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THESIS

100 f-

LIBRARY
Michigan State
University

This is to certify that the
thesis entitled

Calcite Strain Analysis of
The Central Andes:
Northwest Argentina and
Southern Bolivia

presented by

Elizabeth Catherine Hardesty

has been accepted towards fulfillment
of the requirements for the

MS. degree in GeMl Sciences

 

 

 

 

 

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PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
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Calcite Strain Analysis of
The Central Andes:
Northwest Argentina and
Southern Bolivia

By

Elizabeth Catherine Hardesty

A THESIS

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

MASTER OF SCIENCE
Department of Geological Sciences

2006

ABSTRACT
Calcite Strain Analysis of the Central Andes:
Northwest Argentina and Southern Bolivia
By

Elizabeth Catherine Hardesty

Deformation in the Central Andes has previously been interpreted by the use of
kinematic studies, which predict that a generally NW direction of compression has been
present over Andean history. This study conducted a kinematic strain analysis using
calcite twins to examine deformation throughout the Eastern Cordillera, the Subandes,
and the Santa Barbara System, 20° S to 25°S latitude. Samples were analyzed using the
calcite strain gauge technique of Groshong (1974). Resultant shortening axes can be
separated into two main groups, parallel to plate convergence and generally NW; the
latter group is further divided into four distinct trends. Using the relationship between
the maximum shortening axes and bedding, samples were classified as having pre- or
post-folding twin formation, which was used to interpret timing of deformation. Changes
in compression are found to occur at 10 Ma, with a north component of movement that is
implied from derived velocity vectors, and at 2 Ma where shortening directions estimated
by fault kinematic studies trend from NW-SE to NE-SW. The results from this study fit
well with these multiple deformation events, supporting the use of calcite strain analysis

in active mountain belts.

DEDICATION

This manuscript is dedicated to my mom, Ruth Catherine Hardesty, who has

influenced every aspect of my life for the past 25 years.

Mom, your love and support have no measure. I look to you both as a role model
and as a friend. Your dedication to doing the very best is seen in the kindness you exhibit
everyday. You have encouraged me to be a better person and to live by doing the same.
The memories of long conversations, summer road trips, and nighttime movies will
always remain in my mind as ‘our time,’ mother and daughter. I cherish those moments
with all my heart. May our relationship continue to grow as wonderful experiences come

our way. Thank you for all you have done, and all that you do. I love you.

ACKNOWLEDGEMENTS

The funding for this project was provided by the Michigan State University
Department of Geological Sciences. It is gratefully acknowledged that without the
support this project would not have happened. I want to thank the department for its
support and dedication to its students.

I want to especially thank my committee members, Dr. Kazuya F uj ita, Dr. F.
William Carnbray, and Dr. Duncan Sibley, who have gone above and beyond to make
this happen.

I would also like to thank my advisor, Dr. David Hindle for creating this project.
Without his influence and guidance my education would have been incomplete. I wish
him the best in Germany and look forward to future work.

A special thank you to Kaz F ujita for taking on the position of committee chair,
who did so with marvelous grace and ease. The extra hours of work that were put in to
seeing this project through are much appreciated. The guidance and advice you have
given me will always be remembered. I could not have asked for a better chair, thank
you.

The start of my geological career took shape at Wittenberg University where their
wonderful academic program and personable campus life taught me lifelong skills to
succeed. A special thanks to the Math and Geology Departments for their encouragement

and shared experiences which led me down the path to where I am today.

Finally, a very special thank you to all my friends and family whose love and
support have given me the strength I need to get through. Each of you has touched a part
of my life and in some way took part in this task. For that, I am dearly thankful. Much

love to all of you.

TABLE OF CONTENTS

LIST OF TABLES ..................................................................................................... viii
LIST OF FIGURES ..................................................................................................... ix
CHAPTER 1

Introduction .................................................................................................................... 1
CHAPTER 2

Regional Tectonic Setting and Geologic Framework .................................................... 6
Section 2.1 Physiographic/Introduction ......................................................................... 6
Section 2.2 Present Day Tectonics ............................................................................... 11
Section 2.3 Paleozoic Tectonic and Sedimentary Evolution ....................................... 12
Section 2.4 Evolution of the Modern Central Andes ................................................... 18
CHAPTER 3

Previous Kinematic Studies ......................................................................................... 20
Section 3.1 Introduction ............................................................................................... 20
Section 3.2 Previous Kinematic Studies in the Central Andes .................................... 22
3.2.1 Structural style and shortening ............................................................................ 22
3.2.2 Cross section balancing and shortening estimates .............................................. 23
3.2.3 Crustal Thickening and Tectonic Shortening ..................................................... 28
3.2.4 Fault Kinematic Studies ...................................................................................... 30
3.2.5 GPS Studies ........................................................................................................ 33
Section 3.3 .................................................................................................................... 36
CHAPTER 4

Calcite Twinning .......................................................................................................... 39
Section 4.1 Twin Formation and Properties ................................................................ 39
Section 4.2 Previous Stress-Strain Studies .................................................................. 43
CHAPTER 5

Methodology ................................................................................................................ 50
Section 5.1 Introduction ............................................................................................... 50
Section 5.2 Sample Collection ..................................................................................... 54
Section 5.3 Sample Preparation ................................................................................... 54
Section 5.4 Data Collection and Measurements .......................................................... 56
Section 5.5 Processing ................................................................................................. 56
CHAPTER 6

Data and Results .......................................................................................................... 60
Section 6.1 Data ........................................................................................................... 60
Section 6.2 Results ....................................................................................................... 60
6.2.1 Trends ................................................................................................................. 60

vi

6.2.2 Steronets .............................................................................................................. 63

Section 6.3 Errors ......................................................................................................... 71
CHAPTER 7
Discussion .................................................................................................................... 73
Section 7.1 Introduction ............................................................................................... 73
Section 7.2 Plate Convergence Parallel Samples (generally NE trends) ..................... 75
Section 7.3 Others (NW Striking Trends) .................................................................... 80
7.3.1 NNW Trends (Pre-lOMa Deformation) .............................................................. 81
7.3.2 WNW Trends (10-2 Ma Deformation) ............................................................... 82
7.3.3 N-S Trends (Possible 2-3 Ma Deformation) ....................................................... 83
7.3.4 WNW Trends (Deformation post 2 Ma) ............................................................. 84
CHAPTER 8
Conclusions .................................................................................................................. 88
APPENDICIES
Appendix A

Rotating Thin Sections into New Coordinate Systems ......................................... 91
Appendix B

Programs ROTATE and TWINSTS .................................................................... 92
Appendix C

Description of Measurements ............................................................................ 113
Appendix D

Full Data Results ................................................................................................ 114
REFERENCES .......................................................................................................... 241

vii

LIST OF TABLES

Table 1 ................................................................................................................... 52
List of sample site data

Table 2 ................................................................................................................... 58
Input data sheet template. Columns represent: CVIV — azimuth of
optic axis, CVP — plunge of optic axis, KODEC — geographical dip
direction of the optic axis, TWINIC — azimuth of the twin pole,
TWINP — plunge of the twin pole, KODEE — geographical dip
direction of the twin pole, TOTALT — number of microtwins
(striations), THIKM — thickness of the twins, WIDTHN — amount
of the grain that is twinned as a percent of the entire grain.
(Edited from Groshong, 1984)

Table 3 ................................................................................................................... 61
Summary of sample locations and key results

viii

LIST OF FIGURES

Images in this thesis are presented in color.

Figure l .............................................................................................. 2
Digital elevation map of the Pacific coastline of South America showing country

borders, approximate location of the Bolivian Orocline, and the Pacific-Chilean
Trench. Globe included for world reference.

Figure 2 .............................................................................................. 3

Topographic map of the Central Andes showing the tectonic providences, SBS —
Santa Barbara System and SP - Sierra Parnpeanas. Blue rectangle is the

approximate area of the Salta Rifi. (Edited from an image created in GMT,
Wessel and Smith, 1998)

Figure 3 .............................................................................................. 7
Subduction of Nazca Plate beneath South American Plate.

Topography at a vertical exaggeration of 10:], all depths are estimated.
(Adapted from Isacks, 1988)

Figure 4 ............................................................................................... 8
Digital elevation map of South America showing present day regions of
subduction including the two flat slab regions to the north and south.

Figure 5 .............................................................................................. 10
Deformation summary for the Central Andes, a) Distribution of deformation ages
across the South Central Andes (~218). Dark red line at 30 Ma shows the
initiation of main deformation in the region. b) Balanced cross section at 218.
(Modified from Oncken et al., in press)

Figure 6 .............................................................................................. 13
Stratigraphic column of the Santa Barbara System, ~258 (Modified fiom Kley
and Monaldi, 2002)

Figure 7 .............................................................................................. 14

Reconstruction of early Paleozoic land masses.
A. Cambrian ~520 Ma

Approximate location of Ouachita trough in green along Laurentia.
B. Mid-Ordovician ~450 Ma
Ouachita microcontinent and location of F amatinian Orogeny
highlighted in pink.
C. Devonian ~370 Ma

Ouachita terrane placed at its current location along today’s South
America.

(after Dalziel et al., 1994)

ix

Figure 8 .......................................................................................... 16
Chronology of the main tectonic events in the Central Andes (Modified from
Sempere et al., 1997)

Figure 9 .......................................................................................... 24
Shortening estimates from balanced cross sections as well as crustal
cross-sectional area equivalents. (Modified from Kley, 1999)

Figure 10 ......................................................................................... 26
The relationship between block models and balanced cross sections. a) The
geological cross section, b) is restored, c) then shipped of the folded and faulted
cover rocks and simplified to a stack of overlapping basement blocks, d) the
basement blocks restored to their original positions separated by their relative
displacements. (Kley, 1999)

Figure 11 ......................................................................................... 27
Block model of Andean shortening. (A) Early episode of deformation
(25-10 Ma) affecting mostly the eastern Cordillera (EC) and Subandes (SA),
(B) Latter episode of deformation (10-0 Ma) with shortening in the EC almost
fully completed, and (C) Present day showing positions of the major tectonic units
(Adapted from Hindle and Kley, 2002)

Figure 12 .......................................................................................... 29
Derived geological velocity field of the Central Andes of Hindle and Kley
(2002). Small rectangle shows the area with evidence for a northern change in
convergence direction. (Generated using GMT, Wessel and Smith, 1998)

Figure 13 .......................................................................................... 31
Results from previous fault kinematic studies conducted in the Central Andes.
Lines represent estimated shortening directions for deformation, post 1.5 Ma and
pre 3 Ma. CANP, Cabalgamiento Andino Principal (Main Andean Thrust), CFP,
Cabalgamiento Frontal Principal (main frontal Thrust). Compiled with data from
Cladouhos et al., 1994 and Marrett et al., 1994.

Figure 14 .......................................................................................... 35
Velocity vectors for the Central Andes from geological data and GPS.
(A) GPS velocities with respect to the stable interior of South America.
Included are the convergence vector for the Nazca plate derived from GPS data,
GPS NZ-SA, and the predicted global plate motion model NUVEL-IA
(Norabuena et al., 1998). (B) geological velocities averages over 25 Ma.
(C) averaged velocities from the displacement field for 25-10 Ma and
(D) averaged velocities from the displacement field for 10-0 Ma. (From Hindle
et al., 2005; Hindle and Kley, 2002; Kley, 1999).

Figure 15 ........................................................................................... 40
Geometry of calcite e-twinning

(a) Illustration of the relation between twin plane, e, and glide plane, g,
with direction.

(b) Schematic representation of an e-twin shown in e-g cross-section
With c- optic axis, r- rhombohedral plane, t1 — thickness of the
Twin, and t- thickness of the host grain. C and T are the optimum
compression and tension axes. (Modified from Burkhard, 1993
and Groshong, 1972)

Figure 16 ........................................................................................... 42
Twin Type classifications. (Modified from Burkhard, 1993)

Figure 17 ........................................................................................... 45
Referenced x, y, 2 thin section coordinate system determined from U-stage
position.

Rotated coordinate system for remaining thin sections.
a. shows the reference coordinate system as above
b. gives the rotated fixed thin section coordinate system described
in terms of a. (Modified from Groshong, 1974)

Figure 18 ........................................................................................... 47
Geographical Coordinate System.
A. Thin section coordinates as they appear on the U-Stage.
(see Figure 17)
B. Coordinates in geographic space, N-North
C. Plotted coordinates on Steronet. These are the inputs for ROTATE.
Created after Groshong, (hand-drawn)

Figure 19 ........................................................................................... 51
Far left side shows a detailed stratigraphic column at ~23S. Rock Types:
MR—Mudrocks, EV—Evaporites, C—Carbonates, SS—Sandstones. Right
side is a regional correlation chart for Formation and unit names. Sampled unit
shaded in blue — Yacoraite. (Modified from Sempere et al., 1997).

Figure 20 ............................................................................................ 52
Location of the 17 sample sites. (Plotted in GMT, Wessel and Smith, 1998)

Figure 21 ............................................................................................ 53
Yacoraite Formation of the Salta Group (white to gray unit) in (A) the western
flank of a syncline and (B) in extensive thrust faults. It is underlaid by Letcho
red-bed in NW Argentina and Southern Bolivia.

xi

Figure 22 .......................................................................................... 55
Samples from the Yacoraite Formation as seen under the U-stage. A) Type I
twins (parallel striations) indicating low temperatures, B) Type II (possible III)
twins (multiple sets) indicating higher temperatures, C) Low temperature
deformation of quartz grains, D) Pressure solution deformation of ooids. Image
captured on a Polaroid Camera under plain polarized light.

Figure 23 ........................................................................................... 57
A. Universal Stage microscope used for this study.
B. Close-up of the U-stage illustrating the 3D movement allowed
by design.

Figure 24 ........................................................................................... 62
Sample Results. Red dots are sample location, blue vectors are groshong
z-axes. Latitude in degrees S, longitude in degrees W. (Created in GMT,
Wessel and Smith, 1998)

Figure 25 A - Q .............................................................................. 64—69
Individual sample results

Figure 26 ........................................................................................... 70
Sample sites with groshong z-axes and timing classifications. (Created on
GMT, Wessel and Smith, 1998)

Figure 27 ............................................................................................ 76
Fault kinematic results with classified groshong z-axes and sample sites. Lines
represent estimated shortening directions for deformation, post 1.5 Ma and pre 3
Ma. CANP, Cabalgamiento Andino Principal (Main Andean Thrust), CFP,
Cabalgamiento Frontal Principal (Main Frontal Thrust). Compiled with data from
Caldouhos et al., 1994, and Marrett et al., 1994.

Figure 28 ........................................................................................... 79
Satellite image of the study region illustrating N-S compressional trends.
(Original image from Mr. SID, www.mrsid.com)

 

Figure 29 ........................................................................................... 87
Earthquake epicenters for the study region, magnitude 4.1-6.3 (USGS NBIC).
Best-fit double couple solutions (compressional quadrant solid) from moment
tensors show an E-W compression (From Harvard Moment Tensor Catalog,
www.seismology.harvard.edu).

xii

Chapter 1 Introduction

The Andes Mountains are the result of the largest non-collisional convergent plate
margin in the world (Figure 1) and have been the subject of numerous studies with
respect to the timing of deformation and the kinematics of the fold and thrust belts, as
related to tectonic shortening (e.g.,, Echavarria et al., 2003; Allmendinger et al., 1997;
Kley and Monaldi, 1998; Horton, 1999; Kley et al., 1999; Cladouhos et al., 1994;
Sheffels, 1990). The amount of tectonic shortening plays an extremely large part in the
tectonic history of the Andes, in particular, the deformation associated with the uplift of
the world’s second most extensive high-elevation plateau, the Altiplano-Puna in
northwest Argentina and southern Bolivia. This has led to an abundance of previous
studies in the Andes and, more specifically, in the Central Andes, in hopes of gaining a
better understanding of the mechanisms involved with deformation and uplifi (e.g.,
Oncken et al., in press; Marrett and Strecker, 2000; Kley, 1999; Allmendinger et al.,
1997; Sempere et al., 1997; Jordan et al., 1983). However, few studies have been
conducted using microstructures as a mechanical gauge for deformation.

The Central Andes, most often defined as located between latitude 15° S to 28° S,
include parts of Peru, Bolivia, Argentina and Chile (Figure 1). They are comprised from
northwest to southeast of the tectonic provinces of the Western Cordillera, the Altiplano-
Puna Plateau (the Altiplano in Bolivia and the Puna in Argentina), the Eastern Cordillera
(both the Bolivian and Argentine), the Subandes, the Santa Barbara System, the Chaco-

Beni Foreland Basin, and the Sierra Pampeanas (Figure 2).

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The main deformation started in the Central Andes around 25 Ma and is proposed
to have migrated from the northwest to the southeast and occurred in two distinct
episodes, 25-10 Ma and 10-0 Ma. In the south, where deformation is currently taking
place, shortening is thought to be transferring between the Subandes, the Eastern
Cordillera, and the Santa Barbara System. This interplay of recent deformation is
illustrated by varying shortening orientations and deformational events identified both
regionally and locally throughout the study area (e.g., Echavarria et al., 2003; Marrett and
Strecker, 2000; Allmendinger et al., 1997; Cladouhos et al., 1994). Results show that
shortening trends for a number of deforrnational events are different from the plate
convergence direction.

This study conducted a kinematic strain analysis, using calcite twins to determine
the principle strain axes of 17 samples from throughout the Eastern Cordillera, the
Subandes, and the Santa Barbara System (20°S to 25°S) to provide new insights into the
use of microstructures to interpret regional kinematics.

Strain induced twinning in calcite has been used for calcite twin analysis in a
number of studies conducted around the world (e. g., Hindle, 1997; F errill and Groshong,
1993; Groshong et al., 1984). This analysis is noted to be one of the best and most
accurate ways to determine the internal strain of a rock, therefore allowing one to infer
compressional directions (Burkhard, 1993; Groshong, 1974; 1972). The use of calcite
twin measurements to interpret shortening in the Central Andes has never previously
been attempted.

A comparison of the strain results (determined axes of maximum shortening) to

previous fault kinematic studies and regional geological velocity vectors for the Central

Andes show good correlations. The trends in shortening throughout the study area can be
matched to proposed stages of deformation to gain a better understanding of the recent

kinematics and timing of deformation.

Chapter 2 Regional Tectonic Setting and Geologic Framework

Section 2.1 Introduction

The formation of the Andes Mountain belt is associated with the subduction of the
oceanic Nazca plate beneath the South American continent (Figure 3). The Andean
Cordillera extends approximately 6000 km along the West Coast of South America from
Columbia to Chile (Figure 1).

The Nazca plate subducts under the Andean Cordillera in three distinct segments;
under the Central Andes at 30° to the east, under the north (between latitudes 2° and
14°S) at less than 10° to the east (nearly horizontal), and under the south (between
latitudes 28° and 33°S) at the same, nearly horizontal angle (Figure 4) (Allmendinger,
1986; Jordan et al., 1983). These shallow-dipping segments are most commonly referred
to as “flat-slab zones” (Gregory-Wodzicki, 2000) or flat segments (Alhnendinger, 1986).

The north and south flat slab segments resemble each other in terms of plate
geometry but have slightly different structural styles (Kley and Monaldi, 2002; Kley et
al., 1999; Kley and Monaldi, 1998). Above the northern flat slab, a narrow band of folds
is found in a foreland-dipping monocline (Gregory-Wodzicki, 2000). The southern flat-
slab is the cause of overlapping sequences of thin- and thick-skinned structures, and a
zone of currently active tectonics with basement involvement (mostly uplifis)
encompassing the Sierra Parnpeans (Kley and Monaldi, 2002, 1998; Kley, 1999;
Gregory-Wodzicki, 2000; Horton, 1999; Kley and Monaldi, 1998). These segments
represent a northern and a southern limit for along-strike variations within the Central

Andes. These along-strike variations reflect changes seen throughout the Central Andes

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in plate geometry (Gregory-Wodzicki, 2000; Jordan et al., 1983), structural style, and
width, to name a few (Kley and Monaldi, 2002; Kley et al., 1999; Kley and Monaldi,
1998)

The Central Andes reach their greatest width at ~18°S in the Bolivian Orocline
(Figure l) and decreases to both the north and the south of this point (Gregory-Wodzicki,
2000; Kley, 1999; Horton, 1999). From west to east the Central Andes (Figure 5b) are
structurally comprised of (1) the western flank of the magmatic arc and a steep, smooth
western slope (the Western Cordillera); (2) an ~ 4000 m high-elevation hinterland plateau
with internal drainage, remarkably subdued relief, and active volcanism in the north (the
Altiplano-Puna); (3) a Miocene thrust belt system characterized by east-verging thick-
skinned basement thrusts (the Bolivian and Argentine Eastern Cordilleras), resulting on
the east in an uplifted long eastern slope; (4) the Subandean Zone, a fold and thrust belt
with active thin-skinned faulting, (the Inter-andean and the Subandes including the Santa
Barbara System), and finally; (5) the active foreland basin (the Chaco-Beni Foreland
Basin) (Oncken et al., in press; Hindle and Kley, 2002; Gregory-Wodzicki, 2000; Horton,
1999; Allmendinger et al., 1997; Alhnendinger, 1986). These tectonic providences, with
some variation in characteristics, can be traced along the entire Central Andes with the
exception of the Altiplano-Puna, which extends from ~14°S in southern Peru, to ~27°S in
northern Argentina, and the Subandes which terminate to the south at ~23°S (Figure 2)

(Oncken et al., in press).

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Section 2.2 Present Day Tectonics

The Nazca plate is estimated from GPS data to be subducting at a rate of ~68
mm/yr (Klosko et al., 2002; Bevis et al., 1999). It has been suggested that the rate of
subduction has varied (mostly decreased) throughout geologic history, even though the
direction of convergence, relative to the continental margin, has remained relatively
constant at ~079°, as estimated over the past 3 Ma by NUVEL-IA (Oncken et al., in
press; Klosko et al., 2002; Bevis et al., 1999; Norabuena er al., 1998, 1999; DeMets et
al., 1994; Stein et al., 1986).

Along the western edge of the Central Andes, the Nazca plate dips east under the
magmatic arc of the Western Cordillera (Gregory-Wodzicki, 2000). Late Neogene
activity along the eastern onshore forearc created the western flank of the Altiplano and
the Puna (Figure 5a) (Isacks, 1988; Oncken et al., in press). Further to the southeast in
the backarc region under parts of southern Bolivia and Argentina, a fundamental
morphotectonic boundary is found between the Altiplano and northern Puna. This
boundary acts as a north-south transition between a continental basin, composed of
Tertiary and Quaternary sediments, and a basin and range system, of mostly Palaeozoic
sediments (Cladouhos et al., 1994; Cladouhos, 1993; Allmendinger, 1986). These young
basins of the Altiplano-Puna plateau give way to the deep canyon of the Bolivian Eastern
Cordillera in the north, and east-vergent thrusts that dominate the Argentine Eastern
Cordillera to the south. The active Subandean foreland fold-and-thrust belt lies along the
eastern edge of the Cordillera and runs from southern Bolivia to northern Argentina,
terminating around 23°S. Here, the Eastern Cordillera acts as a transition zone between

the northern thin—skinned deformation of the Subandes and the Santa Barbara System,

11

and the thick-skinned deformation of the Sierra Pampeanas (Oncken et al., in press;
Echavarria et al., 2003; Cladouhos, 1993). Earthquakes have been recorded throughout
the Subandes and the Santa Barbara System (~22°-26°S) as well as along the Eastern
Cordillera/Subandes boundary (Oncken et al., in press; Klosko et al., 2002). This recent
crustal seismic activity is related to strike-slip faulting resulting from the NE-SW
compression due to the subducting Nazca plate (Oncken et al., in press, Hindle, 2003).

The currently active foreland basin borders the Central Andes northeast side.

Section 2.3 Paleozoic Tectonic Ed Sedimentary Evolution

Prior to Andean Deformation, this region was a passive margin with deposition
starting in the early Paleozoic, and continuing intermittently throughout the Phanerozoic
(Sempere et al., 1997; Cladouhos et al., 1994). Figure 6 gives a sedimentological history
from Precambrian to Neogene (Kley and Monaldi, 2002).

Today’s Central Andes were located in what is known as the Ouachita trough
segment and was attached to the southern margin of Laurentia at the start of the
Cambrian (Figure 7). The Ouachita segment detached from Laurentia and became its
own small microcontinent. Around the late Cambrian, Laurentia closed the gap between
Gondwana, forcing the microcontinent to accrete. This event is recorded in depositional
history in the Andes by an unconformity between the lower Cambrian and upper
Cambrian sandstone deposits (Figure 6) (Kley and Monaldi, 2002). By mid-Ordovician
(480-440 Ma) the first known mountain-building event, the Famatinian Orogeny, began
along the Gondwana margin that later became the western side of South America. An

early Devonian clockwise movement (410-405 Ma) brought Gondwana closer to

12

 

Figure 6

 

 

Neogene

 

 

Stratigraphic column
of the Santa Barbara
System, ~25S
(Modified from Kley
and Monaldi, 2002)

 

 

Paleogene

4—— Yacoraite Formation

Cretaceous

Devonian

Silurian 3

 

Ordovician

 

 

 

U. Cambrian L‘ 3
_Upper H
Proterozoic
to Lower
Cambrian

 

.>

’1' ‘ ‘ i URENTIA _
/) ‘ my... a) 0/?“ F1gure7
6; /

Ouachita 137/ .
' rr r. Reconstruction of
2.437%” /
J” g lAPETUS

early Paleozoic land masses.

A. Cambrian ~520 Ma
Approximate location of
Ouachita trough in green
along Laurentia.

B. Mid-Ordovician ~450 Ma
Ouachita microcontinent
and location of Famatinian
Orogeny highlighted in pink.

C. Devonian ~370 Ma
Ouachita terrane placed
at its current location along
today’s South America.

(afier Dalziel et al., 1994)

 

Laurentia. Sedimentation fiom the Devonian to the Permian was mostly deep marine
along the margin of Gondwana. These Permian deposits are found today in Bolivia
showing a transgression sequence from the northwest, placing the Central Andes along
the western edge of Gondwana at this time (Sempere et al., 1997). By late Permian the
formation of the super continent, Pangaea, was complete.

Reconstructions of the Pacific suggest that the triple junction between the South
American, the Phoenix, and the F arallon plates moved southward along the western
Andean margin of Pangaea throughout the Cretaceous. Subsequent to the passage of the
triple junction, the F arallon, and later Nazca, plate began subducting under South
America (Sempere et al., 1997). Tectonic activity (Figure 8) at this time included
extensive rifting and the creation of the continental Salta rift system. This large-scale rift
is considered to have four subbasins, a complex geometry, and may have been controlled
by large-scale wrench faulting (Kley et al., 2005; Kley and Monaldi, 2002; Sempere et
al., 1997). Rifting continued with extension and subsidence prevailing along the Central
Andes through the Cretaceous (Kley et al., 2005; Sempere et al., 1997). During active
subsidence stages of the rift a red-bed-sandstone/limestone succession was deposited
including the Salta group in the basin adjacent to northwestern Argentina (Kley et al.,
2005; Sempere et al., 1997).

At ~89 Ma the onset of shortening along the Pacific margin initiated a
compressional regime in the foreland although there were periods of tectonic quiescence
(Gregory-Wodzicki, 2000; Sempere et al., 1997). Around 73 Ma, tectonic activity was
re-activated resulting in drastically increased subsidence in the foreland (Sempere et al.,

1997). This late Cretaceous basin evolved as the distal part of an under-filled foreland

15

Super-

 

 

 

 

 

 

Ase
Epoch/Period Tectonic Events
(Mn) sequence
0 Migrant—a
7 . I
Pliocene -
major deformation in external Eastern Cordillera,
10' activation of CF? 3 m
Miocene I
I
20- foreland basin in sub-Andes and lowlands
major defonnation in Eastern Cordillera,
E activation of CANP system
Oligocene
30" 5 relative tectonic quiescence
I
40.5 I
Eocene = incipient defamatirm in wcstcmpamorrmtandbaa‘n
I
50" -
= foreland basin in Altiplano and Eastern Cordillera
I

 

 

 

Late Cretaceous

Salta Rift Fm
begins

Upper Price

muafionofmmlconvergeecesmp mic-grunge.
mutant-Ironic“. adcnddeCouflm

relative tectonic quiescence

shortenin alon m
l g andmuinptia'ogiof foreland subsidence

 

relative tectonic quiescence

shortening alonglmargr margin .
and in: ation of foreland basin
riftin event in foreland

 

 

MI)"

110-1

Early Cretaceous

120‘

130'-1

140‘

Lower Puca

 

 

150'-

 

tectonic quiescence

expansion of Potosi basin through thermal subsidence

   

extension and/or transtension

 

riftin extension and/or h'anstension

 

Figure 8 Chronology of the main tectonic events in the Central Andes
(Modified from Sempere et al., 1997)

16

 

basin of the active Andean belt and became the Andes continental external foreland basin
during the late Paleocene to early Oligocene (Sempere et al., 1997).

Some amount of deformation must have taken place after the deposition of the
Upper Cretaceous —— Lower Tertiary Salta Group (including the Yacoraite Formation from
which the samples for this study were taken) and before the deposition of upper Miocene
strata (Figure 6). This is apparent by the San Juan del Oro, an angular unconforrnity
found in the Northern Puna and Bolivian Eastern Cordillera at the Paleogene/Neogene
boundary (Figure 6) (Kley et al., 2005; Kley and Monaldi, 2002; Sempere et al., 1997;
Marrett et al., 1994).

By 58 Ma, the foreland sedimentation had fully begun in the current foreland
(Gregory-Wodzicki, 2000). The subduction rate between the Nazca and South America
plates increased around 57 Ma, resulting in tectonic loading and major shortening
throughout the entire Central Andes (Sempere et al., 1997; Pardo-Casas and Molnar,
1987)

Field evidence shows that throughout the late Paleocene through the Miocene
both deformation and deposition occurred in the Andes (Sempere et al., 1997; Marrett et
al., 1994). Deformation continued with spurts of extension and compression during the
Eocene Incaic shortening phase (Oncken et al., in press; Gregory-Wodzicki, 2000).
Major low-angle overthrust fault systems and thick-skinned inversion structures formed
throughout the Western Cordillera (Oncken et al., in press; Jordan et al., 1997; Gregory-
Wodzicki, 2000; Sempere et al., 1997). This structural style suggests that during Eocene-
Oligocene the area might have resembled the present-day Subandean belt (Sempere et al.,

1997)

17

Section 2.4 Evolution of the Modern Central Andes

Many tectonic events suggest that the loci of Andean deformation migrated
southeastward throughout the Eocene to Miocene with continuous foreland deposition
(Oncken et al., in press; Sempere et al., 1997).

Deformation started along the western flank and across the central Altiplano-Puna
plateau ~30 Ma. Gradually, deformation shified to the southeast, where both east- and
west- vergent thrusting and folding occurred throughout the Oligocene with the
development of the southern Altiplano-Puna and Eastern Cordillera (Oncken et al., in
press; Kley and Monaldi, 2002; Gregory-Wodzicki, 2000; Sempere et al., 1997).
Oligocene sedimentation was mostly composed of eroded Mesozoic and Paleozoic rocks
from the west, infilling the foreland basin of the Altiplano, as continuing uplift took place
in the Eastern Cordillera (Sempere et al., 1997).

The most intense deformation in the Central Andes took place throughout the
Miocene (e.g.,, Oncken et al., in press; Hindle, 2003; Alhnendinger et al., 1997; Marrett
et al., 1994). As deformation continued to migrate southeast through the Altiplano-Puna,
the entire Eastern Cordillera formed thrust belts from spurts of compression (Oncken et
al., in press; Kley et al., 2005). Deformation then terminated in the Altiplano-Puna
around late-Miocene, and by ~10 Ma the southern Eastern Cordillera was undergoing its
final main stages of faulting and folding (Oncken et al., in press; Kley and Monaldi,
2002; Hindle and Kley, 2002; Gregory-Wodzicki, 2000; Kley, 1999; Allmendinger et al.,
1997; Sempere et al., 1997; Marrett etal., 1994). This is the proposed end of the first
episode of deformation in the Central Andes. A known period of ceased or diminished

deformation took place between 12-8 Ma in the Eastern Cordillera, as evident from the

18

formation of the San Juan del Oro surface (Oncken et al., in press).

Deformation in the Eastern Cordillera diminished between 9-6 Ma with a transfer
of movement to the Subandean ranges (Echavarria et al., 2003; Kley and Monaldi, 2002;
Hindle and Kley, 2002; Allmendinger et al., 1997). This thin-skinned, foreland fold and
thrust belt, developed to the east during the Miocene (Oncken, et al., in press; Kley and
Monaldi, 2002). The Subandes terminate to the south, into high-angle thrust faults of the
southern Eastern Cordillera where the structural style of foreland thrusting changed at ~5
Ma to these thick-skinned inversion structures as deformation of the Santa Barbara
system began to the east (Oncken et al., in press; Kley and Monaldi, 2002; Kley, 1999;
Gregory-Wodzicki, 2000; Claudouhos, 1993). Deformation is suggested to have
continued until 2 Ma as a direct result of reactivation along normal faults of the ancient
Salta rift system that occurred around 3 Ma, and is possibly still occurring in the southern
Eastern Cordillera (Oncken et al., in press; Hindle et al., 2005; Kley and Monaldi, 2002;
Gregory-Wodzicki, 2000; Marrett et al., 1994). It is generally agreed that there is current
deformation in the region south of the termination of the Subandes in the Santa Barbara
System (Kley et al., 2005; Echavarria et al., 2003; Kley and Monaldi, 2002; Hindle and
Kley, 2002; Gregory-Wodzicki, 2000; Horton, 1999). This is evident by normal and
strike-slip fault movement creating current seismic activity throughout the area (Oncken
et al., in press).

In summary, two main episodes of deformation took place in the Central Andes.
One is estimated to have started ~25 Ma, with movement occurring through ~10 Ma. The
second main episode started ~10 Ma with a significant increase in the amount of

deformation occurring post-3 Ma untill present.

19

Chapter 3 Previous Kinematic Studies

Section 3.1 Introduction

Structural geology involves both dynamic analysis, which examines force and
stress, and kinematic analysis, which examines the deformation due to stress. In this
study, kinematic analysis was used to determine the principle strain axes needed for
interpreting deforrnational events responsible for the development of structures in the
Central'Andes Mountains.

Determining the strain in an active mountain belt can be done using many
techniques. In the Central Andes, large-scale features such as the megathrust faults
bounding the Eastern Cordillera and Subandes illustrate a localized state of deformation,
as large amounts of displacement are accommodated (tens of km of shortening) on only a
few major faults. In contrast, diffuse deformation is evidenced by an abundance of
smaller faults found fi'om a broad distribution of shallow, crustal earthquake hypocenters,
which cut through the region (Oncken et al., in press). With both types of defamation
present in the Central Andes, the scale on which kinematic studies are conducted plays an
important part in interpreting the region’s tectonic history. For example, studies that are
conducted on a smaller scale, such as the use of slickenlines on fault planes to measure
movement, can provide a way to recognize discrete periods of deformation. These
discrete periods often have varying shortening orientations implying that deformation
took place locally. In the Central Andes much of the deformation is localized, therefore,
these smaller scale kinematic studies provide the best data for interpreting the

compressional directions during the complicated history of the region.

20

One technique used for analysis is conducted on a large scale and measures
ground motion directly from geological observations, (e.g., structural shortening and
erosion rates) (Kley, 1999; Horton, 1999; Kley and Monaldi, 1998) or with space
geodetic data (Hindle and Kley, 2002; Norabuena et al., 1998). By using geological data
and observations, tools such as balanced cross sections and plan view restorations, can be
created to interpret the history of deformation (Kley, 1999). For current or recent events,
movement can be measured using Global Positioning System (GPS), Satellite Laser
Ranging (SLR), and the Doppler Orbitography and Radiopositioning Integrated Satellite
System (DORIS), from which velocity and displacement fields can then be created and
are the direct timescale equivalent of the geological observation data (Hindle, 2003;
Hindle and Kley, 2002; Kley, 1999; Norabuena et al., 1998).

On a mid-sized, regional scale, studies have been conducted using fault
kinematics and fold geometries in the Central Andes, yielding good results for local
deformational events (e.g., Allmendinger et al., 1997; Cladouhos et al., 1994; Marrett et
al., 1994). These fault kinematic studies have determined strain in the active mountain
belt by measuring slip directions and fault plane orientations in the field and applying a
strain analysis technique, and result in an orientation for maximum shortening
(Cladouhos, 1993).

In structural geology, classical techniques allow for the calculation of finite and
infinitesimal strain using measurements of cleavage, deformed fossils, and other small-
scale strain indicators. Mechanically induced twins in calcite are a type of strain
indicator. The small strains recorded by the calcite (i.e., twins) are directly related to the

derivatives of previous velocity fields acting on the area (Burkhard, 1993). Therefore,

21

by conducting a kinematic analysis using calcite twins, the internal strain of a rock can be
obtained, which furthermore allows for the direction of maximum shortening to be found.
Both twin data and fault kinematic data give a result that reflects the orientation in which
the total stress was applied during deformation. This similarity allows a direct

comparison between previous fault kinematic studies and the results of this twin study for

the Central Andes, with respect to shortening/compressional direction.

Section 3.2 Previous Kinematic Studies in the Central Andes
3.2.1 Structural style and shortening

The Andean foreland deformation is comprised of three distinctive structural
styles, each relating to an estimated amount of shortening (Kley et al., 1999). They are 1)
thin-skinned thrust belts with detachment along sedimentary cover layers, 2) thick-
skinned thrust belts with structural involvement of basement rocks to 10-20 km depth,
and, 3) foreland basement thrusts that show less than 10% shortening (see Figure 5b)
(Kley et al., 1999). The changes in structural style are said to be controlled by inherited
structure and stratigraphic features of the South American Plate (Kley et al., 1999).
These shortening estimates give thin-skinned thrusts accounting for 40-70% of
shortening, thick-skinned thrust belts as much 20-35%, and foreland basement thrusts
accounting for only 10% of shortening (Kley et al., 1999; Kley and Monaldi, 2002). The
point where the basement becomes involved in thrusting plays a critical role in shortening
estimates (Kley and Monaldi, 2002). For example, a greater shortening estimate is
required to accommodate an area on a cross section filled with thin sedimentary thrust

sheets, than an area filled with thick basement thrusts (Kley et al., 1999; 1996).

22

Therefore, it is safe to state that shortening estimates from balanced cross-sections are
insensitive to changes of the internal structural geometries as long as the assumptions

about the structural style at depth match (Kley et al., 1999; Kley and Monaldi, 1998).

3.2.2 Crosa section ba_lancing and shortening estimates

The use of balanced cross sections in regional thrust systems can provide a good
foundation for estimating regional shortening. Balanced cross sections have estimated
shortening to reach a clear maximum (~250-280 km) at the Bolivian orocline (~18°S),
and diminish north and south it to ~50-200 km (Figure 9) (Hindle and Kley, 2002; Kley,
1999; Kley et al., 1999; Kley and Monaldi, 1998; Allmendinger et al., 1997; Marrett et
al., 1994). The total shortening within the Eastern Cordillera and Subandes remains
constant (between 177 — 230 km) both north and south of the Bolivian orocline (Horton,
1999)

Discrepancies and limitations exist when estimating regional shortening from
balanced cross sections. Cross sections are strongly dependent on the availability of sub
surface data, and estimated magnitudes of translations are highly dependent on
assumptions about unexposed structures at depth. The latter is a large concern in the
internal zones of mountain belts, such as certain parts of the Central Andes (Kley, 1999).
Due to these limitations, shortening estimates of the entire Andean segment (~1500 km
along strike) could be underestimating the real values by as much as 25% (Kley, 1999).

Using balanced cross sections, block models have been created to estimate

shortening over large areas on a more detailed scale, and for different time periods

23

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24

(Hindle, 2003; Hindle and Kley, 2002; Kley, 1999). The first model covered the
Bolivian Orocline region and found 205-260 km of shortening along an E-W profile at
21°S (Figure 10) (Hindle, 2003; Hindle and Kley, 2002; Kley, 1999). This was
applicable to the large Andean region, but lacked detail such as displacement due to
folding and not just faulting (Hindle, 2003; Hindle and Kley, 2002; Kley, 1999).

Hindle and Kley (2002) later created a large Andean ‘block’ model (geological
displacement model) for crustal deformation of the entire Central Andes (Figure 11).
This Andean block model divided the Central Andes into large crustal blocks separated
by fault zones, and applied a block mosaic technique (see Kley, 1999, and Hindle and
Kley, 2002). This gives a deformed picture of the region (Figure 11 C). Next, by
applying the serial simplified cross sections of Kley (1999) to these large crustal blocks, a
retro-deformed picture was created (Figure 11 A). The geological displacement vectors
are then found by connecting known correlation points in the retro-deformed picture to
the deformed picture (Hindle and Kley, 2002). The displacement vectors are then
equivalenced to velocity vectors, which in turn can give shortening estimates (Hindle and
Kley, 2002; Kley, 1999). The results from this large model appear to be accurate for
regional displacement of the Central Andes, as they trend closely to the NUVEL-lA
relative plate convergence vector (Hindle, 2003; Hindle and Kley, 2002; DeMets et al.,
1994; Stein et al., 1986). However, exact shortening amounts cannot be determined due
to the assumptions made for deformation when separating out the large crustal blocks
(Hindle, 2003; Hindle and Kley, 2002).

This method can be applied to different time intervals by decomposing the

displacement history into the two or more time periods. Hindle and Kley, (2002) used

25

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27

25-10 Ma and 10-0 Ma, based on estimated ages for the start of deformation in specific
areas during the two episodes of deformation for the Central Andes. Movement in the
Eastern Cordillera was first pieced together for the 25-10 Ma time period, and the
Subandes and movement to the south was used to estimate the latter time period. Then,
by piecing together the two block pictures time by time, two sets of displacement vectors
were created for the region (Hindle and Kley, 2002). The results of this model are shown
in Figure 12. This larger model (Figure 11) implies that < 20 km of shortening has
occurred in the Eastern Cordillera during the late Neogene, while ~125 km of shortening
has taken place in the Subandes post- 3 Ma (Hindle and Kley, 2002). These are the best

modeled results to date for movement in the Central Andes.

3.2.3 Crustal Thickening and Tectonic Shortening

Isacks (1988) first proposed that the topography of the Andes is largely a result of
crustal thickening produced by crustal shortening. He created a model with the key idea
that “an along-strike variation in the amount of shortening implies the possibility of a
change in the shape of the map view outline of the leading edge of the upper plate”
(Isacks, 1988). Crustal thickening estimates derived from shortening estimates was an
important step forward in kinematic studies in the Central Andes, giving the first wave of
attempts to correlate crustal thickness and shortening to uplift (Hindle et al., 2005; Elger
et al., 2005; McQuarrie and DeCelles, 2001; Kley and Monaldi, 1998; Isacks, 1988).
However, most took this to mean that the two had to be directly related, i.e., the amount
of shortening at the surface must be accounted for by equal crustal thickening. This was

found to not be the case, as < 30% of crustal thickness can be attributed to tectonic

28

—1s° ‘

    

25mm/yr '—>

 

 

280° 285° 290° 295° 300°

I
0 2000 4000 6000 8000

 

 

Red arrows - 25-10 Ma
Bhle arrows - 10-0 Ma

Figure 12 Derived geological velocity field of the Central Andes
of Hindle and Kley (2002). Small rectangle shows the area with
evidence for a northern change in convergence direction.
(Generated using GMT, Wessel and Smith, 1998)

29

shortening in the currently active southern region (Kley and Monaldi, 1998). It is
currently accepted, that the exceptional thickening of the crust under the Andes cannot be
accounted for by the total structural shortening; nor, can structural shortening alone
account for the amount of uplift in the Altiplano-Puna and the Eastern Cordillera
(Oncken et al., in press; Hindle et al., 2005; Yang et al., 2003; Hindle, 2003; McQuarrie
and DeCelles, 2001; Hindle et al., 2000; Kley and Monaldi, 1998). Therefore, some
combination of shortening, crustal thickening, and possibly other mechanisms must be
taking place currently in the Andes (Hindle et al., 2005; Kley and Monaldi, 2002). This
is still being disputed.

Most recently, Hindle et al. (2005) produced a 3-D model for the direct effect of
crustal thickening. Their results give a shortening estimate of ~275 km, taking into
account 2-D shortening and regional crustal thickness changes (movement of material).
The results of this study show crustal thickness and tectonic shortening to be closely
related, and that both need to be taken into account when estimating regional shortening
amounts (Oncken et al., in press; Hindle et al., 2005). These estimates are thought to be
more accurate in light of more recent and widespread, direct measurements of the depth
to the Moho (Hindle et al., 2005; Yuan etal., 2002). Kley and Monaldi (1998) and
Oncken et al. (in press) both give an excellent discussion on how strong (or not) the

correlation is between these two mechanisms.
3.2.4 Fault Kinematic Studies

Shortening estimates from all fault kinematic studies are for post-10 Ma

deformation, and Figure 13 shows the results for two of the main studies with estimated

30

 

I I I
Altiplano Bolivian

Eastern Cordillera

, 23-
. Subandes
E Argentine

Eastern
Argentina Cordillera ,

Chile B, 23

dNVO

Bolivia

 

 

 

 

Er 24
Puna
E: Cladouhos'94 B’
E Marrett'94
— post 1.5 Ma
pre 3 Ma __
25

 

I67 66

l I65

 

 

Figure 13 Results from previous fault kinematic studies conducted in the Central
Andes. Lines represent estimated shortening directions for deformation, post 1.5
Ma and pre 3 Ma. CANP, Cabalgamiento Andino Principal (Main Andean Thrust),
CFP, Cabalgamiento Frontal Principal (Main Frontal Thrust). Compiled with

data from Cladouhos etal., 1994, and Marrett et al., 1994.

31

shortening orientations for pre-3 Ma and post-1.5 Ma.

Early fault kinematic studies were based on fault slip data from along the southern
portion of the Puna (Allmendinger, 1986). Since then, fault orientations from varying
locations throughout the Central Andes, where sediment dates are known making them
ideal for age-dating the deformation, have been used to estimate compressional
directions. Their results illustrate two distinct trends of horizontal shortening, WNW-
ESE and NNE-SSW, for post-10 Ma deformation (e. g., Echavarria et al., 2003; Marrett
and Strecker, 2000; Jordan et al., 1997; Alhnendinger et al., 1997; Marrett et al., 1994;
Cladouhos et al., 1994; Cladouhos, 1993; Allmendinger et al., 1989). This led to a multi-
phase theory for Andean deformation throughout the Central Andes. It was proposed that
generally NW-SE compressional trends correlate to 10 Ma to 2 Ma (dated at 3 Ma by
some studies), and generally NE-SW trend correlate to 2 Ma to present deformation
(Echavarria et al., 2003; Allmendinger et al., 1997; Allmendinger, 1986).

This theory is based on fault slip data that illustrate a distinct change in the
orientation of compression at 2 Ma (or 3 Ma) and has been proposed to have been caused
by increased deformation to the south in the Subandes, which in turn affected structural
styles and deformation throughout the region (Echavarria et al., 2003; Marrett and
Strecker, 2000; Allmendinger et al., 1997; Jordan et al., 1997). The WNW-ESE trend is
found mostly to the south in the Subandes, and NNE-SSW is found further north, in parts
of the Eastern Cordillera and Altiplano-Puna (Echavarria et al., 2003; Marrett and
Strecker, 2000; Allmendinger et al., 1997).

In the early phase (10-2 Ma), a NW-SE shortening direction is said to have led to

uplifi in the region with shortening estimates of <5 km in the Puna (Marrett et al., 1994;

32

Allmendinger et al., 1989; Allmendinger, 1986). This is supported by NNE-SSW
striking thrust faults found in the Altiplano, Puna, and Eastern Cordillera with an average
estimated shortening direction of 120 i20° (Marrett et al., 1994; Cladouhos et al., 1994;
Alhnendinger et al., 1989). At the end of this event at ~8-6 Ma, deformation started in
the south forming the Subandean fold and thrust belt with WNW-ESE trends (Echavan'ia
et al., 2003). Shortening orientations for pre-3 Ma deformation in the south have been
estimated at 275°-299° (Marrett et al., 1994).

The latter phase (2-0 Ma) is characterized by normal and strike-slip faulting with
NE-SW to NNE-SSW shortening (orientations range from 060° - 065°) in the Altiplano-
Puna and parts of the Eastern Cordillera (Allmendinger et al., 1997; Marrett et al., 1994;
Cladouhos et al., 1994). These trends are thought to be the result of the re-activation of
normal faults associated with the Salta Rifi System, with shortening estimates of 5-10 km
(Kley et al., 2005; Kley and Monaldi, 2002; Kley et al., 1999).

Minimum shortening is estimated at 60 km for recent deformation in the
Subandes (Echavarria et al., 2003). Further south, an ENE-WSW shortening takes over
between 2 Ma and 3 Ma as a result of strike-slip faulting (Marrett and Strecker, 2000;
Marrett et al., 1994). Shortening for late Neogene movement across the region was
estimated to be 10-20 km in the Eastern Cordillera and 50 km across the adjacent fold
and thrust belt, yielding a total of 70 km for the Pampean segment in the south

(Allmendinger et al., 1997).

3.2.5 GPS Studies

Regional shortening directions and estimated shortening rates have been found

33

using GPS data and finite displacements from geological observations (e.g., Hindle,
2003; Klosko et al., 2002; Hindle et al., 2005; Hindle and Kley, 2002; Bevis etal., 1999;
Kendrick et al., 1999; Norabuena et al., 1998). GPS studies have estimated shortening
rates across many sections of the Central Andes. The results of numerous GPS-derived
studies have given shortening rate estimates of ~9-15 mm/yr for the active Subandean
fold and thrust belt (Klosko et al., 2002; Bevis et al., 1999; Norabuena et al., 1998), and
9-12 mm/yr for the Central Andes (Oncken et al, in press). GPS shortening estimates are
often compared to geological shortening estimates, found to be 8-15 mm/yr (Klosko et

al., 2002; Hindle et al., 2002; Kendrick et al., 1999).

Average geological velocity vectors were calculated from displacement vectors
for the two main episodes of deformation, 25-10 Ma and 10-0 Ma (see section 3.2.2 for
details). These geological velocity vectors and their orientations were compared to GPS
velocity vectors and have been found to agree to i <5° (Hindle et al., 2005; Klosko et al.,
2002; Kendrick et al., 1999). Figure 14 shows the current GPS data compared to velocity

fields for 25-10 Ma and 10-0 Ma (Hindle and Kley, 2002).

Overall, the estimates from GPS studies appear to match well with the estimated
rates and directions of the 10-0 Ma vectors (Hindle et al., 2002; Klosko et al., 2002;
Norabuena et al., 1998). A comparison between the 25-10 Ma vectors and GPS vectors
show a similar direction, but a slower velocity (Hindle and Kley, 2002). These
comparisons are surprising because they lead to the conclusion that shortening rates are
accelerating over time, while plate convergence is slowing (Hindle and Kley, 2002).
The GPS results from the Subandes are found to be almost identical to permanent

shortening estimates, and therefore are used for a direct comparison (Hindle and Kley,

34

-15°

      
 
  

 

‘20., 25 Ma to Present '20”

time averaged . '-

i ”a '
l -2s-s

 

 

 

e5°w e5°w

-15° -15'

    

/
,. x

 

 

 

 

 

 

 

 

 

/ .- a
25.10 Me n '20. l 10 Ma to Presefl "’ '20
, x
. .r
, w‘ . ’ ,/
-25°S -25°S
0 . . I I '
———o
100 mm yr-l

Figure 14 Velocity vectors for the Central Andes from Geological
Data and GPS. (A) GPS velocities with respect to the stable interior
of South America. Included is the convergence vector for the

Nazca plate dervived fi'om GPS data, GPS NZ-SA, and the predicted
global plate motion model NUVEL-lA (Norabuena et al., 1998). (B)
geological velocities averaged over 25 Ma. (C) averaged velocities
from the displacement field for 25-10 Ma and (D) averaged velocities
from the displacement field for 10-0 Ma. (From Hindle et al.,

2005; Hindle and Kley, 2002; Kley, 1999).

35

2002). This is possible since the majority of shortening in the Subandes has taken place

over the past 3 Ma.

The difference in estimated GPS rates could be accounted for by on the model and
parameters used for calculations. Some parameters that can affect shortening rates
predicted from models are: the location of the site (e. g., near the western edge could be
affected by elastic deformation due to a build-up of strain between large earthquake
events), and the amount of locking (amount of interplate slip locked on the plate
interface) assumed (Hindle, 2003; Norabuena et al., 1998). The best fit, modeled
estimates of shortening rates (as compared to geologic shortening rate estimates) from a
compilation of GPS data, has been found by using the ratio between shortening and
locking at 15 mm/yr: 30mm/yr in the north and 12 min/yr: 38 mm/yr in the south (north
and south being on either side of a transect perpendicular to the trench at 17°S)
(Norabuena et al., 1998). There are many other factors that limit these models, and it

should be noted that they are to be used only as estimates (Kley, 1999).

Section 3.3 Kinematic Timing

While overall shortening of the Central Andes may have commenced in the
Eocene, the majority of the ~250-280 km has accumulated in the last ~30 Ma (Hindle and
Kley, 2002). Earlier pre-Cretaceous folds and some thrusts affect Ordovician strata, but
the amounts of shortening are not thought to be significant (Kley, 1999).

Based on the results from the studies just discussed, the 30 Ma history of Andean
deformation is generally divided into two distinct episodes (e.g., Hindle and Kley, 2002;

Kley, 1999; Allmendinger et al., 1997). The first episode is dated between approximately

36

25-10 Ma (Hindle and Kley, 2002; Kley et al., 1996; Kennan et al., 1995) and mostly
affected the Eastern Cordillera. Deformation during the Eocene started in the Western
Cordillera and then shifted eastward to the Altiplano and the Eastern Cordillera by late
the Paleogene (Gregory-Wodzicki, 2000; Jordan et al., 1997). Deformation during this
first episode is characterized by widespread thrusting throughout the Eastern Cordillera,
and WNW-ESE shortening and subvertical extension in the Puna and Altiplano (Marrett
and Strecker, 2000; Marrett et al., 1994; Cladouhos et al., 1994).

The later episode was almost exclusively accommodated by thrusting in the
Subandes, and is dated between 10 Ma and 2 Ma in both the Puna and southern Altiplano,
and to present for deformation firrther to the south, including the Eastern Cordillera
(where less than 20 km shortening was estimated in the Neogene), the Subandes, and the
Santa Barbara System (Hindle and Kley, 2002; Jordan et al., 1997). This intense period
of deformation is entirely responsible for the creation of the fold and thrust belt to the
east (the Subandes) and the west-vergent thrusts of the Santa Barbara System.

By dividing deformation into these two broad “episodes” it appears that
shortening rates in the foreland thrust belt increase with time, showing an apparent
inverse relationship to the subduction rate (Hindle and Kley, 2002).

Many theories have been proposed that further subdivide the timing of
deformation (Oncken et al., in press; Allmendinger, 1989; Isacks, 1988). The later
episode (10 Ma to present) has been studied a large amount because of the abundance of
data that are available. One proposal is the multi-phase theory of Alhnendinger (1989)
that was given in Section 3.2.4.

This theory and its two distinct phases are further supported by studies using plate

37

kinematic parameters such as, upper plate deformation and plate convergence, changing
geometry and properties in the subducting slab, magrnatism, climate-related variations,
and erosional properties, to name a few (Oncken et al., in press; Hindle et al., 2005;
Marrett and Strecker, 2000; Horton, 1999; Allmendinger et al., 1997; Isacks, 1988).

A tri-phase deformation theory is proposed by Oncken et al. (in press) which
divides the 30 Ma history of deformation into three periods defined by the location of
movement in the region. Figure 5 shows their estimates for the initiation of deformation
over the Central Andes. They propose that from 30-20 Ma deformation affected the entire
plateau including the southern parts of the Puna. In their middle period (19-8 Ma) they
propose a south-eastward continuance of the progression of deformation, with an increase
occurring in the Puna resulting in the start of deformation in the east flank of the plateau.
In the final period (7-0 Ma) they propose that deformation shifted to the flank of the
Altiplano with an increase in shortening in the eastern flank and parts of the Puna. They
note that erosion rates appear to drastically change at both 9-7 Ma and 2-3 Ma, which
would support the Allmendinger, (1989) multi-phase theory for the most recent
deformation.

At present however, it can only be solidly concluded that the two main episodes
of deformation took place in the Central Andes, the first from 25-10 Ma, and the later

from 10 Ma-present, and that changes in compression have occurred post 10 Ma.

38

Chapter 4 Calcite Twinning

Section 4.1 Twin F omafion and Properties

Crystallographers have studied the geometry of calcite and its ability to be
“twinned” for over a century (e. g., Burkhard, 1993; Groshong, 1972; Turner and Orozco,
1976). Caused by low temperature deformation in rocks (generally lower than 300°C),
the mechanical twinning of calcite is a mechanism for accommodating strain by which
the crystal lattice is rotated along discrete planes. Figure 15 shows the principal planes
and geometry of calcite e-twinning (Burkhard, 1993; Groshong, 1974, 1972). In the most
simplified case, an e-twin is formed when shearing takes place along a favorable glide
plane, g, resulting in a rotation of the crystalline lattice, with a relative displacement of
the upper layers of the lattice toward the positive c-axis (Burkhard, 1993; Groshong,
1974, 1972; Turner et al., 1954). This creates a totally new crystallographic orientation
within the grain with respect to the e-g glide system, allowing for a second, and possibly
a third, set of e-twins (e2, e3) to form, if deformation is continued (Burkhard, 1993).

While e-twin gliding is the most favorable coordinate glide system for calcite, it
should be noted that twinning might also occur along the r-plane (Burkhart, 1993).
However, this is only possible as a second twin glide system and can only take place in a
single crystal lamellae within an e-twin formed from a previous deformation. It will not
occur in the entire grain (Burkhard, 1993).

Calcite twins can be formed readily by applying pressure to a single grain of

calcite using only a pocketknife (Burkhard, 1993; Groshong, 1972). This reflects the

39

 

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40

small amount of shear stress (10 MPa) needed for twin formation (Burkhard, 1993;
Groshong, 1974, 1972). Under this low stress, multiple twin sets per grain will ofien
form depending on the temperature, while highly stressed grains will most commonly
display only one set (Burkhard, 1993).

The precise geometry and physical conditions necessary for the formation of
calcite twins allows e-twins to be used as a gauge for measuring the temperature and
amount of deformation in various mountain belts around the world. In terms of
deformation, e-twins can be considered as a zone of perfect simple shear with a unique
sense of shear in the e-g direction parallel to the twin plane (Burkhard, 1993; Hindle,
1997). The amount of simple shear deformation within a grain can be distributed by the
formation of either many thin twin sets (type I) or simply a fewer number of thick twins,
(type II) (Burkhard, 1993). Burkhard (1993) classified e-twins by type with respect to
their appearance under the microscope (Figure 16).

Formation of thick twins is a two-step process in which nucleation (needing a
minimum stress concentration) occurs, followed by the enlargement of an existing thin
twin (Burkhard, 1993). If temperature and shear stress in the sample are taken into
account, it could be easier to widen an existing twin than to create a new one (Burkhard,
1993). Twin type is predominantly a function of deformation temperature, with applied
differential strain rates having only a minor effect (Burkhard, 1993). At temperatures
greater than 300°C, twinning ceases to be a competitive deformation mechanism
(Burkhard, 1993). Therefore, only type I and type II twins are suitable for strain analyses

(Burkhard, 1993; Groshong 1974; 1972).

41

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42

Section 4.; Previous Stress-Strain Studies

The use of calcite twins to determine stress-strain axes in deformed rocks and
their application to tectonic studies was introduced in the 1950’s (Burkhard, 1993;
Groshong, 1974, 1972; Griggs and Miller, 1951). It was first applied to high-grade
marbles where twins generally formed a late, post-crystallization, tectonic overprint
(Burkhard, 1993; Turner and Orozco, 1976; Turner, 1953). The method was refined in
order to determine both the principle directions and the magnitudes of stress for non-
metamorphosed, weakly deformed, sedimentary rocks. This in turn, was used to infer
palaeostress axes (Burkhard, 1993; Groshong, 1972; Turner and Orozco, 1976).
Groshong (1972) quantified the method allowing for the calculation of the total strain in
the sample. This calcite strain gauge technique took into account the thickness of the
twins (Type I vs. Type II) and the relative twinned percentage of the twinned grain. In
doing so, the technique allowed for certain twinsets to be weighted when calculating the
total strain in the sample (Hindle, 1997; Groshong, 1974, 1972). The method is briefly

outlined here, using the coordinate convention of Groshong (1974) (Figure 15).

Shear strain parameters are calculated for individual grains resulting in the expression
2 II
(1) 7,8 =7Zz,-tan(a/2)
i=1

where: 7.23: the shear strain of e with respect to g, n = number of twins, t= width of the

host grain perpendicular to the twin plane, t.- = thickness of a twin lamella and a = the

angle of rotation of the grain edge due to twinning (Groshong, 1974).

43

By simplification of Equation (1) for tensor shear strain and substituting in the value of a

(38.30) one obtains

Les. = 0.347 :1

(2) 2 t

 

i=1

This expression yields the shear strain for each twinset in every calcite grain measured.

Applying the tensor transformation equation for infinitesimal strain (Jaeger and Cook,

reg

 

1969), the shear strain of one twinset, [ J, is transformed into principle axes of

infinitesimal strain.

2
7e 1
(3) [—8]: eg = O —-2—tan¢// 0 ,

 

 

where sex = tam/1 and y/ is the change of an original right angle. The strain for each

twinset (Equation 3) is next transformed into fixed x, y, 2 thin section coordinates. Each
thin section per sample will have unique thin section coordinates defined in terms of a
referenced thin section coordinate system (Figure 17) (See Appendix A) (Groshong,
1972). Each twin set will therefore have a unique equation for strain, with swaps”
representing normal strains and $12,430,823 representing shear strains, in the following

simplified form:

7.»
(4) —2§-=Aq,+B£22+Cq2+D£U+E£23,

where 833 = —(a” + an).

44

U-Stage
East

  

U-Stage
Down

Figure 17 Referenced x, y, 2 thin section coordinate system
determined from U-stage position.

+y'
+1!

+X

Rotated coordinate system for remaining thin sections.
a. shows the reference coordinate system as above,

b. gives the rotated fixed thin section coordinate system
discribed in terms of a. (Modified from Groshong, 1974)

45

where, A-E are the functions of direction cosines between the x, y, 2 thin section

coordinates and the e and g axes. The zero volume-change condition was used.

Measurements of more than 5 twinsets give equations that can be solved
simultaneously by least squares to give the deviatoric strain components. This is applied

to ~60 measured twinsets per sample, and a best fit solution was achieved

ye -
(5) 28 l = '61-’91 +162xi2 + fl3xi3 + fl4xi4 + flsxm

where xi]. are direction cosine functions for the i "' twinset

 

and, A — ,6, are the strain components for the whole sample,

(:61 =8vfl2 =322’fl3 =5mfl4 =£239165 =€32)°

Equation (5) was then used to find a matrix expression for the multiple regression,
(6) )6}. =(XTX)"XTY, j=1,5.

where ,6]. = the least-squares estimate of the strain components in the sample (Groshong,

1972, 1974). The “best fit” strain tensor can be compared to the orientations of the
measured twinsets to test for compatibility between the twinning shear and the whole

sample strain (Hindle, 1997; Burkhard, 1993; Groshong 1974, 1972).

Groshong (1984) developed two FORTRAN programs (called ROTATE and
TWINST) to make analysis faster and easier. ROTATE is used to calculate the
directional cosines for each individual thin section. This program requires the correct
geographic x, y, and 2 plane orientations of individual slides (Figure 18). This is done

manually and requires a short procedure in which the reference line recorded in the field

46

Figure 18 Geographical Coordinate
System.

 

A. Thin section coordinates as they appear
on the U-Stage. (See Figure 17)

Section B. Coordinates in geographic space,
N - North

C. Plotted coordinates on Steronet.
These are the inputs for ROTATE.
Created after Groshong, (hand-drawn)

 

 

 

 

 

 

 

 

 

47

is plotted on a steronet. Then, by the right hand rule, the x, y, and z geographic axes were
determined for each slide. These were then entered into ROTATE. The results are nine

directional cosines for the slide needed for the use of TWINST.

The program TWIN ST allows the input of these direction cosines and all
measured parameters, and calculates a full set of analytical results for the calcite strain
gauge technique. These include the e-g angles for all twinsets that were measured in
rotated geographical coordinates, a negative expected value (NEV) that indicates the
compatibility of the individual twinset result to the best-fit tensor, and three principal
strain tensors (axes) for the sample listed as groshong x, groshong y, and groshong z.

The complete FORTRAN codes are presented in Appendix B.

This calcite strain gauge technique is the most currently utilized for strain analysis
using calcite twins. Groshong (1974) tested his own method of the least-squares strain
gauge calculation by performing a statistical analysis of the results from both
experimentally-derived twins and lab-formed twins and their strain axes. He found that
the orientations of the vertical shortening from the strain interpretation of twinned calcite
matched the vertical strain orientations from lab experiments, thus concluding that the
technique itself was accurate (Groshong, 1974). Groshong et al. (1984) next computed
the angle of precision between individual thin sections strain axes and the overall ‘best’
fit tensor for that sample. These results give an average angle of precision to be i10°-12°

(See section 6.3 for more details).

Twin studies using the Groshong method have been carried out across much of

the fold and thrust belts of the Western Alpine foreland in the French Alps, and the

48

Eastern Helvetica Alps in Switzerland (Hindle, 1997; F errill and Groshong, 1993;
Groshong et al., 1984). These twin studies have yielded good results when compared to
stress and strain analyses conducted with various other twin methods, as well as when
compared to results from studies using different types of data (such as fault kinematic

studies) for the respective regions.

49

 

 

Chapter 5 Methodology

Section 5.1 Introduction

Field work was conducted over a three year period with three separate trips to
Argentina and Bolivia. Oriented samples of Yacoraite limestone (Figure 19) were
collected from 17 sites spanning northwest Argentina and southern Bolivia (20°S to 25°S
latitude) (Figure 20).

The Yacoraite Formation was deposited during the late Cretaceous post-rifi stage
of the Salta Rifi System, and is a member of the Salta Group (and the Balbuena Subgroup
in Argentina). Various stages of rifting caused the deposition of the Salta Group to be
semi-continuous and highly variable in thickness and grain size throughout the study area
(Kley et al., 2005; Kley and Monaldi, 2002; Sempere et al., 1997; Allmendinger et al.,
1997). In the Eastern Cordillera (22°S - 26°S), the thickness of the Salta Group is
estimated at 1000-1800 meters, with the maximum thickness of over 2000 meters at
~23°S (Kley et al., 2005; Sempere et al., 1997). The Yacoraite Formation has an average
thickness between 50 and 100 meters, and is exposed along the flanks of synclines
throughout the region (Kley et al., 2005; Kley and Monaldi, 2002; Sempere et al., 1997).
In the field, it ofien appears as very light colored, white to pink-grey, cliffs (Figure 21)
(Kley et al., 2005). A relatively widespread, yet thin (I to 2 m), gastropod-rich unit was
selected for sampling where available. This unit yields recrystallized, sparitic material
due to replacement of the original bioclastic material, thus making it ideal for

microscopic analysis of the larger calcite grains.

50

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51

 

 

 

Figure 20 Location of the 17 sample sites.
(Plotted in GMT, Wessel and Smith, 1998)

 

Table 1 List of sample site data.

 

 

 

 

 

 

 

 

SAMPLE decimal coords altitude LOCATION
Ion . (W) lat. (S) meters
1 65.083 23.162 4100 Near Abra de Zenta
2d 65.434 23.575 2800 Quebrada de Huichara
3 65.491 23.181 3950 Humahuaca-Casa Grande Road
4 65.624 23.028 3900 Road from Abra Pampa to El Aguilar
5 65.599 23.171 3800 South end of C. Colorado
7 65.179 23.310 4200 Hornocal syncline
8 65.402 23.632 2530 Maimara
9 65.354 23.471 3000 West of Angosto de Pichel
107 65.687 23.702 3914 Susques to Purmamarca
108 64.514 24.317 1120 Sierra Sta Barbara
109 64.480 24.297 1295 Sierra Sta Barbara
110 65.431 25.285 1066 Cabra Corral, Dique.
111 65.351 25.294 1064 Cabra Corral, Dique.
202 65.169 20.599 2618 Camargo, Bolivia
203 65.169 20.599 2618 Camargo, Bolivia
206 65.191 21.274 2463 east of El Puente
30_8 6_5r.319 21.815 2679 South east of Top, Bolivia ‘

 

 

52

 

 

Yacoraite Fm. ’ .. '

 

Figure 21 Yacon'te Formation of the Salta Group (white to grey unit) in
(A) the western flank of a syncline and (B) in extensive thrust faults. It
is underlaid by Letcho red-bed in NW Argentina and Southern Bolivia.

53

 

Section 5.2 Sample Collection

Based on geologic maps and satellite images, sample sites were chosen for their
accessibility, adequate thickness of the unit, and known structures. Exact locations range
in latitude fiom 20.599° S along the eastern boarder of the Altiplano-Puna plateau, to
25.2945o S in the Santa Barbara System. Some sites were sampled twice, varying only in
elevation (Figure 20 and Table 1). If the desired horizon was not available at the site
location, an alternate site was chosen.

At each site, one or more samples about 20 cm x 12 cm in size were taken.
Samples were numbered chronologically relating to the trip on which they were collected
on (i.e. single digits are from the 2001 trip, 100’s are from 2002 trip, and the 200’s were
collected in 2003). Each was marked with a reference arrow to identify its geographic

orientation in azimuth and dip.

Section 5.3 Sample Preparation

From each sample, two or three mutually perpendicular, oriented thin sections
were prepared. All slides were mounted by hand at the Michigan State University (MSU)
Rock Laboratory to ensure accurate orientation and correct identifying labels. A number
of slides were finished at MSU, with the remaining slides completed by PetroGraphics
International in Canada (now known as Vancouver GeoTech Labs). Figure 22 shows an

example of twins in the Yacoraite samples under the microscope.

54

 

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55

Section 5.4 Data Collection and Meflrrements

A Universal Stage microscope (Figure 23) was used to measure poles to twin
planes (e-planes) and c-axes orientations in azimuth and plunge (Figure 15), following
the procedures outlined in Groshong (1972); see Appendix C for detailed description.

The measurements were recorded, along with the number of twins (striations) for
each grain, twin type, and the percent of abundance of twinning in the grain (e. g., Table
2). Approximately 60 twins were measured from either 2 or 3 oriented thin sections of
each sample. Results were plotted on a stereonet after each measurement to assure the
angles between the twin plane and the c-axis were 26° or the angle between el and e; was
46° (Figure 15) (Burkhard, 1993; Groshong, 1972). If an e1,e2 measurement is made, i.e.,
two sets of twins in the same grain were measured, the exact c-axis can be found by
graphical methods. The c-axis was determined by plotting the perpendicular bisector,
then finding the appropriate 26° angle between both twin measurements. This method
yielded the exact c-axis for both twin measurements, and was checked under the

microscope for verification.

Section 5.5 Processing

All measurements were analyzed following the Groshong (1972) strain gauge
method outlined in Section 4.2. Results were acquired by using the two FORTRAN
programs, ROTATE and TWINST (discussed in Section 4.2), created by Groshong and
later modified by Burkhard to conduct the analysis (Groshong, 1986).

First, the program, ROTATE, determined the appropriate direction cosines for

each thin section. Next, the strain tensor program, TWINST, took these corresponding

56

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58

 

direction cosines and the recorded measurements (Table 2) as input, and applied a least
squares method to determine a best-fit strain tensor for the sample (Groshong, 1972).

The orientation of the tensor was then compared to each individual twin set to identify
those that have incompatible orientations and therefore would not have formed in the
determined strain field (Hindle et al., 2000; Hindle and Burkhard, 1999; Burkhard, 1993).
These appear in the results of the program, as negative expected values or NEVs
(Groshong, 1974).

Next, the 10 highest NEVs were eliminated fi'om the sample data set to remove
any significant bias due to heterogeneous strain distributions within the aggregate at the
thin section scale, as well as removing any outliers (Burkhard, 1993). The data were then
reprocessed for strain, using the same least squares method. Finally, the results of the
three principal strain axes are given as groshong x, groshong y, and groshong 2.

For the purpose of this study, the orientation of the 2 strain direction (hereafter
referred to as groshong z-axis) was the desired result. All three axes were plotted on a
steronet with the bedding plane of the sample. This relates the twins to the strata and
structures they were samples from. From this, interpretations of regional deformation

were made.

59

 

 

Chapter 6 Data and Results

Section 6.1 Data

Table 3 summarizes the key parameters and data of this study, including the
desired groshong z-axis result. Appendix D contains full analytical results (including all
raw twinset measurements in azimuth and plunge for e-axis, c-axis, and g-axis, and the

found e, g angles) from TWINST for each sample.

Section 6.2 Results
6.2.1 Trends

The results of this analysis determines the orientations of the three principle strain
axes for 17 samples from various sites throughout the Central Andes, between 20° — 25°
S. Figure 24 shows the twin locations and the derived groshong z—axes. These results
were used to interpret regional trends of compressional directions. For reference,
samples above 22°S are in the northern region, samples from 22°-24°S are in the central
region, and those below 24°S are in the southern region.

The results show two general trends for the groshong z-axis, a general NW-SE
direction, which will include all northwestern striking trends (NNW-SSE), and a
generally NE trending that is approximately parallel to the plate convergence. Both
trends are found in each of the three regions with the central region containing the
majority of the NE—SW. The NE-SW trends match estimated plate convergence vectors
(found for older deformation, 36 Ma- 26 Ma), ~040° (Pardo-Casas and Molnar, 1987), as

well as the GPS estimated NUVEL-lA plate convergence vector for the last 3 Ma, ~079°

60

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61

 

Figure 24 Sample Results. Red dots are sample location,
blue vectors are groshong z-axes. Latitude in degrees S,
longitude in degrees W. (Created in GMT, Wessel and Smith,
1998)

62

(DeMets et al., 1994; Stein et al., 1986).
A summary of samples by trend is listed below:
NW-SE: l, 5, 107, 108, 109, 111, 202, 203, and 208

NE-SW: 2d, 3, 4, 7, 8, 9, 110, and 206

6.2.2 Steronets

Individual sample site results are shown in Figure 25 with plotted steronets and
the three principle strain axes. The steronets were constructed to show the groshong z-
axis (short axis) as it relates to bedding, and allows for the classification into pre- or post-
folding twin creation within the samples. Post-folding formation of the twins is implied
when the groshong z-axes have an almost horizontal plunge that cuts across the fold
limbs nearly perpendicular to strike (e. g., Figure 25H). Some samples were hard to
classify (e.g., horizontal but do not cut the limbs) or were not horizontal (e. g., Figure
25F). These were therefore classified as ambiguous. Pre-folding was implied when the
groshong z-axes lie on or very close (within 10°) to bedding plane (e. g., Figure 25D).
Figure 26 shows the classified results for post-folding vs. pre-folding. A summary of the
classifications is as follows,

Samples Classified as Post-Folding are: 1, 2d, 5, 9, 109, 202, and 208

Samples Classified as Pre-Folding are: 3, 4, 8, 108, and 110

Undefined Samples: 7, 107, 111, 203, and 206

Pre-folding twinning was assigned the age of pre-10 Ma for the samples north of
24°S. This is the said to be the date of a ceasing (or a lag phase) in defamation in the

Eastern Cordillera (e. g., Echavarria et al., 2003; Allmendinger et al., 1997). For samples

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—66° —64° -62° -6

Figure 26 Sample sites with groshong z-axes and timing
classifications. (Created on GMT, Wessel and Smith, 1998)

70

from the central region, an age of pre-9 Ma was assigned based on the average age for
initiation of the main deformation in the Subandes and the Santa Barbara System (e.g.,
Echavarria et al., 2003). The southern region samples can only be interpreted loosely as
pre-3 Ma but post-9 Ma for pre-folding. Post-folding classifications will be assigned
post-10 Ma deformation for the northern and central regions. Post-folding in the southern
region will be interpreted as post- 3Ma as large amounts of current deformation is taking

place in this region.

Section 6.3 Errors

One measure that was statistically tested by Groshong (1974) is the significance
of the number of twin sets measured per thin section. Although only 5 are required for
the calcite strain gauge technique (Groshong, 1972) to be used, Groshong (1974) found
that 50 — 60 twin set measurements per sample yielded small standard deviations. This
study measured ~50 twin sets per sample with the exception on sample 111. Thus, it is
expected that the derived results are accurate.

The measure of NEVs for a sample yields a percentage that can be statistically
interpreted for accuracy. It is accepted that a very good data set yields 25% NEVs
(Groshong, 1984; 1974). The average percentage NEVs for all samples this study was
found to be 28%. Regionally, the northern area yielded a 25.5%, the central 31.6%, and
the southern 26.5%. These are all excellent results, and imply good accuracy.

Another statistical measure for accuracy is the average angle of precision. The
estimated standard error for this measure is i10°-12° for an individual thin section

azimuth as compared to the cleaned total sample ‘best fit’ tensor (Groshong et al., 1984).

71

The results for the study conducted here showed a range from L9" - 24.7° for sample 202
data. When the angle of precision is computed for three individual slides, the average
angle of precision was found to be between 25° and 24.7°. Groshong et al. (1984) stated
that the ideal results are obtained when two perpendicular thin sections are used and ~30
twinsets are measured on each, per sample. For the study conducted here, using the data
from two thin sections at a time for sample 202, the average angles of precision ranged
from 1.9°— 122°. These are generally within the i10°-12° error range given by
Groshong (1984). Therefore, the confidence and accuracy of the data presented from the

study conducted here is high.

72

Chapter 7 Discussion

Section 7.1 Introduction

The groshong z-axes orientations can infer the direction of shortening at the time
of deformation, and when combined with the timing results inferred from their geometric
relationships with bedding, can be used to interpret the kinematic history.

A general trend of NE shortening has been predicted for the Andes throughout
their deformational history (Hindle and Kley, 2002; Hindle, 2002; Norabuena et al.,
1998). This is similar to estimated plate convergence direction (~079°; DeMets et al.,
1994; Norabuena et al., 1998), which is believed to have remained relatively constant
throughout the last 50 Ma (Parado-Casas and Molnar, 1987). Andean geologically
derived velocity vectors (Hindle and Kley, 2002) generally trend at ~075° for 25-10 Ma,
and ~050° for post 10 Ma near the study area (Figure 12) (see Section 3.2.2). It is noticed
that to the southern most vectors trend more northerly. The derived velocity vectors
disagree with a number of the groshong z-axes determined in this thesis and are
incompatible with the general direction of compression predicted from previous local
kinematic studies (e.g., Allmendinger et al., 1997; Cladouhos et al., 1994; Allmendinger,
1986; Norabuena etal., 1999) (see Chapter 3 for studies details).

Given the complexity of the Andes, these samples that have trends different from
the derived velocity vectors and the estimated plate convergence vector have individual
explanations.

Fault kinematic studies can determine the timing of movement relatively

accurately, thus these estimates are more reliable than the results from the twin study,

73

which can only decipher between pre- or post- folding (see section 6.2.2 for dates).
Therefore, data from previous, fault kinematic studies are used to estimate the timing of
recent deformation as predicted by the post-folding twin results. In particular, fault
kinematic studies have indicated a change in orientation at about 2 Ma in the study area
(see section 3.2.4). This is particularly important in the study area where the Cretaceous
age Salta Rifi System is present.

It is expected that twin formation would occur during the first phase of
deformation after deposition, since twins form at very low temperatures and small
amounts of applied strain. However, twins can form at anytime through the
deformational history of a rock as long as stress is applied in the preferred glide plane
direction of the crystals. The samples used in this study were deposited in the late
Cretaceous and have undergone ~30 Ma of Andean deformation (Sempere et al., 1997).
Many of the samples studied here are found to have formed post-folding, that is after the
main phase of deformation. As twin formation represents strain only from the
deformational event in which they formed, the results can be used to infer the
compressional direction of only that event. It is unknown as to why certain tectonic
events trigger twin formation.

The groshong z-axes determined in this study can be divided into two general
groups, those that are sub-parallel to the plate convergence vector (approximately NE
striking), and those that are significantly discordant to the plate convergence vector
(generally WNW to N striking). Both groups contain samples that can be classified as
pre- and post-folding and span the entire study area. Four distinct trends are found for

the groshong z-axes orientations that are different from plate convergence. These non-

74

plate parallel groshong z-axes trend groups appear to represent distinct tectonic regimes,
and are grouped and discussed based on these orientations and deformation events that
are supported by the results of previous kinematic studies as well as geological evidence
in the region. The four groups are: NNW trends with implied pre 10 Ma deformation,
WNW trends with implied 10-2 Ma deformation, Northern trends with implied 2-3 Ma
deformation, and W-WNW trends with implied post 2 Ma deformation. The results of
fault kinematic studies summarized by Cladouhos et a1. (1994) and Marrett et al. (1994)

are compared to the results of this study in Figure 27.

Section 7.2 Plate Convergence Paflllel Samples (generally NE trends)

Sample 7 (44.8°) and 206 (650°). Lie in the Eastern Cordillera and are undefined.

Samples 3 (53.4°), 4 (280°), 8 (287°), and 110 (706°). Were all formed pre-folding
within parts of the Eastern Cordillera. Sample 110 is one of the two southern
most samples.

Sample 2d (653°) and 9 (83.8°). Are classified as post-folding and are from the eastern
side of the Eastern Cordillera. Sample 9 has a shortening direction that is almost

due E-W.

The generally NNE to E trending groshong z-axes are, in general, in the direction
of plate convergence during the two episodes of deformation (25—10 Ma and 10 Ma —
present) in the study area. The estimated plate convergence direction for ~25 Ma is
~040° (Parado-Casas and Molnar, 1987) and for 3 Ma-present is 079° (DeMets et al.,

1994; Stein et al., 1986).

75

 

Altiplano

Bolivia

Argentina
Chile

Puna

 

/ KEY
A Post 1.5 Ma —
Pre 3 Ma

 

 

 

 

 

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Eastern Cordillera

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Er 24

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Post-Folding

Pre-folding —

Undefined — x 2?
I67 I66 I65

 

 

Figure 27 Fault kinematic results with classified groshong z-axes and sample sites.
Lines represent estimated shortening directions for deformation, post 1.5 Ma and

pre 3 Ma. CANP, Cabalgamiento Andino Principal (Main Andean Thrust),
CFP, Cabalgamiento Frontal Principal (Main Frontal Thrust). Compiled with

data from Cladouhos et al., 1994, and Marrett et al., 1994.

76

Samples 4 and 8 have trends of 280° and 287°, respectively, and are both
classified as pre-folding. These trends are significantly more north directed than the
estimated current plate convergence direction. Although plate convergence is said to be
relatively constant over Andean history, Parado-Casas and Molnar (1987) have suggested
that the plate convergence vector for ~42-35 Ma trended at ~03 5°. The trends of the
groshong z-axes and the estimated plate convergence are found to be about the same.
Therefore, it is suggested that these twins formed during deformation that occurred after
the deposition of the Cretaceous sample unit, but before the deposition of Miocene strata,
as evidenced by the angular unconforrnity between them found in northwest Argentina
(Sempere et al., 1997; Marrett et al., 1994).

Sample 3 (53.4°) and Sample 110 (70.6°) are pre-folding and have NE-SW trends.
These match well with the derived velocity vectors as well as trending close to the
estimated plate convergence vector. Deformation in the Eastern Cordillera was initiated
around 25 Ma, with estimated plate convergence direction of ~040°. This deformation is
consistent with the pre-folding classification for sample 3, implying that twins were
formed by a phase of deformation that occurred around 25-10 Ma. However,
deformation in the south began post-10 Ma, thus sample 110 (pre-folding) should be
compared to the later episode (10-2 Ma) derived velocity vectors and current
convergence direction (~79°). The velocity vectors around 24°S show little change
between the 25-10 Ma and 10-0 Ma, therefore, it can be implied that they trend roughly
065° at 10 Ma, matching sample 110. Therefore, the derived velocity vectors and plate
convergence directions are nearly coincident to the groshong z-axes, and furthermore,

explain the NE-SE trends.

77

Sample 9 from the east side of the Argentine Cordillera has a trend closer to E-W
(83.8°) than NE-SW, and has post-folding twin formation. It is accounted for by post-10
Ma movement that is supported by a dominantly E-W velocity vector for the later episode
(10-0 Ma) of deformation determined for the same locality (~24°S, ~65°W). This implies
that an E-W compression may be present on a local scale. It may be an effect of the
missing Subandes to the east. There is also a strong E-W horizontal shortening
determined from a number of large N-S trending thrust faults that affected areas
throughout the Eastern Cordillera south of the termination of the Subandes (Figure 28)
(Cladouhos et al., 1994; Marrett et al., 1994; Allmendinger et al., 1989). Cladouhos et a]
(1994) have determined that this E-W shortening occurred post 1.5 Ma (Figure 27).
These derived trends all match the more E-W groshong z-axis of sample 9 for post-10 Ma
deformation.

Four samples (2d, 7, 9, and 202), all classified as undefined or post-folding, show
NE-SW trends similar to the fault kinematic results for post 1.5 Ma deformation (Figure
29). Recent deformation in the Eastern Cordillera has been affected by the reactivation
and inversion of the Salta Rifi System (Kley et al., 2005). This inversion probably
started pre-3 Ma when deformation initiated in the nearby Santa Barbara system. Fault
kinematic data suggest that there was a change in stress orientation at about 2 Ma with
the more recent deformation having NE-SW shortening (see section 2.4) (Allmendinger
et al., 1997, Jordan et al., 1997; Cladouhos et al., 1994; Allmendinger, 1989).

Cladouhos et al., (1994) also concluded that displacement along Quaternary fault scarps

is NE-SW, as compared to NW-SE on Miocene thrusts. Therefore, these four samples

78

 

79

Figure 28 Satellite Image of the study region illusu'ating N-S compressional trends.

(Origional image from Mr. SID, www.mrsid.com)

could be the result of very late Quaternary deformation that could, to some extent, be

very localized.

Section 7.3 Others (NW Striking Trends)

Based on previous kinematic studies it is proposed that the main deformation in
the Central Andes started in the mid-late Oligocene (~25 Ma) with a general NW
compressional direction in the northern part of the study region (see Chapter 3) (e. g.,
Oncken et al., in press; Allmendinger et al., 1997; Marrett & Strecker; 2002; Cladouhos
et al., 1994; Marrett et al., 1994). This NW trend migrates southeastward into the
Eastern Cordillera and Subandes, until deformation diminishes at approximately 10 Ma
(dates range from 11 Ma to 7 Ma depending on author) (e.g., Echavarria et al., 2003;
Kley, 1999; Sempere et al., 1997; Horton, 1999).

Derived velocity vectors show a change from ~075 to ~050 at ~10 Ma, implying
that a north component of movement is affecting the entire Central Andes (Figure 12)
(Hindle and Kley, 2002; Kley, 1999). In regions to the south, including the Santa
Barbara System, main deformation started around 9 Ma with NW-SE shortening resulting
in major thrust faults (Echavarria et al., 2003; Hindle and Kley, 2002; Allmendinger et
al., 1997). Generally, compressional trends are said to remain NW-SE until ~2 Ma when
a change to NE-SW compression is observed at local scales throughout the study area
(Echavarria et al., 2003; Allmendinger et al., 1997; Cladouhos et al., 1994; Marrett et al.,
1994; Allmendinger et al., 1989). This change suggests that Neogene deformation, as
observed in faults, occurred during two distinct phases; the older is estimated to have

occurred from 10 Ma to approximately 2-3 Ma, while the younger is dated post-2 Ma

80

(Echavarria et al., 2003; Allmendinger et al., 1997; Jordan et al., 1997; Alhnendinger and
Gubbels, 1996; Cladouhos et al., 1994; Marrett et al., 1994; Cladouhos, 1993;
Alhnendinger et al., 1989; Allmendinger, 1986).

The older phase (10-2 Ma) is generally characterized by thrusting with NNE-SSW
striking faults and WNW-ESE shortening (Marrett et al., 1997; Allmendinger et al.,

1997; Cladouhos et al., 1994; Alhnendinger et al., 1989). These thrust faults are thought
to be linked to the thin-skinned deformation caused by the steeply (~30°-40°) subducting
slab (Jordan et al., 1997). Cladouhos et al., (1994) gave average estimated shortening
orientation of 120° : 20° for post-9 Ma deformation throughout the Eastern Cordillera.
The youngest phase of deformation, 2 Ma—present, has confirmed NE-SW shortening
trends in the northern and central parts of the study area (e. g., Alhnendinger et al., 1997;
Jordan et al., 1997; Marrett et al., 1994; Allmendinger, 1989).

Of the samples in this group, 5 are post-folding, 3 are undefined, and l is pre-
folding. These non-plate parallel groshong z—axes orientations fall into four categories,
which appear to represent distinct tectonic regimes. The interplay of shortening between
the Subandes, the Eastern Cordillera, and the Santa Barbara System, is likely to have

strongly influenced deformation patterns.

7.3.1 NNW TrendsJPre- 10 Ma Deformtion)

Sample 203 (152.1°). The northern most sample that lies on the Bolivian Eastern

Cordillera/Subandes boundary and is undefined.

A NNW-SSE compressional direction in the northern part of the study area is

81

responsible for the creation of the present-day fold systems in southern Bolivia (Sempere
et al., 1997). Within the timing constraints from the twin results, this movement could
easily explain the formation of twins in sample 203, which is part of the fold system and
classified as undefined. Therefore, twins were formed during the pre-10 Ma deformation
event that created the fold system.

Furthermore, in the northern Puna and the adjacent Bolivian Eastern Cordillera,
an intense deformation event ~10 Ma is evident by the truncation of reverse faults at the
San Juan de Oro unconforrnity dated at 8.6 Ma (Sempere et al., 1997; Marrett et al.,

1 994).

7.34.2 WNW Trends (10—2 MaL Deformation)
Samples 1 (126.7°) and 208 (127.6°). Both formed post-folding and are located in the

Bolivian Eastern Cordillera.

Sample 1 trends WNW-ESE and is very similar to sample 208 from the north.
They are both were obtained along the Eastern Cordillera and Subandes boundary, and
are classified as post-folding. A difference in direction between the 25-10 Ma derived
velocity vectors and the 10-0 Ma derived velocity vectors imply that NW compression is
taking place through the study area (Figure 12). This northward movement is said to
affect areas as far north as the Bolivian Eastern Cordillera, and could be a result of the
“lower horizon” broadening as the Subandes became more active (post-9 Ma). The post-
folding twin results are evidence for the NW compression and for the recent northward

movement. Also, a change in direction and magnitude is seen in just the 10-0 Ma vectors

82

between those located in the south and those in the north. This difference also implies
that a NW compression is taking place throughout the study area.

The northern Puna and the adjacent Bolivian Eastern Cordillera the San Juan de
Oro is offset by oblique strike-slip faults showing that deformation must have occurred
after 8.6 Ma (Cladouhos et al., 1994). Fault kinematic studies agree that WNW-ESE
(estimates from 122°-127°) shortening took place over the area (e. g., Marrett et al., 1997,
1994; Sempere et al., 1997; Allmendinger et al., 1997; Cladouhos et al., 1994). These
orientations from fault kinematic data therefore support the NW-SE trend and
deformation in the Eastern Cordillera between 10-3 Ma, as indicated by the twin data.

Furthermore, based on a preliminary quantitative analysis using the method of
Hindle et al. (2006), the stress orientation from the derived velocity vectors was
calculated to trend NW-SE (128°) agreeing with the groshong z-axes orientations.
Therefore, samples 1 and 208 are accounted for by regional deformation taking place

between 10-3 Ma.

7.3.3 N-S Trend‘s fl’ossible 2-3 MQeformatiom
Samples 5 (170.4°) and 107 (172.8°). Both samples trend almost N-S, with the formation
of twins post-folding for 5 and undefined for 107.
Sample 202 (azimuth 181.0°). One of the northern most samples that lies on the Bolivian
Eastern Cordillera/Subandes boundary, and shows an almost N-S shortening
trend. It formed post-folding.

Sample 108 (l68.4°). Is from the Santa Barbara System and is pre-folding.

83

Samples 5, 107 and 202 are from the central and northern parts of the study area
(southern Bolivia and northwest Argentina on the Eastern Cordillera/Subandes boundary)
and yield N-S shortening orientations. Sample 108 is located in the Santa Barbara System
but has a similar orientation and is classified as pre-folding. It is widely accepted that the
Santa Barbara System is actively shortening in tandem with the Subandes (Kley and
Monaldi, 2002; Hindle and Kley, 2002; Kley, 1999).

N-S shortening is difficult to explain based on available fault kinematic data.
However, one possibility is that these samples underwent deformation and twin formation
about 2-3 Ma, subsequent to the reactivation and inversion of the Salta Rift (see section
7.2). It is suggested that as the rift closes, material is locally extruded to the north and
south, yielding generally north directed thrusting. Due to the complex structural
relationships and the orientation of the rift segments, local refraction of the shortening
direction to the NNW is plausible. Approximately E-W striking thrusts of unknown age
have been observed in this area (Allmendinger et al. , 1997). However, neither the origin
of the shortening orientation nor the timing of deformation can be clearly identified.

Thus the re-activation of the Salta Rifi System can explain the 4 N-S samples.
7.3.4 WNW Trends (Deformation post-2 Ma)
Sample 109 (115.3°). Formed post-folding and is in the Santa Barbara System.

Sample 111 (110.8°). Trends almost E-W and is undefined.

The southern (24°-26°S) portion of the study area lies south of the lateral

84

termination of the Subandes fold-and-thrust-belt. Here, a unique structural style of thick-
skinned deformation with active thrusting and basement uplifts gives trends different
fi'om those to the north. Three out of four samples in this region have NW-SE trending
groshong z-axes. The southem-most sample (110), discussed earlier, has a NE-SW trend
and is apparently pre-folding. Fault kinematic data indicate that out-of-sequence thrust
sheet motion in the south began post-3 Ma, shows almost exclusively thrust kinematics,
and continues up until the present. In addition, they indicate that a change in
compression direction from NW-SE to NE-SW occurred at ~2 Ma (Echavarria et al.,
2003; Allmendinger et al., 1997; Jordan et al., 1997). This change is particularly well
demonstrated by samples from the southern end of the Puna, 26° S. Samples 109 and
111, which trend at 115.3° and 110.8°, respectively, are consistent with deformation 10-2
Ma while sample 110 (trending 70.6°), is more consistent with the younger phase (2-0
Ma). Thus samples 110 and 111/109 show that a change in compression from NW-SE to
NE-SW occurred in this area post-3 Ma, and are presumably illustrating the found change
in compression at 2 Ma (Allmendinger, 1989). However, sample 110 is classified as pre-
folding. This classification could purely be a result of coincidence, or sample 110 may
represent twinning that developed in some earlier (pre-25 Ma) episode.

Two samples (109 and 111) could both be interpreted as trending almost E-W.
Marrett et al. (1994) gave estimated shortening slightly further south, almost in the
Sierras Pampeanas, of ~107° for strike-slip faults initiated 2 Ma. Mid-Miocene fault data
also show E-W shortening south of the Santa Barbara System (Allmendinger et al.,

1989). These estimates and shortening trends match the results for samples 109 and 111.

85

Shallow earthquakes listed in the Harvard Centroid Moment Tensor catalog (e.g.,
Ekstrom et al., 2005) from the study area indicate roughly E-W compression
(compression axis trends of 64-106°, with an average of 90°:t15°) (Figure 29). These
shallow crustal earthquakes are thought to be occurring as a result of the current thick-
skinned deformation in the south that often incorporates basement rocks (Oncken eta1.,

in press).

86

 

67°W 66°W 65°W 64°W 63°

 

BOL

0. °/\‘\

IVIA

 

J/
2002-05-

ARGENTINA

 
 
  
  

04

 

 

zoos-03.31
199 9-12.30

   

 

2005-03-31

 

 

1993-10-02
0

 

 

 

 

 

 

 

 

W
20° S

21°S

22° S

23° S

24° S

25° S

26° S

Figure 29 Earthquake epicenters for the study region, magnitude
4.1-6.3 (USGS NEIC). Best-fit double couple solutions
(compressional quadrant solid) from moment tensors show an E-W
compression (From Harvard Moment Tensor Catalog,

www.seismology.harvard.edu).

87

Chapter 8 Conclusions

1) Plate convergence parallel samples match derived velocity vectors for both 25-10 Ma
deformation and 10-0 Ma deformation, and are consistent with estimated plate
convergence directions.

a) NNE shortening trends are suggested to have formed pre-25 Ma when plate

convergence had a more northerly azimuth then at present.

b) E-NE shortening trends are accounted for by post-10 Ma plate convergence

estimates and are consistent with local post-10 Ma derived velocity vectors.

2) The non-plate convergence parallel samples are associated with four deformational
episodes and have shortening orientations that are generally in agreement with prior fault
kinematic studies.
a) A deformational event dated pre 10-Ma is associated with NNW shortening
during the creation of the fold system in the Eastern Cordillera.
b) A 10-2 Ma deformational event is associated with WNW shortening and is
suggested to have resulted from velocity differences associated with block
motions.
c) A deformational event suggested to have occurred at 2-3 Ma with N-S
shortening, could be due to local extrusion during the closing of the Salta Rift.
d) A post-2 Ma deformational event that is associated with E-W shortening is due

to recent thrusting found in the study area.

88

3) Classification of samples as pre- or post-folding fit well with the deformation episodes
(25-10 Ma and 10-0 Ma), as well as with Allmendinger’s (1997) multi-phase deformation

theory (10-2 Ma and ~2-0 Ma).

4) More detailed studies conducted on a smaller scale are needed to more adequately

constrain timing, spatial extent and orientation of deformation.

5) The use of microstructures, such as calcite twins, to interpret regional kinematics was
found to give good results when compared to other types of kinematic studies for the

Central Andes. The results gave good insight into the smaller scale kinematics and often
showed local deformation trends. Hopefully, this positive correlation will encourage the

use of calcite twin analysis in other areas.

89

Appendices

90

Appendix A

Rotating Thin Seem into New Coordinate Systems

In order to evaluate data from several thin sections simultaneously, they all must
be referred to in the same coordinate system (Groshong, 1984). This referenced system is
that in which the final strain calculations in TWINST are made. This is accomplished by
first, defining one thin section as the reference coordinate system (Figure 17). The long
side of the referenced thin section is always defined as the positive x direction of a right-
handed coordinate system. The orientation of a vector is specified with respect to the
reference system in terms of its directional angles, al,,Bl, and 7,, from which the
directional cosines to be entered into TWINST can be computed as: cos a,, cos A, and
cos 7, (Figure 17).

Next, the rotated coordinate system is found for the remaining slides of that
sample. The rotated coordinates are described in terms of the reference system by using
the direction angles from the reference system axes to the rotated system axes (Groshong,
1984). The angles between the reference and rotated coordinate axes are then used to
determine the corresponding direction cosines for each slide of a sample. These are then

entered into TWINST (Groshong, 1984).

91

Appendix B: Programs ROTATE and TWINSTS

PROGRAM ROTATE
THIS PROGRAM CALCULATES THE DIRECTION COSINES NEEDED FOR
ROTATION IN "TWINST." TO GET THE RESULTS IN GEOGRAPHIC
COORDINATES (+X = N, +Y = E, +Z = DOWN)
THE THIN SECTION COORDINATES ARE +XI = U-STAGE NORTH

+YI U-STAGE EAST

+ZI = U-STAGE DOWN
TO READ IN AS GEOGRAPHIC COORDINATES,(AZIMUT OF XI=AZXI,
DIP OF XI=DIPXI,ETC.), LOWER HEMISPHERE!
NEGATIVE AXIS ARE CARACTERISED BY A NEGATIVE SIGN OF THE

AZIMUT.(FOR EXAMPLE: NEGATIVE XI-AXIS DIRECTION = U-STAGE SOUTH

=251./60. => AZXI=-251. DIPXI=60.)
CHARACTER FILENAMEI*15, FILENAMEO*15
DIMENSION SLIDENAM(3)

REAL AZXI,AZX,AZYI,AZY,AZZI,AZZ,DIPXI,DIPX,DIPYI,DIPY,DIPZI,DIPZ

REAL ALFA1,ALFA2,ALFA3,BETAl,BETA2,BETA3,GAMA1,GAMA2,GAMA3
REAL AZ,B,C,D, P,Q,Y, ZI, YI,XI

WRITE (*,*) 'INPUT FILE NAME ='

READ (*,99) FILENAMEI
OPEN(UNIT=1,NAME=FILENAMEI,TYPE='OLD')
FORMAT(A15)

WRITE (*,*) 'OUTPUT FILE NAME ='

READ (*,99) FILENAMEO
OPEN(UNIT=2,NAME=FILENAMEO,TYPE='NEW')
READ(1,100)SLIDENAM
READ(1,200)AZXI,DIPXI,AZYI,DIPYI,AZZI,DIPZI
P=180./3.141592653589

Q=1./P

ZI=AZZI/ABS(AZZI)

XI=AZXI/ABS(AZXI)

YI=AZYI/ABS(AZYI)

AZ=ABS(AZZI)

IF(DIPXI.EQ.90.)GOTO 2
IF(DIPYI.EQ.90.)GOTO 2
IF(DIPZI.EQ.90.)GOTO 2
IF(DIPXI.EQ.O.)GOTO l
C=ABS(AZXI)-ABS(AZYI)
B=-l.*COS(C*Q)/TAN(DIPXI*Q)
DIPYI=P*ATAN(B)

DIPYI=ABS(DIPYI)
B=SIN(Q*DIPYI)/COS(Q*DIPXI)
IF(B.GT.1.)B=1.

IF(B.LT.-l.)B=-1.

A=ACOS(B)

C=ACOS(COS(Q*DIPXI)*SIN(A))
DIPZI=90.-P*C

DIPZI=ABS(DIPZI)

IF(DIPZI.GT.90.) DIPZI=l80.-DIPZI
B=-TAN(Q*DIPYI)/TAN(C)

IF(B.GT.1.)B=1.

IF(B.LT.-l.)B=-l.

AZZ=P*ACOS(B)

AZZ=ABS(AZZ)

AZZI=ABS(AZYI)+AZZ

92

IF(AZZI.GT.360.) AZZI=AZZI-360.
AZ=ABS(AZZI-AZ)

IF(AZ.GT.20.) AZZI=ABS(AZYI)-AZZ
IF(AZZI.GT.360.) AZZI=AZZI-360.
IF(AZZI.LT.O.)AZZI=360.+AZZI
AZZI=ZI*AZZI

WRITE(002,700) AZXI,DIPXI,AZYI,DIPYI,AZZI,DIPZI
AZX=AZXI

AZY=AZYI

AZZ=AZZI
IF(AZXI.LT.O.)AZX=-AZXI-180.
IF(AZYI.LT.O.)AZY=-AZYI-180.
IF(AZZI.LT.O.)AZZ=-AZZI-180.
ALFA1=COS(Q*AZX)*COS(Q*DIPXI)
ALFA2=COS(Q*AZY)*COS(Q*DIPYI)
ALFA3=COS(Q*AZZ)*COS(Q*DIPZI)
BETA1=SIN(Q*AZX)*COS(Q*DIPXI)
BETA2=SIN(Q*AZY)*COS(Q*DIPYI)
BETA3=SIN(Q*AZZ)*COS(Q*DIPZI)
DIPX=DIPXI

DIPY=DIPYI

DIPZ=DIPZI
IF(AZXI.LT.O.)DIPX=-DIPXI
IF(AZYI.LT.O.)DIPY=-DIPYI
IF(AZZI.LT.O.)DIPZ=-DIPZI
GAMA1=SIN(Q*DIPX)
GAMA2=SIN(Q*DIPY)
GAMA3=SIN(Q*DIPZ)
WRITE(2,300)SLIDENAm,ALFAl,BETAl,GAMA1,ALFA2,BETA2,GAMA2,
lALFA3,BETA3,GAMA3

FORMAT(3A4)
FORMAT(3(F5.0,F3.0))
FORMAT(1X,3A4,1X,'1',9F7.4)

FORMAT(1X,'ALPHA1 = ',F6.4,'ALPHA2 = ',F6.4,'ALPHA3 = ',F6.4)
FORMAT(1X,'BETA1 = ',F6.4,'BETA2 = ',F6.4,'BETA3 = ',F6.4)
FORMAT(1X,'GAMMA1 = ',F6.4,'GAMMA2 = ',F6.4,'GAMMA3 = ',F6.4)

FORMAT(1X,3(F7.2,'/',F6.2))
CONTINUE
END

93

PROGRAM TWINST
version neuchatel octobre 1982
minor changes feb. 1987 london ont.
(Eigen and Minv routines included in Program)
program by r.h. groshong
purpose: calculated best fit strain tensor from real
shear strain data

first card contains program options

explanation of program options:

idata = 1 print unchanged input data, =0 omit

igepsi = 1 print bearing and plunge of e,c and g axes, the
angle between c and e, and tanpsi/Z, =0 omit

ict = 1 compute and print compression and tension axes,
lamellae spacing index, = O omit

icon = 1 do spang numerical dynamic analysis, = O omit
important: ict must = 1 if icon = 1

idev = 1 print deviations of twinset strains from computed
strain tensor, = 0 omit

icompr = 1 for each data set read in a test value of the
strain tensor, use tofind expected values for
measured twin sets and compute deviations from
measured values. =0 omit.

second card contains special information
explanation of special information

ratio = fraction of actual twin per measured microtwin
thickness
ifudge = effective thickness of thick twins:
= 1 use outer thickness, = 2 use inner thickness
= 3 use average thickness, = 4 not defined properly

explanation of input data variables:
initialization cards, in order

slidea and slideb = thin section i.d. number:
irotat = 0 dont rotate, =1 rotate tocoordinate
system specified by the following direction cosines:
alphal betal gammal (cos from new +xyz axes to t.s. +x
alpha2 beta2 gamma2 (cos from new +xyz axes to t.s. +y
alpha3 beta3 gamma3 (cos from new +xyz axes to t.s. +2

cmbine= is deck to be combined with following deck?
if cmbine = 0 dont combine, = 1 combine with next data set

testtx,testy,testxy,testyz,testxz,testz,theta = optional:
see above test values are the strain components
as fractions indicated by the last letter(s).
theta is 2-d rotation required to put test values into
thin section coordinate system. no rotation, theta = 0

data card variables

grain = grain i.d. number. grain = 999. terminates input
for one slide. if next card is 1.,another data set
is read, if 999. program terminates.

cviv = optic axes, u-stage inner vertical

cvp = optic axes, u-stage n-s

kodec = optic axes, u-stage n—s direction code:
dip e = 2, w = 4

94

twiniv = twin pole, u-stage inner vertical
twinp = twin pole, u—stage e-w
kodee = twin pole, u-stage e-w direction code:
dip n = 1, s = 3
totalm = number ofmicrotwins in microns
thickm = measured thickness of microtwins in microns

totalt = number of thick twins

thicko = measured thickness of thick twins in microns
thicki = measured inner thickness of thick twins in microns
widthn = width of grain normal to win set in microns

widthp = width of grain parallel to twin set in microns

explanation of coordinate system

+x = long axis (length) of thin section = u-stage north

+y short axis (width) of thin section = u-stage east

+2 = normalto xy plane (thickness) of thin section =
u-stage down

additional note
the order of strain components in the subscripted variables
eslide and error is: l=x,2=y,3=xy,4=yz,5=xz,6=z, but in
slistr and conel is: x,xy,y,xz,yz,z (for input into
subroutine eigen)

THIS VERSION HAS HIS OWN EIGEN AND MINV SUBROUTINES!!!
THE ASSIGNMENT OF THE IPUT AND OUTPUTFILES IS INTERACTIV

dimension cviv(150),cvp(150),kodec(150),twiniv(150),
1twinp(150),kodee(150),totalm(150),thickm(150),totalt(150),
2thicko(150),pc(150),qc(150),rc(150),angle(150),
3angcve(150),thicki(150)

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
lgrain,slidenam(3),caxis,taxis,widthn,widthp

integer cmbine

INTEGER AJUN,BJUN,CJUN,DJUN,EJUN,FJUN,GJUN

*JUN = VARIABLES FOR CALCIT OUTPUT

CHARACTER DATAFILE*15,RESULTFILE*15,Resultfile2*15

WRITE (*,*) 'NAME OF INPUT FILE: '

READ (*,1000) DATAFILE

OPEN (UNIT=15,NAME=DATAFILE)

000 FORMAT(A15)

WRITE (*,*) 'OUTPUT FILE: '

READ (*,lOOO) RESULTFILE

OPEN (UNIT=18,NAME=RESULTFILE)

WRITE (*,*) 'File for "Calcite":'

READ (*,1000) RESULTFILE2

OPEN (UNIT=19,name=resultfile2)

read (15,106) idata,iegpsi,ict,icon,idev,icompr

106 format (i2,7x,5(i1,9x))

95

read (15,110)ratio,ifudge
110 format (f5.0,4x,i1)

26 nprev = l
nprev = combined number of twinsets in previous data set(s)
num = O
num = cumulative number of twin sets
27 read(15,10)slidenam,irotat,alpha1,beta1,gammal,
1alpha2,beta2,gamma2,alpha3,beta3,gamma3
10 format(3a4,1x,il,9f7.4)
IF(NPREV.EQ.1) THEN
write (19,1021) slidenam
ENDIF
1021 format(1x,'sample',3a4)

28 read (15,11) cmbine
11 format(il)

if (icompr) 132,132,130
130 read (15,131) testx,testy,testxy,testyz,testxz,testz,theta
131 format(f6.1,3x,f6.1,4x,f6.l,4x,f6.1,4x,f6.l,4x,f6.l,4x,f6.1)
132 continue

n = num + l
3 read(15,1)grain(n),cviv(n),cvp(n),kodec(n),twiniv(n),twinp(n),
1kodee(n),totalm(n),thickm(n),totalt(n),thicko(n),thicki(n),
2widthn(n),widthp(n)
1 format(3f6.2,i1,2f6.2,i1,5f6.2,f7.1,f6.2)
if(grain(n)-999.)2,4,2
2 n=n+1
goto 3
4 num=n-l

numb=num-nprev+1
if(idata) 100,100,101
101 write(18,102) slidenam,numb
102 format(1h ,'thin section ',3a4,5x,'number of twin sets is ',i6)
write(18,103)
103 format(1h ,'grain',3x,'optic axis orientaion',2x,'twin set orient
1ation',5x,'microtwins',12x,'thick twins',22x,'grain widths'/
21h ,10x,'inner vert',2x,'plunge‘,5x,'inner vert',2x,'plunge',3x,
3‘number thickness',2x,'number outer-inner
thickness',4x,'normal to
4, parallel to twin'/)
do 104 i=nprev,num
104 write(18,105)grain(i),cviv(i),cvp(i),kodec(i),twiniv(i),twinp(i),
1kodee(i),totalm(i),thickm(i),totALt(i),thicko(i),thicki(i),
2widthn(i),widthp(i)
105 format(1h ,f5.l,8x,f4.0,5x,f3.0,2x,i1,8x,f4.0,5x,f3.0,2x,i1,5x,
1f4.0,f7.2,6x,f4.0,2f7.2,15x,f6.0,6x,f6.0)
if(irotat.eg.0) go to 100
write(18,107)alpha1,beta1,gamma1,alpha2,beta2,gamma2,

1alpha3,beta3,gamma3
107 format(1h ,'data will be rotated according to the following
direct
lion cosines'/lh ,
2'11 = ',f8.4,4x,'m1 = ',f8.4,4x,'nl = ',f8.4/1h ,

96

3'12 = ',f8.4,4x,'m2 = ',f8.4,4x,'n2 = ',f8.4/lh ,
4'13 = ',f8.4,4x,'m3 ',f8.4,4x,'n3 ',f8.4)

calculate bearing and plunge
danger for systematic orientation error see fn. bearin
100 do 5 i=nprev,num
cviv(i)=bearin(cviv(i),kodec(i))
5 twiniv(i)=bearin(twiniv(i),kodee(i))
cviv and twiniv are now bearings in degrees
variables kodec and kodee are not used past this point

do 6 i= nprev,num
call dircos(cviv(i),cvp(i),pc(i),qc(i),rc(i))
6 call dircos(twiniv(i),twinp(i),dirce(i,l),dirce(i,2),dirce(i,3))

rotate to different coordinate system if required
if(irotat) 33,33,31

31 do 32 i=nprev,num
call rotate(pc(i),qc(i),rc(i),alpha1,a1pha2,alpha3,
1beta1,beta2,beta3,gamma1,gamma2,gamma3)

32 call rotate(dirce(i,1),dirce(i,2),dirce(i,3),
1alpha1,alpha2,alpha3,beta1,beta2,beta3,gammal,gamma2,gamma3)
all directions are in the different coordinate system past here

33 continue

find the acute angle between cv and e in radians (angcve)
do 7 i=nprev,num
a=pc(i)*dirce(i,1)+qc(i)*dirce(i,2)+rc(i)*dirce(i,3)
angle(i)=57.2957795*arcos(a)

check to see that angle between optic axis and e is acute
if(angle(i)-90.)136,136,135
135 pc(i)=-pc(i)
QC(i)=-QC(i)
rc(i)=-rc(i)
136 continue

7 angcve(i)=arcos(abs(a))
do 40 i=nprev,num
call strain(thickm(i),totalm(i),thicko(i),thicki(i),totalt(i),i)
40 call gaxis(pc(i),qc(i),rc(i),dirce(i,1),dirce(i,2),dirce(i,3),
1angcve(i),dircg(i,1),dircg(i,2),dircg(i,3))

if (iegpsi) 112,111,112
112 write(18,8) slidenam,numb,ratio,ifudge
8 format(1h ,'slide ',3a4,’ number of twin sets is',i5,' thicktwi
ln/microtwin ratio = ',f5.3,' thick twin option is ',il)
if(irotat.eq.0) go to 35
write(18,34)
34 format(1h ,'angles are with respect to rotated coordinate

system’/
1)
35 write(18,30)
3O format(1h ,'grain',3x,'bearing c plunge c',4x,'bearing e
plu
lnge e',4x,'angle(c,e)',4x,'bearing g plunge g',7x,

2'tanpsi/2'/)

97

do 41 i=nprev,num
call bearpl(pc(i),qc(i),rc(i),bearc,plunc,kc)
call bearpl(dirce(i,1),dirce(i,2),dirce(i,3),beare,plune,ke)
call bearpl(dircg(i,1),dircg(i,2),dircg(i,3),bearg,plung,kg)
angce=angcve(i)*57.2957795
GJUN=NINT (GRAIN (I) )
if(GJUN.lt.10)GJUN=GJUN+1O
AJUN=NINT(BEARC)
EJUN=NINT(PLUNC)
CJUN=NINT(BEARE)
DJUN=NINT(PLUNE)
EJUN=NINT(BEARG)
EJUN=NINT(PLUNG)
write(19,422)GJUN,AJUN,BJUN,CJUN,DJUN,EJUN,FJUN
41 write(18,42) grain(i),bearc,plunc,beare,plune,angce,bearg,p1ung,
1tenshr(i)
42 format(1h ,f5.1,5x,f5.1,7x,f5.1,8x,f5.1,7x,f5.1,7x,f5.1,10x,f5.1,
17x,f5.1,9x,f9.7)
422 format(1h ,i2,2x,3(i3,2x,i2,3x))
111 continue

c find compression and tension axes, spacing index
if(ict)125,125,120
120 write(18,121) slidenam
121 format(1h ,13x,'dynamic analysis of thin section ',3a4/)
if (irotat.eq.0) go to 126
write(18,34)
126 write(18,122)
122 format(1h ,'grain',6x,'compression axes',9x,'tension axes',9x,
1'no. of lamellae'/
21h ,11x,'bearing plunge',7x,'bearing plunge',7x,'per
millimete
3r'//)
do 123 i=1,num
call ctaxis(pc(i),qC(i),rc(i),dirce(i,1),dirce(i,2),dirce(i,3),
1angcve(i),i)
call bearpl(taxis(i,1),taxis(i,2),taxis(i,3),btens,ptens,k)
call bearpl(caxis(i,1),caxis(i,2),caxis(i,3),bcomp,pcomp,k)
sindex=(totalm(i)+totalt(i))/(widthn(i)*0.001)
123 write(18,124) grain(i),bcomp,pcomp,btens,ptens,sindex
124 format(1h ,f5.1,7x,f5.1,4x,f5.1,9x,f5.1,4x,f5.1,13x,f5.1)

if (cmbine) 114,114,113
113 nprev=num+1

go to 27
114 continue

if (icon.eq.0) go to 125
call spang(num)

125 call data(num)
call regres(num,5)
call tidyup
call prin

if (idev) 141,141,140
140 call deviat(num)

98

141 continue

if (icompr) 134,134,133
133 call cmpare(testx,testy,testxy,testyz,testxz,testz,theta,num)
134 continue

final card is 999. to end run. 1. to begin again
read(15,50) finis
50 format(f10.1)
if (finis.NE.999.) GOTO 26
51 continue
52 format(1x,i3)
stop
end

function bearin(siv,kode)
this fn. only applies if iv reads 0 when the long axis of the
thin section is n-s in the microscope

go to(1,2,3,4),kode
1 bearin=180.-siv
if(bearin) 5,6,6
2 bearin=270.-siv
if(bearin) 5,6,6
3 bearin=360.-siv
if(bearin) 5,6,6
4 bearin=90.-siv
if(bearin) 5,6,6
5 bearin=360.+bearin
siv is stage inner vertical
kode is direction code, 1=n,2=e,3=s,4=w.
6 return
end

subroutine dircos(baring,plunge,p,q,r)
p=cos(plunge*.01745)*cos(baring*.01745)
q=cos(plunge*.01745)*sin(baring*.01745)
r=sin(plunge*.01745)

p=cos(vector,n), q=cos(vector,e.),r=cos(vector,down)
return
end

subroutine
rotate(p,q,r,a11,a12,al3,bet1,bet2,bet3,gam1,gam2,gam3)

rol=al1*p+a12*q+a13*r

rom=bet1*p+bet2*q+bet3*r

r = gam1*p+gam2*q+gam3*r

p = rol
q = rom
return

99

end

subroutine ctaxis(pc,qc,rc,pe,qe,re,angcve,n)
purpose: to calculate direction cosines of compression
and tension axes

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,taxis,widthn,widthp

find t axis
2 a=qc*re-qe*rc
b=pe*rc-pc*re
c=pc*qe-pe*qc
d=(a**2)+(b**2)+(c**2)
if(c) 6, 5, 6
c=.OOOOOOl
if(d) 3, 3, 4
d=.00001
angt=cos(45.*.0174533-angcve)
ya=(qc*c-rc*b)*.70711
yb=(rc*a-pc*c)*.70711
za=(qe*c-re*b)*angt
zb=(re*a-pe*c)*angt

AWONUI

taxis(n,l)=(ya-za)/d
taxis(n,2)=(yb-zb)/d
taxis(n,3)=-(a*(ya-za)+b*(yb-zb))/(c*d)

find c axis
angt=cos(45.*.0174533+angcve)
za=(qe*c-re*b)*angt

zb=(re*a-pe*c)*angt
caxis(n,l)=(ya-za)/d
caxis(n,2)=(yb-zb)/d
caxis(n,3)=-(a*(ya-za)+b*(yb-zb))/(c*d)
return

end

subroutine gaxis(pc,qc,rc,pe,qe,re,angcve,pg,gg,rg)

purpose: to calculate the direction cosines of a vector in the
g-glide direction (pg,qg,rg)

required input: pc,qc,rc;pe,qe,re;angcve

output: pg,qg,rg

find gaxis
2 coscvg=cos(90.*.0174533-angcve)
a=qc*re-qe*rc
b=pe*rc-pc*re
c=pc*qe-pe*qc
d=a**2+b**2+c**2

100

10

p..-

uh.

if (d) 3, 3, 4

d=.OOOOOl
rg=((pe*b-qe*a)*coscvg)/d
qg=((re*a-pe*c)*coscvg)/d
Pg=((qe*c-re*b)*coscvg)/d
return

end

subroutine bearpl(p,q,r,bearin,plunge,k)
PP=P

qq=q+.00001

rr=r
theta=57.29578*atan(pp/qq)
k=0

if(rr) 10,9,9

PP=‘P

qq=-q

rr=-r

k=1

if(pp) 4.1.1

If(qq) 3,2,2
bearin=90.-theta

go to 7

bearin=270.-theta

go to 7

if(qq) 3,2,2
d=57.29578*arcos(rr)
plunge=90.—d
plunge on lower hemisphere,k=0; upper hemisphere,k=1
return

end

subroutine strain(thickm,totalm,thicko,thicki,totalt,i)
purpose: generate strain due to twinning
tenshr is tensor shear strain

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,taxis,widthn,widthp

thickm=ratio*thickm
if (totalt) 6,5,6
go to(1,2,3,4),ifudge

thickt = thicko

go to 5

thickt=thicki

go to 5
thickt=(thicko+thicki)/2.
go to 5

thickt=5000.

tenshr(i)=.347*((thickm*totalm+thickt*totalt)/widthn(i))
return

101

end
subroutine data(n)

purpose: to calculate strain ccoefficient matrix in specified
coordinates for simple shear measurements, zero
volume change

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,taxis,widthn,widthp
dirce = direction cosines of e pole (11,m1,n1)
dircg direction cosines of g glide direction (11,m2,n2)

do 4 i=1,n
coefmx(i,1)=dirce(i,1)*dircg(i,1)-dirce(i,3)*dircg(i,3)
coefmx(i,2)=dirce(i,2)*dircg(i,2)-dirce(i,3)*dircg(i,3)
coefmx(i,3)=dirce(i,1)*dircg(i,2)+dirce(i,2)*dircg(i,1)
coefmx(i,4)=dirce(i,2)*dircg(i,3)+dirce(i,3)*dircg(i,2)

4 coefmx(i,5)=dirce(i,3)*dircg(i,1)+dirce(i,1)*dircg(i,3)

the coef are in order of ex,ey,exy,eyz,exz
return

end

subroutine regres(num,ncol)

purpose: least squares fit, givendata matrix (coefmx) and
measured variable vector (tenshr)

dimension coeftr(5,150),l(5),m(5),covect(25),xy(5)

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
lgrain,slidenam(3),caxis,taxis,widthn,widthp

calculate covariance matrix: (x'x) inverse
do 10 j=1,ncol
do 10 i=1,num
10 coeftr(j,i)=coefmx(i,j)
do 11 j=1,ncol
ji=(j-1)*ncol
do 11 i=1,ncol
zij=0.0
do 12 k=1,num
12 zij=coeftr(j,k)*coefmx(k,i)+zij
11 covect(i+ji)=zij
call minv(covect,ncol,d,l,m)

estimate model parameters: eslide
do 30 i=1,ncol
xy(i)=0.0
do 30 j=1,num
3O xy(i)=coeftr(i,j)*tenshr(j)+xy(i)

102

do 31 i=1,ncol
ii=(i-1)*ncol
eslide(i)=0.0
do 31 j=1,ncol
31 eslide(i)=eslide(i)+covect(j+ii)*xy(j)
eslide(6)=-eslide(1)-eslide(2)

calculate sse
yy=0.0
do 40 i=1,num
4O yy=yy+tenshr(i)**2
bxy=0.0
do 41 i=1,ncol
41 bxy=bxy+eslide(i)*xy(i)
sse=yy-bxy

calculate standard error for model parameters
order of error same as eslide
if(num-ncol) 45,44,45
44 varnce=0.0
go to 46
45 varnce=sse/float(num-ncol)
if(varnce) 58,46,46
46 jdiag=1
do 47 i=1,ncol
if(covect(jdiag))58,49,49
49 error(i)=sqrt(varnce)*sqrt(covect(jdiag))
47 jdiag=jdiag+1+ncol
error(6)=sqrt(error(1)**2+error(2)**2)

print out results
58 write(18,50) num
50 format(1h ,30x,'least squares strain calculation',5x,
1'no. of twin sets = ',i3//)
write(18,52) d

52 format(1h ,15x,'variance-covariance matrix',10x,'determinant =',
1e15.7/)
do 57 i=1,5

57 write(18,53) covect(i),covect(i+5),covect(i+10),covect(i+15),
1covect(i+20)

53 format(1h ,9x,5(e15.7,3x))
write(18,51) sse,varnce

51 format(1h ,11x,'sum of squares of error = ',f15.6,10x,
1'sample variance = ',f15.6/)
write(18,54)

54 format(1h //1h ,20x,'estimated tensor in slide coordinates:

extens
lion is +'/)
write(18,55) eslide

55 format(1h ,'ex=',e14.7,3x,'ey=',e14.7,3x,'exy=',e14.7,3x,
1'eyz=',e14.7,3x,'exz=',e14.7,3x,'ez=',e14.7)
write(18,56)

56 format(1h //1h ,25x,'standard error of strain components'/)
write(18,55) error
return
end

103

1
strai

1
3

16
17

subroutine tidyup

purpose: find principal strains in 3 dimensions

dimension slistr(6),prinax(9)

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,taxis,widthn,widthp

slistr(1)=eslide(1)

slistr(2)=eslide(3)

slistr(3)=eslide(2)

slistr(4)=eslide(5)

slistr(5)=eslide(4)

slistr(6)=eslide(6)

call eigen(slistr,prinax,3,0)

call bearpl(prinax(l),prinax(2),prinax(3),bear1,plung1,k1)
call bearpl(prinax(4),prinax(5),prinax(6),bear2,plun92,k2)
call bearpl(prinax(7),prinax(8),prinax(9),bear3,plung3,k3)
write(18,1)

format(1h ,//1h ,5x,'principal
ns',9x,'bearing',5x,'plunge'/)

write(18,2) slistr(l),bear1,p1ung1

write(18,2) slistr(3),bear2,p1ung2

write(18,2) slistr(6),bear3,plung3

format(1h ,6x,e14.7,12x,f5.1,6x,f5.1)

return

end

subroutine prin
purpose: find principal strains and axes in plane of thin section

angles are positive clockwise because of coordinate system

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,taxis,widthn,widthp

exy=eslide(3)

ex=eslide(l)

ey=eslide(2)
angrdn=(2.*exy)/(ex-ey)
twoang=atan(angrdn)
if(abs(angrdn)-1.5707963) 17,16,16
twoang=twoang+sign(.7853982,angrdn)
ang=twoang*57.29578/2.
fa=(ex-ey)/2.
radius=sqrt((fa**2)+exy**2)
center=(ex+ey)/2.
emin=center+radius
emax=center—radius

104

str

7

8

9

18

19

10

ll

14

print results

write(18,7) slidenam

format(//1h ,'strain in plane of thin section ',3a4,‘ tension is
l+'/)

write(18,8) emax

format(1h ,'maximum compressive strain = ',el4.7)
write(18,9) emin
format(1h ,'minimum compressive strain = ',el4.7)

if(ex-ey) 10,10,18
write(18,19) ang

format(1h ,'angle from y axis to maximum compressive strain axis,
lpositive clockwise = ',el4.7,' degrees')

go to 14

write(18,11) ang

format(1h ,'angle from x axis to maximum compressive strain axis,
lpositive clockwise = ',el4.7,' degrees')

return

end

subroutine deviat(i)

purpose: find expected value of strain in slide coordinates and
deviation from measured value

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
leslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,taxis,widthn,widthp

dimension adev(150),iadev(150)

write(18,2) slidenam

2 format(1h ,10x,'deviations of measured strains from calculated

lains for thin section ',3a4/
21h ,'grain',8x,'tanpsi/2',8x,'expected value',6x,'tanpsi/2 - e.v.
3'/)

do 311 n=1,i
expect=dirce(n,1)*dircg(n,1)*eslide(1)+
1dirce(n,2)*dircg(n,2)*eslide(2)+
2dirce(n,3)*dircg(n,3)*eslide(6)+
3(dirce(n,2)*dircg(n,3)+dircg(n,2)*dirce(
4(dirce(n,3)*dircg(n,1)+dircg(n,3)*dirce(
5(dirce(n,l)*dircg(n,2)+dircg(n,1)*dirce(n,
adev(n)=abs(tenshr(n)-expect)

,3))*eslide(4)+
,1))*eslide(5)+
2))*eslide(3)

SS

311 continue

call sort(adev,i,iadev)

do 3 n=1,i
expect=dirce(n,l)*dircg(n,1)*eslide(1)+
ldirce(n,2)*dircg(n,2)*eslide(2)+
2dirce(n,3)*dircg(n,3)*eslide(6)+

105

3(dirce(n,2)*dircg(n,3)+dircg(n,2)*dirce(n,3))*eslide(4)+

4(dirce(n,3)*dircg(n,1)+dircg(n,3)*dirce(n,1))*eslide(5)+

5(dirce(n,1)*dircg(n,2)+dircg(n,1)*dirce(n,2))*eslide(3)
dev=tenshr(n)-expect

do 312 key=1,i
if(abs(dev).eq.adev(key)) goto 13
312 continue

13 ikey=i-key+1

3 write(18,1) grain(n),tenshr(n),expect,dev,ikey
1 format(1h ,f5.1,5x,f14.9,5x,f14.9,6x,f14.9,i10)
return
end
subroutine cmpare(testx,testy,testxy,testyz,testxz,testz,theta,n)

purpose: find the expected values of twin-set strains froma test
value of strain tensor and their deviations from
measured values.

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,tacis,widthn,widthp

write (18,1) slidenam
1 format(1h ,10x,'deviations of measured strains from test-value
str
lains for thin section ',3a4///
21h ,20x,'the test value strain tensor is:'/)
write (18,2) testx,testy,testxy,testyz,testxz,testz,theta
2 format(1h ,'ex# = ',f7.4,' ey# = ',f7.4,' exy# = ',f7.4,
1' eyz# = ',f7.4,' exz# = ',f7.4,' ez# = ',f7.4//
21h ,10x,'the angle, positive counterclockwise in degrees, from
the
3 unprimed (thin section)'/1h ,21x,'to the primed coordinate
system
4 = ',f6.2///)
if(theta) 3,4,3
3 theta=theta*.01745329
ex=testx*cos(theta)**2+testy*sin(theta)**2+testxy*sin(2.*theta)
ey=testx*sin(theta)**2+testy*cos(theta)**2-testxy*sin(2.*theta)
exy=.5*sin(2.*theta)*(testy-testx)+testxy*cos(2.*theta)
go to 5
4 ex=testx
ey=testy
exy=testxy
5 eyz=testyz
exz=testxz
ez=testz
write(18,6)
6 format(1h ,20x,‘the test-value strain tensor in thin section
coord
linates is:'/)
write(18,7) ex,ey,exy,eyz,exz,ez

106

7 format(1h ,' ex = ',f7.4,' ey = ',f7.4,' exy = ',f7.4,' eyz =

1,f7.4,' exz = ',f7.4,' ez = ',f7.4///)
write(108,8)
8 format(1h ,'grain',8x,'tanpsi/2',8x,'expected value',6x,'tanpsi/2
1- e.v.'/)
sse=0.0
do 9 i=1,n
expect=dirce(i,1)*dircg(i,1)*ex+dirce(i,2)*dircg(i,2)*ey+
1dirce(i,3)*dircg(i,3)*ez+
2(dirce(i,2)*dircg(i,3)+dircg(i,2)*dirce(i,3))*eyz+
3(dirce(i,3)*dircg(i,1)+dircg(i,3)*dirce(i,1))*exz+
4(dirce(i,1)*dircg(i,2)+dircg(i,1)*dirce(i,2))*exy
dev=tenshr(i)-expect
sse=sse+dev**2
9 write(18,10) grain(i),tenshr(i),expect,dev
10 format(1h ,f5.1,5x,f14.9,5x,f14.9,6x,f14.9)
write(18,11)sse
11 format(///1h ,'sum of squares of error = ',f15.6)
return
end

subroutine spang(num)
purpose: calculate spang numerical dynamic analysis.

dimension conels(6),strain(150),prinax(9)

dimension dircg(150,3),dirce(150,3),tenshr(150),coefmx(150,5),
1eslide(6),error(6),grain(150),caxis(150,3),taxis(150,3),
2widthn(150),widthp(150)

common dircg,dirce,tenshr,coefmx,eslide,error,ratio,ifudge,
1grain,slidenam(3),caxis,taxis,widthn,widthp

9 do 10 n=1,num
10 strain(n)=1.0/float(num)
write(18,1l) slidenam,num
11 format(1h ,29x,'spang numerical dynamic analysis'/
11h ,22x,'thin section ',3a4,5x,'number of twin sets = ',i3/)
write(18,12)
12 format(1h ,10x,'nda x',11x,'nda xy',10x,'nda y',11x,'nda xz',10x,
1'nda yz',10x,'nda z'/)
13 do 14 n=1,6
14 conels(n)=0.0
do 15 n=1,num
conels(1)=conels(1)+(taxis(n,1)**2—caxis(n,1)**2)*strain(n)
conels(3)=conels(3)+(taxis(n,2)**2-caxis(n,2)**2)*strain(n)
conels(6)=conels(6)+(taxis(n,3)**2-caxis(n,3)**2)*strain(n)
conels(2)=conels(2)+(taxis(n,1)*taxis(n,2)-
caxis(n,1)*caxis(n,2))*
lstrain(n)
conels(4)=conels(4)+(taxis(n,1)*taxis(n,3)-
caxis(n,l)*caxis(n,3))*
lstrain(n)
15 conels(5)=conels(5)+(taxis(n,2)*taxis(n,3)-
caxis(n,2)*caxis(n,3))*

107

16

17

18
19

99

lstrain(n)

write(18,16) conels

format(1h ,7x,6(f11.7,5x))

call eigen(conels,prinax,3,0)

call bearpl(prinax(l),prinax(2),prinax(3),bear1,plungl,k)
call bearpl(prinax(4),prinax(5),prinax(6),bear2,plung2,k)
call bearpl(prinax(7),prinax(8),prinax(9),bear3,plung3,k)
write(18,17)

format(1h ,10x,'eigenvalues and eigenvectors'/

11h ,12x,'magnitude bearing plunge')

write(18,18) conels(l),bear1,plung1
write(18,18) conels(3),bear2,p1ung2
write(18,18) conels(6),bear3,plung3
format(1h ,11x,f10.6,2x,f7.1,lx,f6.1)
return

end

subroutine sort(v1,n,norder)
dimension v1(1),norder(1)

i=1

i=i+i
if(i.le.n)goto 1
m=i-1

m=m/2
if(m.eq.0)goto 99
k=n-m

do 4 j=1,k

l=j
if(l.lt.1)goto 4
if(vl(1+m).ge.v1(1))goto 4
x=v1(l+m)
ix=norder(1+m)
v1(l+m)=vl(l)
norder(l+m)=norder(l)
v1(l)=x
norder(x)=ix
l=l-m

goto 5

continue

goto 2

continue

return

end

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

C

SUBROUTINE EIGEN

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

10

SUBROUTINE EIGEN(A,R,N,MV)
DIMENSION A(l),R(l)
RANGE=1.0E-6
IF(MV-1) 10,25,10
IQ=-N

DO 20 J=1,N
IQ=IQ+N

DO 20 I=l,N

IJ=IQ+I

R(IJ)=0.0

IF(I-J) 20,15,20

108

15
20
25

3O

35

40

45
50
55
6O

62
65

68

7O
75

78

80
85

90
95
100
105
110

115
120

125

R(IJ)=1.0

CONTINUE

ANORM=0.0

DO 35 I=l,N

DO 35 J=I,N

IF(I-J) 30,35,30
IA=I+(J*J-J)/2
ANORM=ANORM+A(IA)*A(IA)
CONTINUE

IF(ANORM) 165,165,40
ANORM=1.414*SQRT(ANORM)
ANRMX=ANORM*RANGE/FLOAT(N)
IND=0

THR=ANORM

THR=THR/FLOAT(N)

L=1

M=L+1

MQ=(M*M-M)/2

LQ=(L*L—L)/2

LM=L+MQ

IF(ABS(A(LM))-THR) 130,65,65
IND=1

LL=L+LQ

MM=M+MQ
X=O.5*(A(LL)-A(MM))
Y=-A(LM)/SQRT(A(LM)*A(LM)+X*X)
IF(X) 70,75,75

Y=-Y

SINX=Y/ SQRT(2.0*(1.0+( SQRT(1.0-Y*Y))))
SINX2=SINX*SINX

COSX= SQRT(1.0-SINX2)
COSX2=COSX*COSX

SINCS =SINX*COSX
ILQ=N*(L-l)

IMQ=N*(M-1)

DO 125 I=l,N

IQ=(I*I-I)/2

IF(I-L) 80,115,80

IF(I-M) 85,115,90

IM=I+MQ

GO TO 95

IM=M+IQ

IF(I-1) 100,105,105
IL=I+LQ

GO TO 110

IL=L+IQ
X=A(IL)*COSX—A(IM)*SINX
A(IM)=A(IL)*SINX+A(IM)*COSX
A(IL)=X

IF(Mv-1) 120,125,120
ILR=ILQ+I

IMR=IMQ+I
X=R(ILR)*COSX-R(IMR)*SINX
R(IMR)=R(ILR)*SINX+R(IMR)*COSX
R(ILR)=X

CONTINUE
X=2.0*A(LM)*SINCS

109

Y=A(LL)*COSX2+A(MM)*SINXZ—X
X=A(LL)*SINX2+A(MM)*COSX2+X
A(LM)=(A(LL)-A(MM))*SINCS+A(LM)*(COSXZ—SINXZ)
A(LL)=Y
A(MM)=X
130 IF(M—N) 135,140,135
135 M=M+1
GO TO 60
140 IF(L-(N-1)) 145,150,145
145 L=L+1
GO TO 55
150 IF(IND-1) 160,155,160
155 IND=0
GO TO 50
160 IF(THR-ANRMX) 165,165,45
165 IQ=-N
DO 185 I=l,N
IQ=IQ+N
LL=I+(I*I-I)/2
JQ=N*(I-2)
DO 185 J=I,N
JQ=JQ+N
MM=J+(J*J-J)/2
IF(A(LL)-A(MM)) 170,185,185
170 X=A(LL)
A(LL)=A(MM)
A(MM)=X
IF(MV-1) 175,185,175
175 D0 180 K=1,N
ILR=IQ+K
IMR=JQ+K
X=R(ILR)
R(ILR)=R(IMR)
180 R(IMR)=X
185 CONTINUE
RETURN
END
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C SUBROUTINE MINV
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE MINV(A,N,D,L,M)
DIMENSION A(I),L(1),M(1)
D=1.0
NK=-N
DO 80 K=1,N
NK=NK+N
L(K)=K
M(K)=K
KK=NK+K
BIGA=A(KK)
DO 20 J=K,N
IZ=N*(J—1)
DO 20 I=K,N
IJ=IZ+I
10 IF( ABS(BIGA)-ABS(A(IJ))) 15,20,20
15 BIGA=A(IJ)
L(K)=I

110

20

25

30
35

38

4O
45
46
48
50

55

6O
62

65

7O

75

80

100

105

108

M(K)=J

CONTINUE

J=L(K)

IF(J-K) 35,35,25
KI=K-N

00 30 I=l,N
KI=KI+N
HOLD=-A(KI)
JI=KI~K+J
A(KI)=A(JI)
A(JI) =HOLD
I=M(K)

IF(I-K) 45,45,38
JP=N*(I-1)

DO 40 J=1,N
JK=NK+J

JI=JP+J
HOLD=-A(JK)
A(JK)=A(JI)
A(JI)=HOLD

IF (BIGA) 48,46,48
D=0.0

RETURN

DO 55 I=l,N
IF(I-K) 50,55,50
IK=NK+I
A(IK)=A(IK)/(-BIGA)
CONTINUE

DO 65 I=l,N
IK=NK+I
HOLD=A(IK)
IJ=I-N

DO 65 J=1,N
IJ=IJ+N

IF(I-K) 60,65,60
IF(J-K) 62,65,62
KJ=IJ-I+K
A(IJ)=HOLD*A(KJ)+A(IJ)
CONTINUE

KJ=K~N

DO 75 J=1,N
KJ=KJ+N

IF(J-K) 70,75,70
A(KJ)=A(KJ)/BIGA
CONTINUE
D=D*BIGA
A(KK)=1.0/BIGA
CONTINUE

K=N

K=(K-1)

IF(K) 150,150,105
I=L(K)

IF(I-K) 120,120,108
JQ=N*(K-1)
JR=N*(I-1)

DO 110 J=1,N
JK=JQ+J

111

HOLD=A(JK)
JI=JR+J
A(JK)=-A(JI)

110 A(JI)=HOLD

120 J=M(K)
IF(J-K) 100,100,125

125 KI=K-N
DO 130 I=l,N
KI=KI+N
HOLD=A(KI)
JI=KI-K+J
A(KI)=-A(JI)

130 A(JI) =HOLD
GOTO 100

150 RETURN
END

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
c

function arcos(x)
IF(X.GT.1.)X=1.
IF(X.LT.-1.)X=-1.
arcos=acos(x)
return
end

112

Appendix C Description of Measurements

Measuring the pole to the twin plane and c-axes

Measurements were taken by orienting twin lamellae parallel to the cross-hashes
by turning the inner circle on the U-stage. This orients that twin horizontally in space,
thus, relating the measurements to the thin section’s geographic coordinates. The twin
planes were next positioned as close to vertical as possible by rotating the slide along an
E-W horizontal axis using the tambour (Figure 23). This gives the measurement for the
pole to that twin-set in terms of azimuth and plunge amount. The poles to the e-planes
were recorded.

Next, the c-axis was found. The slide was returned to a horizontal position and
placed under cross polar light. A Berek compensator was inserted to determine the
rotational direction (clockwise vs. counterclockwise) for correct location of the vertical
extinction point. A reduction in color (according to the Michel-Levy color chart)
indicated a clockwise rotation, while an increase in color indicated a counterclockwise
rotation. Once the extinction point was reached in one dimension, the orientation of the
c-axis in 3D was then achieved by rotating both the tambour on an E-W axis, and the
goniometers pivotables on a N-S axis to find the point of total extinction. The c-axis

orientation was recorded in terms of azimuth and plunge.

113

Appendix D Full Data Results

114

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0.00
0.00
0.H0
0.00
0.00
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0.0

0.00H
0.0H0
0.H0
0.00H
0.0H
0.000
0.00
0.00

0.00

0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

0.0H

:oHuoom cHnu uo mHm>Hmcm UHEmcxu

0.0H0
0.0H0
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0.00
0.00
0.00
0.00
0.00
0.00
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0.00

167

001M000H0HH.0 INw 00100000000.01quw 0010000000H.0 I000 001M0000000.01I>x0 0010000000H.01I>m 001M0000000.0 wa

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000000.0 I monHuwb mHQEmm 000000.0 I neuum 00 mwumnvm 00 E50
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Ho1m00000HH.01 Houm0000000.0 Honm00000HH.0 H010000H00H.01 00100000000.0
00100000000.01 H01m00000HH.0 00+m0000000.0 H0100000000.01 H01m0000000.o
H01mH000000.0 H010000H00H.01 H01m0000000.01 00+m0000000.0 00+0000000H.01
H01m000000H.01 00100000000.0 H01m0000000.0 00+M000000H.01 00+000HHHOH.0
00+m0000000.o I quCHEumumu xHuumE wUCMHum>oo1mUCmHum>
00 I muom Cqu 00 .OC CoHumHCuHmo CHmuum mwumsvm ummmH

0.00 H.000 00000H.01
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N MUC ~> mUC Nx 06C 0 mUC 0x MUC x MUC
00 I mumm CH3» uo uwnESC 010cm COHuuom CHCu
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0.0 0.00 0.0HH 0.00 0.000 0.00
0.0 0.00 0.00 0.00 0.00H 0.00
0.0 0.00 0.0H0 0.00 0.00H 0.00
0.0 0.00 0.000 0.0 0.00H 0.00
0.H 0.00 0.00 0.0 0.00H 0.00
0.0 0.H0 0.00 0.00 0.H00 0.00
0.0H 0.00 0.00H 0.00 0.00 0.00
0.0H 0.0 0.000 0.00 0.000 0.H0
0.0 0.00 0.00H H.0H 0.H 0.00
0.0 0.00 0.00 0.0H 0.00H 0.0H
0.00 0.00 0.H00 0.00 H.00 0.0H
H.0 H.00 0.000 0.00 0.00H 0.0H
0.0H 0.00 0.000 0.0H 0.00H 0.0H
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0.0 0.00 0.000 0.00 0.00 0.0H
0.0H 0.00 0.00 0.0 0.00H 0.0H

168

0 00HO0H000.0 000000000.01 00000H000.0 0.0
0 00000H000.0 000000000.01 000000000.0 0.0
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HH 00000H000.0 000000000.01 000000000.0 0.0
0H 000000000.0 000H00000.01 000000000.0 0.0
00 0H0000000.01 000000000.0 0H0000000.0 0.H
0 00000H000.0 000000000.01 000H00000.0 0.00
0 000000000.0 000H00000.01 00H000000.0 0.00
0H 000000000.01 000000000.0 0000H0000.0 0.00
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0H 00000H000.0 000000000.01 0H0000000.0 0.00
00 000H00000.0 0H0000000.0 000000000.0 0.0H
00 000000000.01 000000000.0 000000000.0 0.0H
00 H00000000.0 0000H0000.01 HO0H00000.o 0.0H
0 000000000.0 0000H0000.0 00H000000.0 0.0H
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00 000000000.0 000000000.0 000000000.0 0.0H
H 00H000H00.0 00000H000.0 000000H00.0 0.0H
0H 00000H000.0 000000000.01 H00000000.0 0.0H
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00 0000H0000.0 HH0000000.0 000000000.0 0.0
00 000000000.0 H000HH000.0 00000H000.0 0.0
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169

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170

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171

.0 .00m 00.0 00.0 .o H0.0 .mN H .NH .omm N .NH .00 o.mN
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mnufifls» Cflfluo mCfl3u xUHEH mCfl3UOHUflE COHUQ UCUHHO Umm CH3U COflMUCflHHO WHXM UHUQO CHMHD
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m.mm m.wv 0.HHN m.MN v.mNm o.NN
m.mm h.mN m.mMH m.mm h.HmN N.mH
m.NH v.m m.HmH h.NN m.mw o.hH
b.wHH m.OH m.mmH v.mm H.Mb o.wH
0.00H m.bH m.mNm m.Hh h.HhH e.vH
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0.0m m.mH m.th m.or o.mv o.NH
b.mm m.mm o.Nvm m.MN m.mvH o.v
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172

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homoooo.o 0.mN >.Nm e.vN 0.0m N.0mm m.om 0.0 o.Hm
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173

n.0v
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000.H u oHumu cquouofls\c quonnu em

H0.0 .vN
H0.0 .mH
H0.0 .m

H0.0 .0H
H0.0 .N

H0.0 .w

H0.0 .h

H0.0 .
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0

H

HVNQ‘NMKOQOIDCDI‘O
HH

H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
Ho.o
H0.0
H0.0

NOG'LD
NHN

mmmcxoacu umnEdc
mcfizuOHUHE
«N
m.mm
m.mm
N.Hv
o.mN
H.HH
o.NH
m.mm
0.0m

0 mocsHQ w acaummn

o mocsHQ o ocaumwn :Hmuo

Emunxm mumcHUuoou Umumuou ou uuoamwu nufi3 mum meocm

mH nuwm Gas» uo uonesc NumoHcm wnHHm
momm.o I ma ono.o I m6 HmNH.o I mH
oooo.o I Nc mmmm.ou I NE vmmv.o I NH
NmmH.o I Hc vav.ou I H8 oomm.on I HH
mochou coHuuouHu ocHonH0u mcu ou ocHUuooum owumuou ma HHH3 mumn
m .mH .mHm N .NH .vm o.om
H .m .mbN N .NH .vm o.mN
H .HH .mMN N .e .Nom o.mN
H .HH .omH N .v .Nom o.NN
m .0N .mom N .om .mMN o.mN
H .m .NHm v .NH .nm o.mN
H .H .N v .NH .HHH e.vN
H .0 .me v .NH .HHH o.mN
m .w .vON v .nH .owN o.NN
H .mH .voH N .v .mHN 0.0N
H .mH .mmH N .vH .mnN o.mH
H .mm .mON N .VH .th o.>H
m .0N .mmH v .N .mnN o.mH
H .mH .NNN N .N .mmN e.vH
H .mH .mnH N .N .mmN o.mH
H .vm .bmH v .qm .an o.NH
H .vH .VVN v .vm .>MH 0.HH
H .h .NmH N .om .me o.OH
H .Nm .wMN N .om .va o.m
H .wN .HmH N .NH .mHN o.w
H .mH .voH N .NH .mHN o.m
m .NN .H v .H .HHH o.¢
m .NH .m¢ v .H .HHH o.m
H .NN .an v .mH .hn 0.H
CH3u
mmCSHQ uuw> noccH mOCSHQ uuw> u0CCH
coHum ucmHuo umm CH3u conucwHuo mem oHuao chuo
mH mumm CH3» uo umnasc NumoHcm coHuumm chu
m.>v w.m m.mm m.mmH o.Hm
>.>> o.mm m.o m.mmm 0.0m
m.mm r.hN h.hv r.hhH o.mN
m.qm o.>m o.N h.Nmm o.mN
v.0 H.om m.>m o.mmN o.NN
N.mN «.Nmm N.mo a.mmH o.mN
m.mo «.NH m.mH m.va e.vN
H.ov v.Nv m.mv m.mHN o.MN
v.0m m.Hm o.N o.hvm o.NN

m.MN

187

mmMHooo.o
mmOHooo.o
mhmoooo.o
mvaooo.o
mhmoooo.o
mmrHooo.o
vNONooo.o
mNmHooo.o
onoooo.o
Nvaooo.o
mwvHooo.o
mNmHooo.o
hmVHooo.o
homoooo.o
vmvoooo.o
mmNoooo.o
mmmoooo.o
mmNoooo.o
mbmoooo.o
vmooooo.o
wvaooo.o
mmpoooo.o
vmmoooo.o
HMNoooo.o

w.mm
m.HH
o.m

w.mH
m.mm
N.0w
m.vm
b.Hv
m.mN
m.MH
m.N

v.bN
N.mm
v.vN
m.HN
o.v

N.mm
H.ow
H.0H
m.hN
o.m

m.>m
m.mH
m.H

m.>HH
N.mH
h.vm
v.HmN
m.mmH
m.mmH
H.moH
m.m¢N
m.Hm
m.mH
H.mMH
m.Nm
m.me
w.mm
m.mom
v.mm
N.owN
m.mr
m.N¢N
r.hNH
m.HmH
H.HNm
H.No
m.m>N

omommomwmmvmmm

OWCDMNI‘MI‘MMNWOM

uwumEHHHHE uma

meHmEmH no

b.Hm
H.mN
b.0N
m.NN
w.ON
>.mN
m.NN
5.0m
m.mN
H.0N
N.®N
m.oN
0.HN
o.mN
m.mN
m.vN
N.mN
m.mN
v.rN
m.mN
v.MN
m.mN
m.mN
m.mN

.OC

H.mH
h.¢h
m.Hv
m.mv
m.mw
0.Hw
N.mN
h.Nm
m.N

o.Nm
o.mm
m.b

m.vH
N.mH

macsHa

w.mmm
N.HHm
m.mNm
m.v0N
m.mbN
N.h
m.mNm
m.oON
m.m
N.mm
o.mN
¢.mv
m.mON
H.mH

OCHumwn

mwxm COHmeu

m.mw
b.0H
m.wv
w.hN
m.N

w.mH
h.mv
H.wm
m.Nh
m.mv
H.mm
w.mN
h.Hv
H.mw

macsHQ

m.ooH
H.bhH
m.mNH
w.Hmm
m.NH

m.FMH
m.Nm

m.NNm
h.va
m.mNN
o.wON
m.mom
m.mom
o.mvH

mcHumwn

mmxm conmquEou

0.3.
0.2
0.:

00000000000
HNMVMF‘QO‘OHN
HHH

chuo

Emumxm ouMCHUuoou umumuou cu uomammu Sufi: mum mmHocm

NImOHcm
o.NN
H.N
H.mH

m.qu
m.moH
«.mvH
w.mmH
N.NoN
m.m>
e.vON
m.0¢m
H.NmH
N.va
H.mNN
m.mbH
h.>
>.HmH
N.HHN
o.hmH
m.mMH
m.mmH
m.mvH
m.>MN
m.mmN
m.vON
v.mmH
m.hmH

v.b

v.5

m.oH
m.oH
m.mm
h.mH
v.mH

0‘0"
NN H

Hr-immmm

(DIDLOCDCDNNNNWUDONOOO‘OQ'

\OCDGDKOKOFmeO‘ONIDNNCD

N

cofluumm :Hnu no mHm>Hmcm UHEdcxu

m.om

m.om

v.mrH
v.MbH
o.MVN
N.OVN
H.va
H.va
o.mN

h.mmN
b.00N
b.00N
m.hmH
r.hmH
r.th
v.va
v.va
h.mbH
h.th
m.mmN
m.mmN
b.va
h.¢wH
m.mHN

0.0m
o.mN
o.mN
o.NN
o.mN
o.mN
o.¢N
o.mm
o.NN
0.0N
o.mH
o.NH
o.mH
e.vH
o.MH
o.NH
0.HH
0.0H

OOOOOO
HMQ’IDWO‘

188

H.mm m.mNN Nmmhvo.ou

h.w o.Nm NmmmmN.o
wOGSHQ mcHummn wnsuwcoms
mnouow>cmem new mosHm>cmem

mewmvo.on NHoomHo.o vhmvmmo.o Nmmvao.ou ohmmNMN.o vomommH.o
N on: n» mug Nx mun > an: >x mu: x was
Hm I muwm cflzu no awnes: NumOHcm coHuomm cHsu
mmechm UHEmc>o HMUHumEsc ocmmm

o.oq m.mH o.mm N.om m.VHN 0.0m
N.Hm m.m m.¢m w.m m.mmm o.mN
h.mH v.w v.HmH o.mH >.mm o.mN
h.Hv m.H N.mmH m.mN m.MVN o.NN
>.mH o.mv N.NHN m.m m.mHH o.mN
0.0m >.vm H.mNN H.Hv 0.HOH o.mN
m.wm H.mN m.NmH m.mH h.Hm e.vN
o.mm r.hN m.mmH «.mN ¢.mom o.MN
m.mN n.mH m.v¢ w.>H v.mMH o.NN
¢.vv o.N o.H¢N m.HN m.Hmm 0.0N
>.Hv o.mH H.HmH e.vH o.th o.mH
m.mm m.n o.mHN v.Hm m.mHH o.>H
m.Nv h.wN n.0HN m.mq >.mmm o.mH
o.mN m.o b.00N H.mm 0.0HH o.¢H
m.NH m.o m.omm m.om m.omN o.mH
m.m m.Hm 0.HmH m.vN m.>mN o.NH
H.HH m.vm v.mnH m.NN «.mmN 0.HH
m.m m.Nm m.NmH o.mN e.vm o.oH
h.mH m.Nm m.00N H.nH H.mm o.m

m.H v.m m.m>N H.mv N.omH o.m

>.Hv N.wH H.NMN >.v m.mNm o.m

N.HN v.v w.vmm m.Hm o.mmN o.¢

m.nN o.N >.mmH o.NN >.moH o.m

>.w m.HN m.>mN H.mH «.mMH 0.H

m.mm m.>v m.m m.mm m.mmH o.Hm
m.mm >.nh o.mm m.o m.mmm 0.0m
n.Hv m.mm n.>N r.hv h.bhH o.mN
o.mN m.vm o.>m o.N >.Nmm o.mN
H.HH v.0 H.om m.>m o.mmN o.>N
m.NH N.oN v.Nmm N.mm m.mmH o.mN
m.mm m.mm v.NH m.mH m.va e.vN
0.0m H.ov v.Nv m.mv m.wHN o.MN
m.MN ¢.om m.Hm m.N o.hvm o.NN
m.mH v.v H.0NN m.vm m.mmm 0.0N
N.v o.mm m.bmH H.mH N.mHm o.mH
m.m m.vN o.>hH m.mm m.rmm o.mH
m.m v.vm m.vmm e.vm o.mmH o.>H

189

mommmoooo.o
mvvmmoooo.o
VONNHoooo.o
vawboooo.o
mmNNNHooo.o
omoomoooo.o
HNomwoooo.o

hmmeHooo.o
MMMHMNooo.o
HHthoooo.o
memNoooo.o
NmNNhoooo.o
mpmmvoooo.o
oorvmoooo.o

NlmoHcm

mwmuomu No+mm~mmvmm.o u

"NXO

voumememm.o Hum vOImVNmHth.o

'NXW

vouMmmmmme.o uNm voummmmomhm.o

oooooo.o
Helmhvommmw.o
HonmomhmeH.o
HOIMNHwNVHH.o
Houmommmmhm.ou
HoumthoHNH.o

Hm I mumm CH3» no

HN hmMNmoooo.o
m vmmthooo.o
mH homvmoooo.o
Hm mmvrcoooo.01
om bmmmvoooo.ou
Nm mmomvoooo.01
mm Hvamoooo.oI

.>.m I N\Hmacmu msH

mo:

m> Uwuumaxm Nxamacmu

cofiuumm CH3» Hem mcflmuum umumHsonu Ecuu mcamuum nousmmme uo mCOHumH>oU
mmHzxooHo w>HuHmoa .mew :Hmuum 0>HmmquEou Edsflxme cu mem > Eouu mHocm
I chuum m>HmmquEou ESEHGHE

ummOPmNH.o

Gwmuo

moumNFMNNvH.ou u chuum w>Hmmwuano Edefixme

+ mH concwu

h.mH
m.oo
N.mN

mmcsHQ

Vo-mvmomnmm.o unxo co-mmommmmm.o onw

muchOQEoo chuum no

vo-monvam.o «Nxm mo-mvamNHH.o "wa

+ mH concwuxw ”mmuMCHUuoou mUHHm

u mucmHum> mHQEmm oooooo.o
HoanmhmmNH.o HOIMNHvaHH.o Ho
oo+mmmommVH.o HoamHmNNmbH.o Ho
HoumHmNNmpH.o HonmNmoomom.o No
Honmvvmmmmm.on Noanthovm.on oo
HoanvomwwH.o moumwmmMNNm.o Ho

mo+mmonomm.o u acmCHEuoqu x

.oc coHumHsono chuum mmu

NumOHcm coHuumm cflnu no wCMHQ CH c
m.mmN moummwNVHmH.on
m.m>H monmNommHov.on
m.Hm monummvvmmH.o

ocflumwn mchuum HmaHocHum

voummoooomv.o n>w vouflmommNHm.

uOuum Unmucmum

vonmvthNHm.OIn>m vonmmmovhvw.

CH .HOmau UquEHumw

u uOuum no moumsvm wo Esm

Imommmmhm.ou HoumthoHNH.o
Imvvmmmmm.ou HonmoeommmH.o
ImHthovm.OI monmmmmMNNm.o
+m0NmvaN.o HQImoomhomm.on
Iwoomhomm.0I oo+m>mwvaH.o

HHUQE 00CMHHM>OUINUCMHHG>

msvm ummmH

w.H N.NNH NN¢PMN.OI

Hmuum

o xm

X0

0

190

mN
mm

NonmHooo.o
Hmthoooo.o

mmeNoooo.OI

mmoowHooo.o

mmmmooooo.ou

mmommHooo.o
mvommNooo.o
bmmNoHooo.o

mvamoooo.OI

movmoHooo.o
vomHmoooo.o
mommMHooo.o
v¢HNNHooo.o
mommooooo.o

mmONHoooo.OI

hmMNmoooo.o

NoHHmoooo.on

homHHHooo.o
hmmmooooo.o
Nmmmmoooo.o
ovbomoooo.o
HmomHoooo.o

mNhoooooo.0I
mvaNoooo.ou

mmbhmoooo.o
mmhmHHooo.o
mNmHhoooo.o
vmmmhoooo.o

mmmmmoooo.ol

hmanoooo.o
mNmHMNooo.o
mmmmmoooo.o
mmmomoooo.o
vawooooo.o

Hmmmvoooo.0I

mmmmmoooo.o

NNomHoooo.ou

HHmHmoooo.o
HomH¢oooo.o
mmmmNoooo.o

Hmhmooooo.ou

mmmNoHooo.o

whHNmoooo.0I

mNMHoHooo.o

mmooooooo.o
NomNmoooo.o
mHvaoooo.o

mHmmHoooo.OI

mmHhmoooo.o
bwmmooooo.o

Nmmmmoooo.0|

HNNomoooo.o
momNHHooo.o
mHmmvoooo.o
mthmoooo.o
mrmmmoooo.o
HhmmNoooo.o
NvHomoooo.o
mmvmmoooo.o

Ohvmmoooo.on

mmmmooooo.o

ommNmoooo.ou

wwmmmoooo.o

thNmoooo.o:

vvmhvoooo.o
mvmmmoooo.o
hHHhmoooo.o
mmmwvoooo.o
HHmhmoooo.o

NNHvooooo.ou

mmmNhoooo.o
mthooooo.o
Hvamoooo.o
mothoooo.o
Nvmhmoooo.o
H0@Mboooo.o
mmmvNoooo.o
wmhmmoooo.o
movowoooo.o

HHbVHoooo.OI

mmmvvoooo.o

vmmNNoooo.OI
MNNNNoooo.on
wowwooooo.on

mHNMNoooo.o

N®0Mboooo.on

omonoooo.o

wmvmvoooo.on

oommmHooo.o
mmmmoHooo.o
mmmhmoooo.o

mmmvaooo.o
mmmhmoooo.o
oommnHooo.o
bHvNONooo.o
mthmHooo.o
hmmomoooo.o
NNNvaooo.o
mmvaHooo.o
wthmHooo.o
thmvHooo.o
ombwmoooo.o
mbmmqoooo.o
hHmmNoooo.o
ommmmoooo.o
mewNoooo.o
mmmhmoooo.o
wvaooooo.o
mwmvaooo.o
wowmroooo.o
mmmwmoooo.o
MMHMNoooo.o
hwmmHHooo.o
hmmmHHooo.o
mmmvaooo.o
omhmmoooo.o
mmmmmoooo.o
mummvoooo.o
wammNooo.o
oommrHooo.o
bmmomoooo.o
thwvoooo.o
wm¢vHoooo.o
thmHoooo.o
memNoooo.o
hHmwNoooo.o
mNNmHoooo.o
mbNmHoooo.o
mmvaoooo.o
hHmmNoooo.o
hHmmNoooo.o
mmmbmoooo.o

0.0m
o.mN
o.mN

o.hN
0.0N
o.mN
e.vm
o.mm
o.NN
0.0N
o.mH
o.NH
o.mH
o.vH
o.MH

COO
OHN
Hr-Gr-O

OHHMVLDWQ

(nan
NNMM

000000000

0

o.bN
o.mN
e.vN
o.MN
o.NN
0.0N
o.mH
o.NH
o.>H
o.mH
o.mH
o.vH
o.NH
0.HH
0.0H
o.m

191

mhmoooo.o m.m h.an m.MN m.wH n.qh m.mH m.mm 0.HH
wmmoooo.o o.hm w.mNN >.MN m.mm m.NoH H.Hm o.mNH o.m
hmHHooo.o m.om N.mm v.mN m.mm m.mmH H.Hm o.mNH o.m
mhmoooo.o 0.HN m.mvm N.HN m.mm H.om m.mv m.mw o.n
maHoooo.o m.N m.ovN m.mN v.N m.omH 0.0 o.mNH o.m
wmmoooo.o >.Hm m.hmH m.MN H.NH m.mmN m.o o.mNH o.m
mmmoooo.o e.vN m.NHN o.mN v.mw o.mN m.ov m.mN o.m
mmHoooo.o m.mw m.me H.MN H.mH m.MN m.ov m.mN o.N
>mmoooo.o v.mm m.mwN H.om o.>H m.me v.m o.mNm o.H
N\Hmmcmu o mocsHQ o acaummn Hm‘ovaocm m was DHQ m acHumwn o oocsHQ u mcaumwn chuo

Emumxm mumCchooo umumuou ou uumammu nuflz mum mmHocm

H mH coHuao cqu HoHnu 000.H u oHumu cquoHUHe\c ququcu mN mH mumm cqu H0 Hones: H-0HHcm mcHHm
ommm.o- u m: mmov.o n ma loH.o- u mH

oooo.o u «a omvm.o- «2 >mmm.o- n NH

ooom.o- a He mmHm.o- u H5 Nwmm.o a HH

mwchoo coH uuwuHu ocHonH0u mnu ou ocHUuooum vmumuou ma HHHs mumu
.o .ovN 00.0 00.0 .o Ho.o .v H .NH .on v .om .0HN 0.0m
.o .ovN 00.0 00.0 .o Ho.o .m H .mm .NnN v .om .oHN o.mN
.o .oom 00.0 00.0 .o H0.0 .N m .NN .omN N .oH .owH o.>N
.o .oom 00.0 00.0 .o Ho.o .m m .mH .mnN N .oH .owH o.wN
.o .0NH 00.0 00.0 .o Ho.o .N H .ov .ovm v .wN .vnN o.mN
.o .ow 00.0 00.0 .o Ho.o .H m .0 .0H v .¢N .vhN o.¢N
.o .omH 00.0 00.0 .o Ho.o .v H .vm .wNN N .Nm .mvm o.mN
.o .0NH 00.0 00.0 .o Ho.o .v m .NN .vm v .m .mvH 0.HN
.o .omH 00.0 00.0 .o Ho.o .N m .om .N@ v .m .qu 0.0N
.o .omv 00.0 00.0 .o Ho.o .m H .0N .NN N .o .oNH o.mH
.o .om 00.0 00.0 .o Ho.o .N H .o .mm c .mN .mvm o.mH
.o .ovN 00.0 00.0 .o Ho.o .m H .w .0NN v .m .NmH o.mH
.o .oom 00.0 00.0 .o Ho.o .N H .oH .oHN v .oH .th o.mH
.o .oom 00.0 00.0 .o H0.0 .N m .NN .vnH v .oH .me o.VH
.o .oom 00.0 00.0 .o Ho.o .m H .vN .vNN v .vH .mOH o.MH
.o .ovN 00.0 00.0 .o Ho.o .N m .o .mmH v .oH .omN o.NH
.o .OVN 00.0 00.0 .o Ho.o .q H .m .wNm v .oH .omN 0.HH
.o .omH 00.0 00.0 .o Ho.o .N H .m .va v .NN .NOH o.m
.o .0NH 00.0 00.0 .o Ho.o .v H .mH .mHN v .NN .NoH o.m
.o .0NH 00.0 00.0 .o Ho.o .N H .m .va N .0N .wMN 0.5
.o .omH 00.0 00.0 .o Ho.o .H H .0N .vv N .mN .bOH o.m
.o .omH 00.0 00.0 .o Ho.o .N m .Nv .vhH N .mN .hOH o.m
.o .omH 00.0 00.0 .o Ho.o .N H .om .ovH ¢ .om .om o.m
.o .omH oo.o 00.0 .o H0.0 .H H .vH .NOH v .om .om o.N
.o .0NH oo.o oo.o .o Ho.o .m H .H .Nm v .mN .mom o.H
cqu Ou HmHHmuma .ou Hmsuoc mmmconzu uwCCHnuwudo amass: mmmcxownu umnESG mocsHQ pum> uwccH wondHa uuw> uwccH
mcuUHz :Hmum mCqu HUHnu mCquouoHE coHum ucmfiuo umm CH3» conucwHuo mem UHqu CHmuw

mN mH muwm cqu no uwnESC HuoHHcm coHuomm CH2»

192

mbmoooo.o
vmvoooo.o
HMNoooo.o
bvmoooo.o
mhmoooo.o
mbmoooo.o
Hhhoooo.o
hmHHooo.o
mmmoooo.o
hHNoooo.o
hmHHooo.o
HOMHooo.o
Hmmoooo.o
Hmmoooo.o
mhmoooo.o
mmNoooo.o

w.Hm
m.wm
m.o

m.Nv
N.ov
«.mm
w.wH
h.wm
m.VN
m.mm
h.Mb
m.>H
m.om
m.>N
m.b

m.HN

H

v.mHN
N.voH
H.mvN
m.MNH
m.VNH
m.m®N
H.ww
m.mH
m.vom
m.NMN
o.Nv
P.mm
o.NwN
o.mmH
b.Nb
m.NNN

0.0H
h.mH
>.wH
N.NN
m.mm
H.HH

\0

II...
1‘!“
mm

H

0..
HMI—IH

HHWI‘MHI‘MI‘I‘I‘WMN
HHmKOMv-{kaDKDKD

HH

0
m
N

mquHHHHE uma

mmHHmEMH no

m.ON
v.vN
w.NN
v.0N
h.mN
h.vN
m.wN
o.MN
w.MN
m.HN
o.mN
m.HN
m.m~
H.mN
m.wN
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0.. ICIOIOCOOC
VQMQ

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ONONMI‘O‘IOLDLHNOMMON

oo.o
vmm—I

\DmmmVHOHVHWI‘va—Cm

NH

mwcsaa

N.mmH
h.mNH
m.th
n.0NN
m.mbH
N.mmH
o.mmH
m.mmm
v.mmH
b.MHH
H.mvH
>.HHH
N.mh

H.NNH
m.me
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H.Hm

m.mmN
N.mvH
h.om

m.H¢
m.HHm

acaummn

mwxm COfimcwu

mocsaa

0.00

o.MMN
v.omH
H.©OH
m.mh

v.mmN
m.va
w.mmH
o.v0H
m.m0N
m.va
m.mHN
N.MhH
v.0m

e.va
H.mmH
o.omH
m.mmH
N.HvN
m.mHN

h.mmH
m.oHN

ocHummn
mwxm conmmuQEoo

CHmuo

Emumxm wumcHUuoou vmumuou ou pumamwu nufiz mum mmHmcm

HloHHcm
v.5
m.Hm
m.H
m.mH
m.HH
m.mN
m.om
H.mv
m.mm
o.m
0.0H
H.mN
N.mm
m.h
m.Nv
h.mN

m.oo

m.NNN
m.mmm
m.mH

m.er
m.HNH
m.th
v.hmH
v.NmH
m.OMH
m.mmH
m.mmH
H.th
v.v0H
H.0hH
m.mHH

m.NH
o.NH

h.mH
h.mH
H.Nv
m.mH

coauomm :ch wo mHm>Hmcm UHEmc>U

m.mMN
m.mMN
m.bhH
m.hhH
b.MHH
h.MHH
b.50N
m.OhH
w.ohH
h.mvH
m.mmm
N.mbH
b.bNH
r.hNH
m.MMH
m.mm

0.0m
o.mN
o.NN
o.mN
o.mN
e.vN
o.m~
0.HN
0.0N
o.mH
o.mH
o.mH
o.mH
o.vH
o.MH
o.NH

193

mnmoooo.o m.mm m.on m.MN 0.mm N.0NH m.om m.MNH o.m
hmHHooo.o m.0 N.mvH 0.0N m.Nm n.0vm v.0m 0.Nmm o.m
mnmoooo.o m.>m m.mb «.NN m.ov m.mom «.mm 0.Nmm o.N
mNnoooc.o H.hH v.mv m.vN o.mm o.omN m.m0 0.mmm 0.0
mmNoooo.o o.H >.HHm q.eN 0.0p H.0v m.m0 0.mmm o.m
mmNoooo.o m.om v.>¢ 0.MN e.vm 0.HON m.Nm N.mVN o.v
vaHooo.o N.vH 0.ovN 0.¢N o.mv m.mMH N.mw m.H>H 0.H
N\Hmacmu o wucsHa o UGHummn Hw.ovaocm m mu: sHQ m ocwummn o omcsHQ u ocHumwn chuo

Emum>m wumcHUuoou Umumuou ou uuwmmwu :qu mum mmHocm

H mH COHqu CH3» onnu 000.H u OHuwu GquOHUHE\c H3uon£u vN mH muwm CH3» Mo Hwnfidc NI0HHcm mUHHm
0000.0 I ma 0Nvm.0| n ME bmm0.0l u MH
0000.0I I NC 000v.0 u N6 0HhH.0I u NH
000m.0 u H: 0MH0.0 n H8 N0mN.0I n HH
mwGHmOU GOH uuwuflfl OCfi3OHHOM 05H 0“ OGHUHOOUM EmuMUOH wfl HHH3 MUMU
.0 .00H 00.0 00.0 .0 H0.0 .N m .mv .0NH N .0m .00 0.Hm
.0 .00m 00.0 00.0 .0 H0.0 .H m .NM .000 N .Nv .NmN 0.0m
.0 .00m 00.0 00.0 .0 H0.0 .MH m .Nm .Nm N .Nv .NmN 0.0N
.0 .0NH 00.0 00.0 .0 H0.0 .N H .vN .NmH v .NN .00 0.0N
.0 .0NH 00.0 00.0 .0 H0.0 .N m .0 .0mm v .NN .00 0.5N
.0 .0Nv 00.0 00.0 .0 H0.0 .m H .VN .0NN N .0v .00N 0.0N
.0 .0Nv 00.0 00.0 .0 H0.0 .wH m .00 .mmm N .0v .00N 0.vN
.0 .00m 00.0 00.0 .0 H0.0 .m m .0H .0N N .Nv .mvm 0.MN
.0 .0NH 00.0 00.0 .0 H0.0 .H m .NN .vm v .0N .00H 0.HN
.0 .omv 00.0 00.0 .0 H0.0 .v m .vH .vNH N .Nm .mv 0.0N
.0 .0vm 00.0 00.0 .0 H0.0 .MN m .0N .00H N .Nm .mv 0.0H
.0 .v0 00.0 00.0 .0 H0.0 .H m .0H .NmH v .HH .00m 0.0H
.0 .0NH 00.0 00.0 .0 H0.0 .v H .NH .NNN v .HH .00m 0.hH
.0 .vN 00.0 00.0 .0 H0.0 .H H .NH .00H v .VN .05 0.vH
.0 .0NH 00.0 00.0 .0 H0.0 .m m .0H .0N N .ov .mwm 0.NH
.0 .0NH 00.0 00.0 .0 H0.0 .0 m .00 .00H N .ov .mvm 0.HH
.0 .00m 00.0 00.0 .0 H0.0 .MH m .N .00H N .NH .HhN 0.0H
.0 .00m 00.0 00.0 .0 H0.0 .m H .0 .v0N N .NH .HhN 0.0
.0 .0NH 00.0 00.0 .0 H0.0 .v H .0 .v0 v .NN .00N 0.0
.0 .0NH 00.0 00.0 .0 H0.0 .N H .wH .00H v .NN .0mm 0.b
.0 .OVN 00.0 00.0 .0 H0.0 .m m .0 .NNN v .0N .mvm 0.0
.0 .0vN 00.0 00.0 .0 H0.0 .N m .NH .vMN v .0N .mvm 0.0
.0 .OVN 00.0 00.0 .0 H0.0 .N H .0H .NNN N .vm .0H 0.v
.0 .00H 00.0 00.0 .0 H0.0 .h H .0H .00H N .0m .hom 0.H
CH3.» OH HwHfimHMQ .0H HQEHOC mmev—UMEU HQCCHIHwUHHO HwQSHHHC mmmeUflSU HwQEDC MOGDHQ UHw> HNCCH OOCDHQ UHO> HOCCfl
mEUUHHJ CHMHO mCfi3u xUflfiu mCH3UOHUHE GOHUM UCOHHO umm CH3U COHMUCQHHO mflxm UHUQO CHMHO
@N mfi muwm EH3“ HO HQQHEHC NIOHHGQ COfluUOm CHEM“
b.0H N.hm N.0MN b.Nm e.v0 0.0m
m.NH H.¢ H.Nb 0.mm 0.b0H 0.0N

h.0 v.m 0.00N 0.0 v.0mN 0.bN

194

0.0H 0.VH N.00H 0.vv 0.00 0.0N

b.0H 0.0H >.mNH 0.0m o.MMN o.mN
b.0H m.mH m.>mN v.00 v.00H o.eN
N.NN 0.0H m.0NN m.0m H.00H 0.MN
m.mm m.v m.m>H m.h0 0.0N 0.HN
H.HH H.m N.00H m.>¢ ¢.mmN 0.0N
N.0 N.mv 0.m0H H.mN m.va o.mH
m.mm w.mm m.mmm N.mm 0.mmH 0.0H
m.nm v.0 v.0mH m.mm e.voH 0.0H
v.0 0.N b.mHH m.om 0.00N o.mH
v.0 H.mN H.0vH «.mH m.va e.vH
>.0H v.mm >.HHH m.NN m.mHN o.mH
m.m H.m N.m> 0.5m N.m>H o.NH
b.0H o.mH H.NNH m.v v.0m 0.HH
H.HH H.>m m.m0H 5.0 v.me o.m
m.mm v.mm 0.Nm m.v H.mmH 0.0
b.0H m.Nv H.Hm 5.0 0.0mH 0.5
0.m m.o m.mmN >.m m.mmH 0.0
H.HH m.NH N.MVH m.Hm N.HvN o.m
H.HH 0.0N 5.0m m.m0 m.mHN o.m
0.m N.H0 m.Hv 0.0N n.mmH o.N
o.mN v.mH m.HHm N.0v m.OHN 0.H
u mquHHHHE uwa mocsHQ ocHummn mocsHQ mcHumwn
meHwEmH we .0: mmxm concwu mmxm conmmuQEou chuo

Emumxm wumCHnuoou UmumuOH ou uowmmwu cqu mum meocm

NuoHHcm :oHuumm chu we mmeHmcw UHEmCNU

0mm0000.0 H.0v h.HHm 0.0N F.0H m.m0 0.N 0.00N 0.Hm
0HH0000.0 b.0m m.mmN 0.MN 0.HN 0.va m.mm h.m0H 0.0m
vomH000.0 o.NN 0.0Hm 0.0N H.bm m.hmH m.mm h.m0H 0.0N
05m0000.0 v.5v ¢.00N v.0N >.hm m.0vH m.mH m.MMH 0.0N
0b00000.0 v.0v 0.00N H.0N 0.0 0.0HH 0.0H m.MMH o.NN
mHv0000.0 0.mN m.mmm N.MN v.m0 H.mbH 0.0V 0.b0H 0.mN
anH000.0 m.mr m.mN v.bN 0.mH 0.m>H 0.0v 0.h0H 0.vN
0500000.0 a.VH m.MH 0.0N m.h0 0.VVN m.mv H.0HN 0.MN
00N0000.0 v.hH 0.HbN m.VN 0.0m b.NmH 0.N0 H.00N 0.HN
mmN0000.0 0.0m H.0N 0.NN H.0N m.vbN m.m m.th 0.0N
0va000.0 0.Hh 0.FMN N.0N n.0H 0.00 m.m 0.NmN 0.0H
mH¢0000.0 v.00 b.00N N.vN 0.0m v.00 0.m0 e.vm 0.0H
hmHH000.0 v.0 m.bm m.MN 0.00 0.va 0.m0 v.v0 0.bH
0VVH000.0 b.0v 0.0mm H.vN 0.0m 0.0NH v.0H H.0MH 0.vH
0VVH000.0 0.0H H.HN H.vN m.h0 0.va v.0v m.HNN o.NH
mth000.0 v.00 m.m0 0.vN o.NN 0.0NN v.0v m.HNN 0.HH

oomH000.0 0.vm m.NHN N.0N 0.0H 0.00H m.0m m.MNH 0.0H

195

Noummv5vvv0.0| 00+mHHmmmmH.0 H0|m0MHmH0m.0 H0|m0m0000N.0 Nolmva0000.0

Nonmm0N000v.0| H0|m0MHmH0m.0 00+m000NOMH.0 H0|M000VOMN.0 Nolmmv5N5HN.0|
HOIMvammvN.0I H0|M0m0000N.0 H0IMO00v0MN.0 00+mmm05NMH.0 H01m0¢000v0.0|
HonmN05mmmN.0 NOIMva0000.0 Nonmm¢5N5HN.0I H0IM0v000v0.0I 00+m0mmvH5H.0
mo+movvmomv.o u uCMCHEHOuoU xHHumE mocmHum>oonmUCMHum>
mv u mumm cqu we .oc coHumHsono :Hmuum mmumsvm umme
0.05 0.05N mvavH.01
0.0H N.00 mvomm0.0|

m.0 m.0mH m5mmmH.o
mocsHQ ocHHmwn musuHcams
muouom>cmme new mmSHm>cmon

m00v5MH.o- MNmMHmo.o mvmmoNo.on MO5omoo.on mHmHomo.ou m0mvmVH.o
N mu: Nx mos Nx mus N mun >x mus x was
mv u mumm cqu we uwn55c NuoHHcm coHuumm Cch
mHmNHmcm UHEmCNU HmuHqudc ocmmm
H.HH c.5H N.H5N m.mv m.NN o.Hm
m.m m.vv m.NmH m.oH 5.NmN 0.0m
m.mv m.mH v.0mH m.o0 5.NmN o.mN
5.0H o.m 0.00m m.N5 5.mmH 0.0N
5.0H m.Hm 0.mvH m.Hm v.NON o.5N
m.HH m.mH m.v0H 0.05 5.VNm o.mN
m.mm 5.5m m.HOH m.om H.0 o.¢N
5.0H N.0N v.5ON 0.0m 0.Hmm o.MN
m.m N.mm m.mmN N.NN m.NHH 0.HN
m.m H.5 N.N0 n.0v 5.VNm 0.0N
0.Nv m.5N H.mmN N.H0 m.om o.mH
m.HH m.vm N.H5 v.m m.50N o.mH
m.mm n.5v v.mm «.mm N.00N o.5H
5.Hv m.m 0.HNm o.N5 m.N0 o.VH
5.Ho 0.0N o.mHN N.mm o.o o.NH
0.0m m.m0 N.HHN 0.NN «.mm 0.HH
m.mv m.vv 0.HvH o.5N 0.HON o.oH
5.0H m.m o.0NH m.m5 N.mmm o.m
m.mm H.mm H.Hmm m.Hm 0.0vH o.m
5.0H H.m0 5.0H m.H 5.mmN 0.5
0.0N m.mm m.mH H.mN N.omN 0.0
m.m m.¢v m.va o.Nv m.mHH o.m
m.m 0.NH 0.HvN N.m0 0.5 o.«
m.mm m.Nv 5.mmH H.mH m.Hm o.H
5.0H N.5m N.mmN 5.Nm v.v0 0.0m
o.NH H.v H.N5 0.mm 0.50H o.mN
5.0 v.m 0.00N m.m v.omN o.5N

196

Hm 0505m0000.0 mmNON0000.o mm05m0000.0 0.vN
MN v005moooo.0 5NHOH0000.0 HHH550000.0 0.MN
0N MNmmv0000.0 mvmm00000.0 5000HH000.0 0.HN
mv mvaH0000.os 005mm0000.0 0mmmm0000.0 0.0N
mq 0m00H0000.0 000HH0000.0 500HN0000.0 0.0H
0H H5H000000.0 00v0H0000.0 500mHH000.0 0.0H
NH H05mmoooo.0 v0mvm0000.0 mNHomH000.0 0.0H
0v 0mHOH0000.0 «mmNH0000.0 MMHmN0000.0 0.0H
mm 0N50H0000.0| m00Nv0000.0 MMHMN0000.0 e.vH
0H H50000000.0 5m0000000.0n mm05moooo.0 0.mH
5H m50500000.0 NOH0m0000.0n 5HO0N0000.0 o.NH
mN mmmHmoooo.0 00N000000.0 mm05m0000.0 0.HH
0m HO0NN0000.0 m50mH0000.0 00m0m0000.0 0.0
H m50H5H000.0 00N0m0000.0n 500mHH000.0 0.0
HH m¢5000000.0 0Hmmm0000.0| mm0500000.0 0.5
0N 0500v0000.0 N050N0000.0u 05NmH0000.0 0.0
mu 5H0500000.0u N5mmv0000.0 0mmmm0000.0 0.m
0m momvN0000.0 NmmmH0000.0 00m0m0000.0 0.m
0N H00m00000.0 ¢Nm¢v0000.0| 05NOH0000.0 o.N
NN m000m0000.0 5000N0000.0 0m5000000.0 0.H
.>.w n NmeaCmu wCHm> uwuowaxw NmemCmu CHmuo

NnoHHCm COHuomm CHCu now mCHm

momummo ~o+mm5mmHmH.o- u mmHzxuoHo m>HuHmoa

Cum uwumHsonu Eouu mCHmuum Umusmmme uo mCOHHMHme

.mem CHmuum o>HmmquEoo ECEmeE cu mem 5 Eouu wHocm
voum55mN05m.o u CHmuum m>HmmmuQEou ECEHCHE
vOIM0v0Hmmm.0u n CHmuum w>HmmquEoo ECEmeE

mH COHmCmu NIOHHCm COHuomm CHCu uo owHQ CH CHmuum

0.00 0.05 voumNmmmmH0.on
v.0m m.mVN voummNmmomN.ou
m.0 N.0vm woum5va050.o
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voumeNmva.o uNm voumNmmommN.0 uuxw vonqu0MNmN.o u~>w vonmv55NmmN.o n>xm vonmvamHmN.0 u>m vonm5mNMHmm.0 nxw
mucmcoaeoo CHmuum uo Houum Uumucmum
vonmomHHH5v.ouu~w moumOvammm.0nuNxm vonmmom0N5H.ouu v0:Mm00vm0v.0uu>xo voummvmv¢mN.ouu>o vOIM050mmN5.0 nxw

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0.Hm
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198

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.mm .00N
.0N .vm

.N .va

HuHHHCm
vNNm.0 u m8 mNmm.ou
mVM5.0 u NE 000v.0
ommv.0u u H8 oomN.0u
OCHUuouom Uwumuou wn HHH3

v .vN .50H

v .0N .NON

N .0H .NH

N .0N .mvm

v .vv .00N

v .0N .mmH

v .0N .mmH

v .0N .mmH

v .Nm .OVH

N .0N .0Nm

v .VN .00H
mmCCHQ uuob quCH

COHmquHuo mem UHqu

HIHHHCm

0.00N
H.50N
N.¢HN
H.HHN
H.NHH
N.0m
N.0m
N.0m
N.0N
m.Nm
N.NHN

mCHHmmn

0.HN
0.0H
0.0H
0.0H

o.
o.
o.
o.
0.
o.
0.

HMQ‘LOWPW

CHmuo

Cqu mum meaCm

wUHHm
MH
NH
HH
mumo
0.HN
0.0H

CHmuu

CoHuuwm CHCu

199

OOOOOOOOOOOOOO

cu HmHHmuma
mCuUHz CHmuo

H000000.0
50HH000.0
0000000.0
0000000.0
0vv0000.0
0500000.0
H050000.0
0000000.0
NH00000.0
NH00000.0
0500000.0

N\HmmCmu

H mH COH

.ovN
.OVN
.0NH
.000
.OVN
.000
.0N5
.005
.000
.0vHH
.000
.0NOH
.0NOH
.00H

‘OU HQEHOC

("V

H

N

MM

FPI‘NOMHMNOLD
OLDLOOkDr-IOMQ'HV

0 meCHQ

ago cqu oncu

00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0

mmexUHCu HmCCHnuwuso umnEdC
mCqu HUHCu

000.

00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0

0.00 0.0H v.0N 5.00N 0.0 0.0HN 0.5H
v.NON v.NN 0.0 H.vN 0.0N 5.HHN 0.0H
0.00 0.0N 0.H0 v.0 0.00 0.00 0.0H
0.00 0.0N 0.0N N.00H 0.0N 0.v0H 0.vH
0.500 0.5N 5.00 5.v5 0.vN 0.00H 0.0H
0.HOH 0.0N 5.vH 0.HON 0.NH 0.000 o.NH
0.v00 0.0N 0.50 e.va 0.H5 0.00 0.HH
v.v0N 0.0N 0.N0 0.VN N.00 0.0v 0.0
0.00N 0.N0 0.00 5.VN N.NH N.0v 0.5
0.00N 0.N0 0.00 5.VN N.NH N.0v 0.0
0.0NN N.0N 0.0H H.00H 0.0H N.v0H 0.H
OCHmeQ Hm.uva0Cm wocsHa o 0CHummn o mocsHa o 0CHummn CHmuo
Emumam wumCHouooo vmumuou cu uomamwu CuH3 wum mmHocm
H u oHumu CH3u0u0H8\C quonCu «H 0H muwm CH3u no uwnECC NsHHHCm mUHHm
0000.0: I 0C 0000.0: u 06 0VH0.0 u 0H
0000.0 0 NC 00v0.0u u N5 00N0.0n u NH
05Ho.0 n HC 00N0.0: u HE 05v0.0 u HH
mmCHmoo CoHuomuHo 0CH30HH0u mCu ou 0CHUuouom Uwumuou on HHH3 wumo
.0 H0.0 .N H .N0 .owm v .00 .0HN 0.HN
.0 H0.0 .v 0 .0H .05H v .Nv .00N 0.0N
.0 H0.0 .N 0 .0 .0v0 N .0N .NNN 0.0H
.0 H0.0 .0H H .VN .00N v .0 .00H 0.5H
.0 H0.0 .0 H .0 .00N N .HN .000 0.0H
.0 H0.0 .5H H .H0 .N0 0 .00 .N00 0.0H
.0 H0.0 .HH 0 .0N .Nvm v .0N .0v 0.VH
.0 H0.0 .0H H .v0 .00H v .0N .0v 0.0H
.0 H0.0 .0H 0 .vH .v0H N .NH .00 o.NH
.0 H0.0 .0N 0 .00 .0v0 N .N5 .00H 0.HH
.0 H0.0 .0H H .N0 .00 v .00 .000 0.0
.0 H0.0 .0H 0 .00 .00N v .NH .0v0 0.5
.0 H0.0 .0H 0 .00 .00N v .NH .0v0 0.0
.0 H0.0 .0 0 .0H .Nvm N .vH .0NN 0.H
CH3u
mmequCu CwnEdC oOCCHQ uuw> umCCH ooCsHa uum> uwCCH
mCH3uouUHE COHum uCoHuo umm Cqu COHmquHuo mem UHqu CHmHo
vH mH mumm CH3» no umnECC NIHHHCm CoHuowm CHCu
0.00 0.00 5.HOH 5.0H 0.00 0.HN
5.Hv 0.0N v.0HN 0.00 0.00 0.0H
0.0v 0.5N 0.NON 5.00 0.0NH 0.0H
5.00 0.00 «.NON 0.0v 0.00 0.0H
0.50 v.v 0.0NH 0.05 0.0H 0.0
0.0 5.0 5.0HN 0.00 0.HNO 0.5
5.0H N.5N 5.00 0.50 v.00H 0.0
0.HH 0.0 H.0H H.NN 0.00H 0.0

200

0.0 5.0VH 0HNO0N.0n
0.00 0.0 000v5H.0u
H.0 0.00N 050N00.0
muCCHQ OCHHmwn musuHComE
mucuom>C00Hm UCm meHm>C00Hw

005v05H.0u vHH50N0.0u 5000vH0.on 550000H.0 005005N.0 vHOHNN0.0:
N mUC a» MUC Nx MUC 0 00C >x mvC x mUC
0N u muwm CH3» mo umnEdC N-HHHCm COHuuwm CHCu
mHm>Hmcm UHEmC>U HMUHqudC 0Cmam
0.0 0.v0 N.00N H.NH 0.H00 0.HN
5.0H 0.00 N.500 0.0N 0.00H 0.0N
5.0H 0.vN 0.v0 0.0H v.0v0 0.0H
v.VH 0.NH 0.H0 0.H0 N.50H 0.5H
0.00 v.Hv o.NNN 0.N0 0.0 0.0H
0.0H H.0N 0.H0 5.0H 0.NHO 0.0H
0.0H 0.0H 0.H0 0.0H H.55H 0.0H
0.NH 0.0H 0.0NH H.H0 0.0N 0.0H
5.0H v.0 0.5N0 0.HH 5.00N o.NH
0.HN v.00 N.00 H.0H N.00H 0.HH
H.HH N.NN v.05 0.NN 0.v00 0.0
0.5H 0.H 0.N0 0.00 H.0N0 0.5
0.5H 0.H 0.N0 0.00 H.0N0 0.0
5.0H H.0H N.v0 H.HH N.05H 0.H
0.00 0.00 5.HOH 5.0H 0.00 0.HN
5.Hv 0.0N v.0HN 0.00 0.00 0.0H
0.00 0.5N 0.NON 5.00 0.0NH 0.0H
5.00 0.00 0.NON 0.00 0.00 0.0H
0.50 v.v 0.0NH 0.05 0.vH 0.0
0.0 5.0 5.0HN 0.00 0.HNO 0.5
5.0H N.5N 5.00 0.50 v.00H 0.0
0.HH 0.0 H.0H H.NN 0.v0H 0.0
5.Hv 0.0N 0.H0 0.00 0.05H 0.0
0.0N 0.HN N.00 H.00 0.NOH 0.0
5.Hv 0.0H 0.00H N.0 0.00N 0.H
umumEHHHHE uwm moCsHQ 0CHumwn wocsHQ 0CHummn
mmHHoEMH 00 .OC mmxm COHmCmu mmxm COHmmquEou CHmum
Ewum>m mumCHUuoou Uwumuou cu uqummu Cqu mum mmHocm
NuHHHcm CoHuomm CHCu uo mmeHMCm oHEmC>U
00N0000.0 0.0H 0.00N 0.0N 0.N0 0.500 0.00 v.05N 0.HN
0500000.o 0.00 0.00H 0.0N 0.5H 0.0N0 0.0v 0.5H0 0.0N

0500000.0 0.5N v.v0 0.0N H.5 H.0NH 0.0H 0.00H 0.0H

201

v0|0005v000.0 Hum

voum00050N0.0IINm

0 000HOH000.0 0NO0N0000.0 0NHO0H000.0 0.0

NH H500v0000.0n 500050000.0 5HO0N0000.0 0.5

cm 0NOVN0000.0 ¢00N00000.0 000500000.0 0.0

0N 0v00H0000.on 00N500000.0 0HOHv0000.0 0.0

0 05v000000.0 00HH00000.0 000va000.o 0.0

HN 500NN0000.0 00N000000.0 0HON00000.0 0.0

N 05500H000.0 5000H0000.0 000va000.0 0.H
.>.o I N\HmaCmu msHm> Uwuowaxm N\HmQCmu CHmuo

NuHHHCm CoHuomm CHCu Cow mCHmuum nwumHCono scum mCHmuum kusmmwe no mCoHu0H>mU

momuomu N0+m5500000.0u I me3x00Ho w>HuHmom .mem CHmuum w>HmmmumEou ECEmeE cu mem x Ecuu wHoCm

v0:M000N000.0 INxm

00IMNNHv000.01Iwa

+ mH COHmcmuxm

vo-mvavav.o n~>m

v0:M0v0N000.01IN>w

+ 0H COHmcwu

mquCOQEOU CHmuum mo

000000.0 I moCmHum> wHQEmm

HoanvaH00.0|
00+MOH0v000.0
H0|mHO0NHVH.0
00+m00005HH.01
HOIM0055500.0

00+mH00v00H.0
Houmomva00.0|
H0I00H0005N.0I
Hoan005NmN.0
HOIM00eN00H.0

v0+m0H00va.0

0N I mumm CH3u 00 .OC

v01m00000N0.0

VOIMOHN0005.0

v.00
5.0N
H.0H

mmCCHQ

"mmumCHUCoou mUHHm

000000.0

HOIM0H0005N.0I
H0ImH00NHvH.0
00+m0050NOH.0
H0IM5vN50v0.0I
H0|mv0v050H.0|

ucmCHEuwumv

COHuMHCUHmo CHmuum

"%X0

I>xw

00|m0N500HH.0

I CHmuum o>HmmeQEoo ECEHCHE

v0:00000000.0n I CHmuum m>Hmmmuano EdEmeE

NIHHHCm

0.0HH
0.N00
0.00N

0CHumwQ

I uoHum mo moumCUm no 55m
Honm00vNO0H.o
H0u00055500.o
Houmv0v050H.ou
Houm00v5v05.oa
00+MO0H000N.0

H0|mH005NON.0
00+000005HH.01
Honm5vN50v0.0|
00+mHNOHN00.0
H0IM00V5v05.0|

v0:MON0000¢.0

Couuw CumUCmum

v0100000000.0

00|M00005NH.01
v01M0H000vH.0|
00|m0050N¢H.0

mCHmuum HMQHUCHCQ

I>w 00:0000N050.0

I>m v0lm000500N.0

CH Comau UmumEHumm

xHuumE moCmHum>00umUCmHum>

mmumsvm ummmH

CoHuomm CHCu wo wCMHQ CH CHmuum

II
X
0)

Km

202

 

N0¢0N0000.0|

00v000000.0
N00500000.0

H00000000.0I

0vHv00000.0
v0v0v0000.0
0N0000000.0
vHv050000.0
H5HO0H000.0
0H000H000.0
00H5N0000.0

00NOH0000.0u
00NOH0000.0:

0050v0000.0
0N000H000.0
00¢0N0000.0
0050N0000.0
000N00000.0

000000000.0
5Nv0H0000.0

00v000000.0|

0N0000000.0
5HOH00000.0
0vHOH0000.0

0H0500000.0I
5NOH00000.ou
500000000.0|
0HN5N0000.0|

00VHH0000.0
H0vH50000.0
H0vH50000.0
500000000.0
Nv5HH0000.0
05HOHH000.0
vH50HH000.0
500v50000.0

5HO0N0000.0
000500000.0
000500000.0
NNH000000.0
5000HH000.0
v00000000.0
vH0000000.0
50vvv0000.0
000500000.0
000050000.0
000000000.0
00NH00000.0
00NH00000.0
000500000.0
5000HH000.0
000va000.0
N0v0VH000.0
00N5NH000.0

0.HN
0.0N
0.0H
0.5H
0.0H
0.0H
0.VH
0.0H

O O
0'4 N
H H

O

\DCDO‘HHMK‘O‘
Hv-Ir-IN

0000000000

203

00N0000.0
50HH000.0
0500000.0
0v0H000.0
00v0000.0
50HH000.0
0500000.0
50HH000.0
v0v0000.0
05v0000.0
50HH000.0
VNON000.0
0HON000.0
0HON000.0
50HH000.0
00N0000.0

N\HmQCmu

H mH CoH

.00v
.0NH
.00H
.00H
.000
.OVN
.0NH
.0NH
.OVN
.00

.0NH
.0NH
.0NH
.00

.00

.ovN

OOOOOOOOOOOOOOOO

C I C I U U .

ou HmHHmumm .Ou HmEHOC
mCuUHz CHmum

0.0 N.NON
0.50 0.v0N
0.HN 0.N5N
0.VH 0.00H
0.v0 0.50N
H.0N 0.vH0
N.0N 5.v0

v.H H.00

0.0H 5.0HH
0.0N 0.5NH
5.05 N.5v0
0.0N N.00N
0.00 c.00H
0.0 N.0vH
5.0H 5.00H
5.vN H.00N

0 mmCCHQ 0 OCHumwn

uCo CH3» onnu

00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0

mmoCHUHCu uwCCHnumuso umCEdC
mcqu onnu

000.H fl OHUMH CH3uOHUHE\C

HIN0NCm
0.0N v.5v N.5v0
0.0N 5.0V 0.00
0.00 5.00 0.NvH
5.NN 0.0N 0.00
0.HN N.HH 0.00
H.0N N.H0 0.0NH
v.¢N 0.00 0.05N
v.NN 0.00 0.0
0.0N 5.00 0.v
0.H0 H.00 0.00N
N.NN 0.0 5.00N
0.0N 0.00 0.HOH
0.0N H.00 0.0vN
H.0N H.0 N.00N
0.0H 5.00 0.00N
5.H0 0.N0 v.v5
Hm.ova0Cm wOCCHQ m 0CHummn

H0.0 .v
H0.0
H0.0
H0.0

H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0

NNQ‘GDPVKDMVNCDVI‘MV

mmmConCu umnEsC

CoHuumm CHCu no mHm>H0Cm UHEmC>u

0.Nv 0.500 0.00
0.05 H.N5 0.0N
0.00 «.5HH 0.0N
0.00 0.5HH 0.0N
0.00 0.H0 0.0N
0.50 0.00 0.HN
0.50 0.00 0.0N
«.00 0.00 0.0H
N.50 0.00 0.0H
0.H0 0.00H 0.0H
0.0H 0.0v 0.0H
0.00 0.0NN o.NH
0.00 0.0NN 0.HH
v.N 0.00N 0.5

0.00 5.HHO o.N

0.00 0.00H 0.H

u mmCsHQ u 0CHumwn CHmuo

Emumxm mumCHUCOOU kumuou cu uuwamwu Cqu wum mmHocm

quonCu 0H mH mumm Cqu we uwnECC HnN0NCm wUHHm
HNvN.0I I 0C 000H.0| I 08 0v00.0 I 0H
H050.0u I NC 0000.0 I NE 0NvN.0u I NH
05H0.o I HC qv00.0 I HE 0v0H.0 I HH
mmCHmoo CoHuuoHHu 0CH30HHOH mCu cu 0CHUuooum Uwumuou wn HHH3 mumv
0 .0N .00 N .0H .v0 0.00
0 .0H .vNN N .0H .v0H 0.0N
0 .N0 .0¢N N .00 .0HH 0.0N
0 .0H .NON N .00 .0HH 0.0N
H .N .0H v .vH .N00 0.0N
H .v0 .00 q .0H .500 0.HN
H .0H .0HH v .0H .500 0.0N
0 .0H .00 v .0 .NOH 0.0H
0 .NN .v0 N .N .000 0.0H
H .N .HHH v .0N .000 0.vH
H .00 .00H v .N0 .5HH 0.0H
0 .00 .05N N .00 .00N o.NH
0 .0N .NNO N .00 .00N 0.HH
H .0N .NOH N .N .00 0.5
0 .v .00N N .0H .NN o.N
H .0 .N0 v .v0 .Nvm 0.H
Cqu
mOCCHQ uuo> uwCCH woCsHQ uumb uwCCH
COHum quHuo uwm Cqu COHmucmHuo mem UHqu CHmuo

mCquouUHE
0H

m0 mumm CH3“ HO NQQESG

HINONCm COHuuwm CH2»

2(fl1

TII

 

.0 .0vN 00.0 00.0 .0 H0.0 .0 H .0N .00H N .0N .000 0.0N
.0 .00H 00.0 00.0 .0 H0.0 .0 0 .vN .05H N .0N .00H 0.0N
.0 .00 00.0 00.0 .0 H0.0 .0 H .N .NHH w .0 .05H 0.5N
.0 .00 00.0 00.0 .0 H0.0 .5 0 .0H .NOH w .0N .00H 0.0N
.0 .0v 00.0 00.0 .0 H0.0 .0 0 .N .000 v .0N .00 0.0N
.0 .ovN 00.0 00.0 .0 H0.0 .5 0 .w .05N N .0N .v e.vN
.0 .000 00.0 00.0 .0 H0.0 .0H 0 .0 .v00 v .v .N 0.0N
.0 .00H 00.0 00.0 .0 H0.0 .0 0 .0H .00H v .VN .000 o.NN
.0 .00H 00.0 00.0 .0 H0.0 .0 H .0 .NOH N .N0 .00N 0.HN
.0 .0VN 00.0 00.0 .0 H0.0 .0 H .0N .0HH N .0N .05H 0.0N
.0 .000 00.0 00.0 .0 H0.0 .0 0 .0H .NOH q .0N .v00 0.0H
.0 .0NH 00.0 00.0 .0 H0.0 .0 H .N0 .NON v .0H .00H 0.0H
.0 .0NH 00.0 00.0 .0 H0.0 .5H H .0H .0H0 q .0H .00H 0.0H
.0 .0HN 00.0 00.0 .0 H0.0 .N 0 .N0 .00 N .00 .0H o.NH
.0 .0HN 00.0 00.0 .0 H0.0 .0H 0 .0 .0HH N .00 .0H 0.HH
.0 .00H 00.0 00.0 .0 H0.0 .0H 0 .0N .00 N .0N .000 0.0
.0 .N5 00.0 00.0 .0 H0.0 .0 H .0 .00H 0 .00 .N0 0.v
.0 .0NH 00.0 00.0 .0 H0.0 .0 H .v0 .NHN v .00 .00H 0.0
.0 .00 00.0 00.0 .0 H0.0 .q 0 .v .00H v .0 .00N 0.H
Cqu
on HmHHmHmQ .ou HmEHOC mmmCxUHCu umCCHuumuCo uwnEdC mmeHUHCu umnECC wOCCHQ uum> umCCH mesHm umm> uoCCH
mCuUHz CHmuo mCqu HUHCu mCquouoHE CoHum quHuo umm CH3» COHmquHuo mem UHuno CHmum
0N mH muwm CH3u mo umnECC NIN0NCm COHuumm CHCu
0.0 0.00 0.00N 0.5N v.Hv 0.00 <0
0.00 0.05 «.0 0.0 N.v0H 0.0N Mw
5.0H N.0H 0.HHH 5.00 0.00N 0.0N
0.00 N.0N 0.50H 0.5 0.H0 0.0N
0.0H H.5v 0.00H H.0N 5.HON 0.0N
0.00 0.N5 0.NNO 0.0H 0.NOH 0.HN
5.0H H.00 N.00 0.0N 0.05N 0.0N
0.00 0.Hv 0.05 5.00 N.000 0.0H
0.NH N.00 0.05 0.0N 0.0N0 0.0H
0.00H 0.00 0.50H v.HN 0.000 0.vH
0.00 0.v0 N.00 0.00 0.0vN 0.0H
0.00 5.v0 0.00N 0.0H H.HvH 0.NH
5.00 H.55 0.05H H.5 N.00 0.HH
5.00 0.H v.v0N 0.N 0.00H 0.5
0.00 0.5N N.5N0 0.00 H.00H o.N
0.0 5.00 H.00H N.0H 0.0v 0.H
umquHHHHE uma 00CCHQ 0CHummn mmCsHQ OCHummn
meHmEMH 00 .OC mmxm ConCmu mmxm ConmouQEoo CHmuo

Emumxm wumCHvuoou Umumuou ou nowmmmu Cqu wum mmHmCm

 

 

0500000.0
50HH000.0
Nv0H000.0
05v0000.0
0v0v000.0
00HN000.0
NHOH000.0
v00H000.0
v000000.0
0500000.0
0N50000.0
Hv0H000.0
0VVH000.0
0H0v000.0
HN00000.0
0HvN000.0
0000000.0
0va000.0
0v0H000.0
0000000.0

N\HmQCmu

m IRIS.

v.0N
0.00
0.05
0.00
0.00
0.0H
0.0

H.00
0.v0

H mH coHuao cHsu HoHnu

.ovN

00.0

 

 

0.00 0.Hv 0.v5 5.00 N.000 0.0H

0.NH N.00 0.05 0.0N 0.0N0 0.0H
0.00H 0.00 0.50H v.HN 0.000 0.vH
0.00 0.00 N.00 0.00 0.0VN 0.0H
0.00 5.v0 0.00N 0.0H H.HvH 0.NH
5.00 H.55 0.05H H.5 N.00 0.HH
5.00 0.H e.v0N 0.N 0.00H 0.5
0.00 0.5N N.5N0 0.00 H.00H o.N
0.0 5.00 H.00H N.0H 0.0v 0.H

umumEHHHHE uwa mmCsHQ 0CHummn mmCsHQ 0CHummn

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209

 

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210

 

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N500VN000.0
00005H000.0
000500000.0
5000HH000.0
5HO0N0000.0
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HHH550000.0
000HON000.0
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50HO0N000.0
00NHOH000.0
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5000HH000.0
0v0000000.0
005vN0000.0
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0VH000000.0
000NNH000.0
000050000.0
000500000.0
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5000HH000.0
NNNv0H000.0
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50000H000.0
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0.00
0.0N
0.0N
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0.0N
0.0N
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0.0N
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a I O o
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0

000000000000000
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0.0N
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0.0

212

O O O O O O O O O O O O

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0 meCHQ

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00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
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00.0
00.0
00.0
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mmoCquCu umCCH:umuso CmnECC
mcqu oncu

0.0HN H.0N o.NN 0.0N0 0.50 N.00N 0.0
0.00H 0.VN 0.00 0.H5N 0.50 N.00N 0.0
0.NNO 5.0N 0.50 N.00 0.N0 0.0 0.0
0.N0 0.0N 0.N0 5.0H0 0.N0 0.0 0.0
0.H5N 0.00 0.N0 5.N5H 0.00 v.00N o.N
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0 0CHumwn H0.00mH0Cm woCsHQ m OCHumwn o mquHa o OCHummn CHmum
Emum>m quCHUuoou Umu0uou ou uomammu Cqu mum moncm
000.H I OHumu CH3u0u0HE\C H3uonCu 5N mH muom CH3» 00 umCEdC H:00NCm 00HHm
0000.0: I 0C H005.0 I 08 0000.0 I 0H
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0N00.o: I HC 0050.0: I HE 00v5.0 I HH
mmCHmoo CoHuowuHu 0CH30HH0u may on 0CHUuooom Uwumuou ma HHHS wumu
00.0 .0 H0.0 .0H 0 .v .NvH v .N .00N 0.00
00.0 .0 H0.0 .0H 0 .N .00 v .0 .00H 0.0N
00.0 .0 H0.0 .0 0 .0H .0N v .NN .00H 0.5N
00.0 .0 H0.0 .0 0 .0H .05 0 .NN .00H 0.0N
00.0 .0 H0.0 .0 0 .0 .00H q .0H .00H 0.0N
00.0 .0 H0.0 .5 0 .0 .00 v .vH .00H 0.vN
00.0 .0 H0.0 .5H 0 .0 .00 v .v .v0H o.NN
00.0 .0 H0.0 .0 0 .0H .5NH v .v .v0H 0.HN
00.0 .0 H0.0 .0 H .N .v 0 .0H .vHH 0.0N
00.0 .0 H0.0 .0H H .VN .N00 N .N .00 0.0H
00.0 .0 H0.0 .0H H .N .0H0 N .0H .00 0.0H
00.0 .0 H0.0 .0H H .0N .000 N .0H .00 0.5H
00.0 .0 H0.0 .0H 0 .0 .05N N .HH .vH 0.0H
00.0 .0 H0.0 .qN 0 .0N .0NN v .00 .000 0.0H
00.0 .0 H0.0 .0H 0 .Nv .55N v .00 .000 0.vH
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00.0 .0 H0.0 .0H H .0v .00 v .0N .05N 0.HH
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00.0 .0 H0.0 .0 H .0 .Nv0 v .0N .05N 0.0
00.0 .0 H0.0 .0 H .0 .vVN N .0 .000 0.0
00.0 .0 H0.0 .5 H .vN .HON N .0 .000 0.5
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00.0 .0 H0.0 .0N 0 .0N .0HH q .0H .00H 0.v
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mmHHwEMH no

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CoHuumm CHCu uo mmeHMCm UHEMC>U

0.00H
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5.5v0
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214

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N\HmQCmu

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00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
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00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
00.0 00.0 .0
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mmeHUHCu umCCH:umuso uwnEdC
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mmmConCu umCECC
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meHmou COHuowan 0CH30HHOM 02» cu 0CHnuooum uwumuou ma HHHz mumu
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CoHum quHuo umm CH3» COHmquHCo mem oHqu CHmum
mH mumm CH3» uo umnECC N:00NCm CoHuowm CHCu
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216

 

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mmmmmmmmm

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2225

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228

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.>.a : NmemCmu wCHm> Umuuwaxo N\HmQCmu CHmum
N:00NCm COHuowm CHCu H00 mCHmNum UwumHCuHmo Eouu mCHmNum uwusmmme wo mCoHumH>mu
mmmuomn N0+mo05N50N.o: I me3xuoHu w>HuHmoa .mem CHmuum m>HmmmuQEou ECEmeE cu mem 0 Eouu mHqu

v0:m¢0Hv50v.0

"wa

HOIMmNOHva.o INHI

+ 0H COHmCmu

HOImNNmmva.o Ixxm

00:mv00050H.0

I CHmuum 0>Hmmvuaaoo ECEHCHE

00:0N000v5N.o: I CHmuum o>Hmmvuano ECEmeE

N:00NCm

0.00
v.50H
0.00N

0CHNmmn

v0:mHO0H0v0.0

00:00005H5v.0:
00:m00HNO0H.0
00:M0000000.0

mCHmuum HmQHoCHHQ

CoHuowm CHCu no mCmHQ CH CHmuum

IHI HOINN000H00.O Ixm

229

 

00
0H
00
He
0H

0H
5N

0N

50

00

0HHN50000.0:
00050H000.0
NON000000.0
N5N000000.0:
0va0H000.0
00000H000.0
000H00000.0
00050H000.0
0HOH00000.0
00000H000.0
000500000.0:
VNO0HN000.0
5v000H000.0
000000000.0:
5HONN0000.0
0H0000000.0
0H0v5H000.0

00v00H000.0
000NN0000.0:
00N5HH000.0
000v00000.0
50000H000.0:
00Nv00000.0:
00v000000.0
05v50N000.0
N000NH000.0
0000HN000.0
00500N000.0
0v0050000.0
VH500H000.0:
HO0HvN000.0
5005N0000.0
0v0000000.0
0050H0000.0

000000000.0
vv0va000.0
00005H000.0
50N0v0000.0
00va0000.0
00NHOH000.0
000va000.0
000v0v000.0
5HVNON000.0
000000000.0
055NOH000.0
50HO0N000.0
000500000.0
00050H000.0
000000000.0
000000000.0
055NOH000.0

0.00
0.0N
0.0N
0.0N
0.0N
0.VN
0.0N
0.NN
0.HN
0.0H
0.0H
0.5H
0.0H
0.0H
0.0H
0.NH
0.HH

230

OOOOOOOOOOOOOOOOOOOOOOOOO

CH3u ou HmHHmuma
mCuUHz CHmum

0N50000.0
0HON000.0
vv50000.0
0500000.0
000N000.0
v000000.0
00HN000.0
NO0N000.0
N000000.0

N\HmmCmu

 

0 moCsHQ

H mH coHuao cqu qucu

.0Nv
.0N0
.00

.ovN
.00N
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.000
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.00H
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.00

.00

.Ou HmECOC

00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0

mmwchflflu HflCCHIHfiUDO HQQESC

0.000
v.05H
0.0H0
0.0v

0.0vH
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0.HON
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0 0CHwan

0.0N
H.0N
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0.0N
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0.0N
0.VN
0.5N
0.0N

H0.000H0Cm

000.H I OHumN CquouoHE\C

00.0
00.0

00.0.

00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0

mcqu qunu

OOOOOOOOOOOOOOOOOOOOOOOOO

w mmC

mmCHmoo CoH

H0.0
H0.0
H0.0
H0.0
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H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0
H0.0

mmeonCu
mCquoHUHE

.0

.N0
.0H
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.0H
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NwCECC
C0

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0.00 5.HHN
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0.0N 5.Hv

5.N v.0H

0.N0 0.NON

CH0 m 0CHumwn

o wOCCHm

v.50
«.50
0.00
0.00
0.00
0.5

v.5

v.0H
v.0H

U

0.0vN
0.0vN
0.00N
0.00N
0.00N
v.00

«.00

N.0HN
N.0HN

0CHumwn

OOOOOOOOO
HNMQ‘IDKDI‘QO‘

CHmuo

Ewunxm muMCHuNooo caucuou ou powmmmu CuH3 mum mmHoCm
quonzu

mN mH mumm CH3“ HO Hwnfidc
00H5.0: I 0C 0000.0: I 0CH
0000.0 I NC 0N00.0: I NCH
5v00.0: I HC HON0.0 I H8
UUQHHU OCHZOHHOH wfiu Ou DCHUHOUUM OwUMUOH 02 HHH3
0N .0NN N .v0 .00N
00 .05H N .vm .00N
0H .v5 N .NH .00H
.0HN N .vH .va
00 .00N N .vH .vVH
NN .00N N .NN .v0H
00 .000 N .NN .v0H
0H .00N N .0H .NOH
0N .00N N .0H .NOH
00 .00N N .00 .00N
0N .00H N .00 .00N
ON .05 N .0H .v0H
v0 .0NH N .VH .00H
.00N N .0H .0
0N .N00 N .0H .0
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.0HN N .0H .0N0
0N .00N v .0 .ovH
0H .v0N v .0 .ovH
0H .00N v .0 .ovH
0N .NvN N .0H .05H
0H .00N N .0H .05H
0H .vHH N .0H .000
5H .0vN N .0H .000

HMMMMHHHHHHMHHHHMHMMMMHHH

woCsHa uuo> NmCCH
uCoHuo umm CH3»
mH mumm CH3» no amass:

Hum

.0

HI00NCm
005v.0
vH05.0:
000v.0:

wOCCHQ umm> umCCH

ConquHNo mem UHqu
H:00NCm

wUHHm

0.0N

0.NN

OOOOOOOOO
HNMQ‘IOWI‘CDON

CHmuo

CoHuumm CHCu

231

00v0000.0
v¢0N000.0
0050000.0
0va000.0
0050000.0
00N0000.0
000H000.0
0HON000.0
HOH0000.0
HNHN000.0
0vVH000.0
0HON000.0
000N000.0
0000000.0
NO0N000.0
05v0000.0

0.Hv
0.0

N.0v
0.00
0.05
5.5V
0.0v
0.H5
0.N0
5.VH
H.00
v.00
5.0v
H.0

0.0H
0.5V

H

0.50

5.vNN
5.000
0.00

0.00N
H.0N0
0.0NN
H.55

0.5vN
0.00

0.00H
H.H00
0.0NN
0.va
0.N5N
5.05H

5.Hv
5.00H
0.00
0.0v
5.00
5.H0
H.H0
5.H0
5.00
0.05
0.00H
0.00
0.00H
0.0N
5.00
v.HN
5.0H
0.05
0.NHH
0.N0

0.00
0.00H

0.0N
H.0N
5.HN
0.0N
H.0N
H.vN
0.0N
0.vN
v.0N
v.0N
0.HN
0.0N
0.0N
5.0N
N.0N
0.VN

wquHHHHE Non
omHHwEmH 00

.OC

0000500NN0<~5000000N0
H Nf‘tn N mm

HVHNNM

\OLDCDHQ‘Chv-IQIDGDNO‘CDVKDOIONNN

CDN
NM
N

moCsHQ

0.50
H.v0N
0.0N
H.0v
0.N0
5.NON
0.0H
N.0NN
0.0N
0.N0
N.00H
0.0NN
N.00H
0.00N
0.0HN
0.00N
H.va
N.NON
0.50
0.00N

N.HON
0.0N

0CHumoC

moxm ConCmu

0.v0
0.00
0.0N
N.v0
0.00
0.05
0.0N
0.0

H.0H
H.00
5.0

0.0H
0.00
H.0H
0.NN
0.vH
H.00
0.0N

0.H0

wOCCHm

0.000
5.00
H.05N
0.00H
H.HHN
0.000
0.HNN
0.0H
0.00N
0.NOH
0.05N
H.0H0
v.00N
0.00H
0.NNO
0.00H
0.0
N.NOH
0.000
0.H00

H.v00
0.00N

0CHHmmn
mwxm ConmmNQEoo

0.0N
0.0N
0.0N
0.NN
0.HN
0.0N
0.5H
0.0H
0.0H

CHmuo

Emumxm mNMCHONoou vmumuou ou uuwammu Cqu mum mmH0cm

H:00NCm
N.00
0.05
0.0
v.N0
0.HH
0.5
0.0v
0.0H
N.v0
0.H5

0.50N
0.H00
v.HVN
0.05N
0.v5
5.00
v.H0
0.VNN
5.Hv
0.00N
0.0
0.00
0.vv
0.v0N
0.N
N.0v0

0.H5
0.H5
0.NH
0.NH
0.NH
N.0N
N.0N

.0
HHI‘I"

NMMI‘I‘V’VKDKO
555000000

H

COHuumm CHCu wo mHmNHMCm UHEMCNU

0.50N
0.50N
N.5v
v.00N
c.00N
0.0V
0.0V
0.0v
0.00
5.H00
5.H00
0.Nv
0.Nv
0.50N
0.50N
0.0v0

0.0N
0.0N
0.5N
0.0N
0.vN
0.0N
0.NN
0.HN
0.0N
0.5H
0.0H
0.0H
0.0H
0.NH
0.HH
0.0H

232

OOOOOOOOOOOOOOOOOOOOO

Cqu On HmHHmuma
mCuUHz CHmuo

HO0H000.0
e000000.0
H550000.0
NO0N000.0
00v0000.0
005H000.0
000H000.0
N000000.0
N000000.0
0500000.0

N\HmQCmu

H mH COHqu

.00H
.00H
.000
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.0Nv
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.0N5
.0N5
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.OVN
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.00

.00v

.0» HmECOC

 

0.00
N.00
0.00
0.0

v.0v
0.0N
0.00
0.H0
5.0

5.00

0 mmCsHQ

cqu onnu

00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0

mmmCHUHCu NmCCH:umuCo NmnECC

v.N¢H
5.05N
0.0v

0.00N
v.5¢N
N.0vH
H.5N0
v.00H
0.05H
0.00N

0 0CHummn

000.H fl Oflumu Cfl3uOHUflE\C

00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0
00.0

OOOOOOOOOOOOOOOOOOOOO

ICHsu onnu

0.0N
0.NN
5.0N
0.0N
H.0N
N.0N
5.vN
0.0H
5.00
H.0N

Hm.uva0Cm

m moC

H.H0
v.¢N
0.0H
0.00
0.00
0.00
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0.00
0.00
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sHQ

N.500
0.HHH
0.000
0.00
0.00
0.vN
v.00
0.0v0
5.500
0.00H

m 0CHummn

N.00
0.00
0.00
0.00
H.00

o mmCCHQ

0.N0

0.00H
0.00H
0.HOH
0.HOH
N.H0

5.00

N.v00
N.v00
0.NOH

o 0CHwan

Emumxm wumCHUuooo Umumuou cu uumammu Cqu mum meocm

quonCu HN mH muwm Cqu No umnECC N:00NCN wUHHm
0000.0 I 0: 0N00.0: vH05.0: I 0H
00H5.0 I NC 0000.0 005v.o: I NH
5v00.0 I HC HON0.0: 000v.0 I HH
mmCHmou COH uomCHU 0CH30HHow mCu cu 0CHUuooum Umumuou ma HHH3 Numb
H0.0 .0H H .0 .0HH v .0N .5HN 0.0N
H0.0 .0H 0 .0N .NOH v .0N .5HN 0.0N
H0.0 .HH 0 .00 .00H 0 .0N .5HN 0.5N
H0.0 .0N 0 .N .0NH v .0H .00N 0.0N
H0.0 .0H 0 .0N .05H v .0H .00N 0.0N
H0.0 .5 0 .0H .05H v .0 .00N 0.0N
H0.0 .N0 H .0N .NoH v .0 .000 o.NN
H0.0 .50 H .0 .00 v .0 .000 0.HN
H0.0 .N H .N .ov v .0 .000 0.0N
H0.0 .0H H .NH .00 v .0 .v00 0.0H
H0.0 .00 H .v .00N q .0N .0NN 0.0H
H0.0 .0H H .0N .vv0 v .0N .0NN o.NH
H0.0 .0H 0 .0N .05 N .vN .0H0 0.HH
H0.0 .0 0 .0 .00 N .0N .0H0 0.0H
H0.0 .0H H .v .NHO N .vH .0N 0.0
H0.0 .v H .00 .N5N N .vH .0N 0.5
H0.0 .0H H .Nv .N00 v .00 .0HN 0.0
H0.0 .NH H .5N .05N v .00 .vHN 0.0
H0.0 .HH 0 .0N .v0H N .0N .05 0.v
H0.0 .HH 0 .v .00H N .0N .05 0.0
H0.0 .0v 0 .0 .00N N .0N .v0H o.N
mmoConCu umnECC moCsHQ pum> NmCCH moCCHQ uum> NmCCH
mCH3uouoHE CoHum quHuo uwm CH3u COHmucoHuo mem UHqu CHmum
HN mH mumm CH3» «0 umflEdC N:00NCm CoHuumm CHCu
0.vH 0.00 «.0 0.0 v.NvN 0.0N
N.05 0.H0 0.50N H.00 0.00 0.0N
5.00H v.0N 0.0N 0.00 0.05N 0.5N

.233

05v0000.0
v000000.0
N5NH000.0
000N000.0
00NH000.0
vNON000.0
Nv0H000.0
5v5N000.0
00N0000.0
00HN000.0
05v0000.0

 

0.0H
0.HN
N.0v
0.N

0.N¢
v.50
v.0

H.05
0.00
5.00
0.0

u

v.0N

H.NvH
N.00N
0.000
0.00H
0.00H
0.00N
0.NNO
0.00

H.05N
0.v00

0.00H
0.00H
0.00H
0.vH
N.05
5.00H
5.Hv
5.00H
0.00
0.0v
5.00
5.H0
H.H0
5.Hv
5.00
0.05
0.00H
0.00
0.00H
0.0N
5.00
v.HN
5.0H
0.05
0.NHH
0.N0
0.00
0.00H

mumEHHHHE NmQ

00HHwEMH uo

0.5N
5.0N
0.NN
v.NN
0.0N
H.5N
5.0N
0.5N
H.vN
0.vN
N.0N

0.05 0.H0
0.00 0.000
0.N0 0.00H
0.00 0.0
0.H0 0.50N
v.0N 0.0N
N.0 0.50
N.N0 H.v0N
N.00 0.0N
0.0 H.0v
0.0N 0.N0
0.0 5.NON
«.00 0.0H
0.05 N.0NN
0.5N 0.0N
N.0 0.Nv
0.0 N.00H
0.NH 0.0NN
0.N N.00H
H.00 0.00N
0.0N 0.0HN
v.5N 0.00N
H.0H H.va
0.0v N.NON
0.0H 0.50
0.0 0.00N
N.0N N.HON
0.N 0.0N
moCsHQ 0CHNmmn
.OC mwxm ConCwu

wocsHa

0.00H
H.05H
5.00N
v.NvN
0.00
0.05N
0.000
5.00
H.05N
0.00H
H.HHN
0.000
0.HNN
0.0H
0.00N
0.NOH
0.05N
H.0H0
v.00N
0.00H
0.NNO
0.00H
0.0
N.NOH
0.000
0.H00
H.000
0.00N

0CHummn

mmxm ConmmuQEoo

Emumxm mumCHUNooo uwumuou ou uqummu Cqu

N:00NC0
0.N5
5.00
0.5v
5.v0
0.00
0.N0
0.0v
0.0H
0.v
0.0v
0.05

0.00H
0.0H

0.05

0.HHH
H.000
v.000
H.05H
N.HvH
0.0H0
0.0vH
5.0HH

0.00
0.00
0.00
0.00
0.00
0.05
5.Hv
5.Hv
0.0N
0.0N
0.00

CoHuumm CHCu uo mHm>HMCm UHECC>U

v.H0
v.H0
0.H0
0.NH
0.NH
0.0H0
H.HqH
H.HvH
0.00H
0.00H
0.N0

OOOOOOOOO
HNMVIDWI‘QO’I

CHmuo

mum mmHocm

0.0N
0.0N
0.5N
0.0N
0.0N
0.0N
0.NN
0.HN
0.0N
0.0H
0.0H

234

H 0H COHqu CH3» xUHCu 000.H I OHumu CquouUHE\C quxUHC» 0N 0H nuvm CH3» uo umnEdC 0:00NC0 00HHm
5v00.0: I 0C HON0.0 I 0E 000v.0: I 0H
0000.0 I NC 0N00.0: I N8 vH05.0: I NH
00H5.0 I HC 0000.0 I HE 005v.0: I HH

mmCHmou CoH uowNHu 0CH30HHou 0:» o» 0CH0N0000 um»m»ou up HHH3 mumu
.0 .00v 00.0 00.0 .0 H0.0 .0H H .0H .0HN 0 .NH .NOH e.vN
.0 .0Nv 00.0 00.0 .0 H0.0 .v H .0 .0HH N .0 .Hv 0.0N
.0 .0NH 00.0 00.0 .0 H0.0 .0H 0 .0H .00H N .0 .Hv o.NN
.o .0NH 00.0 00.0 .0 H0.0 .NH 0 .NN .NOH N .0N .N5 0.HN
.0 .0NH 00.0 00.0 .0 H0.0 .0H 0 .0 .00H N .0N .N5 0.0N
.0 .00N 00.0 00.0 .0 H0.0 .H0 H .5 .00H N .0 .H00 0.0H
.0 .ovN 00.0 00.0 .0 H0.0 .v0 0 .N .00 N .0 .H00 0.0H
.0 .00N 00.0 00.0 .0 H0.0 .0H 0 .NH .NON N .0N .00 0.0H
.0 .00N 00.0 00.0 .0 H0.0 .0 0 .0H .00H N .0N .00 0.vH
.0 .0NH 00.0 00.0 .0 H0.0 .0 0 .00 .0N0 N .00 .00H 0.0H
.0 .OVN 00.0 00.0 .0 H0.0 .00 H .N .NOH v .0H .00N 0.0H
.0 .OVN 00.0 00.0 .0 H0.0 .VH H .NH .00N v .0H .00N 0.0
.0 .0NH 00.0 00.0 .0 H0.0 .0H 0 .0N .05H v .0N .00N 0.0
.0 .0NH 00.0 00.0 .0 H0.0 .0H 0 .0H .0NN v .0N .00N 0.5
.0 .00H 00.0 00.0 .0 H0.0 .NH 0 .0H .00 q .0H .00N 0.0
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241

 

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