS BETWEEN THIN AND THICK OOID TYPES
v O
o
c n .E
* ♦
-2 -1.5 1 -0.5 0 0 .5 1 1.5 2
increasin q asp erity .
Factor 1
L eg em!
• circ u lar nucleus
A train g u lar n ucleus
* - denotes thin cortex
non fillcd-in symbols are grains with greater than 20% boring on surface
A oval nucleus
X kidney nucleus
■ q uadrate nucleus
X fossil nucleus
shows trend from thin to thick cortex
described by Galehouse (1971) was used. A summary of results is
presented in Table 8. Using the classification system of Bathurst
(1975), results indicate that all ooids analyzed were immature
(containing less than three layers). Ooids with one layer were
dominant, accounting for 81.0% (sample S50) to 99.0% (sample S60)
of all grains in each sample. Grains with two layers were the
second greatest number of grains analyzed, with concentrations
ranging from 0.5% (sample S60) to 17.5% (sample S58). No
identifiable layers accounted for 0.0% (samples S43, S46, S53, and
S58) to 5.5% (sample S50) of the grains in the 23 samples. There
were no grains identified with more than three concentric layers;
the concentration of ooids with three layers ranged from 0.0% to
1.0%.
Discussion
According to the point count of concentric layering in each sample,
all of the samples represent pseudooid to immature ooids,
containing zero to three layers with the majority containing one
layer. In Shoal 1 the samples from the ebb-tidal spill-over lobe
(S38) and the inter-island sand shoal (S39 through S44) had the
highest percentage of ooids with two or more layers (Figure 16).
The percentage of two or more layers ranges from 8% to 15% for
samples from the inter-island sand shoal (S38 through S43). This
reduces to 2.5% to 6.0% for samples from the spill-over area (S44
through S48) (Table 8).
9 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 8. Results of number of outer laminae point count for
all 23 samples. A total of 200 grains per sample were examined.
The majority of the grains examined are immature ooids, containing
only one outer laminae.
92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PERCENTAGE OF GRAINS
WITH 0 ,1 , 2, AND 3 CONCENTRIC LAYERS BY SAMPLE
SAMPLE PERCENT* OF
0 LAYER
GRAINS CONTA
1 LAYER
INING:
2 LAYER 3 LAYER
S38 2.5 82.5 15.0 0.0
S39 1.5 89.5 9.0 0.0
S40 2.0 90.0 8.0 0.0
S41 1.0 88.5 10.5 0.0
S42 2.0 84.5 12.5 1.0
S43 0.0 88.0 12.0 0.0
S44 1.0 93.5 5.5 0.0
S45 1.0 96.0 2.5 0.5
S46 0.0 94.0 6.0 0.0
S47 1.0 93.5 5.5 0.0
S48 1.5 94.5 4.0 0.0
S50 5.5 81.0 13.5 0.0
S51 3.0 91.5 5.0 0.5
S52 2.5 87.0 9.5 1.0
S53 0.0 95.0 5.0 0.0
S54 2.0 91.5 6.0 0.5
S55 3.0 92.0 5.0 0.0
S56 4.5 95.0 0.5 0.0
S57 0.5 88.5 11.0 0.0
S58 0.0 81.5 17.5 1.0
S59 0.5 97.5 2.0 0.0
S60 0.5 99.0 0.5 0.0
S61 1.5 96.0 2.5 0.0
* Percentage of layers determined by point count of 200 grains per sample.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 16. Percentage of grains with two layers for each
sample location. Percentage of grains with two outer laminae
decrease with distance from the open Exuma Sound.
9 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78*11'
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The samples from Shoal 2 also shows a trend with distance from
the shelf-break. The trend indicates that concentrations of higher
concentric layers decrease with distance from the main feeder
channel (Figure 16). This trend is especially obvious with samples
S56 through S58, which show a decrease from 17.5% (S58) at the lip
to 0.5% (S56) at the most inward sample of the spill-over lobe sand
sheet. It appears that the samples from the interior of the spill
over sand sheet (S51, S54, S53, and S56), have the lowest
percentage of grains containing two or more layers.
The samples from the elongate sand bar north of Norman's Pond
Cay (S59, S60, and S61) have differences in layers based on depth.
Samples S59 and S61, both from greater than 6.5 m water depth,
had a higher percentage of grains with two concentric layers than
S60, from 6 feet water depth. Sample S60 may be from a location
where ooid layers are not actively generating. The deeper areas
where more highly layered grains are concentrated may be where
ooids are actively growing. The more shallow regions may be
where older less developed grains are continually being reworked.
This reworking may also be removing outer grain layering, making
grains in these areas appear less mature. This may also be true of
the less mature sands found on the interior of the spill-over lobe of
Shoal 2 and the spill-over lobe area of Shoal 1.
These findings, when combined with the unimodial results of the
size analysis, could be an indication that larger, more mature ooids
96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
are not able to form within this environment. Since all ooids
appear to be pseudo-oolitic (0 layers), superficial (1 layer), or
immature normal ooids (2 layers), it could be an indication that the
energy level created by the currents at LSI are at a level which
allows only one layer to accrete around the available nuclear grain
sizes before grains become too large for additional concentric layers
to accrete (Carozzi, 1960). This would explain both the unimodal
size of the ooid population and the lack of more mature ooids.
Another possible explanation is that ooids are not being actively
generated in this area, since thay are primarily superficial, similar
in size, and show no lateral progression from immature to more
mature grains across the bank margin. If ooids were actively being
generated, one would expect a lateral progression bankward from
immature to mature grains as observed at Joulter's Cay (Harris,
1977).
97
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CONCLUSIONS
The greatest variation in grain characteristics seem to be due to
variations in depositional environment, which are closely related to
the depth of the sampling locations. The depth depends on the
location of the sample on the sand shoals, which tend to shallow
with distance from the open Exuma Sound. Ball (1960) noted a
correlation of water depth, tidal current, and wave action with
sedimentary structures and bedforms.
Results indicate grain-size characteristics within these two shoals
are correlatable with water depth which is related to current
energy, and wave action. Samples from the inter-island areas of
the shoal have similar depositional energy characteristics and very
similar grain-size characteristics. Where there is a rapid change of
depth, the size characteristics also vary. The greatest size
parameter variations occur at areas of the shoal in less than 2 m of
water. Shallow locations such as the relatively flat spill-over lobe
sand-sheet have fine, well-sorted sands. Higher-energy shallow
deposits from spill-over lobe tributary channels and natural levee
areas have coarser, well-sorted positively-skewed sands.
Shape data of each sample also indicates that the differences in
samples are correlateable with depth of water. The inter-island
areas of the shoal with similar water depths have similar grain
shape characteristics. Variations occur either where depths vary
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
greatly over a short distance or in water depths of less than 2 m
(primarily the spill over lobe areas).
The degree of a grains roughness is the controlling factor in grain
shape. This is indicated by both FGSA analyses performed.
Roughness is controlled by the presence and extent of algal boring
on the outer surface of the grain. With the exception of grains with
fossil nuclei, differences in nuclear grain type do not appear to
significantly control differences in overall shape of the grains.
Thus, sample size and shape data indicate that both size and shape
sorting do occur within these sand shoals and that the size and
shape data are correlateable to one another. This sorting is most
pronounced in the areas of the shoal under less than 2 m of water.
Layering characteristics are also related to depth. The most
common ooid type (representing over 80% of grains throughout
both shoals) is the immature ooid containing one accreted layer
around the nuclei (over 90% peloid nuclei). The number of grains
per sample with more than one layer varies with depth. In general,
the further bankward the sample location, the lower the percentage
of grains with two or more layers.
The low percentage of mature grains across the shoal and the
reduction in more mature grains bankward are different than
observations made in other areas of the Bahamas, where ooids
become more mature with distance from the shelf break (Harris,
99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1977; Carney, 1990). This maturing is an indication that ooids are
migrating and maturing as they are transported bankward. Harris
also noted a much higher percentage of mature ooids (ooids with
more than 2 layers) at his location near Joulters Cay. The ooid
sands in the Exuma Cays area are less mature and experience a
decrease in maturity as one progresses bankward. This could be an
indication that ooid grains are: (1) not actively forming and are the
result of erosion of the Pleistocene sand dunes (the composition of
the islands and cays); or (2) forming at a much slower rate in the
Exuma Cays area. The presence of a higher concentration of more
mature ooids could be the result of active carbonate accretion
occuring in the deeper waters of the inter-island sand dunes.
The greatest concentration of ooids occur in the sand sheets created
by coalescing flood-tide dominated spill-over lobes, an indication
that sands are migrating bankwards. This slow bankward sand
migration can be verified in aerial photographs. Also, the spill-over
lobes on the oceanward end of the sand shoal are sediment-starved,
an indication that sands are not actively migrating towards the
shelf-break. With this evidence, one would expect an increase in
ooid maturity bankward, which is not occuring.
These results could also be an indication that the environmental
conditions (ie. availability of nuclei, current and wave energy, and
water chemistry) only allow young (low number of concentric
layers) to develop.
100
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Thus, variations in shape and size characteristics are controlling
factors in the location of different grain types within the ooid sand
shoal system.
Newell and others (1960) observed that ooids decrease in maturity
with distance from the 'oolitic ridge' (the area of less that 6 feet
water depth where ooids are forming) near Bimini. The Exuma
ooids show the opposite, an increase in grain maturity with depth.
The differences between Exuma ooids and those observed near
Joulters Cay and Bimini indicate that bahamian ooids internal
structures and size and shape distribution vary significantly with
location on the bank.
There do not appear to be obvious areas where ooids are forming,
migrating and maturing, and being deposited. This could be an
indication that ooids in this area are not actively forming and are
just being continually reworked and sorted as to their size and
degree of roughness.
101
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References
Aalto, K.R., and Dill, R.F., 1996, Late Pleistocene stratigraphy of a
carbonate platform margin, Exumas, Bahamas, volume 103,
number 1-2, p. 129.
Alder, H.L., and Roessler, E.B., 1977, Introduction to probability and
statistics: W.H. Freeman and Company, New York, 315 p.
Ball, M.M., 1967, Carbonate sand bodies of Florida and the Bahamas:
Journal of Sedimentary Petrology, volume 37, p. 556-591.
Bandat, J.S., and Piersol, A.G., 1971, Random data: Analysis and
measurement procedures: Wiley-Interscience Incorporated,
New York, 407 p.
Bathurst, R. G. C., 1966, Boring Algae, micrite envelopes and
lithification of Molluscan Biosparites: Geologic Journal,
number 5, p. 15-32.
Bathurst, R. G. C., 1975, Carbonate Sediments and Their Diagenesis,
Elsevier Scientific Publishing Company, New York, 658 p.
Bloomfield, P., 1976, Fourier analysis of time series: an
introduction: Wiley-Interscience Incorporated, New York,
258 p.
Boardman, M.R., and Carney, C., 1991, Origin and accumulation of
lime mud in ooid tidal channels, Bahamas: Journal of
Sedimentary Petrology, volume 61, p. 661-680.
Boggs, S., 1992, Petrology of Sedimentary Rocks: Macmillian
Publishing Company, New York, p. 707.
Brigham, E.O., 1974, The fast Fourier transform: Prentice-Hall,
Incorporated, Englewood Cliff, New Jersey, 252 p.
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Carney, C., 1990, A sedimentary model for the ooid shoal complex
at Joulters Cays, Bahamas; sources, sinks and transport;
Geological Society of America, Abstracts With Programs,
volume 22, p. 132.
Carozzi, 1960, Microscopic Sedimentary Petrography: John Wiley &
Sons, Inc., New York, p. 480
Choquette, P. W. and Pray, L. C., 1970, Geological Nomenclature and
Classification of Porosity in Sedimentary Carbonates; Bulletin
American Association Petroleum Geologists, volume 54,
p .207-250.
Davis, J.C., 1973, Statistics and data analysis in geology: John Wiley
& Sons Incorporated, New York, p 646.
Dill, R.F., and Steinen, R.P., 1988, Deposition of Carbonate mud beds
within high energy subtidal sanddunes, Bahamas: (abst.)
Bulletin of the American Association of Petroleum Geologists,
volume 72, no. 2, p. 178-179.
Dill, R.F., Kendall, G.St.C. C, and Steinen, R.P., 1989, Stromatolites,
ooid dunes, hardgrounds, and crusted mud beds, all products
of marine cementation and microbial mats in the subtidal
mixing zone on the eastern margin of the Great Bahama Bank:
(abst.) Bulletin of the American Association of Petroleum
Geologists, volume 73, p. 350.
Dill, R.F., 1991, Subtidal Stromatolites, Ooids and Crusted-Lime
Muds at the Great Bahama Bank Margin: in Osborne, R. H., ed.,
From Shoreline to Abyss, Contributions in Marine Geology in
Honor of Francis Park Shepard, SEPM Special Publication
Number 46, pp. 147-171.
Ehrlich, R., and Weinberg, B., 1970, An exact method for
characterization of grain shape: Journal of Sedimentary
Petrology, volume 40, p. 205-212.
103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Gaffey, S.J., 1983, Formation and infilling of pits in marine ooid
surfaces, Journal of Sedimentary Petrology, volume 53,
number 1, p.193-208.
Galehouse, J.S., 1971, Sieve analysis: in Carver, R. E., editor,
Procedure in Sedimentary Petrology: Wiley-Interscience,
New York, p. 49-68.
Ginsburg, R.N., 1957, Early diagenesis and lithification of shallow
water carbonate sediments in South Florida, in R J. LeBlanc
and J.G. Breeding (editors), Regional Aspects of Carbonate
Deposition: Society of Economic Paleontology, Special
Publication 5, p. 80-90.
Hailey, R.B., and Harris, P.M., 1979, Fresh Water Cementation of a
1000-Year-Old Oolite: Journal of Sedimentary Petrology, v.49,
p .969-988.
Harris, P.M., 1977, Sedimentology of the Joulters Cays Ooid Sand
Shoal, Great Bahama Bank: unpublished doctoral dissertation,
University of Miami, Coral Gables Florida, 451 p.
Hine, A.C., 1977, Lily Bank, Bahamas: History of an active oolite
sand shoal: Journal of Sedimentary Petrology, volume 47,
p. 1554-1581.
Hine, A.C., Wilbur, R.J., and Neumann, A.C., 1981, Carbonate Sand
Bodies Along Contrasting Shallow Bank Margins Facing Open
Seaways in Northern Bahamas: American Association of
Petroleum Geologists Bulletin, volume 65, number 2, p.261-
290.
Hine, A.C., Wilbur, R.J., Bane, J.M., Neumann, A.C., and Lorenson, K.R.,
1981a, Offbank transport of carbonate sands along open
Leeward Bank Margins: Northern Bahamas: Marine Geology,
volume 42, pp.327-348.
104
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Illing, L.V.,1954, Bahamian calcareous sands: American
Association Petroleum Geology Bulletin, volume 38, p. 1-95.
Imbrie, J. and Buchanan, H., 1965, Sedimentary structures in
modem carbonate sands of the Bahamas: in S.E.P.M. Special
Publication Number 12, pp. 149-172.
Ingram, R. L. 1971, Sieve analysis: in Carver, R. E., editor, Procedure
in Sedimentary Petrology, W iley-Interscience, New York,
p. 49- 68.
Kendall, C. G. St. C., Dill, R. F., and Shinn, E., 1990, Guidebook to the
Marine Geology and Tropical Environments of Lee Stocking
Island, The Southern Exumas, Bahamas: KenDill Publishers,
San Diego, California, 61 p.
Lang, J.C., Wicklund, R.I., and Dill, R.F., 1988, Depth and habitat-
related bleaching of reef corals near Lee Stocking Island,
Bahamas: Procedings of the Sixth International Coral Reef
Symposium, Australia, volume 3, p. 269-274.
McLaren, P., 1981, An interpretation of trends in Grain Size
Measures: Journal of Sedimentary Petrology, volume 51,
number 2, p.611-624.
Monty, C., 1967, Distribution and Structure of Recent Stromatolitic
Algal Mats, Eastern Andros Island, Bahamas; Ann. Soc. Geol.
Belg., Bulletin, volume 90, p. 55-100.
Newell, N.D., Purdy, E.G., and Imbrie, J., 1960, Bahamian oolitic sand:
Journal of Geology, volume 68, p. 481-497.
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Osborne, R.H. and Yeh C.C., 1991, Fourier grain-shape analysis of
coastal and inner continental- shelf sand samples: Oceanside
Littoral Cell, Southern Orange and San Diego Counties,
Southern California: in Osborne, R.H., editor, From Shoreline to
Abyss, Contributions in Marine Geology in Honor of Francis
Park Shepard: Society for Sedimentary Geology, Special
Publication Number 46, Tulsa, p.51-66.
Peryt, T. M., 1983, Classification of Coated Grains: in Peryt, T. M.,
editor, Coated Grains, Springer-Verlag, New York, p. 3-7.
Richter, D. K, 1983, Calcareous Ooids: A Synopsis: in Peryt, T. M.,
editor, Coated Grains, Springer-Verlag, New York, p. 71-100.
Robinson, R.A., 1993, Fourier grain-shape analysis of quartz sand
from the eastern and central Santa Barbara littoral call,
Southern California: unpublished doctoral dissertation,
University of Southern California, Los Angeles, California,
151 p.
Schwarcz, H.P., and Shane, R.C., 1969, Measurement of particle
shape by Fourier analysis: Sedimentology, volume 13, p. 213-
231.
Shinn, E.A., Steinen, R.P., Lidz, B.H., and Swart P.K., 1989, "Whitings",
a Sedimentologic Dilemma: Journal of Sedimantary Petrology,
v.59, p .147-161.
Simone, L., 1981, Ooids: A Review: Earth-Science Reviews, volume
16, p. 319-355.
Steinen, R.P., Swart, P.K., Shinn, E.A., and Lidz, B.H., 1988, Bahamian
lime mud: the algae didn't do it: Geological Society of America,
Abstracts With Programs, volume 20, no. 7, p. A209.
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDICES
107
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix A: Grain-Size Data
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
o
vo
SAMPLE 38 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)A 2 f(m - x)A 2 (m - x)A 3 f(m - x)A 3
0 -0.13 0.05 -0.01 -1.69 2.86 0.14 -4.84 -0.24
0 -0.25 0.13 0.14 0.02 -1.44 2.08 0.29 -3.00 -0.42
0.25 - 0.5 0.38 0.28 0.11 -1.19 1.42 0.40 -1.69 -0.47
0.5 - 0.75 0.63 0.37 0.23 -0.94 0.89 0.33 -0.83 -0.31
0.75 - 1 0.88 0.51 0.45 -0.69 0.48 0.24 -0.33 -0.17
1 - 1.25 1.13 0.48 0.54 -0.44 0.19 0.09 -0.09 -0.04
1.25 - 1.5 1.38 29.68 40.81 -0.19 0.04 1.09 -0.01 -0.21
1.5 - 1.75 1.63 57.77 93.88 0.06 0.00 0.20 0.00 0.01
1.75 - 2 1.88 8.99 16.86 0.31 0.10 0.86 0.03 0.26
2 - 2.25 2.13 1.44 3.06 0.56 0.31 0.45 0.17 0.25
2.25 - 2.5 2.38 0.30 0.71 0.81 0.65 0.20 0.53 0.16
2.5 - 2.75 2.63 0.00 0.00 1.06 1.12 0.00 1.19 0.00
2.75 - 3.0 2.88 0.00 0.00 1.31 1.71 0.00 2.24 0.00
3.0 - 3.25 3.13 0.00 0.00 1.56 2.43 0.00 3.79 0.00
3.25 - 3.5 3.38 0.00 0.00 1.81 3.27 0.00 5.92 0.00
3.5 - 3.75 3.63 0.00 0.00 2.06 4.24 0.00 8.72 0.00
3.75 - 4.0 3.88 0.00 0.00 2.31 5.33 0.00 12.30 0.00
Mean (x)= 1.57 Standard Deviation = 0.21 Skewness = -1.33
(0.37 mm)
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 39 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)A 2 f(m - x)A 2 (m - xJA 3 f(m - xJA 3
0 -0.13 0.00 0.00 -1.71 2.94 0.00 -5.04 0.00
0 -0.25 0.13 0.00 0.00 -1.46 2.14 0.00 -3.14 0.00
0.25 - 0.5 0.38 0.00 0.00 -1.21 1.47 0.00 -1.79 0.00
0.5 - 0.75 0.63 0.10 0.06 -0.96 0.93 0.09 -0.90 -0.09
0.75 - 1 0.88 0.15 0.13 -0.71 0.51 0.08 -0.36 -0.05
1 - 1.25 1.13 1.70 1.91 -0.46 0.22 0.37 -0.10 -0.17
1.25 - 1.5 1.38 24.50 33.69 -0.21 0.05 1.13
i i
o
o
-0.24
1.5 - 1.75 1.63 61.55 100.02 0.04 0.00 0.08 0.00 0.00
1 .7 5 -2 1.88 9.81 18.39 0.29 0.08 0.80 0.02 0.23
2 - 2.25 2.13 1.89 4.02 0.54 0.29 0.54 0.15 0.29
2.25 - 2.5 2.38 0.30 0.71 0.79 0.62 0.19 0.48 0.15
2.5 - 2.75 2.63 0.00 0.00 1.04 1.07 0.00 1.11 0.00
2.75 - 3.0 2.88 0.00 0.00 1.29 1.65 0.00 2.13 0.00
3.0 - 3.25 3.13 0.00 0.00 1.54 2.36 0.00 3.62 0.00
3.25 - 3.5 3.38 0.00 0.00 1.79 3.19 0.00 5.69 0.00
3.5 - 3.75 3.63 0.00 0.00 2.04 4.14 0.00 8.44 0.00
3.75 - 4.0 3.88 0.00 0.00 2.29 5.22 0.00 11.94 0.00
Mean (x)= 1.59 Standard Deviation = 0.18 Skewness = 0.19
(0.33 mm)
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 40 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f tm m - x (m - x)A 2 f(m - x)A 2 (m - xJA 3 f(m - xJA 3
0 -0.13 0.00 0.00 -1.95 3.79 0.00 -7.38 0.00
0 -0.25 0.13 0.00 0.00 -1.70 2.88 0.00 -4.89 0.00
0.25 - 0.5 0.38 0.00 0.00 -1.45 2.09 0.00 -3.03 0.00
0.5 - 0.75 0.63 0.00 0.00 -1.20 1.43 0.00 -1.72 0.00
0.75 - 1 0.88 0.00 0.00 -0.95 0.90 0.00 -0.85 0.00
1 - 1.25 1.13 0.05 0.06 -0.70 0.49 0.02 -0.34 -0.02
1.25 - 1.5 1.38 1.01 1.39 -0.45 0.20 0.20 -0.09 -0.09
1.5 - 1.75 1.63 42.76 69.49 -0.20 0.04 1.67 -0.01 -0.33
1 .7 5 -2 1.88 38.53 72.24 0.05 0.00 0.11 0.00 0.01
2 - 2.25 2.13 11.72 24.91 0.30 0.09 1.07 0.03 0.32
2.25 - 2.5 2.38 5.63 13.37 0.55 0.31 1.72 0.17 0.95
2.5 - 2.75 2.63 0.30 0.79 0.80 0.64 0.19 0.52 0.16
2.75 - 3.0 2.88 0.00 0.00 1.05 1.11 0.00 1.17 0.00
3.0 - 3.25 3.13 0.00 0.00 1.30 1.70 0.00 2.21 0.00
3.25 - 3.5 3.38 0.00 0.00 1.55 2.41 0.00 3.74 0.00
3.5 - 3.75 L 3.63 0.00 0.00 1.80 3.25 0.00 5.86 0.00
3.75 - 4.0 3.88 0.00 0.00 2.05 4.21 0.00 8.65 0.00
Mean (x)= 1.82 Standard Deviation = 0.22 Skewness = 0.90
(0.28 mm)
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
to
SAMPLE 41 SIZE DATA
Phi Size
Interval Midpoint
Weight
Percent Product
Deviation from
Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xjA 2 f(m - x)A 2 (m - xjA 3 f(m - x)*3
0 -0.13 0.00 0.00 -1.93 3.71 0.00 -7.16 0.00
0 -0.25 0.13 0.00 0.00 -1.68 2.81 0.00 -4.72 0.00
0.25 - 0.5 0.38 0.00 0.00 -1.43 2.04 0.00 -2.91 0.00
0.5 - 0.75 0.63 0.00 0.00 -1.18 1.39 0.00 -1.63 0.00
0.75 - 1 0.88 0.05 0.04 -0.93 0.86 0.04 -0.80 -0.04
1 - 1.25 1.13 0.05 0.06 -0.68 0.46 0.02 -0.31 -0.02
1.25 - 1.5 1.38 1.57 2.16 -0.43 0.18 0.29 -0.08 -0.12
1.5 - 1.75 1.63 45.74 74.33 -0.18 0.03 1.44 -0.01 -0.26
1.75 - 2 1.88 37.98 71.21 0.07 0.01 0.20 0.00 0.01
2 - 2.25 2.13 9.42 20.02 0.32 0.10 0.98 0.03 0.32
2.25 - 2.5 2.38 4.90 11.64 0.57 0.33 1.61 0.19 0.92
2.5 - 2.75 2.63 0.30 0.79 0.82 0.68 0.20 0.56 0.17
2.75 - 3.0 2.88 0.00 0.00 1.07 1.15 0.00 1.23 0.00
3.0 - 3.25 3.13 0.00 0.00 1.32 1.75 0.00 2.31 0.00
3.25 - 3.5 3.38 0.00 0.00 1.57 2.47 0.00 3.89 0.00
3.5 - 3.75 3.63 0.00 0.00 1.62 3.32 0.00 6.05 0.00
3.75 - 4.0 3.88 0.00 0.00 2.07 4.30 0.00 8.90 0.00
Mean (x)= 1.80 Standard Dev)ation= 0.22 Skewness= 0.94
(0.29 mm)
Product
r—
co
<
£
-1.95 I
-0.65
o
C O
d
t -0.32 I
-0.13 I
-0.18 j
-0.22 1
| 0 0 0
! 0.32 |
G O
C O
d 0.25 I
C O
o
d
| 0 0 0
| 0 0 0
o
o
o
| 0 0 0
| 0 0 0
C O
o>
•
Deviation
Cubed
co
<
1
,5
-5 .0 0
-3.11
-1 .7 7
o>
C O
d
C O
C O
o
o
d
o
d
0.00 I
0 .0 2
0 .1 6
0 .4 9
C M
2 .1 4
3 .6 5
5 .7 3
G O
G O
1 2 .0 0
Skewness=
Product
C M
<
"J
1
E
Tf
V ”
0.45 J
0 9 0
0.33 J
0 .1 9
6 9 0
1 .05
60 0 |
o
d 0.31
9 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 .0 0
0 . 2 5
Deviation
Squared
C M
<
i
£
2 .9 3
2 .1 3
1.47
0 .9 2
0 9 0
C M
o
o
o
0 0 0
8 0 0
o>
C M
d 0 .6 2
00
o
C O
C O
2.37 I
o
C M
C O
co
5 .2 4
Standard Deviation^
Deviation
fro m Mean
X - HI
-1.71
-1.46
-1.21
-0.96 |
-0.71
C O
d
C M
d
0 .0 4
0 .2 9
0 .5 4
0 .7 9
1.04
1 .29
1.54
1 .7 9
2 .0 4
2 .2 9
(0.33 m m )
Product
E
soo-
co
o
d
C O
d 0.23 |
0 .3 2
2 .0 5
3 2 .6 6
9 1 .9 6
G O
C M
5 .1 0
1 .19
0 .1 3
0 0 0
0 0 0
0 0 0
0 0 0
o
o
o 1.59
SAMPLE 4 2 SIZ E DATA
Weight
Percent
0 .3 9
0.21
0.34
0 .3 6
0 .3 7
C M
G O
2 3 .7 5
5 6 .5 9
13.23
2 .4 0
0 .5 0
9 0 0
0 0 0
0.00
0 0 0
0 0 0
0 0 0
M ean (x)=
I Midpoint
S
| -0.13
C O
d 0 .3 8
I 0 .6 3
G O
00
o
C O
T “
G O
C O
1.63
1.88
2 .1 3
2 .3 8
CO
CO
C M 2 .8 8
C O
C O
G O
C O
C O 3 .6 3
3 .8 8
Phi Size
Interval
p h i
o
0 -0.25
| 0.25 - 0.5
| 0.5 - 0.75
| 0.75 - 1 j
lO
C M
Y —
| 1.25 - 1.5 I
I 1.5 - 1.75
| 1.75 - 2
m
C M
C M
«
C M
| 2.25 - 2.5 I
| 2.5 - 2.75
| 2.75 - 3.0
I 3.0 - 3.25
3.25 - 3.5
| 3.5 - 3.75
| 3.75 - 4.0
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 43 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)*2 f(m - x)s2 (m - x)A 3 f(m - x)A 3
0 -0.13 0.16 -0.02 -1.80 3.24 0.52 -5.84 -0.93
0 -0.25 0.13 0.10 0.01 -1.55 2.41 0.24 -3.73 -0.37
0.25 - 0.5 0.38 0.20 0.08 -1.30 1.69 0.34 -2.20 -0.44
0.5 - 0.75 0.63 0.21 0.13 -1.05 1.10 0.23 -1.16 -0.24
0.75 - 1 0.88 0.26 0.23 -0.80 0.64 0.17 -0.51 -0.13
1 - 1.25 1.13 1.48 1.67 -0.55 0.30 0.45 -0.17 -0.25
1.25 - 1.5 1.38 14.52 19.97 -0.30 0.09 1.32 -0.03 -0.40
1.5 - 1.75 1.63 52.50 85.31 -0.05 0.00 0.14 0.00 -0.01
1.75 - 2 1.88 21.87 41.01 0.20 0.04 0.86 0.01 0.17
2 - 2.25 2.13 5.68 12.07 0.45 0.20 1.14 0.09 0.51
2.25 - 2.5 2.38 2.91 6.91 0.70 0.49 1.42 0.34 0.99
2.5 - 2.75 2.63 0.10 0.26 0.95 0.90 0.09 0.85 0.09
2.75 - 3.0 2.88 0.00 0.00 1.20 1.44 0.00 1.72 0.00
3.0 - 3.25 3.13 0.00 0.00 1.45 2.10 0.00 3.04 0.00
3.25 - 3.5 3.38 0.00 0.00 1.70 2.89 0.00 4.90 0.00
3.5 - 3.75 3.63 0.00 0.00 1.95 3.80 0.00 7.40 0.00
3.75 - 4.0 3.88 0.00 0.00 2.20 4.83 0.00 10.63 0.00
Mean (x)= 1.68 Standard Deviation= 0.26 Skewness= -0.56
(0.31 mm)
Product
f ( m - x j* 3 j
1 0 0 0
-0.30 1
-0.25 1
I -0.15 I
-0.09
-0.19
-0.23
I to o
i 0.27
I lfr-0
0.40 |
o
d 0.04 I
| 0 0 0
o
o
d
| 0 0 0
o
o
d
o
d
■
Deviation
Cubed
C O
<
•
£
G O
■ M *
1
O
o
C O
•
a >
C O
1
C O
d
C O
C O
d
■
o >
o
d
•
T " “
o
d
■
o
o
d
C D
O
d 0.17
C O
in
d
G O T f
C M
C M
C O
t* -
C D
0 5
in
C M
N -
0 0
12.30
I I
«
«
o
c
*
0)
Product
C \ J
<
1
o
o
o
C M
d
C M
d
C O
d
C M
d
C O
d
0 5 G O
T —
o 0.87
C D
K
o 0.49
C O
o
d
C O
o
d
o
o
d
o
o
d
o
o
o
o
o
d
C M
C M
o
Deviation
Squared
c v i
<
1
£
2.86
C O
o
c \j
C M
* *
T * *
o >
G O
d
0 0
d
o
C M
d
• M *
O
d
0 0 0
6 0 0
.—
C D
d
in
C O
d
C M▼ —C D
T T
c v i 3.27
M -
C M
C O
C O
in
Standard Deviations
Deviation
fro m Mean
X
•
s
0 5
C O
•
o >
*
o >
d
•
o >
C O
d d
i
o >
d
t
9 0 0
T —
co
o
C O
1 0
d
V " *
G O
d
C O
© C O
C O
1 0 G O
T “ 2.06
C O
C M
Product
£
O
O
d
o
o
9 0 0
d
C O
C M
d
to
C M
44.50
85.25
17.18
4.99
0 0
T “
8 0 0
C O
o
d
0 0 0
0 0 0
o
o
d
0 0 0
N -
in
(0.34 mm]
SAMPLE 4 4 S IZ E DATA
Weight
Percent
o
o
o
o
d
to
d
0 0
d
C O
C M
d
C O
C M
C O
C O
C M
C O 52.46
9.16
in
C O
c m ’
in
N *
o
C O
o
o
C M
o
d
o
o
d
o
o
o
o
o
o
O
O
d
(le a n (x)=
Midpoint
s
C O
d
i
C O
d
G O
C O
d
co
C O
d
G O
C O
d
C O
▼ —
G O
C O
C O
C O
o o
0 0
.—
C O
v —
C M
G O
C O
c m ’
C O
C O
c m ’
0 0
o o
c m ’
C O
co
0 0
C O
C O
C O
CD
C O
0 0
C O
C O
Phi Scale
Interval
s
Q .
o
0 -0.25
| 0.25 - 0.5
| 0 .5 - 0.75
1
lO
r^
o
C M
1.25 - 1.5
| 1 .5 - 1.75
| 1.75 - 2
| 2 - 2.25
| 2.25 - 2.5
1 2 .5 - 2.75
| 2.75 - 3.0
1 3 .0 - 3.25
3.25 - 3.5
| 3 .5 - 3.75
I 3.75 - 4.0
1 15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
Os
SAMPLE 45 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)*2 f(m - x;a2 (m - x;A 3
8
0 -0.13 0.10 -0.01 -1.65 2.71 0.27 -4.46 -0.45
0 -0.25 0.13 0.10 0.01 -1.40 1.95 0.19 -2.72 -0.27
0.25 - 0.5 0.38 0.31 0.12 -1.15 1.31 0.41 -1.50 -0.47
0.5 - 0.75 0.63 0.41 0.26 -0.90 0.80 0.33 -0.72 -0.29
0.75 - 1 0.88 0.68 0.60 -0.65 0.42 0.28 -0.27 -0.18
1 - 1.25 1.13 3.84 4.32 -0.40 0.16 0.60 -0.06 -0.24
1.25 - 1.5 1.38 39.19 53.89 -0.15 0.02 0.83 0.00 -0.12
1.5 - 1.75 1.63 46.20 75.08 0.10 0.01 0.50 0.00 0.05
1.75 - 2 1.88 7.05 13.22 0.35 0.13 0.88 0.04 0.31
2 - 2.25 2.13 1.64 3.49 0.60 0.37 0.60 0.22 0.36
2.25 - 2.5 2.38 0.45 1.07 0.85 0.73 0.33 0.62 0.28
2.5 - 2.75 2.63 0.02 0.05 1.10 1.22 0.02 1.35 0.03
2.75 - 3.0 2.88 0.00 0.00 1.35 1.83 0.00 2.48 0.00
3.0 - 3.25 3.13 0.00 0.00 1.60 2.57 0.00 4.13 0.00
3.25 - 3.5 3.38 0.00 0.00 1.85 3.44 0.00 6.38 0.00
3.5 - 3.75 3.63 0.00 0.00 2.10 4.43 0.00 9.32 0.00
3.75 - 4.0 3.88 0.00 0.00 2.35 5.54 0.00 13.05 0.00
Mean (x)= 1.52 Standard Deviation= 0.23 Skewness= -0.82
(0.35 mm)
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 46 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xJA 2 f(m - x;*2 (m - x)A 3 f(m - x)A 3
0 -0.13 0.20 -0.03 -1.82 3.32 0.66 -6.05 -1.21
0 -0.25 0.13 0.15 0.02 -1.57 2.47 0.37 -3.88 -0.58
0.25 - 0.5 0.38 0.25 0.09 -1.32 1.75 0.44 -2.31 -0.58
0.5 - 0.75 0.63 0.31 0.19 -1.07 1.15 0.36 -1.23 -0.38
0.75 - 1 0.88 0.31 0.27 -0.82 0.68 0.21 -0.56 -0.17
1 - 1.25 1.13 1.57 1.77 -0.57 0.33 0.51 -0.19 -0.29
1.25 - 1.5 1.38 16.56 22.77 -0.32 0.10 1.72 -0.03 -0.55
1.5 - 1.75 1.63 46.25 75.16 -0.07 0.01 0.24 0.00 -0.02
1.75 - 2 1.88 21.29 39.92 0.18 0.03 0.68 0.01 0.12
2 - 2.25 2.13 6.91 14.68 0.43 0.18 1.27 0.08 0.54
2.25 - 2.5 2.38 5.72 13.59 0.68 0.46 2.63 0.31 1.78
2.5 - 2.75 2.63 0.48 1.26 0.93 0.86 0.41 0.80 0.38
2.75 - 3.0 2.88 0.00 0.00 1.18 1.39 0.00 1.64 0.00
3.0 - 3.25 3.13 0.00 0.00 1.43 2.04 0.00 2.91 0.00
3.25 - 3.5 3.38 0.00 0.00 1.68 2.82 0.00 4.73 0.00
3.5 - 3.75 3.63 0.00 0.00 1.93 3.72 0.00 7.17 0.00
3.75 - 4.0 3.88 0.00 0.00 2.18 4.74 0.00 10.33 0.00
Mean (x)= 1.70 Standard Deviation= 0.31 Skewness= -0.33
(0.31 mm)
Reproduced w ith permission o f the copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 47 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x ; a 2
CM
<
•
E E
(m - x)n 3 f(m - x)A 3
0 -0.13 0.80
i
o
©
-1.93 3.71 2.97 -7.14 -5.71
0 -0.25 0.13 0.36 0.05 -1.68 2.81 1.01 -4.71 -1.69
0.25 - 0.5 0.38 0.72 0.27
CO
1
2.03 1.46 -2.90 -2.09
0.5 - 0.75 0.63 0.82 0.51 -1.18 1.38 1.13
i
CO
CO
▼ —
•
-1.33
0.75 - 1 0.88 1.00 0.88 -0.93 0.86 0.86 -0.79 -0.79
1 - 1.25 1.13 3.00 3.38 -0.68 0.46 1.37 -0.31 -0.93
1.25 - 1.5 1.38 14.34 19.72 -0.43 0.18 2.60 -0.08 -1.11
1.5 - 1.75 1.63 27.38 44.49 -0.18 0.03 0.85 -0.01 -0.15
1.75 - 2 1.88 19.64 36.83 0.07 0.01 0.11 0.00 0.01
2 - 2.25 2.13 11.37 24.16 0.32 0.11 1.20 0.03 0.39
2.25 - 2.5 2.38 17.36 41.23 0.57 0.33 5.72 0.19 3.29
2.5 - 2.75 2.63 2.45 6.43 0.82 0.68 1.66 0.56 1.37
2.75 - 3.0 2.88 0.67 1.93 1.07 1.15 0.77 1.24 0.83
3.0 - 3.25 3.13 0.10 0.31 1.32 1.75 0.18 2.32 0.23
3.25 - 3.5 3.38 0.00 0.00 1.57 2.48 0.00 3.90 0.00
3.5 - 3.75 3.63 0.00 0.00 1.82 3.33 0.00 6.07 0.00
3.75 - 4.0 3.88 0.00 0.00 2.07 4.30 0.00 8.92 0.00
Mean (x)= 1.80 Standard Deviations 0.47 Skewness= -0.75
(0.29 mm)
o o
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 48 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)A 2 f(m - x)A 2 (m - x)A 3 f(m - x)A 3'.
0 -0.13 1.63 -0.20 -1.38 1.91 3.11 -2.64 -4.30
0 -0.25 0.13 1.50 0.19 -1.13 1.28 1.92 -1.45 -2.17
0.25 - 0.5 0.38 4.30 1.61 -0.88 0.78 3.34 -0.68 -2.94
0.5 - 0.75 0.63 5.38 3.36 -0.63 0.40 2.14 -0.25 -1.35
0.75 - 1 0.88 4.51 3.95 -0.38 0.15 0.66 -0.06 -0.25
1 - 1.25 1.13 18.72 21.06 -0.13 0.02 0.32 0.00 -0.04
1.25 - 1.5 1.38 40.32 55.44 0.12 0.01 0.57 0.00 0.07
1.5 - 1.75 1.63 18.34 29.80 0.37 0.14 2.49 0.05 0.92
1.75 - 2 1.88 3.71 6.96 0.62 0.38 1.42 0.24 0.88
2 - 2.25 2.13 1.15 2.44 0.87 0.75 0.87 0.66 0.75
2.25 - 2.5 2.38 0.43 1.02 1.12 1.25 0.54 1.40 0.60
2.5 - 2.75 2.63 0.00 0.00 1.37 1.87 0.00 2.56 0.00
2.75 - 3.0 2.88 0.00 0.00 1.62 2.62 0.00 4.24 0.00
3.0 - 3.25 3.13 0.00 0.00 1.87 3.49 0.00 6.53 0.00
3.25 - 3.5 3.38 0.00 0.00 2.12 4.49 0.00 9.51 0.00
3.5 - 3.75 3.63 0.00 0.00 2.37 5.61 0.00 13.29 0.00
3.75 - 4.0 3.88 0.00 0.00 2.62 6.86 0.00 17.96 0.00
Mean (x)= 1.26 Standard Deviations 0.42 Skewness= -1.08
(0.42 mm)
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
to
o
SAMPLE 50 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xJA 2 f(m - xjA 2 (m - x;f t3 f(m - x^A 3
0 -0.13 59.09 -7.39 -0.24 0.06 3.44 -0.01 -0.83
0 -0.25 0.13 14.50 1.81 0.01 0.00 0.00 0.00 0.00
0.25 - 0.5 0.38 12.42 4.66 0.26 0.07 0.83 0.02 0.22
0.5 • 0.75 0.63 5.73 3.58 0.51 0.26 1.48 0.13 0.75
0.75 • 1 0.88 2.81 2.46 0.76 0.58 1.62 0.44 1.23
1 - 1.25 1.13 4.17 4.69 1.01 1.02 4.24 1.03 4.28
1.25 - 1.5 1.38 1.14 1.57 1.26 1.58 1.81 1.99 2.27
1.5 - 1.75 1.63 0.15 0.24 1.51 2.28 0.34 3.43 0.52
1.75 • 2 1.88 0.00 0.00 1.76 3.09 0.00 5.44 0.00
2 - 2.25 2.13 0.00 0.00 2.01 4.04 0.00 8.11 0.00
2.25 - 2.5 2.38 0.00 0.00 2.26 5.10 0.00 11.52 0.00
2.5 • 2.75 2.63 0.00 0.00 2.51 6.29 0.00 15.79 0.00
2.75 - 3.0 2.88 0.00 0.00 2.76 7.61 0.00 21.00 0.00
3.0 - 3.25 3.13 0.00 0.00 3.01 9.05 0.00 27.24 0.00
3.25 - 3.5 3.38 0.00 0.00 3.26 10.62 0.00 34.61 0.00
3.5 - 3.75 3.63 0.00 0.00 3.51 12.31 0.00 43.20 0.00
3.75 - 4.0 3.88 0.00 0.00 3.76 14.13 0.00 53.10 0.00
Mean (x)= 0.12 Standard Deviation^ 0.37 Skewness= 1.65
(0.92 mm
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 51 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xJA 2 3
l
>
N )
(m - x)A 3 f(m - xjA 3
0 -0.13 4.76 -0.60 -1.69 2.85 13.58 -4.82 -22.93
0 -0.25 0.13 1.42 0.18 -1.44 2.07 2.94 -2.98 -4.23
0.25 - 0.5 0.38 2.01 0.75 -1.19 1.41 2.84 -1.68 -3.38
0.5 - 0.75 0.63 1.73 1.08 -0.94 0.88 1.53 -0.83 -1.43
0.75 - 1 0.88 1.94 1.70 -0.69 0.47 0.92 -0.33 -0.63
1-1.25 1.13 6.81 7.66 -0.44 0.19 1.31 -0.08 -0.58
1.25 - 1.5 1.38 15.24 20.96 -0.19 0.04 0.54 -0.01 -0.10
1.5 - 1.75 1.63 25.11 40.80 0.06 0.00 0.09 0.00 0.01
1.75 - 2 1.88 22.80 42.75 0.31 0.10 2.21 0.03 0.69
2 - 2.25 2.13 9.30 19.76 0.56 0.31 2.93 0.18 1.64
2.25 - 2.5 2.38 7.90 18.76 0.81 0.66 5.20 0.53 4.21
2.5 - 2.75 2.63 0.91 2.39 1.06 1.13 1.02 1.19 1.09
2.75 - 3.0 2.88 0.07 0.20 1.31 1.72 0.12 2.25 0.16
3.0 - 3.25 3.13 0.00 0.00 1.56 2.44 0.00 3.80 0.00
3.25 - 3.5 3.38 0.00 0.00 1.81 3.28 0.00 5.94 0.00
3.5 - 3.75 3.63 0.00 0.00 2.06 4.25 0.00 8.75 0.00
3.75 - 4.0 3.88 0.00 0.00 2.31 5.34 0.00 12.34 0.00
Mean (x)= 1.56 Standard Deviation= 0.59 Skewness= -1.22
(0.34 mm
to
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 52 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xJA 2 f(m - xJA 2
?
•
>
CO
f(m - x ;a3
0 -0.13 3.37 -0.42 -1.29 1.66 5.58 -2.13 -7.18
0 -0.25 0.13 2.14 0.27 -1.04 1.07 2.30 -1.11 -2.38
0.25 - 0.5 0.38 4.53 1.70 -0.79 0.62 2.80 -0.49 -2.21
0.5 - 0.75 0.63 5.94 3.71 -0.54 0.29 1.71 -0.15 -0.92
0.75 - 1 0.88 5.97 5.22 -0.29 0.08 0.49 -0.02 -0.14
1 - 1.25 1.13 27.64 31.10 -0.04 0.00 0.04 0.00 0.00
1.25 - 1.5 1.38 33.65 46.27 0.21 0.05 1.53 0.01 0.33
1.5 - 1.75 1.63 13.15 21.37 0.46 0.21 2.82 0.10 1.31
1.75 - 2 1.88 2.96 5.55 0.71 0.51 1.51 0.36 1.07
2 - 2.25 2.13 0.66 1.40 0.96 0.93 0.61 0.89 0.59
2.25 - 2.5 2.38 0.00 0.00 1.21 1.47 0.00 1.79 0.00
2.5 - 2.75 2.63 0.00 0.00 1.46 2.14 0.00 3.13 0.00
2.75 - 3.0 2.88 0.00 0.00 1.71 2.94 0.00 5.03 0.00
3.0 - 3.25 3.13 0.00 0.00 1.96 3.85 0.00 7.57 0.00
3.25 - 3.5 3.38 0.00 0.00 2.21 4.90 0.00 10.84 0.00
3.5 - 3.75 3.63 0.00 0.00 2.46 6.07 0.00 14.95 0.00
3.75 - 4.0 3.88 0.00 0.00 2.71 7.36 0.00 19.98 0.00
Mean (x) = 1.16 Standard Deviation= 0.44 Skewness= -1.12
(0.45 mm
t o
t o
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
t o
u >
SAMPLE 53 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xjA 2 f(m - x;A 2
i
>
CO
f(m - x /3
0 -0.13 0.00 0.00 -2.28 5.18 0.00 -11.79 0.00
0 -0.25 0.13 0.00 0.00 -2.03 4.10 0.00 -8.31 0.00
0.25 - 0.5 0.38 0.20 0.08 -1.78 3.15 0.63 -5.60 -1.12
0.5 - 0.75 0.63 0.14 0.09 -1.53 2.33 0.33 -3.55 -0.50
0.75 - 1 0.88 0.10 0.09 -1.28 1.63 0.16 -2.08 -0.21
1 - 1.25 1.13 0.17 0.19 -1.03 1.05 0.18 -1.08 -0.18
1.25 - 1.5 1.38 0.42 0.58 -0.78 0.60 0.25 -0.47 -0.20
1.5 - 1.75 1.63 5.00 8.13 -0.53 0.28 1.38 -0.15 -0.73
1.75 - 2 1.88 24.36 45.68 -0.28 0.08 1.85 -0.02 -0.51
2 - 2.25 2.13 27.83 59.14 -0.03 0.00 0.02 0.00 0.00
2.25 - 2.5 2.38 35.77 84.95 0.22 0.05 1.80 0.01 0.40
2.5 - 2.75 2.63 4.50 11.81 0.47 0.22 1.01 0.11 0.48
2.75 - 3.0 2.88 1.41 4.05 0.72 0.52 0.74 0.38 0.54
3.0 - 3.25 3.13 0.10 0.31 0.97 0.95 0.09 0.92 0.09
3.25 - 3.5 3.38 0.00 0.00 1.22 1.50 0.00 1.83 0.00
3.5 - 3.75 3.63 0.00 0.00 1.47 2.17 0.00 3.20 0.00
3.75 - 4.0 3.88 0.00 0.00 1.72 2.97 0.00 5.12 0.00
I Iean (x)= 2.15 Standard Deviation^ 0.29 Skewness= -0.79
(0.23 mm
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 54 SIZE DATA
Phi Scale
Interval Midpoint
weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xJA 2 f(m - x)*2
I
co
<
t
,5
f(m - x;*3
0 -0.13 2.50 -0.31 -1.80 3.24 8.10 -5.84 -14.59
0 -0.25 0.13 1.00 0.13 -1.55 2.40 2.40 -3.73 -3.73
0.25 - 0.5 0.38 1.71 0.64 -1.30 1.69 2.89 -2.20 -3.76
0.5 - 0.75 0.63 1.77 1.11 -1.05 1.10 1.95 -1.16 -2.05
0.75 - 1 0.88 1.87 1.64 -0.80 0.64 1.20 -0.51 -0.96
1 - 1.25 1.13 7.51 8.45 -0.55 0.30 2.28 -0.17 -1.25
1.25 - 1.5 1.38 15.23 20.94 -0.30 0.09 1.38 -0.03 -0.41
1.5 - 1.75 1.63 20.71 33.65 -0.05 0.00 0.05 0.00 0.00
1.75 - 2 1.88 20.16 37.80 0.20 0.04 0.80 0.01 0.16
2 - 2.25 2.13 11.34 24.10 0.45 0.20 2.29 0.09 1.03
2.25 - 2.5 2.38 13.02 30.92 0.70 0.49 6.37 0.34 4.46
2.5 - 2.75 2.63 2.37 6.22 0.95 0.90 2.14 0.86 2.03
2.75 - 3.0 2.88 0.68 1.96 1.20 1.44 0.98 1.73 1.17
3.0 - 3.25 3.13 0.10 0.31 1.45 2.10 0.21 3.05 0.30
3.25 - 3.5 3.38 0.00 0.00 1.70 2.89 0.00 4.91 0.00
3.5 - 3.75 3.63 0.00 0.00 1.95 3.80 0.00 7.41 0.00
3.75 - 4.0 3.88 0.00 0.00 2.20 4.84 0.00 10.64 0.00
Mean (x)= 1.68 Standard Deviation= 0.57 Skewness=> -0.93
(0.31 mm
N )
Reproduced w ith permission o f the copyright owner. Further reproduction prohibited without perm ission.
t o
U \
SAMPLE 55 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)r '2 f(m - xJA 2 (m - xJA 3 f(m - xJA 3
0 -0.13 1.55 -0.19 -1.64 2.69 4.17 -4.42 -6.85
0 -0.25 0.13 1.01 0.13 -1.39 1.94 1.95 -2.69 -2.72
0.25 - 0.5 0.38 1.93 0.72 -1.14 1.30 2.51 -1.49 -2.87
0.5 - 0.75 0.63 2.09 1.31 -0.89 0.79 1.66 -0.71 -1.48
0.75 - 1 0.88 2.03 1.78 -0.64 0.41 0.83 -0.26 -0.53
1 - 1.25 1.13 11.31 12.72 -0.39 0.15 1.73 -0.06 -0.68
1.25 - 1.5 1.38 29.31 40.30 -0.14 0.02 0.58 0.00 -0.08
1.5 - 1.75 1.63 30.13 48.96 0.11 0.01 0.36 0.00 0.04
1.75 - 2 1.88 10.37 19.44 0.36 0.13 1.34 0.05 0.48
2 - 2.25 2.13 2.75 5.84 0.61 0.37 1.02 0.23 0.62
2.25 - 2.5 2.38 2.13 5.06 0.86 0.74 1.57 0.63 1.35
2.5 - 2.75 2.63 2.16 5.67 1.11 1.23 2.66 1.36 2.95
2.75 - 3.0 2.88 1.93 5.55 1.36 1.85 3.56 2.51 4.84
3.0 - 3.25 3.13 0.75 2.34 1.61 2.59 1.94 4.16 3.12
3.25 - 3.5 3.38 0.21 0.71 1.86 3.46 0.73 6.42 1.35
3.5 - 3.75 3.63 0.35 1.27 2.11 4.45 1.56 9.38 3.28
3.75 - 4.0 3.88 0.00 0.00 2.36 5.56 0.00 13.13 0.00
Mean (x)= 1.52 Standard Deviation= 0.53 Skewness 0.19
(0.35 mm
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 56 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)*2
C V J
<
1
s
i
>
C o
f(m - xJA 3
0 -0.13 2.37 -0.30 -1.58 2.49 5.91 -3.94 -9.34
0 -0.25 0.13 1.71 0.21 -1.33 1.77 3.02 -2.35 -4.02
0.25 - 0.5 0.38 3.35 1.26 -1.08 1.16 3.90 -1.26 -4.21
0.5 - 0.75 0.63 3.57 2.23 -0.83 0.69 2.46 -0.57 -2.04
0.75 - 1 0.88 3.14 2.75 -0.58 0.34 1.05 -0.19 -0.61
1 - 1.25 1.13 13.29 14.95 -0.33 0.11 1.44 -0.04 -0.47
1.25 - 1.5 1.38 22.94 31.54 -0.08 0.01 0.14 0.00 -0.01
1.5 - 1.75 1.63 21.75 35.34 0.17 0.03 0.63 0.00 0.11
1.75 - 2 1.88 14.57 27.32 0.42 0.18 2.58 0.07 1.08
2 - 2.25 2.13 7.14 15.17 0.67 0.45 3.21 0.30 2.15
2.25 - 2.5 2.38 5.31 12.61 0.92 0.85 4.50 0.78 4.14
2.5 - 2.75 2.63 0.66 1.73 1.17 1.37 0.90 1.60 1.06
2.75 - 3.0 2.88 0.21 0.60 1.42 2.02 0.42 2.87 0.60
3.0 - 3.25 3.13 0.00 0.00 1.67 2.79 0.00 4.66 0.00
3.25 - 3.5 3.38 0.00 0.00 1.92 3.69 0.00 7.09 0.00
3.5 - 3.75 3.63 0.00 0.00 2.17 4.71 0.00 10.23 0.00
3.75 - 4.0 3.88 0.00 0.00 2.42 5.86 0.00 14.19 0.00
Mean (x)= 1.45 Standard deviations 0.55 Skewness -0.70
(0.37 mm
t o
O n
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 57 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)*2 f(m - x)A 2 (m - x)*3 f(m - xJA 3
0 -0.13 0.10 -0.01 -1.42 2.00 0.20 -2.83 -0.28
0 -0.25 0.13 0.29 0.04 -1.17 1.36 0.39 -1.58 -0.46
0.25 - 0.5 0.38 1.47 0.55 -0.92 0.84 1.23 -0.77 -1.13
0.5 - 0.75 0.63 3.32 2.08 -0.67 0.44 1.47 -0.29 -0.98
0.75 - 1 0.88 4.55 3.98 -0.42 0.17 0.78 -0.07 -0.33
1 - 1.25 1.13 31.24 35.15 -0.17 0.03 0.85 0.00 -0.14
1.25 - 1.5 1.38 40.77 56.06 0.08 0.01 0.29 0.00 0.02
1.5 - 1.75 1.63 13.87 22.54 0.33 0.11 1.55 0.04 0.52
1.75 - 2 1.88 3.18 5.96 0.58 0.34 1.09 0.20 0.64
2 - 2.25 2.13 0.77 1.64 0.83 0.70 0.54 0.58 0.45
2.25 - 2.5 2.38 0.44 1.05 1.08 1.18 0.52 1.28 0.56
2.5 - 2.75 2.63 0.00 0.00 1.33 1.78 0.00 2.38 0.00
2.75 - 3.0 2.88 0.00 0.00 1.58 2.51 0.00 3.98 0.00
3.0 - 3.25 3.13 0.00 0.00 1.83 3.37 0.00 6.18 0.00
3.25 - 3.5 3.38 0.00 0.00 2.08 4.35 0.00 9.06 0.00
3.5 - 3.75 3.63 0.00 0.00 2.33 5.45 0.00 12.73 0.00
3.75 - 4.0 3.88 0.00 0.00 2.58 6.68 0.00 17.27 0.00
Mean (x)= 1.29 Standard Deviation^ 0.30 Skewness= -0.42
(0.41 mm
N )
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 58 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)*2 f(m - x)*2 (m - x)*3
if
i i
1
>
0 -0.13 12.52 -1.57 -1.05 1.10 13.73 -1.15 -14.37
0 -0.25 0.13 7.06 0.88 -0.80 0.64 4.49 -0.51 -3.57
0.25 - 0.5 0.38 9.33 3.50 -0.55 0.30 2.79 -0.16 -1.53
0.5 - 0.75 0.63 7.74 4.84 -0.30 0.09 0.68 -0.03 -0.20
0.75 - 1 0.88 6.43 5.63 -0.05 0.00 0.01 0.00 0.00
1 - 1.25 1.13 19.39 21.81 0.20 0.04 0.80 0.01 0.16
1.25 - 1.5 1.38 21.64 29.76 0.45 0.21 4.44 0.09 2.01
1.5 - 1.75 1.63 1 1.32 18.40 0.70 0.49 5.59 0.35 3.93
1.75 - 2 1.88 3.41 6.39 0.95 0.91 3.10 0.87 2.95
2 - 2.25 2.13 0.75 1.59 1.20 1.45 1.09 1.74 1.31
2.25 - 2.5 2.38 0.41 0.97 1.45 2.11 0.87 3.07 1.26
2.5 - 2.75 2.63 0.00 0.00 1.70 2.90 0.00 4.94 0.00
2.75 - 3.0 2.88 0.00 0.00 1.95 3.81 0.00 7.45 0.00
3.0 - 3.25 3.13 0.00 0.00 2.20 4.85 0.00 10.69 0.00
3.25 - 3.5 3.38 0.00 0.00 2.45 6.02 0.00 14.76 0.00
3.5 - 3.75 3.63 0.00 0.00 2.70 7.31 0.00 19.75 0.00
3.75 - 4.0 3.88 0.00 0.00 2.95 8.72 0.00 25.75 0.00
Mean (x)= 0.92 Standard Deviation= 0.61 Skewness= -0.35
(0.53 mm
to
00
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 59 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x;a2 f(m - x)h 2 (m - x)*3
•
>
C o
0
i
O
•a
C O
0.00 0.00 -1.82 3.29 0.00 -5.98 0.00
0 -0.25 0.13 0.00 0.00 -1.57 2.45 0.00 -3.83 0.00
0.25 - 0.5 0.38 0.09 0.03 -1.32 1.73 0.16 -2.27 -0.20
0.5 - 0.75 0.63 0.20 0.13 -1.07 1.13 0.23 -1.21 -0.24
0.75 - 1 0.88 0.32 0.28 -0.82 0.66 0.21 -0.54 -0.17
1 - 1.25 1.13 2.74 3.08 -0.57 0.32 0.88 -0.18 -0.49
1.25 - 1.5 1.38 20.77 28.56 -0.32 0.10 2.06 -0.03 -0.65
1.5 - 1.75 1.63 41.11 66.80 -0.07 0.00 0.17 0.00 -0.01
1.75-2 1.88 22.05 41.34 0.18 0.03 0.75 0.01 0.14
2 - 2.25 2.13 6.40 13.60 0.43 0.19 1.21 0.08 0.53
2.25 - 2.5 2.38 5.67 13.47 0.68 0.47 2.66 0.32 1.82
2.5 - 2.75 2.63 0.60 1.58 0.93 0.87 0.52 0.82 0.49
2.75 - 3.0 2.88 0.05 0.14 1.18 1.40 0.07 1.66 0.08
3.0 - 3.25 3.13 0.00 0.00 1.43 2.06 0.00 2.95 0.0 0
3.25 - 3.5 3.38 0.00 0.00 1.68 2.84 0.00 4.78 0.00
3.5 - 3.75 3.63 0.00 0.00 1.93 3.74 0.00 7.24 0.00
3.75 - 4.0 3.88 0.00 0.00 2.18 4.77 0.00 10.43 0.00
Mean (x)= 1.69 Standard Deviation= 0.30 Skewness= 0.48
(0.31 mm
to
\o
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
u >
o
SAMPLE 60 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product
Deviation
from Mean
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - xJA 2 f(m - x)*2
a
>
C O
f(m - x;*3
0 -0.13 6.94 -0.87 -1.27 1.62 11.28 -2.07 -14.38
0 -0.25 0.13 3.53 0.44 -1.02 1.05 3.71 -1.08 -3.80
0.25 - 0.5 0.38 6.38 2.39 -0.77 0.60 3.83 -0.46 -2.97
0.5 - 0.75 0.63 6.23 3.89 -0.52 0.28 1.72 -0.14 -0.90
0.75 - 1 0.88 5.22 4.57 -0.27 0.08 0.39 -0.02 -0.11
1 - 1.25 1.13 17.69 19.90 -0.02 0.00 0.01 0.00 0.00
1.25 - 1.5 1.38 26.89 36.97 0.23 0.05 1.36 0.01 0.31
1.5 - 1.75 1.63 17.24 28.02 0.48 0.23 3.89 0.11 1.85
1.75 - 2 1.88 6.60 12.38 0.73 0.53 3.47 0.38 2.52
2 - 2.25 2.13 2.16 4.59 0.98 0.95 2.05 0.93 2.00
2.25 - 2.5 2.38 1.00 2.38 1.23 1.50 1.50 1.84 1.84
2.5 - 2.75 2.63 0.12 0.32 1.48 2.18 0.26 3.21 0.39
2.75 - 3.0 2.88 0.00 0.00 1.73 2.98 0.00 5.14 0.00
3.0 - 3.25 3.13 0.00 0.00 1.98 3.90 0.00 7.71 0.00
3.25 - 3.5 3.38 0.00 0.00 2.23 4.95 0.00 11.02 0.00
3.5 - 3.75 3.63 0.00 0.00 2.48 6.13 0.00 15.17 0.00
3.75 - 4.0 3.88 0.00 0.00 2.73 7.43 0.00 20.24 0.00
Mean (x)= 1.15 Standard Deviations 0.58 Skewnesss -0.68
(0.45 mm)
Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without perm ission.
SAMPLE 61 SIZE DATA
Phi Scale
Interval Midpoint
Weight
Percent Product Deviation
Deviation
Squared Product
Deviation
Cubed Product
phi m f fm m - x (m - x)A 2 f(m - x)A 2 (m - x)A 3 f(m - x)A 3
0 -0.13 5.45 -0.68 -0.94 0.88 4.82 -0.83 -4.53
0 -0.25 0.13 6.94 0.87 -0.69 0.48 3.31 -0.33 -2.28
0.25 - 0.5 0.38 16.30 6.11 -0.44 0.19 3.16 -0.09 -1.39
0.5 - 0.75 0.63 15.63 9.77 -0.19 0.04 0.57 -0.01 -0.11
0.75 - 1 0.88 10.91 9.55 0.06 0.00 0.04 0.00 0.00
1 - 1.25 1.13 25.45 28.63 0.31 0.10 2.44 0.03 0.76
1.25 - 1.5 1.38 17.30 23.79 0.56 0.31 5.42 0.18 3.03
1.5 - 1.75 1.63 1.10 1.79 0.81 0.66 0.72 0.53 0.58
1.75-2 1.88 0.91 1.71 1.06 1.12 1.02 1.19 1.08
2 - 2.25 2.13 0.00 0.00 1.31 1.72 0.00 2 .2 5 0.00
2.25 - 2.5 2.38 0.00 0.00 1.56 2.43 0.00 3.79 0.00
2.5 - 2.75 2.63 0.00 0.00 1.81 3.28 0.00 5.93 0.00
2.75 - 3.0 2.88 0.00 0.00 2.06 4.24 0.00 8.74 0.00
3.0 - 3.25 3.13 0.00 0.00 2.31 5.33 0.00 12.32 0.00
3.25 - 3.5 3.38 0.00 0.00 2.56 6.55 0.00 16.77 0.00
3.5 - 3.75 3.63 0.00 0.00 2.81 7.89 0.00 22.18 0.00
3.75 - 4.0 3.88 0.00 0.00 3.06 9.36 0.00 28.65 0.00
Mean (x)= 0.82 Standard Deviations 0.46 Skewnesss -0.29
(0.57 mm
c
60
0 1
o
w
50
0
0.
40
••
£
30
O ) 20
0
£
10
0
Sam ple 38 Size Distribution
> » c m r * . c m K N K N K N N O I N
♦- . • • • N o i N W O O
Midpoint Phi Value
70
I 60
a 50
a 40
- 30
o> 20
0 1
£ 10
0
Sample 39 Size Distribution
CM CM CM CM
Midpoint Phi Size
Sample 40 Size Distribution
50
c
«
u
40
0
Q .
30
* *
£
20
o>
0 1 0
£
0
CM CM CM CM W
Midpoint Phi Value
132
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
| 2 5
S 20
o»
15
10
Sample 47 Size Distribution
M idpoint Phi Value
5 0
c
0
u
4 0
0
a
3 0
* »
£ 2 0
O)
o
0 10
5
Sample 48 Size Distribution
r o o e ^ «) •
M idpoint Phi Values
Sample 50 Size Distribution
® 10
M idpoint Phi Value
133
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sam ple 51 Size Distribution
O 1 0 to 1 0 •e to to 1 0 to 1 0 to 1 0 t o 1 0 0 0
N K o r k. N K . a K O f r * O f r * . O f r * . M
g * * n « » • n o « D O o t o o 0 A
• o © © o oi O f O f ( V e > n O n
M idpoint Phi Value
Sample 52 Size Distribution
M idpoint Phi Value
Sample 53 Size Distribution
4 0
o 30
W
0 )
“ ■ 20
n
& 10
« r * . c u
o — •
M idpoint Phi Value
134
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sample 54 Size Distribution
25
§ 20
o
| 15
£ 10
O )
5 5
N K N N M K M K M K M
^ ^ ^ oi « « w ri o «
Midpoint Phi Value
c
0 1
o
k_
f l »
0.
O)
0 1
£
35
30
25
20
15
10
5
Sample 55 Size Distribution
Midpoint Phi Value
Sample 56 Size Distribution
» 20
Midpoint Phi Value
135
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sample 57 Size Distribution
0 40
u
| 30
£ 20
0 1
0 1 0
^ ^ w w cm cm co co co co
Midpoint Phi Value
Sample 58 Size Distribution
0 20
o >
0 5
CM C M C M CM
Midpoint Phi Value
Sample 59 Size Distribution
* . 50
| 40
|j 30
£ 20
o >
0 1 0
£ _
CM K C M
O — —
Midpoint Phi Value
136
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Sam ple 60 Size Distribution
c
«
0 1
D .
O )
£
3 0
2 5
20
15
1 0
5
0
a n e •
o » - ^ ^
Midpoint Phi Value
Sample 61 Size Distribution
J K 2 0
o >
Midpoint Phi Value
137
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix B: Digitizing Procedure
138
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Steps used in recording maximum projection ooid grain outlines
from a grain mount thin section to the VAX workstation.
D igitizing Procedure:
1) Focus microscope on grain to be digitized.
2) Highlight and select the "Grab Image from Camera" instruction on
com puter screen.
3) Observe the video screen to determine if the grain image is 'clean'. It is
important to get a sharp outline of the image because the computer may
incorrectly interpret an out of focus grain as having high asperity. If the
image is fuzzy, the grain image must be grabbed again. If there are dark
spots outside of the grain boundary, they must be edited out by selecting the
"Remove Bad Pixels" command. After selecting this command the area
containing the dark spot is outlined using the mouse and the command
option to set the spot to zero is given. This erases all dark images from within
the area outlined. If there are light spots within the grain boundary, then
the "Remove Bad Pixels" command is also given and the area is outlined as
explained. The area is then darkened by giving the command to set the
outlined area to one.
4) Highlight and select the "Find Boundary Points" instruction on computer
scree n .
5) If outline of the grain appears accurate then highlight and select the
"Save X-Y Coordinates to File" instruction on the computer screen. If outline
is not accurate then the image must be grabbed again.
6) Program will then ask for a number to assign the grain according to its
type. To identify the grain type the optical path in the microscope is
switched to the oculars and the grain is identified as one of the grain types
described in the classification section. The number corresponding to the
grain type is input into the computer.
7) Switch the microscope optical path back to the video camera and return to
step 1.
139
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

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

PDF

Helicoplacoid echinoderms: Paleoecology of Cambrian soft substrate immobile suspension feeders

PDF

Evolutionary paleoecology and taphonomy of the earliest animals: Evidence from the Neoproterozoic and Cambrian of southwest China

PDF

The characterization of Huntington Beach and Newport Beach through Fourier grain-shape, grain-size, and longshore current analyses

PDF

Barnacles as mudstickers? The paleobiology, paleoecology, and stratigraphic significance of Tamiosoma gregaria in the Pancho Rico Formation, Salinas Valley, California

PDF

Cyclostratigraphy and chronology of the Albian stage (Piobbico core, Italy)

PDF

Quartz Grain-Shape Variation Within An Individual Pluton: Granite Mountain, San Diego County, California

PDF

Biotic recovery from the end-Permian mass extinction: Analysis of biofabric trends in the Lower Triassic Virgin Limestone, southern Nevada

PDF

Holocene sedimentation in the southern Gulf of California and its climatic implications

PDF

Early Jurassic reef eclipse: Paleoecology and sclerochronology of the "Lithiotis" facies bivalves

PDF

Preservation Of Fossil Fish In The Miocene Monterey Formation Of Southern California

PDF

Dynamic fluvial systems and gravel progradation in the Himalayan foreland

PDF

Lateral variability in predation and taphonomic characteristics of turritelline gastropod assemblages from Middle Eocene - Lower Oligocene strata of the Gulf Coastal Plain, United States

PDF

A tectonic model for the formation of the gridded plains on Guinevere Planitia, Venus: Implications for the thickness of the elastic lithosphere

PDF

A proxy for reconstructing histories of carbon oxidation in the Northeast Pacific using the carbon isotopic composition of benthic foraminifera

PDF

Geology and structural evolution of the southern Shadow Mountains, San Bernardino County, California

PDF

Construction of a gabbro body in the Trinity Complex, northern California

PDF

Characterization of geochemical and lithologic variations in Milankovitch cycles: Green River Formation, Wyoming

PDF

A phylogenetic analysis of oological characters: A case study of saurischian dinosaur relationships and avian evolution

PDF

Generation of mutant tissue inhibitor of metalloproteinases-2 (TIMP-2) in the baculovirus expression system

Asset Metadata

Creator Webster, Malcolm Stephen (author)

Core Title Grain-size and Fourier grain-shape sorting of ooids from the Lee Stocking Island area, Exuma Cays, Bahamas

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,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

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

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-14305

Unique identifier UC11337073

Identifier 1384929.pdf (filename),usctheses-c16-14305 (legacy record id)

Legacy Identifier 1384929.pdf

Dmrecord 14305

Document Type Thesis

Rights Webster, Malcolm Stephen

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