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Quartz Grain-Shape Variation Within An Individual Pluton: Granite Mountain, San Diego County, California
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Quartz Grain-Shape Variation Within An Individual Pluton: Granite Mountain, San Diego County, California
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UMI
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313/761-4700 800/521-0600
QUARTZ GRAIN-SHAPE VARIATION WITHIN AN INDIVIDUAL PLUTON:
GRANITE MOUNTAIN, SAN DIEGO COUNTY, CALIFORNIA
By
Dawn Margaret Robinson
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)
December 1995
UMI Number: 1378432
UMI Microform 1378432
Copyright 1996, by UMI Company. AH 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
U N IV E R S IT Y O F S O U T H E R N C A LIF O R N IA
T H E G R A D U A T E S C H O O L
U N IV E R S IT Y P A RK
LO S A N G E L E S . C A L IF O R N IA 0 0 0 0 7
This thesis, written by
iJ C X U ...
under the direction of hJUZ^-.T hesis Committee,
and approved by all its members, has been pre
sented to and accepted by the Dean of The
Graduate School, in partial fulfillment of the
requirements fo r the degree of
-1Z2cl
D tem
D at e.QSk 19 be?'.. .6 j .. 19.95
Chairm an
CONTENTS
Page
FIGURES iv
TABLES vi
ABSTRACT viii
ACKNOWLEDGEMENTS x
INTRODUCTION 1
Objectives of Project 2
Study Areas 2
Location and Accessibility 3
Climate and Vegetation 6
REGIONAL GEOLOGY 7
Areal Geology 7
Geologic History 12
PLUTONIC UNIT 15
SAMPLE COLLECTION 17
SAMPLE PREPARATION 18
FOURIER ANALYSIS 19
Fourier Methodology 21
STRAIN ANALYSIS 25
FRACTURE ANALYSIS 26
ii
STATISTICAL METHODS 28
Introduction 28
Hotelling's T2 Test 28
Analysis Of Variance (ANOVA) 29
Duncan's New Multiple Range Test 30
Factor Analysis 31
Regression Analysis 32
RESULTS 33
Fourier Analysis 33
Factor Analysis 33
Hotelling's T Test 37
Analysis of Variance And Duncan's New Multiple Range Test 37
Strain Analysis 37
Fracture Analysis 42
Fracture Spacing 42
Fracture Ellipsoids 49
Regression 49
DISCUSSION 61
CONCLUSIONS 65
REFERENCES 66
iii
FIGURES
Figure Page
1. Location of principal and secondary study areas showing sampling
locations. The general geological settings of the study areas are
also shown. 4
2. Generalized regional geology map showing geochemical,
geophysical and lithological discontinuities found within the batholith
in southern California. 11
3. Factor analysis plot of the fourier grain shape data. Factor 1
indicates grain elongation. Factor 2 indicates grain asperity. 34
4. Plot of the Hotelling's T2 test results. Black boxes indicate significant
difference in samples. 38
5. Graph of fracture ellipses for sample 1. 50
6. Graph of fracture ellipses for sample 5. 51
7. Graph of fracture ellipses for sample 10. 52
8. Graph of fracture ellipses for sample 15. 53
9. Graph of fracture ellipses for sample 20. 54
10. Graph of fracture ellipses for sample 25. 55
11. Plot of regression analysis between strain ellipse and second fourier
harmonic. 57
iv
12. Plot of regression analysis between fracture ellipse and second
fourier harmonic. 58
13. Plot of regression analysis between fracture and strain ellipses. 60
v
TABLES
Table Page
1. Procedure used in digitizing the two-dimensional outlines of quartz
grains. 22
2. Results of the Factor analysis of fourier grain shape data. 36
3. Results of ANOVA and Duncan Significance testing among the two
sample transect lines. Gray lines indicate Duncan Range Test
grouping at a significance level of 0.05 percent. 40
4. Three-dimensional strain ellipsoid axes for the 25 samples. Q, D,,
and Ds are the lengths of the long, intermediate, and short axis,
respectively. The fabric intensity values are also shown. 41
5. Results of fracture analysis for sample 1. Mean fracture spacing for
this sample is shown in the bottom right corner of the table. 43
6. Results of fracture analysis for sample 5. Mean fracture spacing for
this sample is shown in-the bottom right corner of the table. 44
7. Results of fracture analysis for sample 10. Mean fracture spacing for
this sample is shown in the bottom right corner of the table. 45
8. Results of fracture analysis for sample 15. Mean fracture spacing for
this sample is shown in the bottom right corner of the table. 46
9. Results of fracture analysis for sample 20. Mean fracture spacing for
this sample is shown in the bottom right corner of the table. 47
vi
10. Results of fracture analysis for sample 25. Mean fracture spacing for
this sample is shown in the bottom right corner of the table. 48
11. Fracture ellipsoid axes for the six samples. €[, D,, and Ds are the
lengths of the long, intermediate, and short axis, respectively. 56
vii
ABSTRACT
Most Fourier grain-shape analysis (FGSA) studies of quartz grains have
been conducted under the assumption that individual protoliths generate unique
grain-shape populations. Liu (1993) tested this assumption on 13 plutons of the
Peninsular Ranges batholith and distinguished only three distinct grain-shape
populations; he concluded that regional deformation (ductile strain and
microfracturing) was responsible for homogenizing the grain-shape composition.
This is an attempt to study grain-shape variation within an individual pluton with
well mapped structural features.
Granite Mountain (Gr Mtn), a Mesozoic pluton of the Peninsular Ranges,
was selected for this study. Ninteen samples (#1-19) were collected across an E-
W transect in the western part of Gr Mtn. This transect trends across the Chariot
Canyon fault which cuts part of the western edge of the pluton. Six samples (#20-
25) were collected from a N-S transect from the part of Gr Mtn immediately north
of the La Posta Pluton. Hotelling's T 2 test on all of 25 samples using the first 24
harmonics (a - 0.05) from FGSA, demonstrated that at least 23 percent of the
samples were significantly different from each other. Sample 13 of transect A and
sample 21 of transect B possessed statistically different grain-shape parameters
from other samples within each transect. This may be because of the presence
of intense local deformation. No other significant differences were found within
each transect, although tests suggest that the individual transects differed
statistically from each other.
Strain analysis performed suggested that samples 4 and 13 of transect A
are highly strained. As noted above, this may be due to the presence of intense
local deformation. Regression analysis indicates that a low correlation exists
between fabric intensity (strain analysis) and grain shape (Fourier analysis).
Fracture analysis performed suggested a moderate correlation between
microfracture spacing and grain shape. The fracture analysis correlated better with
the grain shape than the strain analysis. This may be due to overprinting by the
fracture patterns onto the original crystal shape or more likely this may indicate
that the fracture patterns better control the grain shape than do the initial crystal
boundaries. Regression analysis between strain and fracture ellipses resulted in
a moderate correlation which implies that the grains that are strained the most are
also the most fractured.
The above results indicate that large variations may exist in quartz grain-
shape composition within an individual pluton. Great care must be exercised when
selecting a pluton or part of a pluton for local or regional provenance studies.
ACKNOWLEDGEMENTS
I would like to acknowledge the late Dr. Robert H. Osborne, my adviser, for
pointing me in the direction of my project and advising me in the beginning stages
of my research. We will miss him greatly.
I would also like to thank Dr. Donn S. Gorsline for taking over where Dr.
Osborne left off and advising me in the rest of my research. I am also indebted
to Dr. David J. Bottjer and Dr. Charles G. Sammis who helped further my
knowledge and interest in geology. I am grateful to Dr. Scott Paterson for the use
of the Strain Laboratory. Special thanks go to Victoria Todd and Marty Grove for
their advice in choosing a field location. I am also grateful to Rahul Bahadur and
. - j« t —?— —
my brother, Rory Robinson, for help and advice in doing this study.
This project was supported in part by a grant from the Graduate Student
Research Fund provided by the Department of Geological Sciences. Permission
for sampling in the Anza-Borrego Desert was obtained from the Park Headquarters
in Borrego Springs.
x
INTRODUCTION
Numerous workers have quantitatively described the shape of quartz grains
in provenance and sediment budget studies (Mazzullo and Ehrlich, 1983;
Mrakovich and others, 1976; and Osborne and Yeh, 1991). In doing so, these
workers made a basic assumption that the shape of quartz grains from a given
protolith or local source reflects the genetic history of that source with only minor
shape modification occurring during transport. Liu (PhD, 1993) tested this
assumption in his study of 13 distinct plutonic units. Liu concluded that quartz
grain shape varies significantly within plutons and variation is even greater among
plutons of different compositions and textures. Liu's study was the first to directly
address this basic assumption.
Mazzullo and Magenheimer (1987) had concluded that quartz grains in the
fine sand size range exhibit highly non-spherical, angular outlines, numerous
crystalline nodes, grain embayments, and fractures that reflect crystallization and
deformation at elevated temperatures and pressures. This study, however, did not
state what the specific controlling factors of quartz grain shape are.
Liu's study answered many questions regarding what affects quartz grain
shape. He concluded that the shape populations for a group of closely-related
plutons are affected by regional controls. However, his study did not consider an
individual pluton. Many questions were left still unanswered. How much shape
variation occurs within an individual pluton with a narrow chemical composition?
How much of the original quartz crystal shape is found in grus samples? How
1
much affect does fracturing have on the shape of quartz grains? What relation
exists between local zones of deformation and the shape of quartz grains? This
study attempts to answer these questions.
Objectives Of Project
This study examined the grain-shape variation of quartz grains of twenty-
five (25) grus samples occuring within a single plutonic unit, the Granite Mountain
pluton, located in the Peninsular Ranges Batholith, to determine the factors
contributing to the shape of quartz grains. Specifically:
1) To study the occurrence of quartz grain shapes within a single pluton
occurring in the southern California batholith east of Escondido, California to
determine the degree of grain-shape variation.
2) To study the fracture patterns in this pluton to determine what effect it
has on the shape of quartz grains.
3) To study the strain patterns in this pluton to determine what
effect/relation exists between strain patterns, fracture patterns and the shape of
quartz grains.
Study Areas
The Granite Mountain pluton located south of Borrego Springs, California
and east of Escondido, California was chosen for the following reasons:
2
1) The chemical composition of the portion of Granite Mountain pluton
located on Chariot Mountain has been extensively studied by Lampe (M.S. thesis,
UCLA, 1988). Thus, a very narrow chemical composition could be chosen to
eliminate any difference of quartz shape due to variations in chemical composition.
2) The tectonic history of the area is well known and much simpler than the
plutons to the west.
3) Two different types of deformation could be studied: brittle deformation
due to the Chariot Canyon fault and ductile deformation due to the emplacement
of the La Posta pluton to the south and emplacement of the Granite Mountain
pluton.
Location And Accessibility
The study area is located approximately five kilometers east of Escondido,
San Diego county, California (Fig. 1). The Granite Mountain pluton lies within the
eastern portion of the Peninsular Ranges Batholith. Chariot Canyon fault lies on
the western boundary of the primary study area and the Elsinore fault lies to the
east of the primary study area. The primary study area is accessible via dirt roads
leading from Banner to highway S2 in Box Canyon through Rodriquez Canyon and
on Chariot Mountain. These roads are in fairly good shape and are regularly used
by gold mining companies located in Chariot Canyon, and by recreational vehicles.
The secondary area is located between highway S2 on the west and Little
Blair Valley on the east. This is located in the Anza Borrego State Park. The area
3
Figure 1. Location map of study area showing the general geology of the area and
sample locations. HB = biotite-hornblende tonalite (hornblende-biotite facies) of the
Granite Mountain pluton, SB = biotite granodiorite/tonalite (small-biotite facies) of the
Granite Mountain pluton, mb = monzogranite/granodiorite dike, Q = calc-silicate quartzite,
Mg = migmatitic gneiss and schist, G = La Posta pluton, Qal = alluvium.
4
\ Foe^dnd W*Jier
\ ) ~ (5 & V V o lr v “
y * SO T ufy
I Va'Jey
(f/n*3 ■ r-t- Hasan;
/ meters
^Sample Location and
General Geology Map
is accessible via well maintained dirt roads that travel around the periphery of the
pluton outcrop.
Climate And Vegetation
The topography of the area varies from the steep terrane of Chariot and
Granite Mountain to the broad flat terrane of Earthquake and Blair Valleys. Chariot
Canyon peaks at approximately 550 m; whereas, Granite Mountain towers above
the valley floors with a maximum elevation of 1800 m. The lowest elevation in the
Chariot Mountain area is 900 m located in the southeast portion of Rodriguez
Canyon. The Blair Valley area varies in elevation from approximately 840 m to
1000 m.
Chariot Mountain is densely vegetated by low-lying chapparal. Oriflame
Canyon to the south is heavily vegetated by large trees and low-lying brush. Large
Lady bug swarms were encountered in this valley during field work. Rodriguez
Canyon is more of an upper Sonoran type desert climate - sparsely vegetated with
barrel cactus, sage and yucca. Blair Valley area is sparsely vegetated with
moderate to small sized bushes.
The average high temperature recorded in Borrego Springs to the north of
the study area ranges from 68.8 °F (Jan.) in the winter to 107.2°F (July) in the
summer. The average rainfall is only 18 cm per year.(Remeika and Lindsay, 1992)
6
REGIONAL GEOLOGY
This section is divided into two parts. The first is an overview of the areal
geology and the second is a description of the geologic history of the region.
Areal Geology
The Granite Mountain pluton is located within the extensive Peninsular
Ranges Batholith which extends from approximately 34° N, near Riverside,
California, to 28° N in Baja California. However, it is thought to continue to the tip
of the Baja California peninsula underneath Cenozoic cover (Jahns, 1954; Gastil
and others, 1975). This batholith, which trends northwest, is a segment of the
chain of Mesozoic Circum-Pacific batholiths. The Peninsular Ranges Batholith is
1600 km long and 80 to 150 km wide. Todd and others (1994) stated that this
width only represents a fraction of the batholith's original width. On the east, the
batholithic rocks are truncated by the Neogene Salton Trough rift and San Andreas
fault zone (Gastil and others, 1975; Silver and others, 1979) and on the west by
the Coronado Escarpment (Silver and others, 1979).
The Peninsular Ranges Batholith exhibits a change from west to east in
chemical composition, age, size and structural characteristics. East of San Diego,
California, the composition of prebatholithic rocks changes from unmetamorphosed
and lower green schist-facies volcanic arc rock on the west of the batholith to mid-
crustal plutons and upper amphibolite facies metamorphic rocks on the east (Todd
and others, 1994). Plutonic compositions vary from gabbro and tonalite in the west
7
to granodiorite and granite with more alkaline compositions in the east. Tonalite
is thought to be the most abundant rock type in the batholith (Gastil and others,
1975; Gastil, 1983). Batholithic structure also changes from sheeted and diapiric
shapes in the west to elongate shapes with strongly foliated gneissic or mylonitic
textures in the central part of the batholith. The mid- to Late Cretaceous plutons
and eastern parts of the batholith were intruded largely at a late stage, or even
after the regional deformation. These differences seem to result from a difference
in the source rocks for the intruding plutons. According to Todd and others (1994),
Cretaceous plutons in the western part of the batholith intruded oceanic crust;
whereas, the central plutons intruded a "layered sequence of metamorposed,
continentally derived strata and gneissic plutons underlain by transitional (?) crust"
(Todd and others, 1994). Plutons in the eastern portion of the batholith were
emplaced into the North American craton.
These differences found among the plutons within the batholith have led
many workers to subdivide the batholith into difference zones. Silver and others
(1979), using structural, geochemical, geochronological, isotopic and lithological
data, divided the batholith into a western and an eastern zone. The western zone
is characterized by small epizonal plutons of gabbros, quartz gabbros and
tonalites. The eastern zone is characterized by larger mesozonal plutons of
tonalites and low-K20 granodiorites. These two zones are also marked by a
difference in age. The plutons in the western and eastern zones are 120 to 105
m.y. and 105 to 90 m.y., respectively (Silver et al, 1979).
8
Gastil (1983) subdivided the Peninsular Ranges Batholith into five zones,
four of which are present in southern California and Baja California. These four
zones are: 1) the Pacific margin belt; 2) the gabbro belt (west part of the
Peninsular Ranges), composed of gabbro, tonalite and granodiorite; 3) the
leucotonalite belt (eastern Peninsular Ranges), composed of larger, more
homogeneous, and more leucocratic tonalite to granodiorite; and 4) granodiorite-
granite belt which includes large granite plutons with well-formed, large, pink
potassium-feldspar crystals.
Todd and others (1988) recognize three zones within the batholith east of
San Diego. These zones are: 1) a Jurassic to Cretaceous volcanic to
volcanoclastic western zone derived from a volcanic arc; 2) a Triassic to
Cretaceous (?) deep-marine, flysch-type clastic sedimentary central zone derived
from continental crust; and 3) a Precambrian and Paleozoic miogeoclinal eastern
zone.
Todd and others (1988) concluded from a study of 334 granitoids rocks in
the northern Peninsular Ranges batholith that "granitoid rocks formed from the
mixing of basaltic and quartzofeldspathic end-member magmas whose
compositions reflected variations in their source materials". The boundary between
the two different source regions is a north-northwest striking discontinuity that lies
near the center of the batholith and is interpreted as the western margin of major
continental crustal contribution to the batholith. This discontinuity coincides
approximately with lithologic, geochemical and geophysical discontinuities found
9
within the batholith. These discontinuities are shown in Fig. 2. The l-S line is a
division between granitoids primarily derived from a metasedimentary source (S-
type) and those with a mantle-derived origin (l-type). The S-type granitoids have
high p1 8 0 values and8 7 Sr/8 6 Sr initial ratios; whereas, the l-type granitoids have low
p1 8 0 values (values of 5 to 7) and low^Sr/^Sr initial ratios (less than 0.706) (Todd
and Shaw, 1985). Zircon U-Pb data show that the plutons are of two age groups,
one from 120 to 105 m.y. and the other from 105 to 90 m.y. (Silver et al, 1979).
The gabbro line represents the eastern limit of the large gabbro complexes that
typify the western part of the batholith. This line is 5 to 15 km east of the l-S line.
Todd and Shaw (1985) believe that the gabbro line represents the extent of the
western terrane at upper mantle to lower-crustal depths; whereas, the l-S line
represents the terrane boundary at depths deeper than 15 km. The terrane
boundary at the surface is represented by the prebatholithic boundary which was
based on a change in prebatholithic lithology. This interpretation indicates that the
terrane boundary dips steeply to the east which coincides with the dip of regional
structures. The gravity-magnetic boundary indicates the "transition from oceanic
crust intruded by relatively mafic, l-type plutons on the west to continental crust
and sediments intruded by relatively leucocratic late- to post-tectonic plutons on
the east" (Todd and others, 1988).
The l-S line mentioned above roughly coincides with a large Early
Cretaceous shear zone, referred to by Todd and others (1988) as the Cuyama-
Laguna Mountains shear zone (CLMSZ). This zone strikes north-northwest and
10
RIVERSIDE
8 0 STEP
GABBRO
LINE '
G-M /
BOUNDARY
GRANITE MOUNTAIN
* V * V X
^ CLMSZ
NORTH
SAN DIEGO
40 20
KM
Fig. 2. Geochemical, geophysical and lithological discontinuities in
the northern Peninsular Ranges batholith east of San Diego,
California. Double dashes mark the westernmost extent of S-type
granitoids (l-S line). The heavy short dashes represent the
approximate eastern boundary of an area with abundant large
gabbro plutons (gabbro line). The long dashes illustrate the
projected surface trace of modeled contact between western region
of residual gravity and magnetic highs and eastern region of gravity
lows and sparse magnetic anomalies (gravity-magnetic boundary,
G-M boundary). The solid line represents the steep gradient
between plutons with relatively low 8 O values and those with
higher values. The solid line coincides approximately with 105 m.y.
U-Pb age boundary between western and eastern plutons. The
short dash pattern indicates the Cuyamaca-Laguna Mountains
shear zone (CLMSZ). The X marks the location of Granite
Mountain. (Modified after Todd et al., 1988)
dips steeply to the east. It is characterized by 1) strongly flattened and elongated
north-northwest striking, east-dipping plutons; 2) strong foliation and local
development of mylonite gneiss; 3) local hypabyssal textures in plutonic rock types
that occur as hypidiomorphic- to allotriomorphic-granular plutons outside the shear
zone; and 4) emplacement of intermediate and mafic dike swarms (Todd and
others, 1988). The Granite Mountain pluton, which lies to the east of the CLMSZ,
locally underwent complex deformation of early mylonite fabrics and high-grade
metamorphic folds that probably were associated with movements in the shear
zone (Grove, 1987).
Geologic History
During Late Triassic time, a volcanic-plutonic island arc began to
accumulate in the ocean basin off the southwest coast of North America. By
Middle Jurassic time, this arc had extended along the length of the borderland.
During Late Jurassic time, a fringing volcanic arc represented by Santiago Peak
Volcanics probably extended from the continental margin to what is now southern
California southward to an oceanic island in northern Baja California (the Alisitos
Formation)(Silver et al, 1963, 1969).
During the Early Cretaceous, collision of the Santiago Peak-Alisitos arc with
western North America resulted in folding of the continental-margin deposits and
eventual underthrusting of the arc beneath the continental margin (Gastil et al,
1978;1981;Todd and Shaw, 1985). The arc apparently arrived first in the northern
part of peninsular California as indicated by the end of prebatholithic marine
12
deposition and the onset of deformation. By early Cretaceous time, the locus of
magmatic activity in northern part of the batholith had moved eastward from the
Santiago Peak volcanic arc to the vicinity of the Triassic and Jurassic marginal
basin (Todd and others, 1988). The volcanic rocks that were superjacent to the
Early Cretaceous plutons have been removed by erosion. Early Creteceous
plutons intruded the east-dipping suture between the accreted fringing island arc
and the folded marginal basin.
During the Early Cretaceous, regional compression continued in the
batholith east of San Diego (Todd and Shaw, 1979). Deformation was essentially
pervasive in plutons and wallrocks in the western area and early fabrics were
modified by diapiric intrusion. Deformation became concentrated in the east-
dipping CLMSZ. Approximately 100 Ma, locus of magmatism moved eastward into
what had been Paleozoic miogeocline and a markedly different type of magma was
produced (younger, late- to - post tectonic intrusive sequence)(Clinkenbeard et al,
1986; Hill, 1984; Silver et al, 1979; Todd and Shaw, 1986). Although plutons of
the younger sequence are not penetratively deformed, strong fabrics did develop
locally. Between 102 and 98 Ma, shortening in this region changed from a
direction approximately normal to the continental margin (east-northeast) to one
that was subparallel to it (northwest-southeast)(Todd and others, 1988).
Uplift and erosion began in the western part of the batholith while the
younger group of plutons was being emplaced (Gastil et al, 1981). During the
Latest Cretaceous and early Tertiary, a transition from ductile mylonitic deformation
13
to brittle low-angle faulting probably accompanied uplift and unroofing of the
eastern part of the batholith. By the late Paleogene time, the region was
undergoing extension. Lastly, the Late Cretaceous and Paleogene structures were
displaced and reactivated by the Neogene Gulf of California-San Andreas rift-
transform system.
14
PLUTONIC UNIT
The Granite Mountain pluton in the study area is divided in two by the
Elsinore fault with Chariot Mountain on the west and Granite Mountain on the east
(Fig. 1). Lampe (1988) performed a geochemical and petrological study of this
area and concluded that the pluton of Chariot Mountain and the pluton of Granite
Mountain are the same pluton and that this entire pluton should be referred to as
the Granite Mountain pluton. This pluton is asymmetrically zoned and
crystallized from the margins inward producing three mineralogically distinct zones
with internal gradational boundaries. These zones trend in a north-south direction
and are from south to north: a metaluminous, biotite-hornblende tonalite margin
that grades inward to a metaluminous hornblende-biotite tonalite central zone
which, in turn, grades inward to a peraluminous biotite, granodiorite/tonalite core
(Lampe, 1988). Lampe referred to these zones as Hornblende-Biotite (HB), Large-
Biotite (LB) and Smali-Biotite (SB) facies. The boundaries between the facies are
gradational over tens of meters. All samples in the primary study area were taken
from the Hornblende-Biotite Facies (HB). This facies was chosen based on its
location near zones of brittle deformation. Only one facies was sampled to limit
the variation in chemical composition. Samples from the secondary study area are
only known to be tonalite. The tonalite, in the secondary area, is thought to be
part of the Granite Mountain pluton (Grove, per. com., 1994).
The Hornblende-Biotite Facies, which is the dominant facies on both sides
of the Chariot Canyon Fault, is characterized by large euhedral hornblende and
15
biotite books that form a medium- to coarse-grained hypidiomorphic-granular
texture. Foliation is generally parallel to the outer contacts of the pluton. This
foliation is indicated by alignment of mafic minerals and abundant, ellipsoidal mafic
inclusions. As the distance from the margins of the pluton increases, these
inclusions decrease in abundance and become more circular. This facies consists
of hornblende, biotite, plagioclase, quartz, and alkali feldspar. Accessory minerals
consist of sphene, apatite, opaques, zircon and monazite. Plagioclase, which is
subhedral to euhedral, constitues 47 to 52%; whereas, the anhedral quartz
constitues 15 to 23% of this facies. The quartz varies from 1 to 4 mm and
commonly displays undulatory extinction and sutured grain boundaries. Moderate
subgrain development and deformation lamellae occur locally (Lampe, 1988). This
facies crops out as massive, rounded boulders that exhibit a tor weathering
pattern.
16
SAMPLE COLLECTION
Twenty-five grus samples from the Granite Mountain pluton east of
Escondido, California were collected by the author (Fig. 1). At each location,
approximately 2 kg of grus were scraped from the surface of the in situ, weathered
protolith with a small trowel. Oriented rock samples were collected along with the
25 grus samples. The criteria used to collect these samples were: 1)
accessibility and 2) location with respect to the faults in the area and the La Posta
pluton. Six of the 25 samples were used for fracture analysis. The criteria used
for selecting these samples were: 1) the samples should represent as much of
the study area as possible and 2) the samples should be spaced to show
moderate changes in strain and not spaced close enough to be duplicated or only
show small changes in strain.
17
SAMPLE PREPARATION
Quartz grains from the medium (2.0 - 1.0 0; 0.25 - 0.50 mm) sand were
used in this study. Samples were first wet sieved to obtain the desired size
fractions. Wet sieving was performed to minimize breakage and/or attrition of the
quartz grains during sieving. The samples were then boiled in hydrofluoric acid
bath for one minute to remove iron-oxide coatings. The acid residue was removed
by rinsing the samples in de-ionized water. The hydrofluoric acid washing does
not significantly alter the quartz grain shape (Schultz, 1980). Samples were then
dried in convection oven at 40°C.
Samples were examined under a binoccular stereoscopic microscope using
a reflected light source. Quartz grains were hand-picked using a very small brush.
Preparations for fracture analysis involved injecting a medium blue dye deep
into the fractures in the thin sections in order to highlight the cracks and make
them more visible and clear.
18
FOURIER GRAIN SHAPE ANALYSIS
Fourier grain shape analysis (FGSA), which was first introduced by
Schwarcz and Shane (1969) and Ehrlich and Weinberg (1970), has been used to
quantitatively analyze grain shape. Fourier Analysis describes the two-dimensional
shape of grains using "periodic mathematical functions as an infinite series of
summed sine and cosine terms" (Ehrlich and Weinberg, 1970). This method which
can describe the grain's shape as precisely as needed (Ehrlich and Weinberg,
1970), has been used to study a variety of problems especially sediment source
and transport problems. The Fourier Grain Shape Analysis was described in detail
by Osborne and Yeh (1991) and is quoted below.
Ehrlich and Weinberg (1970) describe a closed-form Fourier
method to analyze the observed variation of two-dimensional,
maximum-projection, grain-shape area. Grain shape may be
estimated by an expansion of the periphery radius as a function of
angle about the grain's center of gravity by a Fourier series. 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. Fundamental harmonics are the prime
fractions (1/2, 1/3, 1/4, . . . 1/N), where N equals half the number of
digitized points used to define the periphery of a grain. As the
number of fundamental harmonics is increased, the computed curve
converges with 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 incorporation
of irresolvable high frequencies into lower frequencies (aliasing).
The radius is given by:
19
m = R0 + £ R n CO S(0„ - PAn )
/7 = 1
Where theta is the polar angle measured from an arbitrary reference
line. The first term in the series Ro is equivalent to the average
radius of the grain in the maximum projection orientation. For the
reminder of the terms, n is the harmonic order,. Rn is the harmonic
amplitude, and PAn is the phase angle. The phase angle appears
to provide little additional grain-shape information, and therefore is
not considered further. It is important to note that the n'th harmonic
contributes to the explanation of the observed shape variation as a
figure with n "bumps." For example, the "zeroth" harmonic is a
centered circle with an area equal to that of the maximum projection;
the first harmonic is an off-centered circle; the second is a figure
eight; the third is a trefoil; etc. The center of gravity of the
maximum-projection shape is used as the origin of the radius
expansion to simplify interpretation of the Fourier series.
Coordinates of points along the periphery of the maximum-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
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 or periodic function exists within the data, the amplitude of
the sine and cosine curves with periods close to the natural harmonic
will be considerably larger than the amplitudes of other harmonics in
the sequence.
Although conceptually similar to the closed-form methodology
described by Erhlich 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 estimate of the
continuous spectrum. The FFT algorithm, as its name implies, is
extremely rapid and requires only nlog2 n arithmetic operations
rather than the rf operations as do alterative methods. The reader
is referred to Brigham (1974), Bloomfield (1976), and Bendat and
Piersol (1971) for extensive treatments of the mathematically
complex FFT.
20
Fourier Methodology
The two-dimensional shapes of the grains are recorded using a Video-
Microscope connected to a Digital Corporation VAX - Station 3200 located in the
Sedimentary Petrology Laboratory at the University of Southern California. The
Video-Microscope system consists of a standard binocular petrographic
microscope, a black and white video camera, and a video screen. The Digital
Corporation VAX - Station 3200 includes a keyboard, mouse and Ethernet
Communication Module used for digital communication with other systems. This
VAX - Station is a stand-alone 32-bit work station.
The Fourier digitizing and calculating performed on the grains is
accomplished by using the Grain-Shape Analysis (GSA) program. This program
was written for the Sedimentary Petrology Laboratory at USC by Tim Fogarty and
consists of several complex Fortran routines. The procedure for digitizing the
grains is explained in Table 1. Digitizing the individual quartz grains involves
projecting the two-dimensional image of the quartz grain via the black and white
camera from the microscope to a video screen. The grain image appears dark on
the lighted background. The computer then "grabs" the image of the grain from
the video screen. This is accomplished 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). The boundary points
of the grain are recorded by the computer as Cartesian (x-y) coordinates. The
centroid of the projected grain is also computed and is determined by averaging
21
Table 1. Process algorithm for recording individual maximum project
outlines of quartz grains from dry grain mounts.
Procedure to Digitize Grains:
1) Check to ensure that the microscope lens is at the correct
magnification and the Magnification Factor is appropriate.
2) Find, center, and focus the microscope on the new grain to
digitize.
3) Highlight and then Select "Grab Image from Camera."
4) Visually inspect the new image on the computer screen. If the
image is fuzzy you must re-Grab the image. If there are dust
spots around the outside of the grain, highlight and then Select the
"Remove Bad Pixels" option. Then, set these spots to zero. If
there are glare holes within the grain, highlight and then Select the
"Remove Bad Pixels" option. Then, set these holes to one. There
are some cases when no amount of pixel editing can clean up the
grain image, when this occurs skip and discard this grain and
return to step 1.
5) Highlight and then Select "Find Boundary Points."
6) Visually inspect the chosen boundary point image on the
computer screen. If there are numerous bad points you must re-
Grab the image.
7) If all is good, then highlight and then Select "Save X-Y
Coordinates to File."
8) Return to step 1.
22
the x-y boundary points. These points, or data, are stored for later calculations in
a binary file with a '.BPT' file type identifier extension.
Once the grain boundaries and the centroid of the grain are computed,
these points need to be prepared for Fast Fourier Transform (FFT). This is done
by converting the Cartesian coordinates to polar coordinates. The radius is the
distance from a boundary point to the centroid; the angle used is the angle from
the horizontal line bisecting the centroid to the boundary point. The original data
points are linearly interpolated so that grain points are evenly spaced and centered
about zero. This is done to satisfy the mathematical requirements of the FFT. To
center the data, the mean radius is subtracted from the radius versus angle data.
This radius is later placed in the final amplitude spectrum set.
The amplitudes of each wave number, of which there is a total of 128 for
each grain, are calculated by the following equation (Brigham, 1974):
Fourier Amplitudes = \J(real)2 + (imaginary f
Because the input data is real, half the wave numbers represent reflections and
are therefore omitted from the statistical analysis. This results in amplitude values
for the 64 different wave numbers for each grain. The above described procedure
is termed the standard method. Another method, termed the normalized method,
can also be performed by the GSA program. The normalized method divides the
amplitude values calculated in the standard method by the mean radius or the
amplitude value of the zeroth harmonic. Both methods produce amplitude values
and their respective wave numbers which embody a mathematical representation
23
of the grain. However, the normalized method allows the statistical analysis to be
independent of grain size and reduces the total variance of the sample set. The
amplitude values and their respective wave numbers are stored in a binary data
file with an '.AMP' file type identifier extension for later statistical analysis.
24
STRAIN ANALYSIS
Strain analysis of the pluton was also performed to evaluate the effect of
strain on quartz grain shape. Three orthogonally-oriented, oversized (5 by 7.6 cm)
thin sections were made for each of the 25 oriented rock samples. These thin
sections are approximately 60um thick which is twice as thick as usual. The
doubled thickness of the thin sections is important in the Fracture Analysis and will
be explained in that later section. These thin sections are then individually placed
under a standard petrographic microscope. Measurements of the long and short
axis of at least 50 quartz grains are taken for each thin section and are recorded
by a IBM PC computer. Measurements and calculations are done using the Strain
programs which were written for the Strain Laboratory at the University of Southern
California. The technique of Shimamoto and Ikeda (1976) was used to calculate
two and three-dimensional fabric ellipsoids. Fabric intensity was also calculated.
25
FRACTURE ANALYSIS
Fracture Analysis was done on the pluton in order to ascertain whether and
to what degree fracturing affected the shape of the quartz grains. The thin
sections used for the strain analysis were also used for this portion of the study.
The three orthogonally-oriented thin sections from samples 1, 5, 10, 15, 20, and
21 were analyzed for a total of 18 thin sections. The thicker thin sections were
beneficial in the fracture analysis because they are stronger than the standard thin
sections and therefore, additional fractures are less likely to be produced during
the thin sectioning process. The criteria for selecting the samples were: 1) to space
samples enough to remove duplication and 2) to cover both transects entirely.
Each thin section was placed on a low angle slide magnifier in the Strain
Laboratory. This device magnifies the image by 48x. Two to four quartz grains
were identified in each thin section. The outline and fractures within these grains
were then traced onto an 8 by 17 in. paper sheet. Underwood's (1970) points per
unit length (PL ) method was used to describe the distribution of the microfractures
within a quartz grain. Underwood's method entails counting the number of
intersection points between the microfractures and a set of test lines of known
length. This involved placing a grid, 3.0 by 3.0 cm, with vertical lines 3.0 cm long
and spaced every 3.0 mm onto the selected points on each grain. The points on
each quartz grain were selected so that the grid covered most of the grain. One
to three points were chosen for each grain depending on the size of the grain. In
this study, a linear array was applied at a regular angle increment of 15°
26
measured from a reference frame. The resulting F £(0 ) - the average number of
intersections per unit length in direction (0) exhibits the predominant fracture
direction. This measurement can be easily converted into the average fracture
spacing D(0) in that direction. The D (0-360°) will define a closed figure that
represents an average potential fracture-defined ellipsoid or fracture ellipsoid.
Ellipsoids from the three orthogonal planes were put into a 3-dimensional ellipsoid
using the technique of Shimamoto and Ikeda (1976).
27
STATISTICAL METHODS
Introduction
The statistical methods used in this study are Hotelling's I s test, One-Way
Analysis of Variance, Duncan's New Multiple Range Test, regression analysis and
factor analysis. These tests were calculated using the BMDP Statistical Software
Program for the VAX. Each of the statistical tests are described below.
Hotelling's T 2 Test
Hotelling's T2 Test is a statistical method used to compare the multivariate
means between two sample populations. This method tests the significant
differences between and among the various grus samples. The Hotelling's T2
Test involves determining the multidimensional mean vector for each sample and
the associated variance-covariance matrices (Alder and Roessler, 1977). This test
assumes that the chosen samples are taken from populations having the same
variance-covariance matrix. The inverse of the variance-covariance matrix is
multiplied by the difference from each of the mean vectors using matrix algebra.
This resultant matrix is then multiplied by the number of observations in order to
obtain the I 2 value. Next, the T2 value is multiplied by the resultant of the
difference of the number of observations and the number of measurements and
then divided by the degrees of freedom in order to obtain the F value (Alder and
Roessler, 1977). The Hotelling's T2 Test requires that data consist of random
samples from normally-distributed parent populations that have no interaction
effects (Alder and Roessler, 1977).
28
Analysis Of Variance (ANOVA)
Analysis of variance, or ANOVA, is a mathematical method used to test the
equivalency of samples by partitioning the sum of squares. ANOVA compares the
variance of multiple sample populations as well as subsets of such populations.
The total variance of the tested sample set is divided into one of three categories:
among sample variance, within sample variance and an error term (Alder and
Roessler, 1977). The explanation being that if their variances are similar, then
these sample populations are likely to be from the same parent population. The
three basic assumptions of the ANOVA test are: 1) each set of duplicates is
randomly selected from different populations, 2) each parent population is normally
distributed, and 3) each population has equal variance (Davis, 1986). If the above
assumptions are met then the null hypotheses (H0 ) states that the samples are
equal and are likely derived from the same parent population, with the alternative
(H,) that at least one sample is different.
The ANOVA can be divided into one-way (single classification criteria) and
two-way (two classification criteria) analyses. The one-way analysis was used for
this study. The one-way ANOVA determines the equivalency of multiple samples.
The total variance of the data set can be separated into two sources - variance
within each sample and variance between or among the samples. The
significance level was chosen to be five percent (alpha = 0.05) for all tests.
29
Duncan's New Multiple Range Test
Duncan's New Multiple Range Test was performed in combination with the
ANOVA test. Although the ANOVA test can determine if there is significant
difference between or among multiple samples or sets, it can not identify which
sample or samples are significantly different. The Duncan test is used to identify
that sample or samples which are significantly different. This is accomplished
through a series of the shortest significant ranges which compare differences
between means (Alder and Roessler, 1977). Samples which are not significantly
different are grouped together, whereas dissimilar samples are grouped separately.
The basic assumptions of Duncan's New Multiple Range Test are the same
as the ANOVA assumptions (Alder and Roessler, 1977). In this test, the mean for
each of the chosen samples is determined and placed in a table listed from highest
to lowest. The shortest significant ranges are then computed based on the
number of sample means, the significance level, the number of degrees of
freedom, and the standard error of the mean. The standard error of the mean is
the square root of the within-sample mean square from the analysis of variance
table, divided by the square root of the number of observations on which each of
the means is based (Alder and Roessler, 1977). The difference between any two
sample means is then compared to the shortest significant ranges, and if lower is
considered not significantly different.
30
Factor Analysis
Factor Analysis was developed in the 1930's by experimental psychologists
to study the basic variables needed to account for individual differences in
measurements of abilities or aptitudes (Fruchter, 1954). Factor analysis is an
algebraic procedure which arranges the data along hypothetical axes in order to
gain a new theoretical perspective for the purposes of visually identifying trends
within the data set (Davis, 1986). In this method, there is no significance testing
of the data set and no probability values are generated. The axes or "factors" on
which the data are plotted are determined from eigenvalues and eigenvectors
obtained from the covariance matrix, which is, in turn, obtained from a square "FT
matrix consisting of the original data matrix, multiplied by its transpose (Davis,
1986). This R-mode technique was used in the study to determine the
interrelations between variables. The complexity of large m- (number of variables)
dimensional space of variables (23 harmonics) is reduced using the R-mode
analysis by projecting clusters of original variables onto a new set of axes that
define new variables or factors (David, 1986). The contribution of each variable
on each of the new axes is based on variance. The higher the explained variance
associated with the variable, the greater, the contribution of that variable. The
purpose of factor analysis is to reduce the number of variables while retaining as
much information as possible. The first few factors normally will account for most
of the observed variance. The variance represented by these factors can be
31
estimated by sum of squares for the elements (factor loadings) of the factor's
column in the factor loading matrix.
Regression Analysis
Regression analysis is a mathematical method used to compare two
variables. This method uses a least squares to calculate the best fit of a straight
line to a set of data points. The correlation coefficient, r, represents how well the
straight line fits the data points and thus, how well the two variables correlate to
each other. A perfect straight line fit is denoted by r = 1.0. R is calculated by the
following equation (Lindeburg, 1989):
r = ” £ (* ///) - & > /)(£ //)
l/[ n 5 > 2 - ( £ x f l [n - C Zyfi
32
RESULTS
The results of this study are presented below in three sections: Fourier
Analysis, Strain Analysis and Fracture Analysis. The last section, Regression,
compares the three analyses.
Fourier Analysis
The results of each of the statistical tests are presented in separate sections
below. Those sections are the Factor analysis, Hotelling's T test, ANOVA, and
Duncan's New Multiple Range Test.
Factor Analysis
Factor analysis performs testing on all samples to illustrate which grains are
more or less elongate and which are smoother or rougher. This test was
performed to see if any patterns exist between and within the two sample transects
with respect to grain shape. The results to this test did not indicate any clear
patterns (Fig. 3; Table 2). The data points are scattered over the factor plot in
both the x and y directions. The main cluster of points lies about 0 on the x-axis
and about 0.5 on the y-axis. The grains are scattered enough about the plot to
nullify any conclusions. No differences between or within the two transects can
be defined. The data points are spread evenly enough on the plot to conclude that
the quartz grains show no preferential elongation or roughness.
33
Figure 3. Factor analysis plot of the fourier grain shape data. Factor 1 indicates grain
elongation. Factor 2 indicates grain asperity.
34
Factor 2
Factor Analysis
18
♦
1
♦
9
♦
► 4
24
............
11
19 ' .I'!-..'-
♦
6
♦
♦s
♦
15 *
10
♦
• f
16
< ► 8
17 *
23 ♦
♦
22
12
* '
♦
13
14
*
21
♦
25 ♦
20
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Factor 1
w
c n
Table 2: Results of Factor analysis of fourier
grain shape data.
Sample # Factor 1 Factor 2
1 -0.109 1.041
2 0.354 0.082
3 -1.711 0.226
4 0.516 1.301
5 0.029 0.138
6 1.438 0.563
7 0.58 1.821
8 -0.998 -0.289
9 0.103 1.047
10 -0.26 0.132
11 -0.631 0.42
12 0.841 -0.969
13 -1.209 -1.023
14 1.462 -1.468
15 -0.736 0.28
16 1.994 0.111
17 -0.243 -0.05
18 0.136 1.584
19 -0.151 0.688
20 1.777 -1.562
21 -1.694 -1.785
22 -0.374 -0.587
23 -0.071 -0.36
24 -1.333 0.529
25 0.339 -1.62
Hotelling's T2 Test
The Hotelling's T 2 Test performs sample testing between and among all
samples using the 1 s t through 24th Fourier Harmonics. The results of this test (Fig.
4) indicate that 23 percent of the samples tested as statistically distinct with
respect to grain-shape. Significance level was set at 5 percent (alpha = 0.05).
Analysis Of Variance And Duncan's New Multiple Range Test
ANOVA testing between and among all samples used the 1s t through 24lh
Fourier Harmonics. The ANOVA test indicated that there was significant variance
in the samples. Duncan's test was used in this study to isolate the highly variant
samples (Table 3). Significance level for this test was set at 5 percent (alpha =
0.05). Table 3 shows that samples 20 through 25, the samples from transect B,
are statistically distinct from the samples from transect A. The results from this
test also indicate that sample 13 from transect A and sample 21 from transect B
are statistically distinct with respect to grain shape.
Strain Analysis
Strain analysis of the oriented rock samples was performed to evaluate the
effect of strain on quartz grain shape. The Shimamoto and Ikeda method of
calculating 2-dimensional and 3-dimensional fabric ellipsoids was used. Table 4
shows the results of the strain analysis for this method.
Fabric intensity values for transect A samples ranged from 0.121 to 1.778
and averaged 0.42 for Shimamoto and Ikeda's method. Sample 4 and sample 13
37
Figure 4. Plot of the Hotelling's T2 test results. Black boxes indicate significant difference
in samples.
38
Reflected Results
c o
CD
Table 3: Results of ANOVA and Duncan Significance testing among the two sample transect lines. Gray lines indicate Duncan
Range Test grouping at a significance level of 0.05 percent.
Analysisjin/ariance^
Sample Transect: 1 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
pTobability = 0.46 |
Duncan Range Testing: Sample Transect 1
Sample Transect: 1 | 10 1 6 14 5 2 4 13 18 7 15 16 3 17 12 8 9 11 13
Analysis of Variance: Sample Transect 2 [
Sample Transect: 2 | 20 21 22 23 24 25 |
Probability = 0 .25 {
Duncan Range Testing: Sample Transect 2
Sample Transect: 2 | 22 23 25 24 20 21
Table 4. Three-dimensional strain ellipsoid axes for the 25 samples. DL , D|, and Ds
are the lengths of the long, intermediate, and short axis, respectively. The fabric
intensity values are also shown.
d l illliiP lf f ip iilllE
1 1 1 1 1 1 1 1 1 ® ' I SMS! ! ®®! !
Transect 1
1 1.409 1.23 1 0.244
2 1.505 1.137 1 0.296
3 1.689 1.24 1 0.373
4 9.626 1.205 1 1.778
5 ■ ■ 1.641 1.295 1 0.35
6 1.577 1.231 1 0.322
7 1.462 1.316 1 0.277
8 1.471 1.321 1 0.282
9 1.425 1.191 1 0.25
10 1.582 1.211 1 0.326
11 1.186 1.073 1 0.121
12 1.485 1.307 1 0.285
13 4.573 1.053 1 1.221
14 1.343 1.197 1 0.21
15 1.612 1.298 1 0.338
16 1.472 1.324 1 0.282
17 1.626 1.278 1 0.344
18 1.691 1.248 1 0.373
19 1.55 1.273 1 0.31
Transect 2
20 1.545 1.314 1 0.311
21 1.536 1.205 1 0.304
22 1.698 1.414 1 0.38
23 1.626 1.267 1 0.344
24 1.594 1.396 1 0.34
25 1.324 1.21 1 0.203
have extremely high fabric intensity values (1.778 and 1.221, respectively).
Sample 11 has an extremely low value (0.121).
Fabric intensity values for transect B samples ranged from 0.203 to 0.380
and averaged 0.31 for Shimamoto and Ikeda's method. Sample 22 has a high
fabric intensity value (0.380). Sample 25 shows a low value (0.203).
Fracture Analysis
Discussion of the results of the fracture analysis are divided into two
sections: fracture spacing and fracture ellipsoids.
Fracture Spacing
The average fracture spacing as a function of the measurement angle for
the three orthogonal thin sections for the six selected samples are shown in Tables
5 to 10. These tables also include the maximum, minimum, and average fracture
spacing for each plane. The mean fracture spacing for the sample is given at the
bottom of each table. For the six samples, the mean fracture spacing ranged from
0.12 to 0.22 mm, which is within the very fine sand size range (0.0625 to 0.125
mm). Samples 20 and 25, which are from the same transcect, show similar
fracture spacings. Sample 15 has the smallest fracture spacings; whereas, sample
5 shows the largest fracture spacing. Sample 1, 20, and 25 illustrate intermediate
fracture spacings.
42
Table 5 Results of fracture analysis for sample number: 1
Planes XY
YZ zx
Measurement
Direction
(degrees)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
0 45 6.65 0.15 43 6.35 0.16 32 4.73 0.21
15 42 6.2 0.16 45 6.65 0.15 31 4.58 0.22
30 42 6.2 0.16 46 6.8 0.15 31 4.58 0.22
45 42 6.2 0.16 47 6.94 0.14 29 4.28 0.23
60 45 6.65 0.15 46 6.8 0.15 27 3.99 0.25
75 44 6.5 0.15 47 6.94 0.14 29 4.28 0.23
90 43 6.35 0.16 44 6.5 0.15 32 4.73 0.21
105 44 6.5 0.15 45 6.65 0.15 34 5.02 0.2
120 46 6.8 0.15 42 6.2 0.16 34 5.02 0.2
135 45 6.65 0.15 40 5.91 0.17 34 5.02 0.2
150 48 7.09 0.14 41 6.06 0.17 36 5.32 0.19
165 37 5.47 0.18 42 6.2 0.16 37 5.47 0.18
j Maximum j 48 g 7.09 | 0.18 | 47 j j 6.94 | 0.17 H 37 | 5.47 [ 0.25 |
| Minimum | 37 | 5.47 | 0.14 g 40 g 5.91 g 0.14 g 27 | 3.99 | 0.18 |
I Average | 43.58 j 6.44 | 0.16 j 44 g 6.5 | 0.15 | 32.17 j 4.75 | 0.21 |
Mean Fracture Spacing | 0.173 |
o o
Table 6 Results of fracture analysis for sample number: 5
Planes XY
YZ
zx
Measurement
Direction
(degrees)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
0 40 5.91 0.17 32 4.73 0.21 41 6.06 0.17
15 40 5.91 0.17 28 4.14 0.24 39 5.76 0.17
30 39 5.76 0.17 30 4.43 0.23 39 5.76 0.17
45 34 5.02 0.2 32 4.73 0.21 39 5.76 0.17
60 28 4.14 0.24 35 5.17 0.19 40 5.91 0.17
75 20 2.95 0.34 35 5.17 0.19 41 6.06 0.17
90 15 2.22 0.45 37 5.47 0.18 39 5.76 0.17
105 13 1.92 0.52 36 5.32 0.19 41 6.06 0.17
120 19 2.81 0.36 38 5.61 0.18 41 6.06 0.17
135 21 3.1 0.32 35 5.17 0.19 42 6.2 0.16
150 29 4.28 0.23 34 5.02 0.2 43 6.35 0.16
165 35 5.17 0.19 25 3.69 0.27 39 5.76 0.17
| Maximum | 40 | 5.91 | 0.52 | 38 5.61 0.27 | 43 j 6.35 | 0.17 1
\ Minimum
I 13
| 1.92 | 0.17 | 25 3.69 | 0.18 | 39 | 5.76 | 0.16 1
| Average I 27.75
L _ i ! _ |
0.28 1 33.08 |
! 1
0.21 | 40.33 1 5.96 | 0.17 |
Mear^FractureSpacing [ 0.22
Table 7 Results of fracture analysis for sample number: 10
Planes XY
YZ
zx
Measurement
Direction
(degrees)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
0 59 8.72 0.11 54 7.98 0.13 71 10.49 0.1
15 55 8.13 0.12 57 8.42 0.12 66 9.75 0.1
30 50 7.39 0.14 68 10.05 0.1 64 9.45 0.11
45 50 7.39 0.14 76 11.23 0.09 62 9.16 0.11
60 52 7.68 0.13 77 11.38 0.09 56 8.27 0.12
75 54 7.98 0.13 75 11.08 0.09 54 7.98 0.13
90 53 7.83 0.13 71 10.49 0.1 55 8.13 0.12
105 54 7.98 0.13 71 10.49 0.1 58 8.57 0.12
120 54 7.98 0.13 60 8.86 0.11 59 8.72 0.11
135 55 8.13 0.12 50 7.39 0.14 67 9.9 0.1
150 59 8.72 0.11 43 6.35 0.16 67 9.9 0.1
165 60 8.86 0.11 44 6.5 0.15 69 10.19 0.1
| Maximum i 60 | 8.86 | 0.14 | 77 | 11.38 | 0.16 j
71 | 10.49 I 0.13 I
| Minimum | 50 | 7.39 | 0.11 | 6.35 \ 0.09 | 54 | 7.98 I 0.1 |
| Average | 54.58 8.07 | 0.13 | 62.17 ! 9.19 | 0.12 ] 62.33
L ™ £ £ L J
0.11 |
j Mean Fracture Spacing | ""(H T "*"!
o n
Table 8 Results of fracture analysis for sample number: 15
Planes XY YZ
zx
Measurement
Direction
(degrees)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
0 68 10.05 0.1 74 10.93 0.09 49 7.24 0.14
15 63 9.31 0.11 73 10.78 0.09 49 7.24 0.14
30 59 8.72 0.11 69 10.19 0.1 49 7.24 0.14
45 55 8.13 0.12 60 8.86 0.11 50 7.39 0.14
60 49 7.24 0.14 53 7.83 0.13 49 7.24 0.14
75 49 7.24 0.14 50 7.39 0.14 49 7.24 0.14
90 55 8.13 0.12 48 7.09 0.14 54 7.98 0.13
105 60 8.86 0.11 48 7.09 0.14 56 8.27 0.12
120 63 9.31 0.11 57 8.42 0.12 51 7.53 0.13
135 66 9.75 0.1 64 9.45 0.11 47 6.94 0.14
150 67 9.9 0.1 74 10.93 0.09 48 7.09 0.14
165 69 10.19 0.1 77 11.38 0.09 51 7.53 0.13
| Maximum | 69 | 10.19 | 0.14 g 77 j 11.38~ | 0.14 g 56 | 8.27 | 0.14
| Minimum | 49 | 7.24 g 0.1 | 48 | 7.09 | 0.09 | 47 || 6.94 g 0.12 |
| Average | 60.25 | 8.9 g 0.11 | 62.25 g 9.2 g 0.11 | 50.17 j 7.41 j 0.14 |
| Mean Fracture Spacing
C T >
Table 9 Results of fracture analysis for sample number: 20
Planes XY
YZ zx
Measurement
Direction
(degrees)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
0 48 7.09 0.14 56 8.27 0.12 40 5.91 0.17
15 47 6.94 0.14 55 8.13 0.12 37 5.47 0.18
30 44 6.5 0.15 50 7.39 0.14 33 4.88 0.2
45 38 5.61 0.18 48 7.09 0.14 35 5.17 0.19
60 32 4.73 0.21 47 6.94 0.14 37 5.47 0.18
75 36 5.32 0.19 47 6.94 0.14 42 6.2 0.16
90 46 6.8 0.15 48 7.09 0.14 46 6.8 0.15
105 57 8.42 0.12 53 7.83 0.13 50 7.39 0.14
120 59 8.72 0.11 52 7.68 0.13 50 7.39 0.14
135 57 8.42 0.12 56 8.27 0.12 47 6.94 0.14
150 59 8.72 0.11 55 8.13 0.12 40 5.91 0.17
165 54 7.98 0.13 53 7.83 0.13 36 5.32 0.19
| Maximum 59 j 8.72 |
!.. 56 I 8.27 | 0.14 | 50 | 7.39 I 0.2 1
| Minimum | 32 | 4.73 | 0.11 | 47 | 6.94 | 0.12 | 33 | 4.88 | 0.14 |
| Average 48.08 | 7.1 | 0.15 | 51.67 | 7.63 | 0.13 | 41.08 | 6.07 |
?17 I
8 Mean FractureSpadng \ 0.15
-s i
Table 10 Results of fracture analysis for sample number: 25
Planes XY
YZ
zx
Measurement
Direction
(degrees)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
Points
Points per
Unit Length
(pts/mm)
Average
Spacing
(mm)
0 44 6.5 0.15 41 6.06 0.17 29 4.28 0.23
15 42 6.2 0.16 38 5.61 0.18 33 4.88 0.2
30 41 6.06 0.17 41 6.06 0.17 32 4.73 0.21
45 42 6.2 0.16 49 7.24 0.14 39 5.76 0.17
60 43 6.35 0.16 52 7.68 0.13 43 6.35 0.16
75 44 6.5 0.15 58 8.57 0.12 40 5.91 0.17
90 46 6.8 0.15 60 8.86 0.11 40 5.91 0.17
105 44 6.5 0.15 63 9.31 0.11 42 6.2 0.16
120 43 6.35 0.16 60 8.86 0.11 42 6.2 0.16
135 41 6.06 0.17 58 8.57 0.12 41 6.06 0.17
150 43 6.35 0.16 53 7.83 0.13 35 5.17 0.19
165 45 6.65 0.15 48 7.09 0.14 32 4.73 0.21
j Maximum
-------.46 | 6.8 | 0.17 | 63 |
9:31 I
0.18 | 43 | 6.35 I 0.23 1
| Minimum | 41 | 6.06 j 0.15 | 41 | 6.06 | 0.11 | 32 | 4.73 I 0.16 1
| Average | 43.17 I 6.38 |
—
51.75 |
J ----- 2 , 1 1 ,J
37.33 | 5.52 | 0.18 |
00
Fracture Ellipsoids
If the D(0), maximum and minimum fracture spacing, for each sample is
plotted in a polar coordinate form, a fracture ellipsoid results (Figures 5-10). If all
the observed fractures in each sample do in fact break, the fracture ellipsoids will
resemble the quartz grains shape bounded by the fracture sets. Shimamoto and
Ikeda's method (1976) was used to generate a 3-dimensional ellipsoid for each
rock sample (Table 11).
Regression
Regression analysis was performed to compare the results of the Fourier
analysis to the Strain analysis and the Fracture analysis. Regression analysis
between Fourier Harmonics and Strain ellipse was denoted by the equation:
y = 3.7531 x + 1.2508
This analysis produced a R2 value of 0.0182 which indicates a low correlation
between strain (fabric intensity) and Fourier (grain shape) (Fig. 11).
Regression analysis between Fourier harmonics and Fracture ellipse was
denoted by the equation:
y = 34.671 x + 0.4223
This analysis produced a R 2 value of 0.1063 which indicates a moderate
correlation between fracture (fracture patterns) and fourier (grain shape). This is
a higher correlation with grain shape than the strain analysis showed (Fig. 12).
49
XY Plane YZ Plane
ZX Plane
Figure 5. Graph of fracture ellipses for sample number: 1
c n
o
YZ Plane XY Plane ZX Plane
Figure 6. Graph of fracture ellipses for sample number: 5
XY Plane
345, 1
210 '
195' '165
"150
180
YZ Plane
345, 1
\ 0.4 -
270
210
195' '165
150
180
ZX Plane
345, 1 -
330.
285 ^
270
255 -105
240" 120
225-
150
'165 195'
180
Figure 7. Graph of fracture ellipses for sample number: 10
c n
ro
XY Plane
ZX Plane
Figure 8. Graph of fracture ellipses for sample number: 15
cn
w
XY Plane
o
330
45
300 . <
285
270
105 255
240-
225-
210 '
180
YZ Plane
o
330
0 j 6 -
285 ~
270
255 105
240
2 2 5 '
210
195' "165
180
ZX Plane
o
330
315
300
285
270
255 105
120
135
210 150
195 '165
180
Figure 9. Graph of fracture ellipses for sample number: 20
o n
XY Plane
330
315,
300 a
285 75
270
105 255
240
225'
195' - '165
180
YZ Plane
330
315
300 a
45
0.6 -
0.4 -
285
270
255 105
240- 120
225
150
195' '165
180
ZX Plane
o
„ 345, 1 - J 5
330, >30
315. V ' ■/ >45
■ ' \ 0-6 . /
210
195' - '165
180
150
Figure 10. Graph of fracture ellipses for sample number: 25
c n
O l
Table 11. Fracture ellipsoid axes for the six samples.
Dl , D|, and Ds are the length of the long, intermediate,
and short axis, respectively.
Sample
Dl D, Ds
1 1.673 1.294 1
5 2.592 1.705 1
10 2.029 1.433 1
15 1.85 1.364 1
20 2.126 1.471 1
25 1.899 1.386 1
Strain ellipse R atio (Dl/Ds)
1.6
+ , +
3.7531X+ 1.2508
R2 = 0.0182
1 - -
0.8 -
0.6 -
0.4 -
0.2 -
0 J 1 i 1 i : --------------- ; --------------- 1 --------------- 1 ---------
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Fourier Amplitudes for Second Harmonic
Figure 11. Plot of regression analysis between strain ellipse and second fourier harmonic.
c n
's i
0.09 0.1
Fracture Ellipse R atio (Dl/Ds)
3
2.8 -
2.6
2.4
2.2 -
1.8 - -
1.6 -
1.4
1.2
y = 34.671 x + 0.4223
R2 = 0.1063
0.01 0.02 0.03 0.04 0.05 0.06 0.07
Fourier Amplitudes for Second Harmonic
0.08
Figure 12. Plot of regression analysis between fracture ellipse and second fourier harmonic.
0.09 0.1
c n
o o
Regression analysis between Fracture and Strain Ellipses was denoted by
the equation:
y = 0.1726X + 1.0604
This analysis produced a R2 value of 0.3083. This plot has the best correlation of
all three regression analyses (Fig. 13). This suggests that the fractures observed
in the rock samples were produced by the same stress responsible for
deformation.
59
Strain Ellipse R atio (Dl/Ds)
2.5
2
y = 0.1726x+ 1.0604
R2 = 0.3083
1.5
♦ ♦
1
0.5
0
1 2 0 3 4 5 6
Fracture Ellipse Ratio (Dl/Ds)
Figure 13. Plot of regression analysis between fracture and strain ellipses.
0 3
o
DISCUSSION
The origin of quartz grain shape composition is a very complex matter. It
is difficult to assign a typical grain shape population to a specific rock type
because of the many factors that affect the shape of quartz in a protolith. These
factors include the plastic and brittle deformation of the region, the crystal size
relative to the number of crystals, the crystallographic history of the quartz, the
orientation and spacing of fracture sets, and the grain size selected for study. The
crystallization history of a specific protolith may shape the quartz crystals, but this
shape is not long-lasting because of the plastic and brittle deformation the pluton
undergoes. The deformation may change the shape of the quartz grains to a point
where identification of the original shape is impossible. Thus, the shape of the
quartz grains from a protolith that are studied from grus are more likely a result of
the plastic and brittle deformation of the protolith than any other factor.
The effect of the plastic deformation on the shape of quartz crystals has
been described in numerous papers which used both laboratory experiments and
naturally-deformed rock observations (Hobbs and others, 1976; Young, 1976;
Karato and Masuda, 1989). Plastic deformation can change the shape of the
quartz crystal in terms of crystal form (elongation) and surface texture (asperity).
These shape changes may be a result of deformation, recovery, primary
recrystallization, and/or secondary recrystallization. Artificially strained rocks along
with natual rocks, which can be assumed to have undergone at least some strain,
show more elongation in quartz crystal shape than non-strained rocks (Hobbs and
61
others, 1976; Karato and Masuda, 1989). The asperity of quartz crystals are
changed (i.e. made rougher) by the differential migration of preexisting grain
boundaries (Hobbs and others, 1976).
The effect of brittle deformation on the shape of quartz crystals is not as
well understood. Fractures are however an important feature in igneous rocks and
thus are considered important in shaping the quartz crystals. Fractures are
created by regional tectonism, differential volume changes in heterogeneous rock
bodies, erosional unloading of isotropic rocks or any other process that raises the
local stresses above the local strength (Simmons and Richter, 1976).
Microfractures, though, play a more pivitol role in the shape of quartz grains found
in grus. This occurs because the microfracture spacing is commonly much smaller
than the crystals they transect. Liu (1993) confirmed this in his study by finding
that there were no significant differences in grain elongation between deformed
and undeformed samples. Even though the strained rocks exhibit more elongate
crystals in outcrop, the microfractures when allowed to break, limit the elongation
of the crystals. Liu also discovered that grain size plays an important role in the
amount of information a grain holds. Liu concluded from his study that the larger
the quartz grain studied the more information on the original crystal shape that can
be had. The shape of the smaller grains are more a result of the microfracturing
than of the processes that strained the protolith. This is because as the size of the
grain decreases, the shape becomes more and more a function of the fracture
pattern. In this study, the effect of strain and fracturing on a single pluton was
62
examined in order to see if, and to what extent, each process affected the shape
of the quartz grains found in grus.
Factor analysis tested the selected samples to identify any shape patterns
with regard to grain elongation and asperity. The results to this test indicate that
no clear patterns exist. This suggests that there is variation within the pluton with
respect to grain shape and whatever processes influence the shape of grains are
not prevalent throughout the pluton. The Hotelling's T2 Test and the ANOVA test,
which examine variance in a sample set, indicate that the two transects varied in
grain shape from each other and that there is also significant variation within the
two transects. This implies that significant variation exists within the Granite
Mountain Pluton. Since variation exists within the pluton, the shape of the quartz
grains may be affected by more local controls than previous studies had implied.
Duncan testing highlighted the variant samples within the two transects - sample
13 of transect A and sample 21 of transect B. The variance in these samples may
be caused by geologic phenomena. Sample 13's variance in shape from the rest
of the samples in transect A may be explained by the fact that sample 13 lies on
a portion of the Chariot Canyon Fault. Sample 21 does not lie in any mapped
zone of intense deformation. However, a local zone of intense deformation may
exist but has not been previously mapped.
Strain analysis performed suggests that sample 4 and 13 of transect A are
highly strained. As noted above, sample 13 is highly variant and this was
attributed to sample 13 lying in a portion of the Chariot Canyon Fault. This would
63
explain why this sample is highly strained. Sample 4 does not appear to lie on any
mapped zone of deformation though it could lie in a unmapped zone as does
sample 21. Sample 4, however, does not vary from the other samples in transect
A with respect to grain shape. Regression analysis indicates that a low correlation
exists between fabric intensity (strain analysis) and grain shape (Fourier analysis).
The microfracture spacing correlated moderately well with grain shape.
Better correlation might have been obtained if the samples had been tumbled.
This can be explained by the fact that not all of the fractures transecting the quartz
grains have broken in the grus samples. The strain analysis correlated less with
grain shape than did fracture analysis. This may be due to overprinting by the
fracture patterns onto the original crystal shape or more likely this may indicate
that the fracture patterns better control the grain shape than does the initial crystal
boundaries. Regression analysis between strain and fracture ellipses resulted in
a moderate correlation which implies that the grains that are strained the most are
also the most fractured.
64
CONCLUSIONS
Fourier grain-shape analysis, Strain analysis, and Fracture analysis were
performed on 25 samples collected from the Granite Mountain Pluton, San Diego
County, California to determine what relation exists between strain, microfractures,
and the shape of quartz grains. Fourier analysis was used to mathematically
describe the shape of quartz grains. Strain analysis was used to identify the fabric
intensity of different portions of the pluton so as to correlate these with grain
shape. Fracture analysis was used to identify the fracture patterns in the quartz
grains in order to relate these to grain shape.
Based on these analyses, the following conclusions can be made.
1) The Fourier testing presented in this study indicates that large variations in
quartz grain shape may exist within an individual pluton.
2) Fabric patterns do not correlate well with grain shape.
3) The variation in quartz grain-shape is caused by local zones of intense tectonic
deformation.
4) Fracture analysis indicates that fracture patterns affect grain-shape more than
strain.
5) Great care must be exercised when selecting plutonic bodies as specific
sources for local or regional provenance studies.
65
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Asset Metadata
Creator
Robinson, Dawn Margaret
(author)
Core Title
Quartz Grain-Shape Variation Within An Individual Pluton: Granite Mountain, San Diego County, California
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 S. (
committee chair
), Bottjer, David J. (
committee member
), Sammis, Charles G. (
committee member
)
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c18-9452
Unique identifier
UC11357652
Identifier
1378432.pdf (filename),usctheses-c18-9452 (legacy record id)
Legacy Identifier
1378432-0.pdf
Dmrecord
9452
Document Type
Thesis
Rights
Robinson, Dawn Margaret
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