’51

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TEXTURAL ADJUSTMENTS DURING
REGIONAL METAMORPHISM

THESIS FOR THE DEGREE OF M. S.
MICHIGAN STATE UNIVERSITY

MICHAEL PATRICK RYAN

I973

.'-. ‘A‘xm “*w’o- u gdmrm

ABSTRACT

TEXTURAL ADJUSTMENTS DURING REGIONAL METAMORPHISM

by

Michael Patrick Ryan

Petrographic thin sections of regionally-metamorphosed
Thunderhead Sandstone have received quantitative textural evalua-
tion. Interior and exterior components of surface area vol.-
have been measured for quartz and plagioclase phases from 24 sites
over the regional gradient. Statistical testing of components of
variance within and between sampling sites indicate that quartz
surface area components are very sensitive to local (outcrop-scale)
conditions while plagioclase surface area is more responsive to
regional effects. The textural mosaics formed by phase association
were next modeled as states in a Markov chain. For non-collapsed
chains, grain size variation in quartz and alkali feldspar influenced
the amount of Markovity or determinism in the rock texture. Removal
of grain size effects by chain collapsing suggested that a limiting
value exists for the strength of neighborhood phase associations,
and that the amount of site-to-site variation in determinism

decreases with distance up the metamorphic gradient.

TEXTURAL ADJUSTMENTS DURING REGIONAL METAMORPHISM

BY

Michael Patrick Ryan

A Thesis

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

Master of Science

Department of Geology

1973

ACKNOWLEDGEMENTS

I thank Dr. Thomas A. Vogel for introducing me to rock textural
problems and for providing guidance in the development of the
research.

Dr. Charles Spooner kindly machined my "spinner randomizer"
for use on a petrographic microscope stage.

My wife Masako was a constant source of encouragement, and

deserves special thanks.

ii

TABLE OF CONTENTS

Page No.
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 1
PART I GRAIN BOUNDARY TEXTURES
Discussion of the Model . . . . . . . 4
Application of Quantitative Stereology . . . . . . 9
Surface Area Changes with Metamorphic Grade . . . . l3
Variance in Surface Area . . . . . . . . . . . . . 15
Regression . . . . . . . . . . . . . . . . . . . . 24
Residuals from Regression . . . . . . . . . . . . . 29
PART II GRAIN AGGREGATE TEXTURES
Mosaic Patterns and Grain Aggregate Textural Changes 35
Textural Mosaics . . . . . . . . . . . . . . . . 35
Testing the Mosaic Model . . . . . . . . . . . . . 36
Method . . . . . . . . . . . . . . . . . . . . . . 39
Results: Non-collapsed Chains . . . . . . . . . . 43
Collapsed Chains . . . . . . . . . . . . . . . . . 49
Conclusions . . . . . . . . . . . . . . . . . . . . 54
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 58

iii

LIST OF TABLES

Table 1: Sites 8, 15, 17,
Analysis of Variance:

Table 2: Sites 8, 15, 17,
Analysis of Variance:

Table 3: Sites 8, 15, 17,
Analysis of Variance:

Table 4: Sites 8, 15, 17,
Analysis of Variance:

Table 5: Sites 8, 17

Analysis of Variance:

Table 6: Sites 8, 17

Analysis of Variance:

Table 7: Sites 8, 22

Analysis of Variance:

Table 8: Sites 8, 15

Analysis of Variance:

Table 9: Sites 17, 22

Analysis of Variance:

22
Quartz-Quartz Sv .

22
Quartz-Others Sv .

22
Plagioclase-Plagioclase Sv

22

Plagioclase-Other Sv .

Quartz-Quartz Sv .

Quartz-Others Sv .

Quartz-Others Sv .

Plagioclase-Plagioclase Sv

Plagioclase-Others Sv

iv

Page No.

20

21

21

21

22

22

23

23

23

Figure
Figure

Figure

Figure
Figure
Figure
Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

10.

11.

12.

13.

14.

15.

LIST OF FIGURES

Nomenclature of Surface Area Types .
Model for Changes in Surface Area

Sketch Map of the Gatlinburg, Tennessee-
Cherokee, North Carolina Area

Sketch Map of Regional Isograds
Variation in Quartz-Quartz Sv
Variation in Quartz-Other Sv .
Variation in Plagioclase—Plagioclase Sv
Variation in Plagioclase-Other Sv

Quartz-Quartz v§_Quartz-Other Grain
Boundaries .

Plagioclase-Plagioclase v§_Plagioclase-Other
Grain Boundaries .

Distribution of the Residuals from Regression
(Quartz Boundaries)

Distribution of the Residuals from Regression
(Plagioclase Boundaries)

Residual Distribution for Quartz and
Plagioclase

Page No.

10

14

16

17

18

25

28

30

31

34

37

4O

Figure

Figure

Figure

Figure

Figure

Figure

Figure

16.

17.

18.

19.

20.

21.

22.

Rose Diagrams for Development of Anisotropy
in Rock Texture .

-2 Loge A (Non-collapsed Chains Perpendicular
Traverses)

Model for Markov Test Statistic v§_Distance
Up Metamorphic Gradient .

-2 Log A (Non-collapsed Chains, Parallel
Traverses)

-2 Log A (Perpendicular Traverses, Collapsed
Chains

-2 Loge A (Perpendicular Traverses, Collapsed
Chains: Quartz, Plagioclase, Others

Quartz, Kspar, Others) .

-2 Log A (Perpendicular Traverses; Collapsed
Chains; Quartz, K-spar, Others) .

vi

Page No.

41

44

47

48

51

53

55

INTRODUCTION

 

Ehrlich et a1. (1972) have discussed the general concept of
rock texture in regional metamorphism and the information textural
parameters can carry. They demonstrated that the surface area and
the shape of plagioclase grains are highly responsive to changes in
metamorphism. Moreover, in the metamorphosed granodiorite they
studied, these textural variables proved more responsive to metamorphic
conditions than compositional variables.

This paper represents a further attempt to evaluate the response
of selected textural variables to changes in the metamorphic environ—
ment.

Allen and Ragland (2) have reported chemical as well as textural
variation in the Thunderhead Sandstone, from Gatlingburg, Tennessee
to Cherokee, North Carolina. The Thunderhead Sandstone is a region-
ally metamorphosed arkose, of medium-to-coarse grain size. It is
Precambrian in age, and is believed to have undergone prograde meta-
morphism in the Devonian, following overthrusting into its present
location during the Ordovician (3).

A number of factors suggested using the Thunderhead Sandstone
as a testing area for further textural work:

1) Relative homogeneity in composition

2) A facies range from greenschist to upper amphibolite

3) Massive bedding and numerous roadcuts made possible an
adequate sampling plan

4) Lack of appreciable penetrative deformation

There are important similarities and differences between the
Thunderhead Sandstone used for this study, and the Cross Lake Gneiss
of Ontario used for a prior textural study (4). Both bodies have
undergone prograde regional metamorphism from west to east within a
distance of 20-25 miles, and in both cases, metamorphism ranged from
greenschist to amphibolite facies. Differences between the Thunderhead
(a meta-arkose) and the Cross Lake Gneiss (a meta-granodiorite) are
compositional and textural. Modal composition in the Thunderhead
Sandstone is 36% to 66% quartz, about 25% plagioclase, and an average
of 21% micas, of which biotite predominates a 'The compsoition of
the Cross Lake Gneiss is approximately 24% quartz, 54% plagioclase,
12% biotite and 2% muscovite (4). In the Thunderhead Sandstone,
exposures in greenschist grade have preserved relict sedimentary
textures, including graded bedding and cross bedding. In the Cross
Lake Gneiss, primary igneous textures are preserved in the low-grade
sector, including parallel alignment of plagioclase (4).

Rock textures may be specified by examination of two broad
variable groups: grain boundary-based variables and grain aggregate-

based variables. This paper will use surface area per unit volume--

a boundary parameter and phase mosaic patterns--a grain aggregate
parameter, to quantitatively test the textural effects of regional
metamorphism on the Thunderhead Sandstone. For those portions of
this study involving surface area, quartz and plagioclase alone are
considered, while the mosaic study involves all major phases in the
rock.

Adjustments in the rock fabric to the changing physical condi-
tions (T, deviatoric stress) of regional metamorphism produce
continual changes in the topologic network of grain boundaries and
the type and orientation of phases making up the neighborhood of a
given grain or aggregate of grains (5). Stressed grains repair
structural damage through polygonalization-recrystallization
processes (6), as well as solid-state diffusion. Stressed aggregates
of grains approach textural--and metamorphic-equilibria through
neighbor selection when stability limits of old neighbors have broken
down (7). Additionally, large aggregates of grains may organize
themselves into "super neighborhoods" through compositional banding

processes (8).

PART I

GRAIN BOUNDARY TEXTURES

DISCUSSION OF THE MODEL

 

There are two components in the total surface area of a grain:
interior, or polygonal-surface area and exterior surface area
(Figure 1). These two types may be termed a-a and 0-8 respectively,
where a-a implies that two grains of the same phase meet at a boundary,
and a-B implies the junction of two different phases. These may also
be termed like-like or unlike boundaries, respectively.

Our model estimates changes in both components of surface area
during regional metamorphism (Figure 2). In initially unmetamorphosed
sediments (left side of figure), most of the total surface area is
exterior, or a-B. Only relatively minor amounts of a-a occur, and
these are often diagenetically generated fractures or the chance
agglutination of two grains of the same phase. Rapid increases in
the a-a component occur as stored strain is relieved through poly-
gonalization and recrystallization (6). Increases in temperature
facilitate structural repair by increasing the ease of recrystalli-
zation, such that the surface area in the interior of a phase (q-u)
soon comprises most of the total surface area (as illustrated by the

large hump over the brittle sector).

Figure l. Nomenclature of Surface Area Types.

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Figure 2. .Model for changes in surface area in
quartz and plagioclase, in response to

the changing (P,T) conditions during
regional metamorphism.

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Relief of stored strain reduces the driving force producing
recrystallization (6), while maintained--or increased--temperatures
will aid grain growth (9). Both these effects will cause a
relative reduction in like-like (a-a) boundaries. Grain growth
should be expected to continue up the gradient, effecting a sub-
stantial reduction in a-a surface area through the elimination of
a-a boundaries. It would be expected that the final Svaa value
would approach, but not equal, that in the original sedimentary
fabric. Impurity levels within a phase would be expected to block
some grain boundary migration (10), and therefore the elimination
of subboundaries within phase interiors would not go to completion.
This difference between a-a surface area in the sedimentary and
equilibrium metamorphic rock is denoted ASvaa. Exterior Sv would
be expected to remain approximately constant, until the integrity of
grain margins begins breakdown by like-phase agglutination in areas
of semi-plastic flow. The final equilibrium Sv texture should be
characterized by a relatively higher level of a-B boundaries, due to

the enhanced stability of a-B margins at higher grades of meta-

morphism (7).

SAMPLING
Sampling within the Thunderhead Sandstone (Figure 3) was

carried out at twenty-one individual sites along U.S. Route 441

Figure 3.

Sketch map of the Gatlinburg, Tennessee-
Cherokee, North Carolina area
(after King, 1964).

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from Gatlinburg, Tenessee to Cherokee, North Carolina. The overall
direction of the sample traverse is coincident with the regional
metamorphic gradient, and approximately perpendicular to all mapped
isograds (Figure 4).

From the samples obtained, 36 samples were selected for textural
examination. Sixteen of these were candidates for a subsequent
analysis of variance which followed the preliminary examination.
Samples were slabbed for thin-sectioning perpendicular to the
direction of elongation of eliptical quartz grains, or the apparent
foliation of the rock fabric as a whole. This provided for uniformity
of orientation of each thin section with respect to the inferred
regional stress field producing foliation.

Thin sections were stained for plagioclase and alkali feldspar
with rhodizonic acid and sodium cobaltinitride using a procedure

developed by Bailey and Stevens (11).

APPLICATION OF QUANTITATIVE STEREOLOGY

 

Recent developments in metallography have provided means of
making three-dimensional form and structural inferences from two-
dimensional microstructure (12). These metallographic approaches
provide, for example, a means of abstracting volumetric surface area

from observed phase boundaries in thin sections. It was therefore

Figure 4.

Sketch map of the location of
regional isograds (after King, 1964).

10

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11

possible to examine the extent of polygonalization and recrystalli-
zation in the quartz and plagioclase phases of the Thunderhead
SandStone, and test the recrystallization model by the application
of stereologic surface area measurements.

Recrystallization of quartz and plagioclase involves energy
reductions which cause adjustments in total surface area. Total
surface area has an outer, or unlike phase to phase contact as well
as an inner or like-like phase contact. Therefore both these bound-
ary types must be counted in polygonalization-recrystallization
studies. Subboundaries, or interior borders are a-u type contacts,
while exterior, or grain-matrix margins are a-B types. Surface
areas for both types of contacts are generated from the basic
observation N1, the number of intersected margins per unit line.

The polygonal (interior, a-a ) surface area per unit volume is given
by

S = 2N (l)
v 1

while exterior (a-B ) surface area per unit volume is

S = 4N (2)
v 1

Coefficients of 2 and 4, for expressions 1 and 2 respectively,
account for both the interfacial areas at an a—a margin in the

first case, and, in the second case, the fact that the outer

12

surficial area of the a-B margin will be counted twice since the
outer surface will necessarily close upon itself. Full development
of (l) and (2) may be found in Underwood (13) and DeHoff and
Rhines (14). Operational determination of N1 uses the method of
random secants (13). Stained thin sections were examined on a
Leitz petrographic microscope using a flat stage, 8X occular, 10X
objective, and Chayes point counter. For each thin section, 30
test lines were applied. Each test line measured 1.18 mm, making
a total traverse length of 35.4 mm per thin section. The position
of each traverse was randomized with respect to x-y position (in
the plane of the stage) under the objective, and angular orientation
(8) relative to the microscope axis. Cross hairs within the occular
provided the test secant. Visual traverses were made along the test
line, and a-a, a-B observations were recorded on a Swift point
counter for both quartz and plagioclase; i.e., the following bound-
aries were counted:

1) quartz-quartz

2) quartz-others

3) plagioclase-plagioclase

4) plagioclase-others
Counts were accumulated until a total of 30 randomly-oriented

traverses had been completed. Total counts were then normalized to

13

N1 by division by the total cumulative traverse length. From N ,

Sv was then available by relations (1) and (2).

RESULTS
The effects of the regional metamorphic gradient on surface
area in quartz and plagioclase are presented in the form of
1) plots of surface area vs. distance up the metamorphic
gradient
2) the analysis of variance of surface area for selected sites
3) regression of u-u surface area onto a-B surface area

4) evaluation of the residuals from regression..

SURFACE AREA CHANGES WITH METAMORPHIC GRADE

 

Values of quartz-quartz, quartz-other, plagioclase-plagioclase,
and plagioclase-other surface areas per unit volume (nmzmm's) have
been determined for a number of sites occupying various positions
within the regional metamorphic gradient. Sample sites are identi-
fied along the absissa in Figures 5-8. The position of a site on
the absissa was obtained by projecting normals from map localities
onto a line perpendicular to the regional mapped isograds.

Examination of quartz-quartz Sv (open circles, Figure 5)
reveals an early series of high values, which declines substantially

by site 10, then undergoes a moderate rise between sites 13 to 18,

Figure 5.

Variation in the surface area of quartz-quartz
contacts as a function of distance up the
regional metamorphic gradient.

14

mm.:_2 om

mwh<ozdmm <>OZ<O

mmJQE/‘m ._<_CZ_.

m—

N._.m<DO\th<DO

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0F

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ow

A
%_wwzww3 s

15

and declines slightly by site 22. This is in general agreement
with what we would anticipate with the model of Figure 2.

For quartz-other Sv (Figure 6), consideration of open-circled
values shows a fairly steady series, with a slight but noticeable
dip from site 8 to site 21. This is also behavior which might be
expected by considering the a-B trend as outlined in the surface
area model.

Variation in surface area for plagioclase-plagioclase bound-
aries (Figure 7) shows two rises, one centered over sample site 1
and a second centered over sample site 13.

The variation in plagioclase-other surface area (Figure 8)
shows fairly steady variation about an average value near 10 mmzmm'3.
A small downward movement in values, however, occurs between sites
13 and 18.

Deviation from the surface area model in plagioclase occurs
in overall low a-a values and the failure of a a values to stand
substantially above a-B values--especially in the early low-grade

SBCtOI‘.

VARIANCE IN SURFACE AREA

 

The spread in Sv values for outcrops which received multiple
testing (such as sites 1 and 2 with two values each) suggested an

evaluation of the variance in surface area at selected sites.

Figure 6.

Variation in the surface area of quartz-other
contacts as a function of distance up the
regional metamorphic gradient.

16

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m
C
C
O
o o
. .7 u a
O C
O O o. O O 0
O C C O C
O.
0
0 O
cwc.O\~Cm:O
mmumoZQmm m>0c<0 o

coimCm> meta momtsm
3353 22:50

A
(€_WWZWW) S

Figure 7.

Variation in the surface area of plagioclase-
plagioclase contacts as a function of distance
up the regional metamorphic gradient.

17

 

mmiz om 2 or m

C C
u. g m a m . a. o
o
o o o o o
o o
o
o o o o
o
o o o.
o
.N
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S
A
mm<._oo.o<$\mm<soo_o<i m
w
329.5% <>oz<o zo:<_m<> <mm< moimaw We
$5.25 ._<_:z_o w...

Figure 8.

Variation in the surface area of plagioclase-
other contacts as a function of distance up
the regional metamorphic gradient.

18

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op

ON

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(‘0
A
(€_ww aWW) s

mmIHO\ mw<400_0<4a

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19

Meaningful evaluation of changes in SV over the metamorphic
gradient are critically dependent on a knowledge of the extent
of variation within an outcrop or sample site.

From the total spread of sample sites, four sites were chosen
at random for the analysis of variance. From available samples
for each site (generally 10 to 15), four samples were randomly
selected for subsequent thin sectioning and surface area measure-
ments by methods described earlier. Those samples involved in
the analysis of variance are represented by black dots above their
sample sites on Figures 5 to 8.

The analysis of variance decomposes the total variance (all
samples at all sites) into a component within the sample site and
a component between the sample sites. The magnitude of the differ-
ence between these two components is determined through the F test
statistic. The null hypothesis (Ho) states that the values of Sv
from all samples at all sites, come from the same population. The
alternate hypothesis (Hi) states that SV values from different
sample sites come from different populations. Rejection of the
null hypothesis at a given level of significance requires exceeding
corresponding tabled values of F. Details of the computational
steps and complete discussions of analysis of variance are given

by Sokal and Rohlf (1969) and Griffiths (1967).

20

Results of the analysis of variance a-a, a-B SV in quartz and
plagioclase are presented in Tables 1 through 4. These evaluate
the components of variance for sample sites 8, 15, 17 and 22. This
is a range of 12 miles on the metamorphic gradient, although repre-
sentation of the entire gradient was assured through the process of
random selection. Rejection of the null hypothesis at an a-level of
.05 requires an F statistic value of 3.49 or greater. In no instance
was this value met, and the null hypothesis has failed to be rejected.
We conclude, therefore, that from the sample sites selected to
represent the metamorphic gradient, there are sites which contain as
much variation within themselves as between sites over the gradient

as a whole.

TABLE 1: SITES 8, 15, 17, 22

Analysis of variance: Quartz-Quartz SV

Source df. EE. M§_ ‘E
Among sites 3 370.216 123.405 1.47
within sites 12 1001.353 83.446

Total 15 1371.569

21

TABLE 2: SITES 8, 15, 17, 22

Analysis of variance: Quartz-others Sv

Source df; §§_ MS .5
Among sites 3 274.912 91.637 0.804
within sites 12 1366.540 113.878
Total 15 1641.452

TABLE 3: SITES 8, 15, 17, 22
Analysis of variance: Plagioclase-Plagioclase Sv

Source i g E F
Among sites 3 35.502 11.834 0.745
within sites 12 190.481 15.873
Total 15 225.983

TABLE 4: SITES 8, 15, 17, 22
Analysis of variance: Plagioclase-other Sv
Source if; s3 MS 5
Among sites 3 344.211 114.737 1.601
within sites 12 859.851 71.654

Total 15 1204.062

22

The 4 site-l6 sample analyses were broken down into a number
of smaller analyses involving two sample sites. Results of these
breakdowns are presented in Tables 5 through 9. Reduction in the
number of sites changes the degrees of freedom for both the "among
sites” and the "within sites” sources of variation. This requires
comparison of the calculated F statistic with new tabulated values.
Rejection of the null hypothesis now requires an F value of 5.99

for significance at the 95% level, and 13.7 for an a-level of .01.

TABLE 5: SITES 8, 17

Analysis of variance: Quartz-Quartz Sv

Source df. ‘ss MS .5
Among sites 1 368.833 368.833
4.108
within sites 6 538.694 89.782
Total 7
TABLE 6: SITES 8, 17
Analysis of variance: Quartz-Others Sv
Source df. gs M§_ E_
Among sites 1 33.620 33.620
0.471
within sites 6 427.392 71.232

Total 7 461.012

TABLE 7:

Analysis of variance:

Source df.
Among sites 1
within sites 6
Total 7

TABLE 8:

Analysis of variance:

 

Source df.
Among sites 1
within sites 6
Total 7

TABLE 9:

Analysis of variance:

Source df.
Among sites 1
within sites 6

Total 7

SITES 8, 22

Quartz-Others Sv

s_s fi
266.805 266.805
290.573 48.428
SITES 8, 15

Plagioclase-Plagioclase Sv

:22 118.
125.091 125.091
22.404 3.734

SITES 17,22

Plagioclase-Others S

V
g: 14.5.
286.084 286.084
268.284 44.714
554.368

23

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5.509

| "11

33.50

I"?!

6.398

24

Highly significant rejection of H0 (a = .005) for plagioclase-
plagioclase Sv at sites 8 and 15 (Table 8) shows that differences
in the relative amounts of recrystallization and grain growth are
present.

Significant rejection of Ho (a = .05) for plagioclase-others SV
between sites 17 and 22 (Table 9) show that differences in the outer
component of Sv (a-B ) are present. In the surface area model, these
sites correspond to points in the higher-grade rocks where semi-
plastic behaviour should become increasingly important. Hence,
semi-plastic agglutination of plagioclase between sites 17 and 22

may explain the substantial reduction in Sv‘

REGRESSION

 

The regression of u-a Sv on a-B Sv for quartz is shown in
Figure 9. Values of the simple correlation coefficient (0), and
the multiple correlation coefficient (R2) are 0.5339 and 0.2851
respectively. In the analysis of variance for overall regression,
the slope 81’ (here 81 is an estimator for the parametric slope 131,
and should not lye confused with a 8 phase or grain boundary) of
0.5741 was significant at the 99.9% level.

The regression line divides the graph into two fields. Strong

deviation from regression in field 1 indicates samples that have

the great bulk of their total Sv taken up by u-a subboundaries

Figure 9.

Grain boundary diagram, showing the amount of
total surface area in quartz which is allocated
to subboundaries (quartz-quartz) and to neighbor
boundaries (quartz-other). A diagonal from the
origin would divide this into two fields: upper
field suggests large amount of recrystallization;
lower field suggests granulation trend.

25

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z_<¢o Npm<ao z. awhk<0m

U

600

00'

0°.

ZIJBnO—ZIJBOO

saglepunoa

26

(1-13-A and l-lO-b). These occupy the a—a peak in the surface area
model. Samples deviating strongly form regression in field 11 have
relatively few a-a boundaries, and most of the total Sv is exterior
(sample 17-2).

Samples involved in the SV analysis of variance are indicated
by geometric shapes. Substantial scatter in values for a single
outcrop site (Figure 9) is shown in plots for site 17 (triangles)
and site 22 (circles). At site 17, separation of 17—2 form the main
cluster indicates that recrystallization has been relatively sur-
pressed. Very large a-a Sv and a-B SV values for sample 17-4 indi—
cates a large relative increase in both recrystallization and dis-
persion of the quartz phase. This difference in Sv behavior between
17-4 and the 17-1, 17-3 cluster may not be explained by differences
in quartz content (samples 17-4, and 17-1 contain 42.75% and 46.75%
quartz respectively).

Marked scatter also occurs in plots of the Sv components for
samples from site 22. In this case there is an approximately linear
range of (a-a Sv, a-B Sv) values for the series 22-2A, 22-4, 22-5
and 22-6. The range in modal % quartz for these samples is 45.75 to
49.50--a separation of less than 5%. Explanation for such large
differences in recrystallization within one sample site may lie in

proximity to pelitic interbeds, and/or point-to—point differences in

27

deviatoric stress. At site 17, for example, samples l7-l, l7~3 were
relatively removed from pelitic layers, while 17-2 and 17-4 were
quite close. Sample 1'74 was the closest of all, being one foot
below a two-ibot-thick pelitic layer.

For the regression of a-a on a-B Sv in plagioclase (Figure 10),
analysis of variance for overall regression shows 81 = 0.2615 at the
99.9% level of significance.

For plagioclase Sv’ as in quartz Sv’ site 1 shows strong devia-
tion from regression (in field 1) indicating high levels of recrystal-
lization. Samples from site 22 (circles) show scatter in their plots.
The plagioclase content of these rocks varies from 22.25% to 30.25%.

0

The variance in modal 6 is small (8%) and does not have a systematic
relationship with 8v“ The explanation for scatter in Sv within a
single outcrop appears to lie outside the variation in modal % (as in
quartz).

For quartz-quartz Sv at sites 8 and 17 (Table 5), standards
must be reduced to a 90% significance level for rejection of Ho.
For quartz—quartz Sv variation among all four sample sites considered
in the original analysis of variance (Table 1), the most significant
differences (from a consideration of Figure 5) appear to be between

sites 8 and 17. The failure to reject H0 at the 95% level of

significance, however, indicates that substantial difficulties may

Figure 10.

Grain boundary diagram for plagioclase.
See Figure 9 caption also.

28

 

 

mm_c_wuc.som cmcuo.nom_a

com 000

m m__w .0
m. 35 O
A_ m~_m 4

mm mfim m_QEmm«

 

mm:m m>0c<

mSG 322.0

0.
mm.m<gz:0m

oom oov oom
D
O
O
D 0
D i
1 D
U
i
Z_<m0 mm<._OO_O<4n_

com

2 _

DD@

00..

m whk<0m

OOP

OON

00m

'69|d_'58|d

seglepunog

29

lie in the way of using quartz SV as an estimator of position on
the regional metamorphic gradient. Similar variations in quartz SV
with metamorphic grade were found in the Cross Lake Pluton in an

earlier textural study.

RESIDUALS FROM REGRESSION

 

Figures 11 and 12 plot the deviations of individual observations
from regressing a-a Sv on u-B Sv for quartz and plagioclase respec-
tively. These residuals are plotted over the positions their sample
sites occupy on the metamorphic gradient. The upper portion of each
figure contains samples which have a predominance of a-a -type Sv'

The lower portion contains those samples which have the larger portion
of their total Sv tied up in the outer, or a—B component. Plotting
residuals in this manner permits an evaluation of trends in the vari-
ance of Sv up the metamorphic gradient as well as an examination of

g the goodness of fit to the assumptions of least-square regression (18).

Both Figures 11 and 12 show a non-random behavior of Sv variance
in the distance sequence plot. For both quartz and plagioclase,
variance from regression decreases from early large positive values
(site 1) through zero to large negative values near sites 7-11. Both
quartz and plagioclase show subsequent reductions in negative vari-
ance through zero to sizable positive variances. This second "high"

is centered on site 17 for quartz and on sites 13-15 for plagioclase.

Figure 11.

(Non-random) distribution of the residuals
from regression for all quartz boundary types.

30

38.2.: Ezm_o<me 0.:amoz<pm: a: moz<hm_o
mm on m. o. n

3.58 «2% 35 S «:33: 3 5 av a fl
.oz 35 Barnum

D
motmucsom 3.2321522? co nommmcwom mo_.mc:=onla=mua

mucmcanoo Tmuczom Ntmao to... cozzntufla .ngmmm

 

.0.

A PPIBUJHSEI-A

Figure 12.

Distribution of the residuals from regression
for plagioclase boundary types.

31

382:: «cogmbo 2:30:33: a: 3:339

 

an an. em a
«ufiaxva an: a.«:« 3: new a n
.02 25.. 32.8
.1
U
DU \l/
U a \\ In. a
0 D D D /
.1 < D \
.1 //< D \ V
/ o \\ u
D n. <//I\O D /
.4 4
0 /U
a /
0
D U/

mmtmucaom :Zmzuffluqu :9 33033. mats—ocaoalazmuu

35.33.30 32:53 32033:; co“. 5:33:30

.233”.

 

Apmewnsa-A

32

In the case of quartz, a final decline through zero to negative
values occurs between sites 18-22. Variance in plagioclase appears
to tail off and distribute itself widely about the zero line. In
general, rises and declines in variance for quartz are fairly tightly
grouped, while those for plagioclase show more spread.

If distance up the netamorphic gradient had no effect on the
regression data, we should expect a fairly horizontal band of
residual plots. This band would be centered about the zero-deviation
line. The sinuous variation in deviations for quartz and plagioclase,
(dashed line in Figures 11 and 12) plus the apparent synchronous
rise and fall of these deviations indicates that the ratio of a-a
to a-B surface area is highly dependent on position within the gradient.
This is what one might expect from consideration of the surface area
model (Figure 2), as the model essentially tries to anticipate
changes in the ratio of a-a Sv to a-B Sv with distance. The second
group of large positive values in Figures 11 and 12 show a relative
increase in importance of a—a subboundaries from sites 7-11 to sites
13-17. This implies a second location of high amounts of recrystal-
lization. This second "high" coincides with the location where the
Greenbrier Fault system intersects the sample traverse (19).

The effects of local deformation in those sectors of the gradi-

ent where we should expect brittle or semi-plastic response are

33

shown in Figure 2. Cross-hatched areas indicate the effect on the
a-a and a-B components of Sv'

The distributions of the residuals from regression are shown
in Figure 13. Quartz residuals show clear non-normal distribution
and.areskewed to the right. Plagioclase residuals are approximately
normally distributed.

Two assumptions of least-square regression are normal distribu-
tion of residuals about the zero deviation line, and horizontal
banding of the residual plots. In quartz, both assumptions have
been violated, while in plagioclase only the horizontal distribution
condition is not met.

Failure of the residuals to meet the assumptions of least-square
regression indicates that the components of Sv in quartz and plagio-
clase do not have a purely linear variation with metamorphic grade.
Instead, the components of Sv show sinusoidal variation up the

metamorphic gradient.

Figure 13.

Residual distribution for quartz and plagioclase.

34

 

—_._ ._ Q—H—I‘

FREQUENCY

DISTRIBUTION OF REGRESSION RESIDUALS FOR SV SV

Below Lune

an

Quartz

S Regressed On 5

v“ v

an

Plagioclase

SV Regressed On 8

u .p

0 Above Lune

Distance From Regressnon Lune (arbitrary UI'IIIS)

35

w

GRAIN AGGREGATE TEXTURES

MOSAIC PATTERNS AND GRAIN AGGREGATE TEXTURAL CHANGES

In this section, textural changes developed in the rock fabric
are modeled in terms of mosaic pattern changes to regional metamor—
phism. These changes involve aggregates of grains and their chang-
ing associations with neighbors as the physical conditions (P, T)
of metamorphism change. The general textural model is therefore
extended to include neighborhood changes and their expected effect
on the textural mosaic. The mosaic model is tested by making
estimations of the amount of Markov character present in the phase

aggregations.

TEXTURAL MOSAICS

 

The imposition of the changing P, T, and deviatoric stress
components of a regional metamoprhic gradient upon sedimentary rock
fabrics will induce textural disequilibria. Readjustments to
equilibrium by changes in surface area have been discussed in a
former section. This section will examine those textural changes
which alter the phase mosaic.

For grain aggregates, readjustment to textural equilibrium

involves the orientation of phases into directions of preferred

36

growth, until compositional layering is produced in directions
perpendicular to the greatest local principal stress component (8).
Such an ordering should produce neighborhood mosaics with rythmic
phase repetitions, also in directions coincident with the differential
stress. The end stage of such a mosaic model would be a banded rock
fabric.

It should therefore be possible to examine the effects of
regional metamorphism on the Thunderhead Sandstone by comparing the

textures of sampled rocks with the metamorphic mosaic model.

TESTING THE MOSAIC MODEL

 

The sequences of mineral phases generated by traverses across
rock fabrics may be conceived of as states in a Markov process.
Such conceptualization provides a means of quantitatively estimating
the strength of association between aggregations of phases within
the rock fabric. Vistelius (20) and Kretz (21) have domonstrated
the utility and power of Markov approaches to rock textural evaluation.
In a first-order Markov process, the state currently occupied
influences the nature of the next succeeding state. Passage from
state to state is termed a transition, and knowledge of the total
variation in the composition of states, and their relative proportions,
permits probabilistic statements to be made about transitions,

providing the identity of the initial, or starting state, is known.

37

The evaluation of modal variations within the Thunderhead Sand-
stone permitted assignments of Mineral phases to states in the
Markov process. Two coding formats were used, and the results of

each format compared. The initial scheme followed the code:

1 = quartz
2 = plagioclase
3 = others

State 3, "others" consisted of mica, alkali feldspar plus very small
amounts of incidental opaques and calcite. A second code lumped

plagioclase and alkali feldspar together, and the new format was

1 = quartz
2 = feldspar
3 = others

where "others" were now almost totally micas.
The coded states and their transition probabilities may be viewed

schematically (Figure 14, below) (22).
Pu

8' 1?.
4%
13:0

Pu. I923 . P33

38

Pij is the assigned transition probability of passage from state i
to state j. In the case of i = l, j = 2, Pij is the probability of
passage from a quartz to a feldspar observation under coding format 2.
When i = j, Pij becomes the likelihood of a phase observation
succeeding itself, e.g., a mica observation followed by another mica
observation.

Observed transitions are compiled in the form of a transition

frequency matrix. For both coding formats, the three states form

the 3x3 matrix:

1 2 3
1 I N N N -\
11 12 13
2 N N N
21 22 23
3 N N N
31 32 33 J

 

 

\

where 1, 2, 3 are coded states and the nij's are the total observed
phase—phase transitions (23).

The transition probability matrix is formed by row-summing the
transition frequency matrix, and dividing each frequency element by

its row sum:

1 P.
[IP]= 2
3

 

 

39

All rows will now sum to 1, since states mu§£_succeed each other.
Testing for Markov character follows the method of Anderson and
Goodman (24). The null hypothesis states that events (in this case
phases) are independently distributed. Rejection of H0 in favor of
the alternate establishes Markov character. The computational form

of the test statistic is
P..
-2 Lo A = E N Ln (—ll)
ge " ij E,
J
where nij are observed transition frequencies; Pij is the transition
probability from the ijth cell; and Pj are marginal probabilities

from the j'th column, formed by column totaling the transition

frequency matrix, and dividing by the grand total:

P.=EN../ 53.11..
1 13 ' 1] 1]

The test statistic is distributed as X2 with (n-l)2 degrees of
freedom. The relative magnitude of -210ge A provides a measure of
the strength of association of the coded phases, and is therefore a
measure of the amount of textural determinism in the Thunderhead
Sandstone rock fabric. This should hence monitor the neighborhood

changes wrought by regional metamorphism.

METHOD
Samples selected were the same as those chosen for the earlier

surface area studies. Slabbing for thin section preparation was done

\_

MI

 

fig?) ("Z

40

in a plane perpendicular to the maximal lineation in mineral phases,
and foliation in the rock fabric. Therefore the planes of examina-
tion contained the intermediate elliptical (x-y) axes of distended
mineral phases, as opposed to the maximum (z) axes of elongation

(see Figure 15 below).

 

c: I303]

//V7uega«ugook7rzr

_.;::::> fiquAAér
62/

2
flflI

 

 

C) i

 

 

Since in nearly all fabrics, varying amounts of anisotropy

were present, each fabric sample was examined in two primary direc-
tions, one perpendicular and the other parallel to lineation. A
similar approach was taken by Pielou (25) who examined vegetation
mosaics developed under conditions of strong prevailing wind. In
each thin section, the position of maximum anisotropy was determined
by construction of a series of Rose orientation diagrams (Figure 16).
Unit-length traverses were made of the rock fabric on 15° intervals.

At each interval, observations of intersected quartz-matrix and

Figure 16.

Rose diagrams for development of
anisotropy in rock texture.

41

2-4A

 

3 60

 

 

l-IOB

 

180

360

 

270

 

 

 

 

I-ISA

POLAR PROJECTIONS OF ROCK FABRIC TRENDS

42

plagioclase-matrix grain boundaries were recorded. These observa-
tions were then plotted on polar graph paper to construct the fabric
Rose (13). Directions of maximal and minimal anisotropy are loci

of minimal and maximal peak modes, respectively.

For each rose diagram, two angles are determined that relate the
orientation of fabric anisotropy to the Chayes point counter affixed
to the microscope stage. One angle relates the direction perpendicular
to fabric anisotropy with the microscope axis, and the other relates
the direction parallel to detected anisotropy to the axis. These
angles are 0 and 011, respectively. It is therefore possible to
mount the rock thin section in the counter and turn the stage through
some angle 6 which will position the rock fabric for traverses
perpendicular or parallel to the anisotropy as identified by the roses.
The traversing of thin sections was performed on a Leitz petrographic
microscope, using a 16 power objective and 3.5 occular. Trials with
various combinations of occulars and objectives were performed,
until a match was found which provided minimal redundancy (several
cross—hairs falling in the same phase), and maximized the amount of
total observed variation without loss of information (periodicity
of phase changes shorter than cross-hair spacing).

For each 6 value, as determined by the rose diagrams, 25

traverses were performed. The starting position of each traverse

43

was randomized with respect to the x-y plane of the thin section,
however each traverse in a group of 25 was performed parallel to the
orientation angle 6. All traverses started on the left cross-hair
and ended on the right. For each traverse, the phase intersected by
the cross-hair was noted and recorded. The eleven observations per
traverse formed a chain of ten transitions. Each thin section would
therefore be tested by 275 data points in each of the two cardinal
rock fabric directions. This generated 250 transitions perpendicular
to the direction of lineation and 250 transitions parallel to the
direction of lineation. Phase observation data points from each
traverse were key punched into data cards. These cards were then
evaluated by a modified Fortran routine of Harbaugh and Bonham-
Carter (26), which formed transition frequency and transition
probability matrices. Matrices so formed were further tested for

Markov character by calculation of ~210ge A on a desk calculator.

RESULTS

Non-Collapsed Chains

 

For perpendicular-to-fabric traverses, values of -210ge A vs.
distance up metamorphic grade are plotted in Figure 17. Dotted
horizontal lines indicate the u-levels for rejection of the null

hypothesis of independence of association among the phases quartz,

Figure 17.

Degree of determinism in texture as
a function of distance up the regional
gradient.

44

mwn___2

 

Om m. op
9 / 1
mo.uu
5.”...
om
on
9.
cm
wmmIHO ...0<._anmhm<30 -mmtstpm
Sm
mz_<Io ammaatjoo 202
mummm><¢»

m<430_ozwamwa

 

v 9901 a-

45

plagioclase and others (alkali-feldspar and mica). Examination at
the a = .01 level shows a mixture of random and non-random associa:
tion, with sample sites 4, l3 and 18 showing high levels of determinism
in their textures, while others are relatively subdued.

Inspection of some observed data points for sample site 1
(low -21n A value) and site 4 (high value) explain the large variability
in determinism. For site 1, an example traverse was: 12323313221;
for site 4: 21111211111. The runs of quartz observations at site 4
are a function of grain size. Larger-than-average quartz grains
receive a proportionately larger number of cross-hairs of the test
transect. The effect of runs generated by large-sized grains on the
transition frequency and transition probability matrices is to "load-

up” the diagonal cells. Such an effect is seen in the transitions

 

 

 

at site 4:
QTZ. PLAG. OTHER
QTZ. 82 21 17 120
PLAG. 25 18 ll 54
OTHER 16 15 45 I 76
123 54 73
.492 .216 .292

The large frequency of quartz-quartz contacts, and other-other
contacts is due to the relatively large grain sizes in quartz and

alkali-feldspar, respectively. Since 250 transitions are taken per

46

directional traverse, inflation of like-like cell values, leads to
diminution of the off-diagonal a-B cells. It is this grain-size
effect which produces a "premature" and abnormally high amount of
determinism.

Explanation of the effect of grain size on the test statistic
for Markovity is provided by the mosaic model (Figure 18). Traverses
taken parallel to the fabric, Figure 19, show similar perturbations
in -21n A due to grain size. We should be able to expect, in the
conversion of an arkose to a meta-arkose, that initially rounded or
semi-rounded quartz and alkali feldspar grains would become more
distended through tectonism , so that progressively elliptical shapes
would be produced as distance up the gradient increases. (The effect
of such shape changes on traverse observations parallel to the fabric,
is to increase the likelihood of "runs”, and hence increase -21n A.)

Comparison of Figures 17 and 19 shows high values for site 4
for both traverses. The implication is that large grain sizes
affected both test directions, and that those grains are relatively
well-rounded, since the G-statistic values are nearly the same for
both perpendicular and parallel tests. For sites 11, 18, 24, 23
and 20, a substantially higher parallel test value indicates a sig-
nificant flattening of the overall phase shape. For site 11, this

is a flattening of both quartz and alkali feldspar. For sites at the

Figure 18.

Model of anticipated levels of textural
determinism as a function of distance
up the regional gradient.

47

 

H2m_o<mw o_Immo_2<pms_ a: moz<hm_o

wz_oz<m ._<zo_._._mon_s_ou a zo:<mz_._

 

oz_mo._m>mo o.— mso um;

,

 

 

 

 

 

_ \

m._.zm_s__omm ._<z_o_mo z. >p_.__m<_m<>.m

22:23:35: 10:14“; to 83 .<

U>m amw0m<f mm_oz

20.2533 z_§o\mm<za do 152:5 mod docs.

 

OIlSIlVlS 1831 All/\OMHVW

98012—

Y

Figure 19.

Development of determinism in rock texture
as a function of distance up the regional
gradient.

48

302:: “c0330 3:33:20: 3..

mm om ma 0H

 

reformmifitmzo 533m
2220 nomamzooncoz

momcm>mcp .822;

83335
m

 

 

ON

.m

:V

138012—

onsnms 1581 MMOMBW

49

higher-grade end, i.e. 18, 24, 23, and 20, the flattening is
primarily in quartz, since alkali feldspar begins breaking down to
brown biotite at the staurolite isograd (about site 15). Such
distensions in the over-all quartz phase are likely recrystallization

adjustments to applied stress.

COLLAPSED CHAINS

 

The noise imposed on the -21n A spectrum by grain-size effects
may be removed by collapsing the observation chain (25). Such
collapsing provides a means of examining the strength of association
between unlike phases. Indeed, this kind of textural information may
only be abstracted through the collapsing process.

Sample traverses presented earlier were: 12323313221, and
21111211111, from sites 1 and 4 respectively. Their collapsed forms
are 123231321, and 2121 respectively.

It is important to note that the collapsing operation produces
an "artificial" texture of unit grain size, and, of course, one without
like-like (a-a) grain boundaries. It must, therefore, be evaluated
in conjunction with the non-collapsed results for evaluation of the
"real” texture.

The effect of collapsing on the transition frequency matrix
reduces the diagonal (like-like) cell frequencies to zero. The fre-

quency matrix for site 4 (perpendicular testing) now looks like:

50

QTZ. PLAG. OTHER
QTZ. 0 21 17‘I
PLAG. 25 0 11
OTHER 16 15 0
K. /

 

 

Elimination of non-zero diagonal elements throws all the probability
of state-state transitions into the off-diagonal cells in the

transition probability matrix:

Q PL. 0
Q ( o .710 .289 I
PL. .820 0 .179
o .473 .526 0
\ J

 

 

This results in relatively large -21n A values, and strongly determin-
istic "textures", as in Figure 20.

Kullback, et a1. (1962) have reported that specification of
zero-valued elements under the null hypothesis will reduce the number
of degrees of freedom by one for each zero. This is in agreement
with Pielou (1965). This causes a drop in degrees of freedom from
four to two for comparison of -21n A with X2.

Substantial site-toesite‘variation occurs in the strengths of
phase associations. Comparison of a low -21n A at site 4 and a high
value at site 6 reveals as much variation in large-scale textural
phase associations as in nearly all 24 miles of prograde traverse.

Examination of transition frequency matrices for non-collapsed

Figure 20.

Development of determinism in rock texture
as a function of distance up the regional
gradient.

51

Amm__Eg aco_nm.o o_nacoemuo2 a: mocm~m_o

om ma ofi m

   
 

 

 

.m._m;~o www.mu-.m:onmmaaum

0
L0

mc_m;o nomamZoo

mmmcm>mcp .m_:2u:ma_om

‘V‘DA ‘

C
O
H

E

vasom— QIISIIBIS 1561 Kunowew

52

treatments of sites 4 and 6 reveal a substantial number of long

alkali feldspar "runs" at site 4, and a significant decrease in run
length at site 6. The reduction in alkali feldspar grain size between
sites permitted a relative increase in the number of quartz-other
plagioclase-other contacts in samples gathered at site 6. This a-B
type contact increase resulted in an increase in Markov character
between sites 4 and 6.

Removal of alkali feldspar from the "others" state, and a lump-
ing with plagioclase to form the state "feldspar" permits a new
comparison to be made (Figure 21). Dashed lines tracing the values
of -21n A for quartz-feldspar-others chains, closely correspond to
values fer non—lumped quartz-plagioclase-others. Departure from good
fit occurs, however, between sites 15 to 18 inclusive. Examination
of the transition frequency matrices shows a large conditional
probability shift from column 3 (others) to column 2 (feldspar) when
comparisons of the non-lumped and lumped formats at site 15 are made.
This results from the removal of an appreciable number of transitions
involving alkali feldspar from "others", and insertion in "feldspar".
As K-feldspar continues to break down to biotite the departure from
fit lessens, and gocui agreement is restored by site 24, indicating

absence of alkali feldspar from the rock fabric.

Figure 21.

Levels of determinism in rock texture for
two formats of aggregates as a function of
distance up the regional gradient.

53

73:83 23:35 25305322 a: 3:320
mm om .fl 3 m

umzmmnlmszo C333... ”Ntmzoumgmam

uzom I 22:0 ”.92; ”Ntmzonmopmam
mEmco 33230

3238; 5.36.53:

— DHSHBIS 1561 MIonJew

 

 

54

Plotting a "best-fit" straight line through values of -21n A,
for both coding formats, does not provide the overall increase
initially suspected (Figure 22). Ho: 8 = 0 for the regression equa-
tion is not rejected at a = .05 with 16 degrees of freedom. It is
of interest to note, however, that departures from this best fit line
reduce with distance up the metamorphic gradient. For both coding
formats, the reductions are comparable in magnitude. Hence, it appears
that collapsed-chain textural determinism may approach some limiting

value. This suggests classic stochastic convergence.

CONCLUSIONS

 

We have presented models t0'predict changes in surface area and
changes in neighborhood mosaic patterns with increased metamorphic
grade.

Results of several analyses of variance indicate that substantial
variation in both the like (a-a) and unlike (u-B) components of surface
area can occur in quartz within a single sample site. This indicates
that quartz surface area may be too sensitive a parameter for region—
al comparisons of recrystallization and grain growth. Significant
differences in both the components of plagioclase surface area between
sample sites indicate that plagioclase may be most suited for region-
al comparisons. This is in general agreement with the results of an

earlier study (1).

Figure 22.

Bouncing level of determinism in rock texture
as a function of distance up the regional gradient.

55

Ame-Zea u:o_um.o oztr_oEmHm2 a: wucmHm_o
om mg 0“ m

mtmfotmamEmduNtmao $3.3m

m:_m:o cmmam__oo

mwmto>map .m_:o_u:macom

 

 

09

E

Y3801'3_

OHSHBIS 1591 KHAOHJBW

56

Results of the least-squares regression of the two components
of surface area, and the evaluation of the residuals from regression,
indicates that the ratio of like (a-u) to unlike (u-B) surface area
does not change linearly with increased metamorphic grade. This is
true for both quartz and plagioclase. Higher order terms in the
regression equation appear necessary to account for the sinusoidal
behavior of the surface area ratios with increased metamorphic grade.

It appears that the contributions of initial sedimentary facies
(in terms of pelitic interbedding) and local stress fields may explain
variations in surface area not explained by the regression of one
component on another.

Textural mosaics were investigated by permitting phases to
simulate states in a first—order Markov chain. The rock fabric was
examined in directions perpendicular and parallel to the anisotropy
of mineral phases.

For non-collapsed chains, grain size variation in quartz and
alkali feldspar influenced the amount of Markovity, or determinism
of phases in the rock fabric.

Removal of grain-size effects by chain collapsing, permitted the
examination of neighborhood changes induced by regional metamorphism.
This examination suggests that a limiting value exists for the

strength of neighborhood phase associations, and that values obtained

57

at individual sample sites converge on this limit in a stochastic
manner with increasing metamorphic grade.

This work represents a pilot study in a long-range project. It
has attempted to outline some of the problems confronting textural
work in regional metamorphic environments.

From the results of this study, we suggest:

1) Future work to define the effects that small-scale variations
in sedimentary facies, and local variations in the stress
field, have on surface area.

2) Increased reliance on approaches which examine all compon-
ents of variance.

3) Future work to investigate the capabilities of Markov
approaches to textural mosaics.

4) Efforts to couple the solid-state physics (i.e.: micro-
mechanics, diffusional processes and associated creep)
with small-scale textural evaluations (statistically

augmented) on an outcrop scale.

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

11)

58

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12)

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59

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26)

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