.4-

viz.

1.

599s

n
A.
*w.

w
é

.1

\4:

‘~

I
u
cm

a\»

:. '
..~. m.
tffié'x‘ 1.
..
w,”

- J...
..,.
(1

l:' —v‘
{V

a
v. “$.73” >35."
6.. ‘3. ‘fi...

6%"..1.
.M‘J; "
~ “ .
“‘3 57.

v": ~

w-fi .Q'I
“.._
z“

. é ‘

‘ v‘.‘ m :.

4“}. w‘ ‘ .r ‘ '3‘. c i, a. .363 Sgt...“

41:1:1 ‘D:>v-I0‘ {I Wfi‘i‘v.‘
4&3}. ~‘ ' z ..., ~..__.‘

“ ":1 a ' J; ‘9'" ‘7‘.

a
‘ 4 mi‘
I
u

, go
.’:..“"‘-.<’xt:
’03?! I

‘3

.5?
1%:

\
l a;

Mo.
A».
.u..

i.
fir? 3

‘9..-

‘“ y...
-W -. a§4w
4‘57..v »~.-

"' .W‘-..
"‘. ...~.-

. .»a.

.u

.1.
~.-,..- A

 

sm/ LI IBRARIES

WWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWW WWWWW WWW

30’ LIBRARY
Michigan State
Unlverslty

 

 

 

 

|

 

 

 

 

 

 

This is to certify that the

thesis entitled

CRYSTAL SIZE DISTRIBUTION COMPARISON
IN ORDOVICIAN DOLOMITES

presented by

ROBERT CRAIG BROWN

has been accepted towards fulfillment
of the requirements for

MASTER degreein SCIENCE

 

 

Major professor

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

W ”GENREWRNBOXtor-MMMMMMWM
W To AVOID FINES Mum on or bdon mm.

W DATE DUE DATE DUE DATE DUE

W

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU I. An mm Action/Equal OW lm
WM‘

 

 

CRYSTAL SIZE DISTRIBUTION COMPARISON
IN ORDOVICIAN DOLOMITES

by

Robert Craig Brown

A THESIS

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

MASTER OF SCIENCE

Department of Geological Sciences

1994

ABSTRACT

CRYSTAL SIZE DISTRIBUTION COMPARISON IN ORDOVICIAN DOLOMITES

By

Robert Craig Brown

Crystal size distributions (CSDs) vary according to nucleation and growth. CSDs are
compared within and between the Trenton Formation (Middle Ordovician) and the
Saluda Formation (Upper Ordovician) dolomites, and to theoretical models (site-satura-
tion, Johnson-Mehl). Comparisons are made by 1) t-test of standard deviations of nor-
malized CSDs, 2) Kolmogorov-Smimov goodness-of-fit (K-S) test between CSDs, 3)
K-S test of CSDs to normal, lognormal, and gamma distributions, and 4) t-test of the
gamma distribution shape factor, alpha. Dolomite CSDs are more closely represented by
the gamma distribution than the normal or lognormal distributions. Trenton CSDs are
not significantly different from each other despite significant differences in mean grain
size. The pattern of CSD shape does not change relative to mean grain size. Saluda
CSDs are not different from each other, but are different from Trenton CSDs.

Theoretical models do not resemble the dolomite CSDs.

Acknowledgements

Many thanks go the the MSU Geology Department Faculty and Staff, for their assistance,
encouragement, and financial support. I appreciate the opportunity to study under the
guidance of Duncan F. Sibley, Michael A. Velbel, and David T. Long. I appreciate being
able to meet and talk with Aureal T. Cross, John T. Wilband, Thomas A. Vogel, Grahm
Larson, F.W. Cambray, Hugh Bennett, and Bob Anstey.

My thanks goes to Jill and Tom Stebbins for welcoming me into their busy and wonder-
ful household in Okemos. I would like to acknowledge my friends (whose advice to fin-
ish as soon as possible was promptly ignored, yet they remain good friends) Myung Yi,
Abdule Muhanna, Mohammad Ghavidal-Syooki, Mounir Saad, and 800 Meen Wee.
Acknowledgement should also go to Sgt. McCloud (Dave Cook) and his sidekick crony
in crime, Chester (Erin Lynch) for welcoming me to MSU. I want to thank my family

for their humor throughout this ordeal.

iii

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................... vi
LIST OF FIGURES ................................................................................................. viii
INTRODUCTION .................................................................................................. 1
GENERAL GEOLOGIC SETTINGS OF SAMPLE DOLOMITES ..................... 3
Trenton Formation Dolomite ............................................................................. 3
Saluda Formation Dolomite ............................................................................... 7
COMPUTER - GENERATED MICROSTRUCTU RES AND ANALYSES ........ 12
METHODS ........................................ . ..................................................................... 18
Method of Crystal Size Distribution Measurement ............................................ 18
Stereology of CSD Determination ...................................................................... 18
Statistical Analyses ............................................................................................. 24
Method Reproducibility ...................................................................................... 32
CSD DATA ............................................................................................................. 43
Trenton Formation ............................................................................................... 43
Saluda Formation ................................................................................................ 50
Theoretical Computer - Generated Microstructures ........................................... 5 3
Analysis and Comparison Between Formation and Theoretical CSDs .............. 55
DISCUSSION ......................................................................................................... 58
CONCLUSIONS ..................................................................................................... 63
APPENDD( A
Thin-Section Description, Photographs And Drawing ........................................ 65
APPENDD( B
Two-Sample Kolmogorov—Smimov Goodness-Of-Fit Tests ............................... 82

iv

TABLE OF CONTENTS (cont’d)

APPENDIX C

Normalized Crystal Size Distribution Frequency Histograms And

Crystal Size Distribution To Thin-Section Sample Key ...................................... 88
BIBLIOGRAPHY ................................................................................................... 127

10

ll

12

l3

14

LIST OF TABLES

EAQE

Two-Sample Kolmogorov-Smirnov Test Evidence of
Reproducibility On Measured Crystal Size Distribution Data ................ 41
Comparison of Statistical Values of Duplicate CSD Counts
and Thin-Section Samples ....................................................................... 42
Trenton Formation CSD Statistical Values ....................................... 44-45
Two Sample K-S Tests Between Thin-Section TLl Clasts .................... 47
Two Sample K-S Tests Between Thin-Section TL2 Clasts .................... 47
Two Sample K-S Tests Between Thin-Section TL3 Clasts .................... 48
Two Sample K-S Tests Between Thin-Section TL7 Clasts .................... 48
Two Sample K—S Tests Between Thin-Section TL8 Clasts .................... 49
Two Sample K-S Tests Between Thin-Section TL9 Clasts .................... 49
Two Sample K-S Tests Between Thin-Section TLll Clasts ................... 49
Saluda Formation CSD Statistical Values ............................................... 52
Two-Sample Kolmogorov-Smimov Goodness-Of-Fit Tests Between
Saluda Formation Samples ..................................................................... 53
Theoretical Computer-Generated Microstmcture CSD Statistical Values .......... 54

Two-Sample Kolmogorov-Smirnov Goodness-Of-Fit Tests Between
Normalized Theoretical Computer-Generated Microstructure CSDs ..... 55

vi

15

LIST OF TABLES (cont’d)

Comparison of Mean and Standard Deviations of the Means and
Standard Deviations of the Alpha, Normalized StandardDeviation,

Skewness, and Inclusive Graphic Skewness Values for the Saluda
and Trenton Formations .......................................................................... 56

vii

FIGURE

LIST OF FIGURES

Regional sample location map of theTrenton Formation (middle
Ordovician) core samples within the Michigan Basin and the
Saluda Formation (upper Ordovician) outcrop samples on the

western flank of the Cincinnati Arch. ..................................................

Detail map of the Trenton Formation core sample location with the
well lease names listed. The wells from which core samples were

investigated in this study are circled (after Miller, 1988). ...................

Photomicrograph of Trenton Formation limestone conglomerate

showing rounded quartz grain matrix ..................................................

Detail map of the Saluda Formation (upper Ordovician) outcrop

sample location (after Walters, 1988). .................................................

General stratigraphy of the Cincinnatian Series as determined by

various authors (from Davis, 1986). ....................................................

Computer generated microstructures (from Fridy et al. 1992) with
corresponding CSD frequency histograms. Nucleation and growth
models are a) Johnson-Mehl, b) Site-Saturation (cellular), and

c) Site- Saturation with weakly clustered nuclei. ................................

Size histogram of circles measured from intersections on several
sphere sizes is the sum of the individual disu'ibutions shown by the

differently shaded bars (after Russ, 1986). .........................................

CSD frequency histograms of Boi Doi dolomite from Aruba,
Netherlands Antilles. Histograms are from a) thin-section, and

b) disaggregated grain-mount. .............................................................

viii

..... 4

..... 6

..... 7

..... 8

..... 9

..... l3

..... 20

..... 21

FIGURE

10

11

12

13

14

15

16

LIST OF FIGURES (cont’d)

a) Shaded grains show those measured in a line point count, and

b) the corresponding CSD frequency histogram. ............................

Densities of the gamma and lognormal distributions with
parameters selected to give the maximum value .54 at x=1

(after Breiman, 1973). ....................................................................

a) frequency histograms, and b) cumulative relative frequency
distributions of Gamma distributions using a constant [3 (scale)

value and different or (shape) values. .............................................

a) frequency histograms, and b) cumulative relative frequency
distributions of Gamma distributions using a constant or (shape)

value and different B (scale) values. ...............................................

a) frequency histograms, and b) cumulative relative frequency
distributions of Gamma distributions using equal or (shape) and B

(scale) values. .................................................................................

Two of the three frequency histograms of line point counts of
Trenton clast TLlA. (Note: size data is measured data and not

normalized.) ....................................................................................

Respective cumulative relative frequency distributions of the
frequency histograms of Trenton clast TLlA shown in Figure 14.

Two of the three frequency histograms of line point counts of
Trenton clast TLlB. The solid line is a fitted gamma distribution.

(Note: size data is measured data and not normalized.) .................

......... 23

.......... 28

.......... 29

.......... 30

.......... 31

.......... 33

......... 34

.......... 35

FIGURE

17

18

19

20

21

22

23

LIST OF FIGURES (cont’d)

Respective cumulative relative frequency distributions of frequency

histograms of Trenton clast TLlB shown in Figure 16. ....................

Frequency histograms of duplicate line point counts of Boi Doi
dolomite from Aruba, Netherlands Antilles. The solid line is a
fitted gamma distribution. (Note: size data is measured data and

not normalized.) ................................................................................

Respective cumulative relative frequency distributions of the
frequency histograms of the Boi Doi dolomite shown in Figure 18.

Frequency histograms of line point counts of duplicate thin-section
samples of the same clast from the Trenton Formation. (Note: size

data is measured data and not normalized.) ......................................

Respective cumulative relative frequency distributions of the

frequency histograms shown in Figure 20. .......................................

Two of the eight frequency histograms of the Saluda dolomite

samples. .............................................................................................

Kolmogorov-Smirnov goodness-of-fit test cumulative relative
frequency distribution showing the consistent differences

between the Saluda and Trenton Formation CSDs. ..........................

EAGE

....... 36

....... 37

....... 38

....... 39

....... 4O

....... 51

....... 58

INTRODUCTION

The crystal size distribution (CSD) of a single phase, polycrystalline solid will vary
according to the nucleation and crystal growth behavior during the transformation, or
recrystallization, of that solid. Friedman (1965) recognized the importance of CSDs
in describing the character of carbonate rocks such as dolomite, by classifying those
with a relatively uniform CSD as equigranular and those with a polymodal CSD as
inequigranular. Sibley and Gregg (1987) suggested that unimodal (equigranular) dis-
tributions result from a single nucleation event in a homogeneous substrate, and that
polymodal (inequigranular) distributions result from nucleation in an inhomogeneous
substrate, or multiple nucleation events. Marsh (1988) used CSDs to study the kinet-
ics of crystallization in metamorphic and plutonic rocks. Marsh’s basis for using
CSD data was that it yields quantitative kinetic data that can be applied to
understanding geochemical systems independent of the development of exact kinetic

theory for the system under consideration (Marsh, 1988, p.278).

Many experimental CSDs have been observed, particularly in the material science
field, often showing coarsely skewed, lognormal shapes to the distributions. This
fact, and the effect of nucleation and crystal growth behavior on the crystal size dis-
tribution, has been investigated using a number of computer models in which vary-
ing nucleation and crystal growth processes can be chosen to generate a polycrystalline
solid (Mahin, Hanson, and Morris, 1976, 1980; Saetre, Hunderi, and Nes, 1986;

Marthinsen et al., 1989). A range of computer generated CSDs with specific crystal '

2
nucleation and growth processes can be compared to experimentally derived CSDs to
assess the nucleation and growth characteristics of these systems. In this study, three
computer-generated CSDs are used to evaluate experimental size distributions measured
in dolomites. Dolomite from the Trenton Formation, Middle Ordovician, of Michigan,
and the Saluda Formation, Cincinnatian Series, Upper Ordovician, of Indiana were inves-
tigated in this study. Rocks from these formations were chosen because of the different
mean grain sizes within the formations and different temperatures of dolomitization

between the formations.

The major limit of CSD data is that there is more than one way (nucleation and growth
kinetics) of generating a given size distribution. For example, a transformation with an
increasing nucleation rate and a constant growth rate may have a similar CSD to one
with a constant nucleation rate and decreasing growth rate. Alternatively, differing CSD
characteristics will result if a constant growth rate is maintained and the nucleation rate is
varied. This is illustrated by several computer generated CSDs (Saetre et al., 1986;
Marthinsen et al., 1989; Frost & Thompson, 1987). Similarly, Larikov (1986) generated
nearly identical percent transformation sigmoidal graphs using a constant growth rate,
but using different nucleation frequencies.

The purpose of this study is to compare the shape of CSDs from within a given popula-
tion (formation), between populations (formations), and to theoretical CSDs, to place
constraints on the interpretation of CSDs, thereby illuminating the influences of the dif-

fering conditions under which dolomites form.

GENERAL GEOLOGIC SETTINGS OF SAMPLE DOLOMITES

Samples from two locations were investigated for this study. The first sample location is
the epigenetic, fracture-related dolomite from the Trenton Formation, Middle
Ordovician, within the Michigan Basin. The Trenton Formation samples are cored inter-
vals from wells located in Jackson County, Michigan. Figure 1 shows the sample loca-
tion in reference to the Michigan Basin. The second sample location is the Saluda
Formation, Upper Ordovician, located in Jefferson County of southeastern Indiana.
Figure 1 shows the Saluda Formation sample location in reference to the Cincinnati Arch

and Illinois Basin.

Trenton Formation Dolomite

The Trenton Formation overlies the St. Peter Sandstone (Lower Ordovician) and
generally grades into the overlying Utica Shale (Upper Ordovician). The thickness of the
Trenton Formation ranges from about 50 meters in the northeast to about 150 meters in
the southeast of Michigan. The southeastward thickening of the formation probably rep-
resents carbonate platform development in that area. The top of the Trenton appears to
be a regionally extensive hardground (Keith, 1985). The Trenton Formation is approxi-
mately 110 meters thick in the study sample location of Jackson County, Michigan. The
Trenton Formation in this location is probably deposited in a deep subtidal environment

(Wilson and Sungepta, 1985).

Three types of dolomites have been recognized in the Trenton Formation of the Michigan

THENTON FORMATION
CORE SAMPLE LOCATION

     

Permian

lllllll

L'" "Min.

IIII

 

 

Pennsylvanian

 

 

Devonian

 

Ordovician

  
 
 

  

mi W

 

 

 

 

 

 

 

SALUDA FORMATION
OUTCROP SAMPLE LOCATION

figure I Regional sample location map of the Trenton Formation (middle
Ordovician) core samples within the Michigan Basin and the Saluda
Formation (upper Ordovician) outcrop samples on the western flank of the
Cincinnati Arch.

5
Basin (Taylor and Sibley, 1986). A ‘cap’ dolomite exists at the upper few meters of the
Trenton that is in contact with the Utica Shale and is distinctly ferroan (approximately 7
mole % FeCO3). A ‘fracture-related’ dolomite exists which is related to subsurface
fractures, and structures of the basin. It is characterized by linear trends of epigenetic
dolomites such as that found along the northwest-trending Albion-Scipio Trend which
transects southeastern Jackson County, Michigan. A ‘regional’ dolomite is confined to
the southwestern and western edges of the basin and does not extend into the study area.
The Trenton core samples used in this study are considered to be part of the fracture-
related dolomites taken from Jackson County, Michigan (depths of approximately 4850
to 4930 feet below sea level). Most of the formation in the study area is limestone, but
the cored intervals for this study contain partially and completely dolomitized strata.
Figure 2 is a local area map showing the well locations (from Miller, 1988). Much of the
Trenton Formation in the study area consists of a mudstone or wackestone clast
limestone. The dolomite is slightly calcium rich having a mean of 51 mole % Ca [based
on position of d(104)], (Miller, 1988). Taylor and Sibley (1986) calculated a temperature

of precipitation of approximately 80°C by using oxygen isotope data.

The samples from these locations and depths were chosen for study because they are
dolomitized intraclastic limestones which show significant textural variations between
the clasts of the conglomerate. The textural variations of clasts in close proximity elimi-
nates differences in overall solution chemistry or temperature as a control on the result-

ing dolomite textures.

The clasts range in size from a few millimeters to several centimeters in diameter. The
clasts are generally surrounded by a matrix of carbonate mud and quartz silt. The silt is
not found within the clasts, or within cemented fractures of some clasts, which shows the
rocks to be true conglomerates, not collapse breccias. Dolomitization followed the lithifr-

cation and subsequent deposition of the conglomerate as evidenced by the fact that the

A32 .552 .33 0288 v.8 beam £5 E 839395 203 BEES 28 523 Sec
«:03 2F .33.: 3.5: 9.8. :03 05 .23 5:82 0389. 28 392.com :95; 05 .8 9:: =83 N 8:9...—

 

 

hT- ocmxz<:
A

a a e 2 V O- 32.52:
mmmoo zepzmmh

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o a... N—
593....
_ a... Tu
. . A.“ V63 5:: p 2... . 3 z
W— ._. 5.3:. 5:: \ .92.. .0258 5.3.: .
m h .0 2. 03 2 p
a . 2.22... 36.:
E :03 \ a?“ .83 o.
5.3:. 52“. W
19. 9: x03
.. z 2 <1
7363 o :
ZOSZ<2
P N m
m w
.
.

 

 

 

 

.ll.. . . w . 2
ME >>

 

 

 

 

 

Figure 3 Photomicrograph of Trenton Formation limestone conglomerate showing
rounded quartz grain matrix.

Photographs of the thin-section, and drawings outlining and labeling the clasts are shown
in Appendix A. A brief description of each clast studied in this investigation is also

given in Appendix A.
Saluda Formation Dolomite

The Saluda Formation samples analyzed in this study were obtained from a road cut
along Highway 421, in Jefferson County of southeastern Indiana, approximately 3 miles
north of Madison, Indiana, near the Kentucky-Indiana border. Figure 4 is a detail sample
location map showing the location of the road cut. This site is located on the western
flank of the Cincinnati dome/arch, toward the Illinois basin. The Saluda Formation is

Upper Ordovician and part of the Richmond Group of the Cincinnatian Series.

 

_._.._. _.RIOHMONOa] IT
I : WAYNE '
' l.._..1 “““ 'I I
I nusu | : . PREBLE :
i I UNON I
INDIANA I I FAYETTE : .._.. ...._-_.. —-i
i i__..—---—.-.—| OHIO
l- "—' I FRANKLIN I BUTLER I
' HAMBURG l = ¢'
In = ° . I
I DECATUR ) H: U Q” . H
i ' I
' /--I/ may : cmcmmn
—‘ IDEARBORN

= VERSAWLLES ' \-"’ .
l . , \
, \.‘\@ \ .

i JENNINGS-1.. .._I!” ~ —1"_1.l.._.,_ ._.r‘
! '4’ErFFERSON

.. I !SWITZERLANQ <\ ‘ .
I" ' 'uverrson .._. I ,1 @5/
i SCOTT ' \. \./ CARR/OLL w
. I TRIMBLE ' ./

"""""-'-\ agorono’

 

iIn--=i ' “m /,5.é/ " ‘ KENTUCKY
I
I-“@ {SKY IGHT I I N
VEDW‘” ' 20 munfl
I)‘ LOUISVILLE
JEFFERSON

 

 

 

fir SAMPLE OUTCROP LOCATION

Figure 4 Detail map of the Saluda Formation (upper Ordovician) outcrop sample
location (after Walters, 1988).

9

dolomite in the partially dolomitized samples tends to form around the edges of the
clasts. Figure 3 is a photomicrograph showing the edge of a clast and the rounded quartz
in the matrix.

Figure 5 shows the general stratigraphy of the Cincinnatian Series as determined by vari-
ous authors (from Davis, 1986). Following the work of Walters (1988), the Saluda lies
above the Liberty Formation and generally lies below, but interfingers with the
Whitewater Formation above it. The Saluda thickens to the south and the Whitewater
thickens to the north. The thickness of the Saluda is approximately 60 feet in the study
area (Brown & Lineback, 1966).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

us us Mum SI 0000.“ '40.. cor-011.500 sumo: swowo untrue-Iv 3.1m
It“ cc»:- on... a in uremic" «ma. III. 3 l nun-m in... u .4. ma. then. tout tam. mt
a ea a hoe. ma non mm mm a 5-0.. mm an. and. run but It". vim tau
(um mates
. Wltfl'“ mi mu minute-
a 3"!“ a, ‘ Wit-LL: ...
. ‘ WH'EMTgl ,I Hull 0'
2'! '- mum I mum man In. ....... ‘
- p \
5 H 253‘ “W” uwoa mum \\
5 mount I m. \
'i 2 . Luann wit
5 g ’3‘; um“ <"‘" '0"
‘ 'U
2 5 ,3. “M"“u' mu noun MI
E E -‘ cLAmvut ”I. - '0"
i K i “nature“ m
H mm 3
c
U ————I
a 3 3 cum 1
___r m
i . awn annual " I I
- ml.
2 .1. “W I 3' L8 W ”W g I: am!
i g 3; comm“: ma. cm'WI-u o 3 wt:
‘2’ 5' “new! W ““‘W‘ ““‘w‘ u
0 g ammo”; mum
M
m.
. g It you L/ "awn! 2
:1: mu m
* M
sour—care “’9‘ u
3 2 ‘0" ,u on KO“ m In
I! -' (comm W

 

 

 

 

 

 

 

 

 

 

 

FIGURE 5 General stratigraphy of the Cincinnatian Series as determined by various
authors .(from Davis, 1986).

The Saluda is predominantly dolomite. Brown and Lineback (1966) indiCate a distinc-
tive contact at the base of the Saluda with the underlying strata. However, other authors

describe the base of the Saluda to be gradational with the underlying strata, which is the

10

case at the sample location for this work. A distinctive zone of colonial corals exists
near the base of the Saluda. The Saluda is predominantly overlain by, and grades into,
the Whitewater Formation, which also contains a variety of limestone types interbedded
with calcareous shales. In much of Jefferson County and Clark County to the south, the
Saluda is disconforrnably overlain by the Silurian Brassfield Limestone (Brown &
Lineback, 1966). Post-Ordovician erosion removed the uppermost Ordovician and low-
ermost Silurian strata, and in places the Saluda and Whitewater formations are overlain

by upper lower Silurian strata (Walters, 1988 ref. of Hattin, 1961) .

At Madison, Indiana the Saluda consists of a section of thinly to thickly-bedded, biotur-
bated, dolomitized mudstones and wackestones, that is interbedded with lime grainstone
lenses and overlain by approximately 15 meters of laminated, dolomitized mudstone. All
the samples obtained for this study are mudstones from interbedded grainstones and

mudstones.

Overlying the interbedded grainstones and mudstones are laminated, dolomitized mud-
stones which contain occasional mudcracks and rip-up clasts, but show no evidence of
evaporite deposition. The laminated, mudstone section is completely dolomitized, as is
the upper bioturbated mudstone portion of the mudstone-grainstone facies. The dolomite
contains 44-48 mole % Mg [based on position of d(104)]. The amount of dolomite in the
mudstone decreases down section, however, and partially dolomitized bioturbated mud-
stones are found approximately 10 meters below the base of the laminated mudstone
facies. Mudstones with 50% dolomite occur as much as 20 meters below the base of the

laminated mudstone facies.

The grainstone lenses contain fragments of brachiopods, bryozoans, trilobites, and

crinoids. The wackestones contain fragments of bryozoans and brachiopods. The

ll

grainstone lenses are also limestones or partially dolomitized, and the dolomite is gener-
ally confined to the mud found within the sheltered pores of the grainstone. The grain-
stone lenses are approximately 5 to 30 cm thick. They appear to be storm-washed
deposits, as indicated by typically undulating bases with stacked and concave down bra-
chiopods, overlain by crinoidal and bryozoan fragments, and terminate with relatively
flat tops. The grainstones often pinch out laterally within a few meters. Deeper in the

section, the grainstones are thinner and laterally more continuous.

The dolomite is unimodal planar and either does not replace allochems, or replaces them
non-mimetically. Dolomite cement partially fills fossil molds (formerly aragonite), the
remainder of which is filled with coarse, equant, orange cathodoluminescent (CL) calcite
spar. The dolomite crystals have thin CL zones, and often have corroded interiors. The
CL zones can be correlated through the upper 20 meters of the section, including the
grainstone-mudstone facies. The zones in the dolomite deeper in the section are too faint
to correlate, but those in the upper section indicate that the dolomitizing solutions were

the same for the grainstones as for the mudstones.

The facies control on dolomite distribution in the Saluda is consistent with early diage-
netic dolomitization. Hatfield (1965) suggested brines. Regardless of the water chem-
istry, the lack of deep burial in the area (Beaumont et al., 1988) is consistent with

dolomitization at low temperatures.

COMPUTER - GENERATED MICROSTRUCTURES AND ANALYSES

Mahin, Hanson and Morris (1976), developed a computer model to construct single-
phase, polycrystalline microstructures for the purpose of characterizing the generation of
grain shape. The model is sufficiently general to treat any nucleation and growth process
in a one-phase solid. Because most crystal size distribution analyses are conducted in
two dimensions, a planar section from the computer-generated microstructure unit cube
was also generated. Two nucleation and growth models were used to illustrate the
technique (Figure 6). The site saturation model, also referred to as the cellular model,
begins with randomly-distributed nucleation sites in an isotropic, one-phase solid, which
all nucleate simultaneously and grow uniformly as equi-sized spheres until impingement.
Following impingement, the grains have planar boundaries to each other and grow
according to the free space available. In the Johnson-Mehl model, nuclei are randomly
distributed, form at a constant rate within the unit cube, and grow uniformly until
impingement. The nucleation sites and times are random. This results in the unit cube
being filled with grains of varying sizes and ages throughout the transformation, and in
grain boundaries which are hyperboloids of revolution. In both models the growth rate is
constant. A third microstructure, included in Figure 6, is a site saturation model with the
nucleation sites being weakly clustered. The corresponding CSD frequency histograms
are also presented with each microstructure in Figure 6. These microstructure prints are
provided by Dr. Knut Marthinsen, Department of Physics and Mathematics, Norwegian
Institute of Technology, Trondheim, Norway, (Fridy, Marthinsen, Rouns, Lippert, Nes,
and Richmond, 1992).

12

‘

 

In «a
s- ' t
4 I.
‘*" ‘.hv‘b f
r

mama ’ I
393%“

L

‘C

 

   
  

$1
I
D
3%
(0
'34"!

b

i
v!
5..
9::

{9?
is;
Q"

é‘
0:
B:-
13:
O
.5
5

'Iiméfizgflfi

€‘ .wflhw 'v“
. 5 ‘A
.521.» ~ g"

 

I'm ”Autogr-

 

— I l u . fifi—r

v I
e- ..
F 1
4
uv- _
a
u- _
’ .
r .
I‘ .4
l‘ . .
... _
1
4
.,
n . l . A
.u h. n.

. n J

frcquuncg

 

 

 

 

 

 

KHJNSMEL.NormSiZI

e '>— 7
0' l
75 a I J
“9 I i I
..- i l .2
xc : l i

l . l—I—‘frh I [—1

 

   
    

I:

3.

Ob
\

E

a,

.0.
n‘ 1

a

      
  
 

frcquuncu

Q
h
3
9
s3
v
,5.

      
  

 
  
    
   

It
.‘
61%.
at
.'""hn

a
‘ia:

 

 

 

 

 

A
EV.
'5

 

 

 

   

  

  

         

.1" . : ’V I ..l l-' I-l l
«:- u w w ... w KHSITSAT.Nor-m$izc

 

1.7

v ‘Ofl‘t'li‘
mgaJtém '

fruquuncu

 

 

 

-e.n m 0.0 ... e.-

KHSSUKCLoNormSiZI

C)

Computer generated microstructures (from Fridy et al. 1992) with
corresponding CSD frequency histograms. Nucleation and growth models
are a) lohnson-Mehl, b) Site-Saturation (cellular), and c) Site- Saturation
with weakly clustered nuclei.

14

The goal of Mahin, Hanson and Morris (1976) was to relate the topological features of
well-defined microstructures to the nucleation and growth laws which generated them.
“Physical experiments are limited by reproducibility, and the lack of total environmental
control. The theoretical analysis, based on known statistical theorems, provides the abili-
ty to reproduce the sections and transformation control, but is limited by the scarcity of
well defined models and theorems. Valid computer simulation, on the other hand, is able
to extend the attributes of the theoretical work to include highly detailed two-dimension-
al representations of the progression of a transformation in time and space, as well as
detailed three-dimensional information for any time or space.” (Mahin, Hanson and
Morris, 1976, page 39-40). For example, serial sections through microstructures of theo-
retical nucleation and growth models are useful aspects of computer-generated
microstructures for crystal size and shape analyses. Mahin, Hansen and Morris (1976)
concluded that it is possible to demonstrate theoretically that microstructures of a given
model type (site saturation, Johnson-Mehl, etc.) will be geometrically equivalent, regard-
less of the nucleation/growth ratio (Nv/G). They generated nearly identical,
logarithmic-like, CSD frequency histograms for two Johnson-Mehl model
microstructures. One of the Johnson-Mehl microstructures had a nucleation-to-growth
ratio of 40 grains per unit volume, and the other had 244 grains per unit volume.
Although the mean grain size changed, the shape of the CSDs remained the same. They
concluded that the results followed the theoretical predictions in all cases, indicating that

the simulation is valid at least for simple processes.

Mahin, Hanson and Morris (1980) investigated the nature of the distributions of quanti-
ties such as the number of sides, grain areas, and intercept lengths of a line transecting
the grains on a planar section of site saturation, and Johnson-Mehl model
microstructures. The frequency distributions of normalized grain areas and grain diame-

ters did reveal qualitative differences between the site saturation and Johnson-Mehl

15

microstructures. The distribution of intercept lengths did not show as distinct a

difference in the frequency histograms of the CSDs of the two microstructures.

Saetre, Hunderi and Nes (1986), constructed microstructures from the site saturation and
Johnson-Mehl nucleation and growth models as well, and studied three additional mod-
els. A third model consisted of a decreasing nucleation rate accompanied by a constant
growth rate. A fourth model incorporated an increasing nucleation rate with a constant
growth rate, and a fifth model was composed of a constant nucleation rate and a decreas-
ing growth rate. By holding the growth rate the same in the first four models, the effect
of nucleation frequency on crystal size distribution can be seen. The models with an
increasing nucleation rate or a decreasing growth rate were quite similar, and were the

ones resulting in the most lognormal-like distributions.

An increasing nucleation frequency, and consequently the relative nucleation rate, results
in a more coarsely skewed CSD than the site saturation model because younger, smaller
grains will develop before all available space is consumed by the growth of the older
grains. Generally, as the nucleation frequency increases, the nucleation density increas-
es, and greater number of younger, smaller grains will be allowed to form in the uncon-
sumed space of the unit cube. The resulting grain size distribution will contain a smaller
mean grain size, a smaller mode, and a more coarsely-skewed distribution than a
Johnson-Mehl model with the same growth rate. By holding nucleation frequency con-
stant, the effect of varying growth rates may be viewed. An increasing growth rate, rela-
tive to a constant growth rate, would shorten the completion time of the transformation,
and decrease the time and space available for new nucleation sites to form throughout the
transformation. The space will be consumed at a relatively faster pace by. the growing
grains, thereby decreasing the number of subsequent nucleation events which can take

place during the transformation. The resulting CSD would show a slightly less

16
coarsely-skewed distribution than a transformation with the same nucleation frequency
and a constant growth rate. The opposite would be true for a corresponding decreasing
growth rate. It would seem unlikely that nucleation would continue at a constant rate/fre-
quency if the growth of existing grains is decreasing, unless the growth rates were some—
how a surface-reaction-controlled process. Saetre, Hunderi & Nes (1986) produce several
CSD histograms from the models described above which show that an increase in the
nucleation rate serves to increase the number and peak frequency of small grains. This
will lower the mean crystal size, and, generally, increase the size to mean-size ratio. This
subsequently spreads out the distribution of the interrnediately-sized grains, and produces

a more lognormal-like normalized CSD.

Marthinsen, Lohne and Nes (1989) produced similar frequency histograms for both par-
tially- and fully-recrystallized microstructures in both the site saturation and Johnson-
Mehl models. The partially-recrystallized structures were investigated because the other
simulated microstructures did not allow for any grain competition or grain growth after
impingement, which would happen in real structures. The comparison of partially- and
fully-recrystallized microstructures shows that the shape of the distribution remains
essentially the same, and that the effect of impingement serves only to lower the peak
frequency and consequently broaden the distribution. However, the effect of
impingement appeared to show a greater influence on the site-saturation model CSD than

on the Johnson-Mehl model CSD.

Marthinsen, Lohne and Nes (1989) also introduced non-uniformity with respect to the
distribution of recrystallization nuclei and to the growth of new grains. This was done
because experiments have shown that the recrystallization process is exceedingly inho-
mogeneous. Two methods of introducing non-uniformity were used in their study. The

first method introduced non-uniformity by dividing a lohnson-Mehl model unit cube into

17
two areas, with one area having a much higher nucleation density than the other. The
other method divided the recrystallized nuclei into classes, each of which was associated
with a different decreasing growth rate. This second method was simulated using site
saturation (instantaneous nucleation), Johnson-Mehl (constant nucleation), and increas-
ing nucleation rates. The nuclei were distributed among the classes lognormally, in that
the highest growth rate was assigned to the class with the fewest nuclei. The model of
classes with different decreasing growth rates is based on a model for particle-stimulated
nucleation of recrystallization in which it is assumed that the nucleation of recrystalliza-
tion is restricted to the deformation zones surrounding large particles. The deformation
zones and the amount of stored deformational energy is proportional to the particle size.
The stored def ormational energy is the driving force for the growth of the recrystallized
grain. It is largest at the particle, and decreases throughout the deformation zone. Thus,
the initial growth rate is largest at the largest particles. The modeling of lognormally dis-
tributed nuclei growth rates is based on the lognormal grain size distribution often
observed in commercial alloys. The relevant aspect of the simulations to this study is the
modeling of many different growth rates for many grains within the same microstructure,
such as in flux-limited growth. The effect of altering the nucleation rates by creating the
two zones with different nucleation densities did not significantly change the resulting
CSD from that of a straight Johnson-Mehl nucleation and growth model. For the models
with the introduction of classes of grains with different decreasing growth rates, none of
the CSDs closely simulated the lognormal CSD. The CSDs with site saturation and
Johnson-Mehl nucleation kinetics were broader, and subsequently had slightly lower
peak frequencies, than their counterparts with isotropic, constant growth rates. The
model with increasing nucleation rate was most similar to the lognormal distribution, and
compared favorably to the increasing nucleation rate and decreasing growth rate models
developed by Saetre, Hunderi & Nes. Again, it seems unlikely that an increasing nucle-
ation rate would occur with a constant growth rate, or in this case classes with different

decreasing growth rates, without a surface-reaction-controlling factor.

METHODS

Method of Crystal Size Distribution Measurement

In this study the CSDs of the thin-sections from the Trenton and Saluda were determined
by taking line point count measurements. The line point counting method is conducted
by traversing across a thin-section (or dolomite clast in the case of the Trenton) in which
all of the crystals which touch the cross-hairs of the ocular along that traverse are includ-
ed in the count. The longest diameter of each crystal encountered during the traverse of
the thin section is measured and recorded. The grains on the edges of the clast or thin
section were not measured to eliminate boundary effects. At the end of the traverse, the
thin-section or clast is off-set approximately 1.5 to 2 times the size of the larger-sized
grains measured in the first traverse, and a second traverse is begun. Those grains large
enough to cross two traverses were counted only once. The number of grains measured
per sample ranged from 199 to 300. The purpose of the line point counting method of
CSD measurement described above is to minimize the bias toward the larger grains, in
comparison to the normal point counting method. The method does not completely elim-

inate the large grain bias.

Stereology of CSD Determination

The two-dimensional view of a microstructure obtained by slicing a planar section
through the unit cube will show a different size distribution than would be observed for

the true grain diameters viewed in 3-dimension. The resulting distribution is generally

18

l9

coarsely-skewed; that is, fewer large grains are observed. This occurs because the proba-
bility of obtaining a longest-axis cross section of all crystals encountered by a planar cut
through the polycrystalline unit cube is low compared to obtaining some smallerportion
of the crystals within the planar section, or thin section (Lorenz, 1989; Russ, 1986). This
fact was illustrated by Krumbein (1935) in his size distribution comparison between a
thin section and disaggregated grains of the St. Peter sandstone. There is, however, no
accurate way to theoretically determine the relationship between true and apparent sizes

for irregular objects of unknown size distribution.

The probability of obtaining a particular circle diameter is related to the vertical
thickness of a slice of the sphere with that size (Russ, 1986). Cashman and Marsh (1988)
showed that the CSD, or density distribution curve for the apparent size of uniformly-
sized spheres in thin section, could be calculated. The attempt to determine or calculate
the true sizes and distributions becomes problematic when dealing with spheres of differ-
ent sizes. The apparent size distribution is affected not only by the probability that the
apparent diameter of any one sphere will be smaller than its true diameter due to the
effect of sectioning, but also because there exists a greater chance of intersecting a large
sphere than a small one (Cashman and Marsh, 1988). Russ (1986) gave an example
where the smaller grain sizes observed in thin section may be contributed to from the
smaller portions of larger grains as well as grains with that true diameter. The frequency
distribution of each size will add, giving rise to a complex histogram such as that shown

in Figure 7.

20

Frequency

 

40
Section Diameter (urn)

FIGURE 7 Size histogram of circles measured from intersections on several sphere
sizes is the sum of the individual distributions shown by the differently
shaded bars (after Russ, 1986).

The problem of true and apparent grain sizes was investigated in this study by conduct-
ing an empirical check of size distributions of dolomite in both two and three
dimensions. A CSD was determined on a friable dolomite sample from Aruba,
Netherlands Antilles (BD6TS). A second CSD was determined from a grain mount of
disaggregated grains from the same sample (BD6GM). The diameters measured in the
grain mounts are true diameters. Figure 8 shows the frequency histograms and cumula-
tive frequency distribution curves of the CSD’s resulting from the grain mount and thin
section line point counts. As in the St. Peter sandstone example conducted by Krumbein,
the histograms and cumulative frequency distribution curves show that the CSDs
between the two and three dimension have changed, and not merely shifted. However,
these graphs indicate that the bias due to thin sectioning of dolomites is generally minor

because the dolomite crystals tend to maintain an equant form.

In the line point count, it is apparent that a line placed randomly across a polycrystalline

microstructure may intersect more of the larger grains than the smaller ones, resulting in

21

Frcqucncg Histogram

 

1
.1
4
fl
4
:4
d
J
.1
.4

UNITS I 1 x 10' um

 

frequencg
8
I I I I I I I 7 I I I I I I T l T I I I '
A
l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

..
. #J

h
Irrrrlrrrrlaarrlrrrr

'1
’_J

 

 

UNITS - 1 x 10' um

 

3.

.... I

l l A A A I .l A A A l j J I A l A L I A

fr-quancg
I
I I I I l I 'I I I I I I I I I I I I I I
l
l
J
l
J

I l l l l I l l l l l l l I I l l A l l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i

r-
)-
i
P

 

BD$GM.sizc

figure 8 CSD frequency histograms of Boi Doi dolomite from Aruba, Netherlands
Antilles. Histograms are from a) thin-section, and b) disaggregated grain-
tmmm.

22
the distribution being slightly more finely skewed than a CSD including all grains.

Figure 9 shows the microstructure of a site saturation model on which the grains
measured in the line point count have been shaded. It is apparent that more of the small-
er-grained areas are excluded from the line point count than if all of the grains were mea-
sured. However, it is also apparent that more of the smaller grains are included than if a
grid-based point count were completed. For the purposes of this study it is assumed that
if the same method of measuring grain sizes and determining CSDs is applied to all
experimental samples and computer-generated models, the resulting CSDs will represent
the nucleation and growth processes of the sample. The problem of the difference in the
true and apparent CSDs is diminished in this study because both the experimental and
theoretical CSDs are determined using the same method of measurement from a two-

dimensional view of the microstructures.

Saetre, Hunderi and Nes (1986) point out the problem of the smaller grains being lost in
experimental CSD analyses because of either the sample preparation procedures, or the
limiting resolving power of the technique used to image, identify, and measure the
grains. They propose using a cut-off effect in the computer-generated microstructures, to
eliminate small grains in order to simulate the experimental effect in the computer mod-
els. They removed all grains smaller than 0.153 of the mean grain area. The cut-off
effect is not very noticeable on the linear or logarithmic scale frequency histograms. It is
quite noticeable, however, when it is plotted as a cumulative frequency distribution. This
cut-off gives the tendency towards a more lognormal distribution for the Johnson-Mehl
model. They note that when comparing experimental distributions to theoretical ones,
the cut-off effect is relatively unimportant when comparing probability densities, but is
substantial when comparing cumulative distributions, noting that cumulative
distributions are more sensitive to variations at the small areas. It might be noted that the

line point count method for the experimental CSDs may slightly exaggerate this cut-off

frequency

Figure9

y~ 1 «'11:,

  

  
   
   

lglfigéNg
gall: s' .
to .3/9‘gQ‘é‘fi’g’iv'fi‘i-‘Wc‘;

   

 
  
  
 
      

 

 

 

 

 

 

 

 

 

 

, , l.
a) ’73.). , , \I'L‘Zh “‘3?" ‘1': il|nf§

_-"®a£\mpb’s~>3-Y:O;‘i IVA“

|—' fr fi r I ' '

a. _ F—
i.
[—1
KMSITSQT.sizc

a) Shaded grains show those measured in a line point count, and b) the

corresponding CSD frequency histogram.

24

effect by eliminating a greater number of the small grains from the count and tending to
produce a more normal-like distribution. However, the line point count would most like-
ly simulate this cut-off effect in the computer-generated models. The cut-off effect was
applied to the experimental CSDs as well as to the computer-generated microstructure
CSDs, and it was found that it made very little difference in the resulting cumulative fre-
quency distribution curves. For this reason a cut-off effect was not applied to the com-

puter-generated model CSDs when comparing them to the empirical CSDs.
Statistical Analyses

Five statistical methods of comparing the CSDs were applied to this study, to character-
ize the differences in shape of the CSDs. Two of the statistical methods rely on the
Kolmogorov-Smirnov goodness-of-fit test As indicated above, comparing the cumula—
tive distributions is a more sensitive measurement of the variations in small areas than
that of the frequency histograms. The Kolmogorov-Smimov test is a nonparametric sta-
tistical procedure which measures the difference between two cumulative distribution
functions. The test was originally developed for continuous distributions. However, it
can be applied to discrete distributions as well, though the critical values tend to be over-
conservative with discrete distributions [i.e. the true may be less than the nominal a
(Neave and Worthington, 1988, p.90)]. The Kolmogorov-Smirnov test determines the
differences between two distributions by measuring the maximum vertical distance
(Maximum D) between each cumulative distribution function at any point in the two dis-
tributions. Using the STATGRAPHICS Statistical Program, version 4.2, the two distrib-
utions may be a theoretical distribution compared to an experimental distribution
(one-sample test) or two experimental distributions (two-sample test). The number of n
values do not have to be the same in each distribution to perform the test The two-tailed

test is sensitive to differences in location (central tendency). in dispersion, in skewness,

25
etc. (Siegel, 1956, p.127). It is the best known of several distribution-free procedures

which compare two (2) cumulative distribution functions in order to test for differences
of any kind between the distributions of the populations from which the samples were
obtained. The Kolmogorov-Smimov test is best used in situations where it is perhaps
unclear what kind of differences to expect between populations, or where expected dif-
ferences do not fit into the usual categories of location or spread (Neave and
Worthington, 1988, p. 149-153). The Kolmogorov-Smimov test is probably more power-
ful than the chi-square test in most situations (Conover, 1971, p 295). The most obvious
advantage of the Kolmogorov-Smirnov test is that it is not necessary to group observa-
tions into arbitrary categories; for this reason it is more sensitive to deviations in the tails

of distributions where frequencies are low than is the chi-square test (Davis, 1986).

The first method used a one-sample Kolmogorov-Smirnov test to evaluate the goodness-
of-fit of each CSD to a normal (Gaussian) and lognormal distribution calculated from the
mean and standard deviation of the CSD at hand. It was also used to evaluate the good-
ness-of-fit of each CSD to a corresponding gamma distribution. The results of the test
were evaluated by examining the significance level at which the null hypothesis (that the
experimental and theoretical distributions are from the same population) could be reject-
ed without a type 1 error. The null hypothesis was rejected if the significant level was

less than 0.05.

In the second statistical method, the CSDs for each sample were normalized by dividing
each measurement by the corresponding CSD mean value. This placed each distribution
at a central location equal to 1. The resulting difference in the cumulative frequency
distributions of the CSDs would then only be characterized by the differences in shape or
spread, and not in location. The CSDs were run through the two-sample

Kolmogorov-Smimov goodness-of-fit test provided by the STATGRAPHICS statistical

26

program. Again, an arbitrary limit of 0.05 significance value has been selected, and the

test data yield a general relationship of the CSDs.

The third, fourth and fifth statistical methods yield numerical values which characterize
the CSD shape. T-tests were conducted with these values to establish their similarity or

difference as CSD shape characterizing values.

The third statistical method calculated the normalized standard deviation (NSD) follow-
ing work of Tweed, Hansen, and Ralph (1983). Tweed, Hansen and Ralph (1983) com-
pared grain size distributions before and after recrystallization grain growth and noted
that variances of distributions can be directly compared only if the distributions have the
same mean. Since the data in their study approximated a lognormal distribution, the dis-
tributions were normalized after scaling geometrically (Tweed, Hansen and Ralph, 1983,
p.2237). The change in the normalized geometric standard deviation before and after
grain growth could then be compared quantitatively. They followed the method
described by Moore (1969). The CSDs in this study were not all close to lognormal and,
thus, scaling them geometrically would not be appropriate. Therefore, the standard devi-
ations of the normalized CSDs were compared in this study, and are termed the normal-

ized standard deviations.

The fourth statistical method used to characterize the CSD shape was skewness. Both
the inclusive graphic skewness, as described by Folk (1980), and skewness calculated by
the STATGRAPHICS statistical program are included in this study.

The fifth statistical value characterizing the CSD shape is the gamma distribution shape
factor alpha ((1) derived from each CSD using the STATGRAPHICS program. The

general shape of the dolomite CSDs shows relatively low probabilities for intervals

27

close to zero, with the probability increasing for a period as the interval moves to the
right (positive direction) and then decreasing at a more gradual rate as the interval moves
further to the extreme positive region of the distribution. A class of functions that serve
as good models for this type of distribution behavior is the gamma class. The gamma
probability density function used in the STATGRAPHICS program is given by the equa-

tion:

f(x) = [3a xa-le-flx
Na)

 

where 0t is termed the gamma distribution “shape parameter” and [3 is termed the gamma
distribution “scale parameter”, (Bury, 1975, p.299). The gamma F(a) function is defined
by:

I“ = Ixa"le”dx
0

The tails of the exponential, gamma, and lognormal distributions all decrease rapidly. For
x large, the tail of the gamma distribution is dominated by the term e'X/B. Figure 10
(after Breiman, 1973) demonstrated the differences between the lognormal and gamma

distributions where in each distribution the maximum of each occurs at x = l.

28

.f (X)
//_\\
.5 _ / \
/ \
/ \
/ \
.4 H ’ \

 

 

2 —- I \
I
I
' _ ’/’/ \QOGNORMAL
/ \\\‘
r’ 1 I 1 1 x
o r 2 3 4

FIGURE 10 Densities of the gamma and lognormal distribution with parameters
selected to give maximum value .54 at x=l (after Breiman, 1973).

A series of gamma distributions is shown in Figures 11, 12, and 13, to illustrate the char-
acteristics of gamma distributions with different alpha and beta values. Figure 11a
illustrates the shape of several gamma distributions which have varying alpha values and
a beta value of l, and 11b shows the corresponding cumulative frequency distributions of
11a. Figure 12a shows the shape of several gamma distributions which have a constant
alpha and varying beta values, and 12b shows the corresponding cumulative frequency
distributions from the gamma distributions in 12a. Figures 13a and 13b show the shape
of the density distribution and the corresponding cumulative frequency distribution for
several gamma distributions which have equal alpha and beta values. When CSD data is
normalized, the value of the gamma distribution scale factor, beta, will become equal to
the value of the gamma distribution shape factor, alpha.. The alpha value does not
change between the normalized (NormSize) and directly measured (Size) CSD data. The
alpha value defines the shape of the CSD in terms of the gamma distribution that best

represents the CSD data, either as the directly measured data or the normalized data.

29

 

 

 

 

 

 

 

a
Prob. Don-itu Fen. __ 2 1
Guam.
-- 2.61
n". '- _‘-.. T-'_ '.-'--.' 3-71...
' u 3.51”
. , 4 1'
1
a) ..
I.
X
Cum. Dist. Fan. __
Gamma

 

 

 

l
buflyflfi
O
i‘ F ww-

 

 

 

 

 

 

 

 

 

_ r
'0‘--:7—;'.:.:7.3 oooo
b ---- ' '. .3 1-
b ... 1fi
h
4
... _—- ...—.._- .._... -' -—.—-' “_.— — —— —— — ——
r- 1
b .
p.
d
0.. i-
)- ’ 4
l
r . d
b
1
.0. ’—
L .
l 1
.- ‘.
. q
p
q
... r— - .__ -- .._.-.1
p d
1- q
p .
1 1
b l
. I
J x . A .L
O I O O I. I.

figure 11 a) frequency histograms, and b) cumulative relative frequency
distributions of Gamma distributions using a constant B (scale) value and

different a (shape) values.

30

Prob. Dun-itu Fen.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a a
— 3 .05
Gamma
.. 3 .0.
E ..... a 2:
q
e.e—- _
:I ~ 3
JJ ’ ‘ ‘
.d 0.6— : _:
e . - «
F i .
'0 0.3— 1‘ _:
e : :
.0 ~ -
0 ea— _.
L i I
D. : .
...— L
C I
.P- —
a, a 1 r 1 r . J r r 1 r 1
e a e u so to an
X
I a ‘
Cum. D&.te Fen. _ 3 ..s
Gamm-
" 3 .0.
Y T Y '3‘ ru
° 3 108
..... a 21
. d
n .
o _.
L .
O. .
. d
E — —I
3 J
u .1
d
bl : 1 " .
e e e a u u on

figure 12 a) frequency histograms, and b) cumulative relative frequency
distributions of Gamma distributions using a constant a (shape) value and

different 3 (scale) values.

31

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

Prob. Danastu Fen. __ 2.7 2.7
Gamma
I - " 3 3
. ' r ' ‘ I i f ' 3.78123
* -- 3.3 aJe
. ""° ‘0‘ ‘35
3 ' H—‘ .
*J 4
'4
. <
c ~—-——- 9' --
I .
‘D .
O .
.D
o a
L .
a. ‘ 1
l
l .
- 1
a) . - . . .
0 I I 8 C O
X
. a a
Cum. Osat. Fen. __ 2.7 2.7
Gamma
°- 3 3
is ' ' L: are? e
'- 3.8 3.8
‘°°" ‘05 ‘15
. II
.n .
O --_.m" .._--"-___-_-_.-_
L .
n. J
O q
E - --—- ;_
:r , .
U ' ’ 1
_ _ _ m_- --- 14
’_’"I‘;1'.'“'1“' ...L....
O I I l e I
X

figure 13 a) frequency histograms, and b) cumulative relative frequency
distributions of Gamma distributions using equal a (shape) and B (scale)
values.

32
It is evident from Figures 11b, 12b, and 13b that relatively minor variation exists
between the cumulative frequency distributions which have equal alpha and beta values
compared to the variations observed between cumulative frequency distributions where
one gamma distribution variable (alpha or beta) is held constant and the other changes.
The Kolmogorov-Smimov goodness-of—fit tests were completed between normalized

CSDs, each of which have a beta value equal to its corresponding alpha value.

Method Reproducibility

For evidence of reproducibility in the line point count method, three CSD counts on each
of two clasts within the Trenton formation core were conducted. Two CSD counts were
also conducted on the Netherlands Antilles sample (BD6TS). Figure 14 shows two of
thethree frequency histograms, and Figure 15 shows the respective cumulative frequency
curves from the TLlA clast of the Trenton Formation. Figure 16 shows two of the three
frequency histograms, and Figure 17 shows the respective cumulative frequency curves
from the TLlB clast of the Trenton Formation. Figure 18 shows the frequency
histograms and Figure 19 shows the respective cumualtive frequency curves from the
Netherlands Antillies sample. The histograms and relative cumulative frequency distribu-
tions are comparing the direct measurements taken (size) and are not the normalized dis-
tributions (NormSize). It is evident from all of the histograms and cumulative frequency
curves that relatively good reproducibility is obtained for the method. Similarly, a dupli-
cate thin section sample of the same clast was made, and the grain sizes were measured
as described above (clast/count TL4B and TL13B). The resulting frequency histograms
are shown on Figure 20, and the respective cumulative frequency distribution curves are
shown in Figure 21. Table 1 shows the two-sample Kolmogorov-Smirnov goodness-of-
fit test significance levels for the respective clasts and counts. The significance levels

indicate that the distributions are not significantly different.

33

Fraquanog Histogram

 

I V r I v r 1 I Y 1 vi T I V if T

froquancu
8
.....q.......
L
,//’l
l

 

 

 

 

 

 

 

 

 

 

 

 

 

L .
ac — \ j
u - _
e r— —f"/' i l o—- '1
A L l 4 L l a I
I. .0 .0 .0 no “0
TLlA.siza
I I t I f I
.0 '— _-
u— L

1

m “L E
3: NH 2
m C _' .
a": K -
U
L
k.

 

 

 

 

 

 

 

 

 

 

 

)—
)-
)-

 

 

‘l. I. .0 .0 II. “I

TL192.aiza

figure 14 Two of the three frequency histograms of line point counts of Trenton
clast TLlA. (Note: size data is measured data and not normalized.)

34

Cumulatiua Ralatiua Fraquanciaa

 

 

 

 

 

 

 

I r Y I ‘ ' I ' ' I r ' I ' T I
{.0 '— _-
L 4
t-
.. P. —I
L
1
+5 .. _ _
. L .
u 1- at
L r- d
a a. t— —
r d
. 1
I. '— .—
r.
L
. I— —___—/ _-
J . - ' I l L 1 1; L
‘1. I. .0 a. I“ I“
TL19.arza
l T I I 'Y I r I
IO. _ u-
q
5 '4
.0 — —
L ..
. /
E .. l-D / «III
m v- o‘ d
u - -
L .
m u _- _1
0- t
" '1
I. '- / -I
)- '1
r- 1
. _ r
I . r l . . l a A I a L 1 x x .l

 

 

 

'3. .0 .0 on It. ‘6.

TLlna.aiza

figure 15 Respective cumulative relative frequency distributions of the frequency
histograms of Trenton clast TLlA shown in Figure 14.

35

Fraquancy Hiatogram

 

l I I I I r ' V I I I T r 4T r I v V l

T umrs - r x 10' um

. I
~ ‘
.4
h .
O.- a—
. a
" ct
h

/1_

frequency
8
I
l
/l’

u— .—
L

 

 

 

 

 

 

 

 

 

 

 

 

 

1
e — _J
l a . l . . l . L L a 1 l . . I l
’3. I. . .0 ea “0 no I"
TL18.siza
, . ., - ., . ., - ., . .,
.0 .—

UNITS 2 1 x 10‘ um

..—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

J

g..- \_ _'

m "'s' __ ‘

3

U \

U u— ' _

a \ .

k .
TL182.aiza

figure 16 Two of the three frequency histograms of line point counts of Trenton
clast TLlB. The solid line is a fitted gamma distribution. (Note: size data
is measured data and not normalized.)

36

Cumulatiu- Rolatiu. Frequoncicn

 

 

 

 

 

 

 

 

 

 

 

I I l T I fl I fi l
IO. r— —:
" ”' UNITS . 1 x 10' um —
4; «'- ‘
u b I
U - .
L D ‘
a I. I- -
I. — _
O F'- o—" ‘
A l l A l l A l A I
'l. .0 u .0 I“ no I”
TL18.sizc
u l I l I f O 1 v .
e -— _
u _ —
. UNITS - 1 x10'um .
*é’ .. L _‘
U ' .
u p ‘
L b 1
u O. I.- .—
0. _ ‘
I. I— q
. _
l L l J l A l 4 I L
“I. I. .0 .0 “C It. 8?.
TL182.sizc

Figure 17 Respective cumulative relative frequency distributions of frequency
histograms of Trenton clast TLlB shown in Figure 16.

37

Froqu-ncu Histogram

 

' 1 I v v I 1 I v v ' v V T I’ T 1 v Y 1 l ‘7 v v r I
60

UNITS O‘I1O‘Ufll

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.... r— _
3
§ r r _
3 n“ _ .4
a . — .
u p — d
L _ — ‘
" ~ FL— .
.L J r—r-m _
l L l l L l. il.l
. I. I. a 6. I.
806Tstsize
u— r If ' I v T
UNITS-IxIO'um
ao- [— r j
m _ .
U __ .
c .
m _—
3 ~- [— _
U’
U _r—
L
@-
806T82.sizo

Figure 18 Frequency histograms of duplicate line point counts of Boi Doi dolomite
from Aruba, Netherlands Antilles. The solid line is a fitted gamma
distribution. (Note: size data is measured data and not normalized.)

38

Cumulative Relative Frequenciee

 

 

 

 

I T I 'fi r If T I T I ' f
I“ _-
h- d
b 4
I- q
..— e-
b d
I ums-uro'um ‘
p- -1
g “P- —I
u + «
u l- .

L .

n ‘0— d
O. , .
"l— a-
r 4
h- d
h 1
O— —I

l A A A A 1 A A A A 1 L A A A l L A A A l A A A A l

. I. .0 fl 6. .0

O
BDSTS.saze
T I I

 

.
\ 4

.
I l 1 l l I

 

l ' T ' I V V ' l I j— ' I I V 1 l ' V I l
h \ I
I A A A I A A A I t g .1 I

 

 

 

BDBTSZ . Ii 2.

Figure 19 Respective cumulative relative frequency distributions of the frequency
histograms of the Boi Doi dolomite shown in Figure 18.

39

Frequency Hietograe

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

f ' r r I I ' 1 I fl I
.0 _- —
r- d
D C
D q
_
'- d
u - umrs . Ix IO'um -
b d
? F— el
3' ’ ‘
u- at
g a '— — .-
U ,_ ‘
b ..
3 _ r“ .
g P _r_ -— d
L " f r j
5— - F" .
b e
—

b .
I. b -
v- e
h ‘1
,. .4
I I l d
O —4

J- L A I A 1 l A L _A. l A A. ‘— 4 l I A L A l L J_. L L

'l. O. .0 I“ I” .0.

a
TL4B.srze

I l I " I r T I
.0 '— —I
P C
u- q
r- d
" __ UNITS - I x 10' um "
a. — —I

i-

. 1
3| L _J— .
U ’ ‘
a — _
E . .
3 i —' ‘

_ .
r 1
U' _ f— .
m n I— _ .—
L . “ .
‘ P- u
r- q
I" d
8. _ -
y- d
D Q
n d
. m [‘1 -
O '- 7 I-

l 4 A A A I A A A A l A A #A l A A A A I A A A A l

.I. O. .0 I“ b" .0.

TL138.aize

Figure 20 Frequency histograms of line point counts of duplicate thin-section
samples of the same clast from the Trenton Formation. (Note: size data
isnwmmmddflaamlmnnmmmmuflo

4o

Cumulative Relative Frequenciee

 

  

UNITS -1x10'vm

 

percent

 

 

 

 

 

 

 

 

O. i— .-
" «I
.
I-
I. '— _
h ..
. .
. .
I D— -—
A A A i L A A A l A A A A L - A A A l A A A A l
'8. u .0 lea I” .40
.
TL4B.srze
I r t r T I f T '
IO. P— ____ _
i .
.
r- d
a. — —
” ums - 1x10'um ‘
. -
. -
2 ~- -'
u * -
0 ~ -
L > -
Bl .. - _
D. _ .
b -I
p. .
u — -
. r
. .
. .
. _.
j 4 L I A l 4 g I 4‘ A l A L I
30 u .0 lo. I” .00

TL138.eize

Figure 21 Respective cumulative relative frequency distributions of the frequency
histograms shown in Figure 20.

41

TABLE 1
Two-Sample Kolmogorov-Smimov Test Evidence of
Reproducibility On Measured Crystal Size Distribution Data

 

Clast/Count K-S Significance K-S SnifiA— of
Level of CSD Data Normalized CSD Data

 

TLIAZ TL1A3 ' TLlAZ TLIAS

 

.7870 .2098 ; .7870 .5175

 

.6527 § .5842

 

 

 

 

 

TL13B g TL13B

.0659 , .517§

Boarsz g Bosrsz .
.2923 T .2923 i

 

Table 2 shows the comparative mean, the standard deviation, the normalized standard
deviation, the skewness (as calculated by STATGRAPHICS), the inclusive graphic skew-
ness (Folk, 1980), the value of the gamma distribution shape factor a (alpha), and the

one-sample K-S significance value to the normal, lognormal, and gamma theoretical dis-

tributions.

42

TABLE 2
Comparison of Statistical Values of Duplicate CSD Counts and Thin-Section Samples

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TLIA— 26.—— 88 16 49 .6134 1. 537 3.265 2. 700
11.1112 I 26.32 I 15.56 I .5914 I 1.004 I .169 5'0 .0634 MI .007 I .3302 I 2.613
TLlA3 27.34 16.98 .6208 1.231 .323 .0012 .158 .5011 2.581
“1* 1—6 20.94 .5669 1.639 .065 .0300 _ .0569 _——3—.038___—
1L1132 38.43 21.82 .5678 1.627 .157 .1900 .001 .0524 2.544
11.1133 38.51 23.01 .5974 1.301 .175 .0024 .0088 .3566 2.764
BD6TS 21.46 9.31 .4341 .0050 .0262 .3921 3.55-6 .0019 3.768
BD6TSZ 21.04 8.61 .4093 -.0808 -.0340 .2934 1.95.7 .0005 4.258
TL4B _______A_ 65.21 41.91 .6427 1.199 .278 .0023 .727 _. 2.382—
1L138 69.05 40.26 .5831 I 1.056 .205 .0005 .0987 .7293 2.824
”“T- .. . o vratron ‘——"’ —“""————“————_‘ ' ‘

alpha = Gamma Distribution Shape Factor lGSK = Inclusive Graphic Skewness

N = Kolmogorov-Smirnov Test Significance Level to a Normal Distribution SK = ST ATGRAPHICS Skewness

L = Kolmogorov-Smirnov Test Significance Level to a Lognormal Distribution
G = Kolmogorov-Smimov Test Significance Level to a Gamma Distribution

The values presented in Table 2 show that relatively good correlation exists for the
STATGRAPHICS skewness, the normalized standard deviation, and the gamma distribu-
tion shape factor (alpha) as CSD shape descriptors. The mean and standard deviation

values also indicate relatively good reproducibility of the line point count method.

The size distributions obtained for the Trenton and Saluda Dolomites were compared to
each other, and to the three computer—generated models. CSD measurements on the
computer-generated microstructures of the Johnson-Mehl and site saturation nucleation
and growth models, obtained from Dr. Knut Marthinsen, were also conducted by the line

point count method.

CSD DATA
Trenton Formation

' In the Trenton Formation samples, CSDs of fifty-seven clasts in twelve thin-sections of
core were measured. The CSDs within the Trenton Formation contained a range of mean
grain sizes from approximately 103 um (microns) to 690 um. Table 3 lists the mean, nor-
malized standard deviation (NSD), STATGRAPHICS skewness (SK), inclusive graphic
skewness (IGSK), and gamma distribution shape factor alpha (a) of the gamma distribu-
tions fitted to the CSDs by the STATGRAPHICS program. The table also shows the sig-
nificance values for the one-sample Kolmogorov-Smirnov goodness-of—fit test of the
normal (N), lognormal (L), and gamma (G) distributions, fitted to the Trenton CSDs by
the STATGRAPHICS program;

Almost all of the CSDs are coarsely skewed, and, as can be seen by Table 3, the skewness
varies considerably between clasts within the same thin-section. There is no correlation
between mean grain size and skewness. X—Y plots of the skewness, normalized standard
deviation, and alpha values to the mean grain size values yield shotgun patterns. The
mean significance level for goodness-of-fit to a normal distribution for the Trenton sam-
ples is 0.046. Nine of the fifty-seven samples (approx. 15.8%) have a significance level
greater than 0.05 for the Kolmogorov-Smimov goodness-of—fit test to a normal distribu-
tion. The mean significance level for the Kolmogorov-Smirnov goodness-of-fit test to a
lognormal distribution is 0.080. Twenty-six of the fifty-seven samples (approx. 45.6%)

have a significance level greater than 0.05 for the Kolmogorov-Smirnov goodness-of—fit

43

AL4

TABLE 3
Trenton Formation CSD Statistical Values

Normal Lognormal

0.0 l

Alpha
.69 89
.61313

2. 81 4

3.03783

2.54382
.76443

O 8

 

45
TABLE 3 (cont’d)

 

Normal Lognormal Gamma Alpha

0.088 0.6169 .88956

3-0.002§-_ 0.0839 0.8383 3.24926

20.000034: 0.5184 0.122 2.64872

‘7‘ I I: 0.222 0.2922 .68066

.68 . LI:.0,II3 ng.1} I ' 0.1573 2.18132

9 . . . . Q i. -‘ .6349 2.517 1

.45 . . ‘ ’II' 13.3 .0733 3.87437
.11 . . . 31.‘ _‘_i“‘ .6839 2.42907
.91 . . }I. .‘- 0. 0 9 .8156 3. 8985
.64 . . . ;D.V03piii 0.19866 .5798 2.71994
.79 . . . 70.120237, 0.07603 .3081 3.63656
.6 . . . 0.0804 y . . 7- .4353 3.62261
.07 . . . f7;7'-::j 70. ['71. .1945 3.66526
.26 . . . _ip.’: >fl,1 0.32612“ .4358 3.36934
.93 . . . J .‘13U-p; 0.05073 .6351 3.1558
.91 . . . '0.006545. 0.060908 .3966 3.79039
.53 . . . 3.0.43555H..8~ ‘_ ; phé. 1 4;: 4.55155
.54 . . . g '. ...: 02.;jhu‘i ut7l39‘. 260886
.43 . . . 370.60593.‘_. ‘3 .1509 2.37001
.63 . . . . .. l . . g . 36 . 7 4
.76 . . . I 0.05275755312 ‘1‘ 2.68302
.96 . . . T 0.09693 3.13785
.4 . . . 7' ; .4 r. 18
.75 . . . 20.099663, ".V H. 5: .3406 3.0576
.78 . . . L.T _ ->; ... p 75 .3212 2.8285
33.76 . . .35, i j; 03117445 .9593 2.13452
34.51 . . . :1. h_.¥";‘ 8“ .2773 2.5821?
33.79 . . . ii.rliT»;;'l0.37035x. .3932 2.0578
33.38 . . ’2' I ‘V:_'l .7 _(.fl: .5091 2.56273
13! 69.05 . 831 . 334.3‘:_§ 70.098746. .7293 2.82419

H.512. I Normalized Standard Deviation All.“ I Gamma Distribution Shape

W I Kolmogorov-Smirnov Toot Significance Level to a Normal Distribution 93‘ I Inclusive Graphic Skewness

W I Kolmogorov-Smirnov Test Significance Level to a Lognormal Distribution 5‘ I STATGRAPHICS Skewness
Lima I Kolmogorov-Smirnov Test Significance Level to a Gamma Distribution

 

46

test to a lognormal disuibution. The mean goodness-of-fit significance level to a gamma
disuibution is 0.440. Fifty-four out of the fifty-seven samples (approx. 94.7%) have a

significance level greater than 0.05 to a gamma distribution.

Table 3 shows that the gamma distribution has very few Kolmogorov-Smirnov goodness-
of-fit values less than 0.05, and can probably best describe most of the CSD shapes rela-
tive to the other distribution types. It is apparent that the gamma distribution shape
factor may be a good value to represent the shape of each CSD, and can be quantitatively

compared to determine CSD shape variability.

The Trenton core sample CSDs were divided into two groups based on mean grain size
to determine if trends in the shape of the CSDs were present in the alpha, skewness, and
normalized standard deviation values of the two groups. A large mean grain size group
and a small mean grain size group were evaluated. The small mean group contained
those CSDs with a mean grain size between 113 and 313nm. The large mean group con-
tained those CSDs with a mean grain size between 315 and 652 pm. A two-sample t-test
was performed between the mean, alpha, normalized standard deviation, and skewness
values in each group. A significance level less than 0.05 was used to reject the null
hypothesis. The two-sample t-test between the alpha values resulted in a significance
value of 0.15. The two-sample t-test between the normalized standard deviation values
of the two groups resulted in a significance value of 0.56. A two-sample t-test
significance value of 0.096 was obtained for the inclusive graphic skewness values of the
two groups. The significance value for the two-sample t-test between the STATGRAPH-
ICS skewness values was 0.98. The significance value for the two-sample t=test
between the mean grain sizes was 5.3 E—l3. Thus, the null hypothesis that there is a dif-

ference in the shape of the Trenton CSDs based on mean grain size is rejected.

47

Tables 4 through 10 show significance level results of the normalized CSD two-sample
Kolmogorov-Smimov goodness-of-fit test between clasts from the same thin-section.

The significance levels less than 0.05 are shaded.

TABLE 4
Two Sample K-S Tests Between Thin-Section TL1 Clasts

1A3 I l I l

0. 70 0.5175 0.5842 0 5175 0.7212 ”.. : . 0.2923

. 4 . . .4

.4

0.7870

0.6427

.14

 

TABLE 5
Two Sample K-S Tests Between Thin-Section TLZ Clasts

 

TLZB I TLZC 11.21)

 

MA am: 99956

 

11.213 1 ”01.84175 N 06527 I

 

 

 

 

 

 

11.2c I 0.8475

 

TABLE 6

48

Two Sample K-S Tests Between Thin-Section TL3 Clasts

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Clast 11.38 TL3C TL3F TL3G 11.311 11.31 TL3] 1L3K 11.31. TL3M
TL3A 0.3953 0.5175 0.1212 “0.0096 0.4543 0.6527 0.8996 0.7870 0.2485 0.7212
11.38 0.5842 0.1465 00007 0.1759 0.5175 0.2923 0.5842 3933737. 0.1759
11.3c 0.175910..02082 0.6527 0.3412 0.5842 0.7212 0.2098 0.6527
TL3F 00001 0.2485 0.3412 0.3953 0.3953 0.1212040424.’
TL3G ‘ 0.0530 00031 _‘2 0.0056 0.0162 0.042.400.0812
run “"6154; 6.7176 6.9566 "6.2485 6.15.. 3
11.31 0.7212 0.9408 }-0.0337 0.4543
11.31 0.7870 0.12485: 0.4543
11.311 0.0530 0.5842
11.3L 0.1465
TABLE7

Two Sample K-S Tests Between Thin—Section TL7 Clasts

 

 

 

 

1L78 11.71: TL7D 11.713
TL7A 0.2485 0.1465 0.1759 50.0013;
11.78 0.0659 0.3412 00208
TL7C 0.8475 00424

 

 

TL7D

 

 

 

 

0.0659

 

 

 

49

TABLE 8
Two Sample K-S Tests Between Thin-Section TL8 Clasts

TL8D

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 9
Two Sample K-S Tests Between Thin-Section TL9 Clasts

 

TL9B TL9C

 

11.9.4 0.2098 511.330.0424?

 

ma 90162

 

TL9C

 

 

 

 

 

 

TABLE 10
Two Sample K-S Tests Between Thin—Section TLll Clasts

 

Clast TLllC TLllD TLllE TLllF

 

TLllA 0.5842 0.8475 0.1759 0.6527

 

TLllB

99974 90973 07212 0-1212

 

1111:: 0.7212

0.2098

0.6527

 

TLllD

0.0996

0.6527

 

TLllE

0.2098

 

 

TLllF

 

 

 

 

 

 

 

 

50
From Tables 4 through 10 it appears that about one CSD (clast) is significantly different

in shape from most of the other CSDs (clasts) in the same thin-section.

The normalized CSD two-sample Kolmogorov-Smimov goodness-of-fit tests between all
normalized Trenton samples are presented as a table in Appendix B. All two-sample
Kolmogorov-Smimov goodness-of-fit significance levels less than 0.05 are shaded in the
table of Appendix B. Of the 1,596 comparisons betWeen the Trenton clast CSDs, 1,290
(81%) show goodness-of-fit values >0.05. indicating that they are from the same popula-
tion. Of the 306 comparisons (19%) with goodness-of—frt values <0.05, 174 (57%) of
those are from 4 of the 57 clasts. The clasts include TLlD, TL2A, TL3G, and TL9C.
The majority of the Trenton CSDs are not significantly different in shape from each

other, though the mean grain sizes do vary significantly.

Saluda Formation

Eight CSDs from seven thin-sections of hand samples from the Saluda Formation were
measured by the line point count method. The mean grain size of the CSDs of the mud-
stones measured decreased down section, and ranged from 310m to 69 um. Figure 22
shows two of the eight normalized CSD frequency histograms. The normalized frequen-
cy histograms of the CSDs are also included in Appendix C. Table 11 lists the mean, the
normalized standard deviation (NSD), the STATGRAPHICS skewness (SK), the inclu-
sive graphic skewness (IGSK), and the gamma distribution shape factor alpha (a) for the
Saluda sample CSDs. It also lists the significance values for the one-sample
Kolmogorov-Smirnov goodness-of-fit tests of the normal, lognormal, and gamma distrib-

ution fitting to the Saluda Formation CSDs.

51

Pruquoncg Histogram

 

7"

I 1 r *rfo'fi 11* 1 1

00'- —1

D d

P d

I _ I

.0— .-

D d

[ ... ..__ 3

1. F—' .

3 “f — 1

C ’ ‘

a * ‘

3 a:- +_ ...:

. 1‘1- .
U'
2
fl.

llllll

1'1171

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p
L
I.
1
1
1.
1

.
.
T.
b
llllLlJl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 . f- T 1 1

...—. —.

1- _ 1

1. .

1. a

_ .1
3... ...

h _. .1

a . __ .
.- .

5 . _ .
3 ..- -
0' , -— -
I . _‘ __ .
k . .
“- . .
ae— -‘

1- .1

. .1

. .

. r n .

e- n -1
1.4 L1. . . .1. L 4 l . 2 14—1

 

,
.

M88914DS.NormSizc

Figure 22 Two of the eight frequency histograms of the Saluda dolomite samples.

52

TABLE 11
Saluda Formation CSD Statistical Values

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample Mean NSD SK IGSK Normal Lognormal Gamma Alpha
b849OIDSSZ 68.905 0.4963 0.6592 0.2679 0.00004 , 0.004}; 0.2932 3.7044
MS4901DS.SH 67.253 0.4012 0.5253 0.125 :. 0.0001: W021! 0.0501 6.1786
MS4904DS 57.512 0.4530 0.7654 0.1145, 0.0873 0026? 0.2579 4.5784
MSB903DS 55.675 0.4978 1.055 0.1472 0.1551 00576 0.2013 3.8924
MSB904DS 53.801 0.4668 1.1053 .1515 0.02946 0.4254 0.5647 4.9075
MSB907DS 37.023 0.4990 0.7085 0.319 0.0049 0.1053 0.1373 3.9175
M58912DS 49.711 0.5217 0.6341 0.2661 15.0.0279 0.122 0.5755 3.4214
MSB914DS 30.741 0.5662 1.4115 0.4500 ,’;10..0001‘ 0.1005 35.0.0243 3.5505
m - Normalized Standard Deviation m . Gamma Distribution Shape Factor

m1 = Kolmogorov-Smirnov Test Significance Level to a Normal Distribution 19.55 : Inclusive Graphic Skewness

m1 = Kolmogorov-Smirnov Test Significance Level to a Lognormal Distribution SK 1: STATGRAPHICS Skewness
mm s Kolmogorov-Smimov Test Significance Level to a Gamma Distribution

 

All of the Saluda Formation sample normalized CSDs are coarsely skewed. Table 11
shows that skewness also varies moderately between the Saluda Formation samples. As
with the Trenton samples, there appears to be very little correlation between mean grain

size and skewness in the Saluda dolomite samples.

The mean significance level for goodness-of-fit to a normal distribution is 0.035. Two of
the eight samples have a significance level greater than 0.05 for Kolmogorov-Smirnov
goodness-of-fit test to a normal distribution. The mean significance level for goodness-
of-fit to a lognormal distribution is 0.108. Five of the eight samples have a significance
level greater than 0.05 for Kolmogorov-Smirnov goodness-of-fit test to a lognormal dis-
tribution. The mean goodness-of—fit significance level to a gamma disuibution is 0.263,

and seven out of the eight samples have a significance level greater than 0.05.

53

Tables 12 shows the results of the normalized CSD two-sample Kolmogorov-Smimov

goodness-of-fit test between the Saluda Formation samples.

TABLE 12
Two-Sample Kolmogorov-Smimov Goodness-Of—Fit Tests
Between Saluda Formation Samples

Sample MS49OIDS. 1115490405 M88912 5 115391405 M58903 5 M58904DS 1115590705
11549010552 g;.g....,.;.;,»,.03.,...; 0.2533 0.4440 0.0940 0.4145 0.3644 0.2965

145490105511 0.3231 537;; .. , :j -__g-..- 1 _g .;;_:~.,; , , _ f 0.6578 .:I._,j:,-f ._.g __

5154904135 5,31,. .. __ _.g 0.4653 0. 63 0.1053

M5891zos 0.700 0.2497 0.6240
11151191405 0.0968 ._ _j, 0.3896
M88903DS 0.5934 0.2030

MSB904DS 0.2382

 

was

Of the 28 Saluda CSD comparisons, 7 (25%) show goodness-of-fit values <0.05. Of
those 7, 5 (71%) of them are from the sample MS4901DS.SH. However, the majority

are not significantly different from each other.

Theoretical Computer - Generated Microstructures

It is expected that the CSDs for the computer-generated models will vary according to
the differing nucleation and growth parameters used to generate them. Those differences
should be reflected in the differences in the appearance of the C805, and in the statistical

values characterizing the CSD shape, as well as in the normalized CSD two-sample

54
Kolmogorov-Smimov goodness-of-fit tests. The normalized frequency histograms are
also shown in Appendix C. The CSD for the site saturation model is finely skewed, the
Johnson-Mehl model is more normally distributed, and the site saturation model with
weakly clustered nuclei is quite normally distributed. Table 13 lists the statistical values

for the theoretical models, as was done for the Trenton and Saluda Formations.

TABLE 13
Theoretical Computer-Generated Microstructure CSD Statistical Values

_ Normal Lognormal

 

 

KMJNSMEL 0.2896 3 110.000.37.in I

J KMSSWKCL 0000065 T

 

  

 

 

 

 

 

 

 

 

 

KMSITSAT = Site Saturation (Cellul) Nucleation and Growth Model
KMJNSMEL = Johnson-Mehl Nucleation and Growth Model
KMSSWKCL = Site Saturation Model With Weakly Clustered Nuclei

E512 = Normalized Standard Deviation Alpha = Gamma Distribution Shape Factor
W = Kolmogorov-Smimov Test Significance Level to a Normal Distribution m 4: Inclusive Graphic Skewness
mm = Kolmogorov-Smirnov Test Significance Level to a Lognormal Distribution SE = STATGRAPHICS Skewness

9.110.101 = Kolmogorov-Smimov Test Significance Level to a Gamma Distribution

 

The gamma distribution shape factor does not adequately describe these distributions.
The weakly clustered site saturation model is quite normally distributed. The Johnson-
Mehl model is somewhat normally distributed, but is slightly finely skewed, as can be
seen on Figure 6. The site saturation model is quite finely skewed and does not compare

to a normal, lognormal, or gamma distribution.

Table 14 shows the results of the two-sample Kolmogorov-Smimov goodness-of-fit test
between the normalized CSDs of the three theoretical nucleation and growth models used

in this study.

55

TABLE 14
Two-Sample Kolmogorov-Smimov Goodness-Of-Fit Tests
Between Normalized Theoretical Computer-Generated Microstructure CSDs

 

 

 

Model KMJNSMEL KMSSWKCL I
KMSITSAT . ' ‘ 0.04524“ " .7 ‘- : . p L 0.053175}, 3:: .7 '
KMJNSMEL A I A H A H J ' ... 0.13512)

 

 

 

 

The results of the statistical analyses of the theoretical models shows that the site satura—
tion and Johnson-Mehl models differ according to the nucleation and growth kinetics
used to generate them. As would be expected, the J ohnson-Mehl model has an increase
in the frequency of smaller grains over the site saturation model (Figure 6). The effect of
weakly clustered nuclei in a site saturation model appears to broaden the distribution, and
to increase the number of small grains, thereby making the CSD less finely skewed than
the site saturation model with random nucleation sites. The resulting weakly clustered
model CSD mimics the shape of the Johnson-Mehl model, as can be seen by the
Kolmogorov-Smirnov goodness-of-fit test value in Table 14, but it still maintains a lower
frequency of the smaller grains than the Johnson-Mehl model. This illustrates the effect

of varying the location of nuclei on the resulting CSD.

Analysis and Comparison Between Formation and Theoretical CSDs

The two-sample Kolmogorov-Smirnov goodness-of-fit values of the Saluda normalized

CSDs to the Trenton and computer-generated normalized CSDs are presented in the table

56
of Appendix B. The goodness-of-fit values in Appendix B show that of the 456 compar-

isons between the Saluda and the Trenton samples, 243 (53.3%) have values <0.05, indi-
cating that those samples are not from the same population. Five of the eight Saluda
samples account for 204 (84%) of the 243 goodness-of-fit values that are <0.05. These
include MS4901.SZ, MS4901.SH, M84904, M8894, and MS8914. Thus, a majority of
the normalized CSDs for the Saluda Formation samples are significantly different from

those of the Trenton Formation samples.

The means and standard deviations of the alpha, normalized standard deviations, STAT-
GRAPHICS skewness, and inclusive graphic skewness values for the Trenton and Saluda

CSDs are presented in Table 15

TABLE 15
Comparison of Mean and Standard Deviations of the Means and Standard Deviations
of the Alpha, Normalized Standard Deviation, Skewness, and Inclusive
Graphic Skewness Values for the Saluda and Trenton Formations

   
   
  

        
   
   

    

 

     

    

  

 

 

    

      
 

  

 

     
 

   

 

 

    
 

SALUDA FM.
CSD Shape Descriptor Mean Standard Dev. ‘ 5131193! 0 Dev.
Alpha 21.269 0.923 0,542
Normalized Standard Dev. 0.488 0.049 0.107
FTATGRAPHICS skewness 0-353 0302 1.089
0.222 0.087 0.1 17

 

 

 

   

This table shows significant differences between the alpha values of the two formations,
and between the normalized standard deviation values of the two formations. There is

moderate-to-low difference between the STATGRAPHICS skewness values between the

57

two formations, and very little difference between the inclusive graphic skewness values
of each formation. Two—sample t-tests performed between the shape descriptors of the
two formations resulted in similar conclusions. Significance levels less than 0.05 result
in rejection of the null hypothesis. The two-sample t-tests for the alpha and normalized
standard deviation values of the two formations yielded significance levels of 1.7 E9
and 0.0015 respectively. The two-sample t-test for the STATGRAPHICS skewness and
inclusive graphic skewness values of the two formations yielded significance levels of

0.1853 and 0.8184 respectively.

The table in Appendix B also shows that the theoretical model CSDs are significantly
different from both the Saluda and Trenton Formation samples. There are no goodness-
of-fit values greater than 0.05 for the site saturation model. The Kolmogorov-Smimov
goodness-of-fit tests between the weakly clustered site saturation model and the Trenton
Formation samples have only two significance values greater than 0.05 out of the 62
comparisons. Kolmogorov-Smirnov goodness-of—fit tests between the weakly clustered
site saturation model and the eight Saluda Formation samples resulted in only one signif-
icance value greater than 0.05. The J ohnson-Mehl model goodness-of-fit to the Trenton
Formation samples resulted in nineteen significance values greater than 0.05 out of the
62 tests. Three of the eight goodness-of-fit tests between the Johnson-Mehl and Saluda
Formation samples resulted in values greater than 0.05. This indicates that the J ohnson-
Mehl model is the closest of the three theoretical models to the dolomite CSDs, but all

theoretical models have relatively poor representation of the experimental data.

DISCUSSION

CSD shape comparison between the Saluda and the Trenton samples appear to show the
Saluda Formation sample CSDs have slightly lower frequencies of very small grains.
Figure 23 is a cumulative frequency graph of Saluda and Trenton Formation samples

which illustrates the CSD behavior observed between the two formations.

c.o.1=.'a -—- TL11£.NortaSiz¢
.4 H3091408.Nom3

' W V 1 1—7 r 1 v T Y —r 1* r V mr Y t
8 ... A

 

c.d.f‘.

 

 

 

A; L A. 1 A] A 4 1 # A L A 1 g; 4 J L
I

8 I 3

ubscruatian

FIGURE 23 Kolmogorov-Smirnov goodness-of-fit test cumulative relative
frequency distribution showing the consistent differences between
the Saluda and Trenton Formation CSDs.

The lower number of small grains in the normalized Saluda sample CSDs, relative to the

58

59
number observed in the Trenton, implies a lower nucleation to growth ratio in the Saluda
Formation than that of the higher temperature Trenton Formation samples. It cannot be
determined if the lower ratio in the Saluda is due to a decreasing nucleation rate, an
increasing growth rate, or both, relative to those of the Trenton samples. Occasionally,
much larger grain growth, also termed “run-away growth”, is also evident in the higher
temperature Trenton samples, and can be associated with elevated temperatures. Run-

away growth was not observed in the Saluda Formation samples.

The values of skewness did not show significant differences between the Trenton and
Saluda samples, as is evident by the two-sample t-test results shown previously, as
opposed to the gamma distribution shape factor alpha. It may be that the skewness fac-
tors do not detect significant differences between the CSDs due to the nature of the skew-
ness statistic. Groeneveld (1991) compared several measures of skewness of univariate
distributions, and used Hampel’s influence function to clarify the similarities and differ-
ences among the measures of skewness. “Skewness, like kurtosis, is a qualitative proper-
ty of a distribution... A general concept of skewness as a location- scale-free
deformation of the probability mass of a symmetric distribution emerges. Positive skew—
ness can be thought of as resulting from movement of mass at the right of the median
from the center to the right tail of the distribution together with movement of mass at the
left of the median from the left tail to the center of the distribution,” (Groeneveld, 1991,
p.97). The steps outlined by Hartmann (1988) indicate that the gamma distribution shape
factor (alpha) and the normalized standard deviation values may be better descriptors of
the CSDs than skewness values. “Instead of using a goodness-of—fit parameter to some-
thing which is only assumed, I propose the following procedure:

1) Make a decision about the statistical system, thus, the right descrip-

tive statistics to be used.

2) Estimate the parameters of the experimental data.

60
3) Check the goodness-of-fit to the theoretical distributions for the pur-

poses of quality control,” (Hartrnann, 1988, p.915).

Use of the gamma disuibution in describing CSDs is also supported in work by Vaz and
Fortes (1988) in which they show the gamma distribution to have the type of asymmetry

observed in actual grain size distributions.

The majority of CSDs in this study do not resemble lognormal distributions. It is com-
mon to find lognormally shaped CSDs in materials believed to have undergone aggrad-
ing neomorphism by Ostwald ripening (recrystallization due to surface free energy
differences whereby large crystals grow at the expense of smaller crystals). An aggregate
of grains can reduce its total interfacial free energy by forming grains as large as possi-
ble, thereby reducing the total interface area (Vernon, 1975). The Trenton and Saluda
Formations do not have lognormally shaped CSDs and do not show petrographic
evidence of neomorphism. Recent dolomite crystal size distribution studies (Gregg and
Howard, 1990; Gregg and Shelton, 1990) have found lognormally shaped distributions in
dolomites. Using the line point count method with scanning electron microscopy, Gregg
and Howard (1990) determined CSDs on Recent dolomites forming in peritidal
savannahs on the Caribbean island of Ambergris Cay, Belize. The Belize samples had an
average Kolmogorov-Smimov goodness-of-fit test significance level of 0.17 to a normal
distribution, and 0.58 to a gamma distribution, whereas the average for a lognormal dis-
tribution was 0.69. Only two of the normal disuibution tests had significance levels less
than 0.05, and none of the lognormal or gamma distribution tests had significance levels
less than 0.05. The submicron to micron sizes of the Belize dolomites are within the
range in which surface free energies can contribute to the stability of a crystal. The log-
normal distributions are therefore consistent with the hypothesized Ostwald ripening

process. Gregg and Shelton (1990) also determined the CSDs of the back reef facies

61

dolomite of the Bonneterre Dolomite in southeastern Missouri. The Bonneterre Dolomite
forms the lower part of an upper Cambrian platform carbonate sequence which is a pri-
mary host to the Mississippi Valley-type sulfide ore deposits of that region. The resulting
CSDs were all coarsely skewed and typically lognormally distributed. The Bonneterre
samples had a mean Kolmogorov-Smimov goodness-of-fit test significance level of
approximately 0.14 to the normal distribution, and 0.25 to the lognormal distribution.
The lognormal distributions observed in the Bonneterre dolomite could be attributed to
further dolomitization and neomorphism during the sulfide mineralization. It is assumed,
for lack of other evidence, that the neomorphism was driven by surface energy (e. g.
Ostwald ripening) during the regional mineralization. The lack of neomorphism in the
Saluda dolomite is suggested by the presence of well preserved CL zoning. The dolomite
probably did undergo partial re-equilibration of unstable cores. However, that would be a

compositionally driven process and not a surface energy driven one.

The thickness of contemporary CL zones can be used to distinguish flux-limited crystal
growth from surface-reaction-limited crystal growth (Kretz, 1974; Carlson, 1989).
Heterogeneity in the flux of dolomitizing solution is based on Pingitore’s (1982) concept
of macropore and micropore solute transport. In macropores the solute may be transport-
ed under hydraulic gradient whereas in micropores, or in isolated intragranular pores
which form culs-de—sac off the flow path, the solute is subject to transported by diffusion.
The chemical isolation, and the ability to exchange ions between these two water/solute
regimes, determines the openness of the system to dolomitization, the degree of textural
preservation, and the resulting trace-element chemistry of the dolomite. Assumptions
made for this model are that for most of a given volume of rock solute transport is by dif-
fusion, that a much smaller volume receives solute by advective flux, and that there is a
continuum between advective flux and diffusion flux. In flux-limited crystal growth,

contemporaneous CL zones in crystals of different sizes will vary with the radius of the

62

crystal. The larger grains presumably receive a greater flux of solute from which growth
occurs, and will grow at a quicker rate than smaller grains, which receive a smaller flux
of solute. The larger grains will subsequently grow thicker CL zones than those of the
contemporaneous smaller grain CL zones. In surface-reaction-limited crystal growth, the
contemporaneous CL zones will have a constant thickness regardless of the crystal diam-
eter. The variation in crystal size results only from the age of the crystal. Nordeng and
Sibley (1990) conducted such a study on the Saluda Formation dolomite and found that
the contemporaneous CL zone thicknesses were a function of the crystal diameter, and

therefore fit a flux-limited model.

The theoretical models indicate that the CSD skewness could be augmented if the
preferred nucleation sites were slightly clustered, and not homogeneously or randomly
distributed. Qualitatively, only clast TLlD, and possibly TL3G, of the Trenton dolomite
clasts had noticeably ‘clustered’ sizes. Petrographic inspection suggests that these clasts
may have initially incorporated two textural sizes within them, because groups of small
dolomite crystals were distinct and did not necessarily grade into the surrounding larger
crystals, as seen in the theoretical model. The CSDs for these clasts were among those

most different from the other Trenton CSDs. Clustering in the Saluda was not apparent.

CONCLUSIONS

Several characteristics of the CSDs observed in this study can be noted.

1)

2)

3)

4)

The CSDs for almost all samples are coarsely skewed with the exception of the
computer- generated microstructures.

The shape of the majority of CSDs for the Trenton and Saluda Formations are
represented more closely by the gamma-type distributions than they are by the
lognormal or normal distributions. This is evident by the greater percent of
Kolmogorov-Smimov goodness-of-fit values >005 for the gamma distributions
than the lognormal or normal distributions.

The majority of the Trenton CSDs have a similar shape regardless of their mean
grain size. This is evident by the 81% of the goodness-of-fit values >0.05
between Trenton samples, and the two-sample t-tests of the mean grain sizes, and
the alpha values between the large mean grain size Trenton clasts and those of the
small mean grain size Trenton clasts. In addition, the X - Y plots of the alpha and
NSD values of all Trenton samples against the corresponding sample mean grain
size values showed no linear trends.

The shapes of the majority of the Trenton CSDs show significantly different dis-
tributions than those of the Saluda Formation. This is evident by the mean and
standard deviation values of the respective alpha and normalized standard devia-
tion CSD shape descriptors, and a two-sample t-test conducted on those values.

It is also evident by the 53.3 % of the goodness-of-fit values <0.05 between the

Trenton and Saluda samples

63

64

5) The mean dolomite crystal size decreases down section in the Saluda Formation.
This down section decrease in mean grain size is consistent with the flux-limited
growth identified by the Nordeng and Sibley (1990) CL zone thickness study.

6) Lognorrnally shaped CSDs may be supplemental evidence of neomorphism of
dolomite. This is evident by the lognormal distributions of the Belize modern
dolomite and the Upper Cambrian, Bonneterre dolomite CSD studies by Gregg et
al., and by the lack of evidence of neomorphism in the Saluda samples.

7) CSDs of the computer-generated microstructures do not resemble those of the

Trenton or Saluda Formations.

Further study of the limestone Trenton clast CSDs would be required to compare the dif-
ference between the dolomite and precursor limestone CSDs. A similar relationship
between the mean grain size and CSD in the limestone clasts as observed in the dolomite
would indicate that the precurson limestone texture exerts significant control of the
nucleation and growth of the dolomite. In addition, further studies in similar geologic
settings are needed to determine if the differences between the Saluda and Trenton sam-

ples are a consistent characteristic of CSD shape between the different settings.

APPENDICIES

APPENDIX A

Thin-Section Descriptions, Photographs, and Drawings

APPENDIX A

Thin-Section Description, Photographs, and Drawings

We:
L1- 12 C3 1321 4931: (TLl)
Elm 129591100921

; one pop>

Fine to medium grained, planar dolomite.

Fine to medium grained, planar dolomite.

Very-fine to fine grained, planar dolomite.

Very-fine to fine grained, planar dolomite with a few large echinoid
replaced grains. some clays and minor porosity.

Medium to coarse grained, planar dolomite.

Fine to medium grained, planar dolomite.

Fine to medium grained, planar dolomite with a silica replaced
brachiopod.

small amount of anhydrite and some clays which allowed more plucking
from minor porosity.

TL 1- 12 C3 855 4891: (TL2)

Ll-

it

I'

r; or m pow

>_pow ?

Coarse grained planar dolomite with some plucking during sample
preparation.
Medium to coarse grained, planar dolomite.
Fine to medium grained, planar dolomite with some plucking.
Medium to coarse grained, planar dolomite with some plucking.
2 C1 Bl: (TL3)
Medium to coarse grained, porous, non-planar, with significant clays
between crystals. Vug?
Fine to medium grained, planar dolomite.
Fine to medium grained, planar dolomite.
Fine to coarse grained, porous, non-planar dolomite, with some anhydrite
and significant clays between crystals. Vug?
Fine to coarse grained, porous, non-planar dolomite, with some anhydrite
and significant clays between crystals. Vug?
Very-fine to fine grained, planar dolomite. Dirty, with pyrite.
Fine to medium grained, planar dolomite. °
Medium to coarse grained, planar dolomite with minor porosity.
Fine to medium grained, planar dolomite with some porosity between

clasts;

65

66

f-a

Medium to coarse grained, planar dolomite with some porosity between

clasts.

Medium to coarse grained, planar dolomite.

Fine to medium grained, planar dolomite with some clays between crystals

and minor porosity.

. Medium to coarse grained, planar dolomite with an area (vug?) of fine to
medium grained, porous dolomite which has more clays.

N. Medium to coarse grained, planar dolomite.

L1-12 C3 B2. (T134)

A. Coarse grained, porous, planar dolomite with a few anhydrite grains and

some plucked grains.

B. Coarse grained, porous, planar dolomite with some plucked grains. No
anhydrite grains.

Ll-12 Cl BS: (TLS)

I(. Coarse grained, porous, planar dolomite with some pore filling clays,
much anhydrite and plucking.

L. Medium to very-coarse grained, porous, planar dolomite with some
anhydrite, pore filling clays and plucking.

"' W. Fine to medium grained, dirty, planar dolomite(?), with minor porosity (in
one area), some plucking and a stylolitic boundary.

Luck 1-12 C1 BS 485?: (TL6)

* 11. Medium grained, porous, planar dolomite with some plucked grains.
(Same as TL7E) Partial?

L1-12 C1 BS: (TL7)

A. Fine to medium grained, porous, planar dolomite with a moderate amount
of clays and silt size quartz grains in the pore spaces and between crystal
grams.

Medium to coarse grained, porous, planar dolomite with a few large, run-away
growth dolomite rhombs, and minor amount of clays in the pore spaces.
Medium to coarse grained, very porous, planar dolomite with an
appreciable amount of anhydrite and pore filling clays.

Medium to coarse grained, very porous, planar dolomite with some
anhydrite and pore filling clays.

Fine to medium grained, porous, planar dolomite with a minor amount of

pore filling clays.

Luck 486495 (C 1 B8?): (TL8)

A. Fine to medium grained, moderately porous, planar dolomite filling a
fossil mold and non-mimetically replacing it. A moderate amount of pore
filling clay and a small amount of anhydrite.

B. Fine to medium grained, slightly porous, planar dolomite with a minor
amount of pyrite.

C. Fine to medium grained, porous, planar dolomite with a minor amount of
pyrite.

D. Medium to coarse grained, very porous, non-planar dolomite with a

moderate amount of anhydrite.

3!"?5

1719.0!”

67

E. Fine to medium grained, slightly porous, planar dolomite with a moderate
' amount of clays in the pore spaces, a minor amount of pyrite, and a dingy
appearance.

F. Fine to medium grained, slightly porous, planar dolomite with a minor
amount of pyrite and a dingy appearance.

G. Fine to medium grained, planar dolomite with minor porosity,, a minor
amount of pyrite, and a dingy appearance.

Luck 1-12 C1 B5 4852172: (TL9) (same as 6, 7, and S?)

A. Fine to medium grained, porous, planar dolomite with a minor amount of
pore filling clays.

B. Very-fine to fine grained, moderately porous, planar dolomite with a
significant amount of clays in the pore spaces and between grains. Some
anhydrite and a large, replaced echinoid grain.

C. Medium to coarse grained, porous, planar dolomite with a minor amount
of pore filling clays.

D. Medium to coarse grained, porous, planar dolomite.

Luck 1- 12 C3 BS 4891: (TLlO) (same as TL2?)

A. Coarse grained, porous, planar dolomite.

B. Medium to coarse grained, porous, planar dolomite.

C. Coarse grained, very porous, planar dolomite with a minor amount of
pore filling clays.

Luck 1-12 C2 B1 4867: (TLll)

A. Medium to coarse grained, very porous, planar dolomite, with a minor
amount of pore filling clays.

B. Fine to coarse grained, very porous, planar dolomite, with an appreciable
amount of pore filling clays.

C. Medium grained, porous, planar dolomite with a minor amount of pore
filling clays.

D. Medium to coarse grained, very porous, planar dolomite with one large
calcite crystal, and a minor amount of pore filling clays.

E. Medium to coarse grained, porous, planar dolomite with a minor amount
of pore filling clays.

F. Medium to coarse grained, moderately porous, planar dolomite.

G. Medium to coarse grained, porous, planar dolomite with a minor amount
of pore filling clays.

Luck 1-12 C3 B21: ('1‘L12)

A. Fine to coarse grained, very porous, planar dolomite with an appreciable
amount of pore filling clays and a few, very large, replaced, echinoid
grains.

Ll-12 C3 B2 4882: (TLl3) (mirror of TL4B)

A. Same as TIAB, but with an anhydrite grain present and also a heavier

amount of pore filling clays.

68

SALUDA Formation Samples

3-28-89

#4
#7d
#7
#15

#20
#22

#23

Very fine to fine grained, non-planar dolomite with minimal porosity.
Fine grained, non-planar dolomite with minimal porosity.

Partially dolomitized section of thinsection. Very fine grained,
mudstoned.

Grainstone with partially dolomitized matrix between, or within some
allochems/grains.

Non-planar dolomite with some echinoid grains replaced.

Partially dolomitized area, euhedral dolomite, some of which outline
former grainstone particles/allochems. Rhombs are cemented within, or
growing within, large calcite crystals. Some pyrite and si, especially near
contact with the completely dolomitized area. Completely dolomitized
area, non-planar, very fine grained with occ. glaucanite grain, and
laminations.

Nearly completely dolomitized. In areas where there is some calcite
cement, the grains that are completely dolomitized appear to be non-
planar. There are a few fossil molds replaced with calcite cement and are
partially dolomitized.

Grain Mount Method

#22

One large piece of partial dolomite was soaked in a 1% solution of HCl
for 4 days. The solution was changed approximately every 12 hours by
decanting the old solution without disturbing the sediment. The large
sample was removed and the sediment was removed with an eye dropper,
placed on a slide and allowed to air dry. This residue was then brushed
onto a slide coated with Canada balsam for measurement.

 

 

 

 

TL - 1 (TL 1 - 12 C3 B21 4931)

 

 

 

 

 

 

 

TL - l CLAST DRAWING

 

 

70

 

 

 

 

TL-2 (TL1-12C33554891)

 

 

 

 

 

 

 

TL - 2 CLAST DRAWING

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AST DRAWING

72

 

 

 

 

TL-4 (Ll-12C3324882)

 

 

 

“’1

 

 

 

 

TL - 4 CLAS'I' DRAWING

 

 

73

 

 

 

 

TL~5 (LI-IZCIBS)

 

 

 

 

 

 

 

 

TL - 5 CLASI‘ DRAWING

 

 

74

 

 

 

 

TL-6 (LUCKl-12C135485?)

 

 

 

 

 

 

 

 

TL - 6 CLASP DRAWING

 

 

75

 

 

 

 

 

TL-7 (Ll-IZCIBS)

 

 

 

 

 

 

 

 

 

TL - ‘7 CLAST DRAWING

76

 

 

 

 

 

TL - 8 (LUCK 4864175 C1 B8?)

 

 

 

 

 

 

 

 

 

TL-8 CLASTDRAWING

77

 

- 12 C1 BS 4852%)

 

 

 

 

 

 

 

 

 

 

 

 

 

TL - 9 CLASI' DRAWING

78

 

 

 

 

TL - 10 (LUCK 1 - 12 C3 BS 4891)

 

 

 

 

 

 

 

 

 

TL - IO CLAST DRAWING

 

 

79

 

 

 

TL - ll (LUCK I - 12 C2 31 4867)

 

 

 

 

 

 

 

 

TL - 11 CLAST DRAWING

 

80

 

 

 

 

TL-IZ (LUCKl-12C3821)

 

 

 

 

 

 

 

 

TL - 12 CLAST DRAWING

 

81

 

 

 

 

TL-l3 (Ll-12C3324882Hmln’orofTL-4)

 

 

 

 

 

 

 

 

TL - 13 CLAST DRAWING

 

 

APPENDIX B

Two-Sample Kolmogorov-Smirnov Goodness-Of-Fit Tests

LPPENDIX B

“ov-Smirnov Goodness-Of-Fit Tests

 

 

 

 

     

.. 300. .
_ 09.0.0

 

L

005.0

 

 

 

 

 

 

 

 

 

80nd 05nd N 3.5.0 800.0 500.0
88.0 300.0 000 «.0 053.0 «13.0
.5... IS... 05... 0:20. wSF

a 5k

 

 

 

 

v _.vmd
«09.0
180.0
_. $0.0

«a x .
580.0
mevod

 

 

 

 

. m 0% 09.3030.

0.20226.

53:020.
903 50
500.0 400
8:0 80

 

 

 

 

 

 

 

   

a. 1% 1 11““4H

«30.0 800.0 «30.0 wt:

y... ...»... .. . . . H .... 05...
«:40 008.0 030.0 05.0 22.0 09

800.0 99.0 9.90 92.0 a1.
l.1|1
88.0 800.0 508.0 250 «05»
033 05.0 81.0 800.0 900.0 02
99.0 800.0 83.0 9.80 0:00 9:0.
990 000.0 88.0 9.8.0 002.0 92....
«5.0 020.0 «30.0 020.0 2.05.0 <5...
05» 8:» SS» 9.: 05.: «<50. 5: 280030

 

 

 

 

 

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TWO SAMPLE KOLMOGOROV - SMIRNOV TEST FOR NORMALIZED CSD'S (size lave. size)

 

 

5150 .L 113-50-ssaup005) AOUleS—A0.10301u[0)l aldums-oml

fl XIGNEIddV

 

 

 

TWO SAMPLE KOLMOGOROV - SMIRNOV TEST FOR NORMALIZED CSD‘s (size / ave. size)

 

 

 

 

TWO SAMPLE KOLMOGOROV - SMIRNOV TEST FOR NORMALIZED CSD's (size / ave. size)

178

 

 

 

 

TWO SAMPLE KOLMOGOROV - SMIRNOV TEST FOR NORMALIZED CSD's (size / ave. size) <0.0S

98

 

 

 

 

 

TWO SAMPLE KOLMOGOROV - SMIRNOV TEST FOR NORMALIZED CSD's (size / ave. size)

0.1212 0.6527

 

 

 

TWO SAMPLE KOLMOGOROV - SMIRNOV TEST FOR NORMALIZED CSD'S (size / ave. size)

 

 

[.8

 

APPENDIX C

Normalized Crystal Size Distribution Frequency Histograms
and Crystal Size Distribuiton to Thin-section/Sample Key

APPENDIX C

Normalized Crystal Size Distribution Frequency Histograms And Crystal Size
Distribution To Thin-Section Sample Key

THIN SECTION NAMES FOR CSD GRAPH NAMES

Gilliam: W Slims

Trenton Formation, Jackson Co., Michigan

TL-l TL 1 - 12 C3 B21 A-I 9

TL-2 TL 1 - 12 C3 855 4891 A-D 4

TL-3 L l - 12 C1 Bl A-C.F-M 11

TL-4 L l - 12 C3 B2 AB 2

TL-S L 1 - 12 C1 BS K,L,W 3

TL-6 Luck 1 - 12 C1 BS 485? H l

TL-7 Total Luck 1 - 12 C1 BS 485? A-E S

TL-8 Total Luck (C1 B8 ?) 4864 1/2 A-G 7

TL-9 Total Luck 1 - 12 C1 BS 4852 “2 AD 4

TL-lO Total Luck 1 - 12 C3 B5 4891 A-C 3

TL-ll Total Luck 1 - 12 C2 B1 4867 A-G 7

TL-12 Total Luck 1 - 12 C3 321 A 1

TL-13 Total Luck 1 - 12 C3 BZ 4882 B 1
(Mirror of TL4B)

Netherland Antilles, Aruba Dolomite

BD6TS BD6 (Boi Doi Thin Section, two CSD counts)

BD6GM BD6 (Boi Doi Grain Mount, one CSD count)

Saluda Formation, Jefferson Co., Indiana

4901.82 MS4901DS (500 grain CSD count)

4901.811 MS4901DS (445 grain CSD count)

4904 MS4904D8

893 MS893DS

894 M8894DS

897 M8897DS

8912 M88912DS

8914 M88912DS

Computer Generated Microstructures

KMSITSAT Site Saturation (Cellular) Nucleation and Growth

KMJNSMEL Johmon-Mehl Nucleation and Growth

KMSSWKCL Site Saturation Nucleation and Growth With Weakly Clustered Nuclei

88

frequency

frequency

89

 

 

 

 

 

 

 

 

 

L
"ii i).—

 

 

. I '1L—i—q‘l—i {—7
TLlA.N0rmSize

 

 

 

 

 

 

 

 

l '1

 

 

l 1 1 l r 1 . 1 l 3 l

 

 

-I.l 0.. LI ...

TL192.N0rmSize

 

90

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

J1141|4|14IJJ|4|1— . «J 4 _ .1.JJ _ a q a 4 A O _ . q a _ . a a d 4 q 0‘—
l L 6. ft 1
. . e .
L e . . L
.. L.
. . m e i
L . .
. m U .. h L
e Z - 1
. em 1 .2
T - 1 .1 a.
I m 1
L E r i
1 .. . a .
- _. N -
II L . L
. 1 .. m .
. _ W1 . 1 i
T . L 1 1
L r _ . T . .
e . F
T _ 1 .. _ .
. w . . .7 H r.
v r — 1 V W i
0. I 1 # L
. FIE: . L .
- .2 r .
T—lLLiLlLiL- rrr r.._LLlel_! . - [thlLiPLiPLIL [1-1. - L .. ...- _lir _ . _ . F L b
u u u ... ... . u u « ...

JUCIJUILt Janina-LL

8..

TL18.N0rmSizc

91

 

11. - .I‘ -1.—|4ldJIaidiflli_ ._lJIdI .1—1111Jl—I-J13#

 

TL182.N0rmSize

 

 

mucmjfiuah

 

 

 

 

 

 

 

 

 

 

— 1.11_._ _ _1— 7—44..qu .... ‘I_|‘wlal—1-i—.1<. _t— -1_.i#
_
e
—\
_ -
_

_ .
.LLILIPLlrLlrhiEiEi—LLIPLIEEFM _

n u u a n u 6

JUCUJUULL

TL183.N0rmSize

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

JOCIJUILk

1110114114191—1.‘ 14411—141414: ._..—11141 .4141._ 1.1111 jj
T 1
I I
L
_
_
_

. e -

T - 1

_
e

L e j .

rt — b|b r r b p b p r — p b h u — p p p p F b n n n h

u u a u .6. 6

8..

TL1C.N0rmSize

 

 

 

 

 

 

8.. r—

JDCIJUILh

A.

88

‘8

TLlD.N0rmSizo

93

 

i—‘ldlll~)i -|_‘ 111 rfiJl—ll1 11— I 1—[411141'4'11—11

 

 

 

mucujwflak

TLlE.N0rmSize

 

e

 

 

 

 

 

 

 

 

TL1F.N0rmSiz-

 

 

i—IJIJZ - |_ .q ...I-Ilel-HI1'1I-llflvu—J’wtldllfl .11.. . 111-.1—1
L

3

h .

4

L

W. 4

fl _
_ ..
_

F1|I| . .
H -

_ r . _ _ . _ . . . . 0

u a .6. u a

JUCIJUILh

94

IAIJI— . .1— _ giniJi—JIIAI- _.—1I<l¢.11fl11_.—1141..._ _.1—11

W. L

 

 

1 .

TL18.N0rmSize

 

 

JUCUJFflLh

 

_lI—.1_.. _1— -t_i._1—I~l_l:-.—.11“'1<'d|—l- 01—1.—

 

TL1H.N0rmSize

 

JUCIJUILL

95

 

 

 

 

 

 

« a u

JUCIJUILt

1411.1—l_ _1-.q.1ql 01—1. flail-IA 1‘! .... .1—11111— al..|~|.¢. —..

r
L
J

L

 

rIFrpL—pbpb_.ppp—£LL—prpb_lrlrirlrr

TL11.N0rmSizc

711.1 . . I. l— .14 . .qllJuli—tlt..-l.fll||dltilqlllal...l-1|a . ...—J

 

— A

 

 

 

.1.

 

 

JOCIJUILh

TL29.N0rmSizI

96

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1]"— q_-____|.111 11- 1.11111
_ 4 ...—«14144.04.—

 

 

T
. n.
L
L
L -
L
L
L
-11L 1--1M1111-1- -111111. -- -
L .
PbPhiFrhhh—thbbbLthhhbth
u u a u u .

nonlnfiuat

.-

TL28.N0rmSize

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

JOCIJUlah

141141.-. 1 .-_..-..iJ 11¢ — q q q q «i. «l—
J.
_ _filll
L
. L
i; L
i _L
r
#1...
L
L
L
1— pr b bP-bL+- _ ha -F
u a u u 6

TLac.N0rmSizI

97

 

 

-_.q a . ~ _ a q 4 «aijljiJ141-«|1_11411—JJ|4|41_-J 1WJ114J. .1-.—.-.01-|...l- a q 0 0 JJ 1. J a q _ 1 q a +1—

I

l 61

T L

[jar—rm
rLL.
0
TI
1

 

8

 

 

 

 

 

 

 

 

1
1
TLBD.N0rmSiz¢

 

 

 

L 1!... . L

— huh-L.~b phbbe p—L Lirphhbh— —PPhL—-h pb—hbrh—hpbP—bbbP—r

. a . . . .
u a a .. u u a n 6

G

 

 

l

 

 

 

 

JUCIJUILk JUCIJUILb

TL39.NormSiz-

 

98

 

— |4|_l|n_v _\._|,dlr.r-‘ 1-..Jl—|I‘<A| _I . ‘|<|l—l.<|.<l|lau _‘

 

TL33.NormSizo

 

 

 

 

 

 

JOEIJUILh

 

_ . _ — _ _. _u—‘_‘JJI—I- _,I_x

 

 

JUCIJUILL

TLSC.NormSizo

 

 

99

 

_ _Ifllnd'ul— -: .1— ... —. ..l— ‘ql _.l—Ifi 4|I—Il—IV—.'dl_[¢‘_ _

TL3F.NormSizc

 

JUCUJUILh

 

i.

 

_ . _ _._ — _ —r .I-wfi'J -I-,Jl_.—?~‘ .vu-YJ,-I1.¢ 1‘ql

_L

[]]d lill FLTTw— F? r—

 

r!

 

_L._ .L » .FLLLILIEIFLIrLLLIELIErL
u u u u u n o

JUCIJUILt

 

 

TL38.NormSizn

 

fr-qucncg

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l

hm

1..

TL3H.NormSizc

 

frcqulncu

 

 

 

 

 

 

_ . [—1

 

 

 

 

L .
.'.!'1..'HW

 

l A

 

 

0.. 1.! 1.. I.‘

TL31.NormSizo

I. ..l._A| AI >l_ J...‘ ._l_|_.l

_l‘ I I.__L.L-LA|,.I L..J 4-1

A I I l l JA_l -.l ——L——l—u

 

101

.II. I ‘ I . .' ; I'D ll. 1! II V ‘IV .I‘ II. n j I .l ‘v . . I ‘l ‘1' .JJI '
J] a. _ - _ d Jluld‘ll— _ a la Jl— «I'd J q IH II— fill- . . - Inn .Jllldl— n nlfll‘ild a 4'1

[—l—ll—l

TL3K.NormSizc

 

 

 

_r7

[I

LL
TL3J.NormSLz¢

V A A
.
I l I I I1 I

 

# T
A . rl- 4HI.
4 v

 

 

 

rill it}! . I'L

.rl—llrrlbo.—PL»k—.>»p—-»F.FLI —».,.._P.»»_.-..—F».»
.

u a u .o. u u n u o

 

 

 

 

 

 

 

 

JUCIJUILh JOCOJUILh

1' IL V. I u

102

j

r

r

fill

 

 

LLLIPL
u u

_l

JUCUJUULh

 

JJIdJIIfiI—l11nlfildl1djll—1— .14'JJ1_ 11.!- 1‘. 3411—1

.b. EtLtLl—ILI - .rr~ 1% -

TL3L.NormSizc

 

fil—l. I4 _ _y‘111141-1.llq11-,‘.l~. 4.1—.14....‘14;1_l.—1 .

 

 

 

 

 

 

 

TL3M.NormSizo

 

 

JUCIJUILh

KB

 

JijldJI— «J . .1 — q q 4 41—--. 1111—.111-14. 4.1—-.4 . .. _lnllll‘ob :1 .le . ,- . . -. 1
_ . . . . _ . _ - . d - - 410.4 _ a J . . d#

TI

r 1

A

, I A

A
. A

H 1
fl A

r

 

 

TL4A.NormSizc

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TL4B.NormSizo

 

 

. T l
h .
hrLLf—pp.»—»|PP~__».V—*lplphr —. p p P— p . b p — . . u p — . p p .
u a u a H O O O N O O
O 3 I

JUCUJUILL JDCIJUILL

 

 

 

 

 

 

 

 

 

TLSK.NormSizc

 

 

JJIqu. . . . _ a _ 4 q firwJJJJ;
f
_L
r i
t We A
._
T

_

_
1’. _ . — . _ . _ —l
u n u a n n o

JUEmJUULL

 

. “_‘l‘fit _‘14 |..1,.11_1J1\_

1

 

 

— h p b — p n p

JUCIJUILh

 

 

1..

TLSL.NormSizc

frcquoncg

froqucncg

O.

8.

MB

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Y Y Y I * T I * l ' ' ' I I
_ _
L F“ J
_ 4

1
b- —I ‘-
l
— .-
1
" ‘1
~ J
1
P G
r—— —— J
b _ .
P—-‘ i
_ I
L. ..
. 4
. 1— _ -;
F 7
’ '1
p- -‘
_ 1—, _1 -
. 1 1 1 -
_ 1 1 l I 1 r1 _'
1 A 1 A A J 1 L A . 1 L A L '

..0‘ .0. ‘0. .0. 3..

O
TLSU.NarmS;zI
1 T I Y V f f T j
?
—— .3
1
...

 

‘IY1U'T'Y'r7TI‘IIYrIII'rYfiT

 

 

 

 

 

 

 

 

 

 

 

 

_1
J

r-
1.

1
1
1
r

TLBH.NormSizc

_.l._n -u _AL..I...' 4.1.1 .I .1-|-4_.1...I..1._|--a. s u 1

106

 

J11-.I~ _ _ ...l--.x _.1‘.J..-qII—I.— ... .. 191— ,_1‘- ‘1.1-.... .14. v—#

1

Y L

r F 1

 

 

 

 

 

 

 

 

 

 

A
F L
l

1. 1

 

 

bP-bb—pbh»—bpbPPb-P-—-PPP—rPF-r

 

 

“ . . a n . .
. t I

JUCIJUILL

8n.

TL7A.NormSiz¢

 

141111.411 . .._ -. q. u — d W q _ 4 q — J11! 411-111

#

 

 

 

 

 

I .0 F—
80 r—
O

JUCIJUILh

It

TL7B.NormSizo

107

 

 

 

4141-1d141.— u . . «141. q 41‘ Tq11q _.IJL..|41.IJ O 11114-- 41 q . «1— q 4 a . —1- q 1.14 d 1.141411
r. . I J

v

 

 

 

 

 

I _1_
Hm
TL7C.NormSiz¢

 

 

 

 

 

 

 

 

 

 

 

 

TL7D.NormSizo

 

 

f
v r Flllllll'u'l A
_1 ..
I IA .- T i
o
F p h h b h P P rh — P b b h — h h h P h p p h b L — — — .1 .11bl » PL b — b h h h — b h b P b h F P P
u u a u .0. o u u a u .0. o

JUCIJUILh JOCIJUILb

108

 

fl

v

1
—
L

 

”fl

. F
Y _11,

L
v 1.11.;
|_ A

 

 

. a . .
u I u no

JUCIJUOLt

d d u d . _ 1 «11.41314144111114141—1111411:91—11

A

4

L

 

.1
F1— ...up pl. plLrL b b L h h b r p b rrh - h1—1.

..o ‘

TL7E.NormSizc

 

 

 

 

 

 

 

 

 

 

 

1.17.1. . . . 7.-JI.1]|41~JJ1311414J1_1.11.«J-J
j m L
_H L
v L
f
T 1
I _.11 1
_
_
_
T _ _ 1
Y _
#
_.i! 4
- 1
71—1Pu1—1r——b 51- h — h P b h — b P h b — b b P P1P F. p h blr
« u a a u u o

JUCIDUILh

 

lo.

TLBA.NormSizc

ND

1-1]1.. . .dn..-.-11-.1._- .JI.1..--_11I.1.1.-.._ ..-. -. _1 1._- .1. . . _.-. . 1111—11.. ..1 4.14141 . . ... .. ...;

T 1 . 1
. r
V Y A
. . FA

 

 

_- .----- .
1........w......11.w. .

 

TLBB.NormSiz¢

TL8C.NormSizc

 

W1—
1
1

 

 

 

 

. r 111--. .
. 1 . _
.1111 U , .11.

T L I r 1
—» ..p-rL1r1.—I1FIF1_1IPIL1»1P1_.__-pnn—zbluerhlr L p r»: P —L p h p — p p b p — PL » p p
0
o

o O O
u u a u ..o. o u

 

 

 

 

 

 

 

 

a ‘

JUCIJUIL$ JUCIJUILk

 

froqucncg

frcqucncg

H0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1 fl 1 T a:
1 1
1 _. g

1

* a | .
L I 1 1 1‘11 .—. ‘1

1g 1 1 A 1 1

-l.1 0.. L. l.. 3..
TLBD.NormSizn
I 14—1—1
. i
_
,._

I l 4_l_l #Jg _l__l--l.l_

 

 

 

TL8E.NormSizc

I.'— 4
; , 1
r 1 _
. 1 111 r1 7] -

1H

 

 

. q d q q d d 1 d d —

q d 1 4 —

1 d 4 d —

 

ll.1llll ‘lll,

 

 

 

 

_

JOCIJUIL‘

.
I

 

p P b b b1b b.11—1LI—rl

r.

; L A A

1..

TL8F.NarmSizn

 

T

71—14114 4.. -.- —...- a ..< .- 1—141J14141dulq141J1411dJ11c1diJ 1—1

r17

 

 

 

 

 

 

 

 

 

 

 

 

.11—1rtblLI

W F---

 

..--.L
I
4

.
r

 

|L1~11—1—L1.>1Ir11—1 —1h1h1PL1—LL- .F1—..—.- .

a u .o.

JUCIJUOLt

L

k

A

TL80.NormSizc

 

H2

 

 

.._.—[411%

 

 

 

 

TLSA.NormSiza

 

 

JDCUJUULh

|y_yl11. _ ‘1 _‘. 1‘1“41_J>J|11‘_

~1AI:.1_;< w—l 4|.l. J A141

[—1

 

 

 

EEK—...P—b»
a

 

u.—.F»._..-.h

JUCUJUIL;

i

TLSB.NormSizc

 

H3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

JUCIJUIgh

1—---...... _J.~...l.1_ .....-Ju. .fl...q!...1Jl_€1-4 . _._ A... . .-_l
1 L
T LA
1 _-L ‘
.l llvlll 1
:!LL
T — L
_ l A
.11
A
il — I.
r A
V 4
.1. j
I _ P
, fl A
F A
I _ 1
r _ 4
L
r r1 4
f 1
— — D h b h b Lr h b!_ b h b P — h P b h F b r h b — b b h F—
a a u u ... .. .

..O

TLSC.NormSizc

1'_ Jlfll n: ¢ - —.- - 'acl—l ..I—u- dildl «IIAIJ ln'qlldlad'qlq-.4" .. -, —|u

g

 

 

 

 

rLLL — h p p p — h b no» — bk b -

 

 

 

JUCIJUILb

C
a.

TL90.NormSizo

frequencu

fr-qu-ncy

H4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

u ' _W '_
T
r T‘ — '
t _
[1W ‘
IIi
—. .m‘9 ah
-‘ - TL10A.HarmSi¥e . '
r
3 i
E i
-_ i
; 3
E h 3
il l ,g “

TL103.NormSizc

H5

ll11].JIJJIJI .nIJJJIJlqul 1114i nl—ldIl-II-Iy-VI—ol

 

 

 

1 .

TL10C.NormSiza

 

 

_ _ _ ._ ..F_Lh._ prL
u u n u n u -
JOCOJUULh

r

 

 

 

 

I!—,l<l. _|< \-l — JI— ‘- I-lI—| A—IQQJ'J‘J. _V qJ.‘l—'—¢JIJ I—l.v_ll

 

 

u u a ... u .

JUCIJUILt

8..

TL11A.NormSiz¢

frequency

froqucncg

H6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x r " 1 I T I I i
_ 1
— —;
; HTL :
}' '_'|'—‘ '
‘ 1 1 A 1 . x .
... ... 1 a n I 3.. ..-
TL118.NarmSizc
1 I I l ‘
r‘ :
._ . ...
L i L
- ’ 3
. I I
I
.. x _
p ‘ _'
a l L—m {—1 j
I L 1 . . 1 . 1 '
... ... ‘u. la. 3.. ‘..

 

 

TL110.NormSiz¢

H7

 

JI—I—‘I—Wiyl—JIW-‘W I_.|<I‘-|Iu JI.-lqld'ql<I—J‘.JIJ\ . —.J

 

 

 

 

 

TL110.NormSize

a.

 

 

_
, f I! :ili iii!!!
rll 1|: :3.
Ail‘llll‘
I—>+p._>...—-...—..-.—.P>F—
u u a u u a

JUCIJUUL;

 

I—lul<.1‘4l—. ‘L_!~'—A.— 1 . - . — < _ . d d u u - _ _

 

 

 

 

_foL>—»FLp—-.p._-p.—....—

TL11E.NarmSizc

 

 

u u a u u o

JUCIJUILL

118

I

 

 

 

 

 

 

 

JlldJlldl Jt-—l.nld...ldllq|-—|4Jcldl_—l _.l.‘ . .lA-lql—lnj.-sq.l--'—IJ

i

L

'A

— h b p b — P h h L — P p n h P b P h p — b b 5|..th

JUCIJUIgh

 

4..

8..

TL11F.NormSizc

 

 

 

 

 

 

 

 

 

Jollil , _ . I _ _ _ q ._9 q 14‘ - .-..‘uflA
r A
f A
_ A
f _ A
_ F . _ . . _ L _ p . L
m m u u a .

JUCUJUILL

3‘

u

'1

TL118.NarmSizn

H9

 

 

 

T_

JUCflJUflLh

 

TL129.NormSizl

 

v

i

Id}... _ . _ ... _ _I—‘fi1.-|-5- — . - d.4| d J - _r_ —

TL138.NarmSizo

 

 

 

 

JUCIJUILh

no

r.

 

41JJ4_ _1_ — _ —!_|-|4—JI—‘-!_I._ - _ —J‘1_Jl_.-..¢ _._}

LII

 

 

JUCIDUOLh

 

 

MS490108.N0rmSizn

I_‘-:‘_lq _ —‘ .-.I—v<.‘_-<ll—v-_l- —|»a|-. 14.jldl4 _¢_I

 

 

 

 

LIPIVIIrurplLL1_P_-..._....—>..._

JUEIJUIL;

 

MS4901DS.NormShort

frnquoncg

frcquoncu

O.

I.

II

I.

121

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

h_I I i I T l I I ' I I 1.]
P
r I
I
. _1 ...
b _I
" I
. I— .1
_ 7
I- _ [—1 CI.
» -i
_ ._.. _1'
- r—d I d:
’ I——: I 7
_ I I I I—I_ :
. I I I 1 . a I": Fla. 5
I— . _t A _-
I ' . . A 1 L4 . 4 .¥ I 1 A1 . 4 . . LA I. 1 I
o 0.0 3 LI a_ 3.0 a
MS4904DS.NormSizc
T I T
L _._ l:
- 1
i- r— J
I' ‘.
L _. —
C 4.
i- —I I—1 3
I LII— *
L 1 7 I I I :——I _
1 l A - . 4 l , . A A l 1 .
'0. 0.. I-. Co. 3..

"$89303.Norm3i2l

n2

Y.

v

If‘rv f1 Y #7 Y ' Y Y Y

jfifi Y Y

 

—h b PI» — FLIP rh h p p P — hi-ILILII— tItvlh-IrrbthI—I

filI—o¢..-.__.-——_,.‘.—-_._._._l.—a-__..._

 

 

 

 

 

 

 

 

u a u

JUCIJUILL

 

L l A L A A 4'

I1

 

M8894DS.NormSizc

I

' V T T V 1 V

I Y— T 'Y' T I 7

v
T

 

J.:d..—.JI .,— u q a .._ -oqI-I..l—

I‘ll-.-.L.I_l—JJI¢.I— _ -,_ . _

m
H
_l .

 

 

 

 

 

 

F47?

 

 

 

 

 

 

 

 

 

 

LuthL'th.IEL—pbbhbthP—bbbb—hbPb?

A L44 ‘ .

L

 

 

JUCIJUULh

...

M3897DS.NormSizc

fraquencg

fraquancu

n3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
M3891203.NormSizc

 

 

IILI

Us

l

 

 

M88914D$.Norm812l

U4

jInIJ‘JII-II— I14lJI_ I-—IJI— -.fi .1. IquITflI-Id JII—I _I.—II—IJ
T

 

 

 

 

 

 

u u a u

mucuawflLm

 

 

 

 

.
I.

 

rIpIPI_ . —I_ ILILI P - —LIL.|PI—I —I,._L.Ir|FIIhvo1—I._ILIILIII—II

I;

 

‘O.

KHSITSAT.NormSize

T

7

T ffi—j‘ v

 

Ifllq...l-n “4-1—3: _IJII- —Iq« d J- _..-- I. q — q ~II4II—J

 

II.

 

 

 

 

 

 

 

 

 

 

 

 

1 F. -

. g

fl r _ H
mm 4

r L, A

, I

LIL, IhIh IA—III—f..- I!—II—.LLI- ~I..— IrLILouIPI LIIrLIIIC

u u u . . .

EUCUDUILh

0.?

KMJNSMELoNDrmSiZI

U5

T

 

.II—JI‘._ _I—I—II-I-I-. _. WIJI- _ — _..I1I-I< I—I—u- V_ — _

 

 

 

 

 

LA+A'

KMSSUKCL.NormSize

 

FLILI» I _.lrIrIpIpLIrlle Lirg
u u u o

JUCUJUNLt

 

 

 

 

 

JUCUJUOLh

 

BDSGM.NormSiz¢

 

n6

 

 

 

 

 

 

 

BDBTS.NarmSiz¢

 

 

JUCOJUmLL

 

—| -I. — I4 : —I..II—IVJIAII—I-I—IIJII—IIJII-I,_ .fig

_w

41 A

 

 

 

I 1
I I
I .
I
t I I
I
I ‘_ L

 

BDST32.NormSizn

 

DUEmJUULk

BIBLIOGRAPHY

Beaumont, C., Quinlan, G., and Hamilton, 1., 1988
Orogeny and Stratigraphy: Numerical models of the Paleozoic in the eastern interior
of North America. Tectonics, 7 (3), 389-416.

Breiman, Leo

Statistigg: With a Viaw Toward Applications. Houghton Mifflin Co., Boston, MA,
1973.

Brown, George D. Jr., and Lineback, Jerry A., 1966
Lithostratigraphy of Cincinnatian Series (upper Ordovician) in southeastern Indiana.
American Association of Petroleum Geologists Bulletin, 50(5) 1018-1032.

Bury, Karl V.
' ' M 1 in A 1i i . John Wiley & Sons, New York, 1975.

Carlson, W.D., 1989
The significance of intergranular diffusion to the mechanisms and kinetics of porphy-
roblast crystallization. Contributions to Mineralogy and Petrology, 103 (1) pp. 1-24.

Cashman, K.V., and Marsh, B.D., 1988
Crystal Size Distribution (CSD) in Rocks and the Kinetics and Dynamics of
Crystallization II: Makaopuhi lava lake. Contributions to Mineralogy and Petrology,
99, 292-305.

Conover, W.J.
Wm. John H. Wiley & Sons, Inc., New York, 1971.

Cumings, ER, 1908
The stratigraphy and paleontology of the Cincinnati Series of Indiana. Indiana
Department of Geology and Natural Resources Annual Report, 32, 607-1188.

Davis, John C.

W. 2nd edition, John Wiley & Sons, Inc., New
York, 1986.

127

128

Davis, R.A., 1986
Cincinnati Region: Ordovician stratigraphy near the southwest comer of Ohio. In
'01» 1 a1 0 i fAmri . n nn' F1] -10: - o rn ‘ tin.
Geological Society of America, 1986.

Folk, Robert L.
1 f im R k . Hemphil Publishing Co., Austin, Texas, 1980.

Friedman, G.M., 1965
Terminology of crystallization textures and fabrics in sedimentary rocks. Journal of
Sedimentary Petrology, 35, 643-655.

Fridy, J .M., Marthinsen, K., Rouns, T.N., Lippert, K.B., Nes, 13., and Richmond, 0.,
Characterization of 3-D particle distributions and effects on recrystallization studied
by computer simulation. in Proc. of ICAA3, Tronheim, Norway, June 22-26, 1992.

Frost, H.J., and Thompson, C.V., 1987
The effect of nucleation conditions on the topology and geometry of two-dimensional
grain structures. Acta Metallurgica, 35 (2), pp. 529-540

Gregg, J .M., and Gerdemann, P.E.
Sedimentary facies, diagenesis, and ore distribution in the Bonneterre Formation

(Cambrian), southeast Missouri. In: Fi 1d i r ri f
0. ‘fith' 0-" .fi‘rau ‘Aln!’ 010' 14040 |Jl‘010' Eds.

Gregg, J .M., Palmer, J.M. and Kurtz, V.E., 1989, 43-55.

Gregg, J .M., and Howard, S., 1990
Crystallographic and mineralogic studies of Recent, peritidal dolomites, Ambergris
Cay, Belize. (Abstract). Geological Society of America Annual Meetings, 22, 179.

Gregg, J .M., and Shelton, KL, 1990
Dolomitization and dolomite neomorphism in the back reef facies of the Bonneterre

and Davis Formations (Cambrian), southeastern Missouri. Journal of Sedimentary
Petrology, 60, 539-562.

Gregg, J.M., and Sibley, DE, 1984
Epigenetic dolomitization and the origin of xenotopic dolomite texture. Journal of
Sedimentary Petrology, 54, 908-934.

Groeneveld, Richard A., 1991
An influence function approach to describing the skewness of a distribution. The
American Statistician, 45 (2), 97-102.

Hartmann, Daniel, 1988
The Goodness-of-fit to Ideal Gauss and Rosin Distributions: A new grain-size para-
meter. Discussion. Journal of Sedimentary Petrology, 58, 5, 913-917.

129

Hatfield, Craig Bond, 1968
Stratigraphy and paleoecology of the Saluda Formation (Cincinnatian) in Indiana,
Ohio, and Kentucky. Geological Society of America, Special Paper Number 95.

Holland, SM, 1993
Sequence Stratigraphy of a Carbonate-Clastic Ramp: The Cincinnatian Series (Upper
Ordovician) in its type area. Geological Society of America Bulletin, 105, 306-322.

Keith, B., 1985
Facies diagenesis and the upper contact of the Trenton Limestone of northern Indiana.

In: wovician and Silurian Rogkg 9f me Mighigan Baain. Cercone, K.R. and Judai,
J .M. (Eds), Michigan Basin Geological Society Special Publication No. 4, pp. 15-32.

Kretz, R., 1974
Some models for the rate of crystallization of garnet in metamorphic rocks. Lithos, 7,
pp. 123-131.

Krumbein, W.C., 1935
Thin-section mechanical analysis of indurated sediments. Journal of Geology, 43,
482-496.

Lorenz, B., 1989
Simulation of grain-size distrubutions in nucleation and growth processes. Acta
Metalurgica, 37 (10), pp. 2689-2692.

Larikov, L.N., Karpovich, V.V., and Dneprenko, V.N., 1989
Computer analysis of regularities of nucleation and crystal growth in a solid. Cryst.
Res. Technol., 24(6), 579-583.

Mahin, K.W., Hanson, K., and Morris, J .W., Jr.
The computer simulation of homogeneous nucleation and growth processes. In

Cgmputar Simglatign far Matgrials Applicatigna, 1976, (ed., Arsenault, R., Simmons,
J., and Beeler, J .), National Bureau of Standards, Gaithersburg.

Mahin, K.W., Hanson, K., and Morris, J .W., Jr., 1980
Comparative analysis of the cellular and J ohnson-Mehl microstructures through com-
puter simulation. Acta Metallurgica, 28, 443-453.

Marsh, B.D., 1988
Crystal Size Distribution (CSD) in Rocks and the Kinetics and Dynamics of
Crystallization 1: Theory. Contributions to Mineralogy and Petrology, 99, 277-291.

Marthinsen, K., Lohne, 0., and Nes, E., 1989
The development of recrystallization microstructures studied experimentally and by
computer simulation. Acta Metalurgica, 37 (1), 135-145.

130

Miller, Michael, 1988

Dolomitization and Porosity Evolotion. PhD. Disertation, Michigan State University,
East Lansing, Michigan.

Moore, P.G.

Prinoiolos of Sgtiatical Tochniguea, Second Edition, pp. 164-199. Cambridge
University Press, 1969.

Neave, HR, and Worthington, P.L.
Distg'ootion-Froo Toots. Unwin Hyman, London, 1988.

Nordeng, S. and Sibley, DE, 1990
Diffusion Limited Growth of Dolomite, Saluda Formation, (Ordovician, Indiana).
(Abstract). Geological Society of America Annual Meeting, 22, A178.

Pingitore, N.E., Jr., 1982
The Role of Diffusion During Carbonate Diagenesis. Journal of Sedimentary
Petrology, 52, 27-40.

Russ, J .C.
Size distributions. In W, Chapter 4, pp. 53-72, Plenum Press, 1986.

Saetre, T.O., Hunderi, 0., and Nes, E., 1985
Computer Simulation of Primary Recrystallization Microstructures: The effects of
nucleation and growth kinetics. Acta Metallurgica, 34(6), 981-987.

Sibley, DR, 1990
Unstable to stable transformations during dolomitization. Journal of Geology, 98,
739-748.

Sibley, DE, and Gregg, J .M., 1987
Classification of dolomite rock textures. Journal of Sedimentary Petrology, 57, 967-
975.

Siegel, Sydney
WW McGraw Hill. 1956.

Taylor, T.R., and Sibley, DE, 1986
Petrographic and geochemical characteristics of dolomite types and the origin of fer-
roan dolomite in the Trenton Formation, Ordovician, Michigan Basin, USA.
Sedimentology, 33, 61-66.

131

Tweed, Cherry J., Hanson, Niels, and Ralph, Brian, 1983
Grain growth in samples of aluminum containing alumina particles. Metallugical
Transactions A, 14A, 2235-2243.

Vaz, M.Fatima, and Fortes, M.A., 1988

Grain Size Distribution: The Lognorrnal and Gamma Distribution Functions. Scripta
METALLURGICA, 22, 35-40.

Vernon, R.,

Reactions in microstructure development. In Metamorphic Processes, Halstead Press,
John Wiley & Sons, N.Y., 1975

Walters, Sylvia J., 1988
Th w-imn 010? .no_ ....lm: Ev°t n ofa‘ ...10 F011.on n‘l‘
rdovi ian 0 Hi hwa 421 eff r onC nt Indiana. unpublished Masters thesis,
University of Cincinnati, Cincinnati, Ohio.

Wilson, J .L., and Sengupta, A., 1985
The Trenton Formation in the Michigan Basin and environs: Pertinent questions about
its stratigraphy and diagenesis. In Cercone, K. R. and Budai, J. M. (Eds. ), Ordovician

and Silurian rocks of the Michigan Basin. MiohigaoB gin leoo ogic cg Sooi roty Specr cial
Pluoi roation No.4 ,.pp 1- l3.