The distribution of some selected alkali metals and ......The Stronghold Granite is located in the...

145
The distribution of some selected alkali metals and alkaline earths in the Stronghold granite, Cochise County, Arizona Item Type text; Dissertation-Reproduction (electronic) Authors Bock, Charles Mitchell, 1935- Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 06/07/2021 16:04:46 Link to Item http://hdl.handle.net/10150/565605

Transcript of The distribution of some selected alkali metals and ......The Stronghold Granite is located in the...

  • The distribution of some selected alkali metals and alkalineearths in the Stronghold granite, Cochise County, Arizona

    Item Type text; Dissertation-Reproduction (electronic)

    Authors Bock, Charles Mitchell, 1935-

    Publisher The University of Arizona.

    Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.

    Download date 06/07/2021 16:04:46

    Link to Item http://hdl.handle.net/10150/565605

    http://hdl.handle.net/10150/565605

  • THE DISTRIBUTION OF SOME SELECTED ALKALI METALS

    AND ALKALINE EARTHS IN THE STRONGHOLD

    GRANITE, COCHISE COUNTY, ARIZONA

    A Thesis Submitted to the Faculty of the

    DEPARTMENT OF GEOLOGY

    In P a rtia l Fulfillm ent of the Requirem ents For the Degree of

    DOCTOR OF PHILOSOPHY

    THE .UNIVERSITY OF ARIZONA

    •r-'C harles Mi Bock

  • ERRATA

    page 26, Table 4.Stronghold Granite

    k2o CaO

    Average

    Stronghold Granite

    5.75 0.50 should read

    Average 4.95 0.59

    page 27, Table 5 .Average o f rhyolite

    dikes associated with the Stronghold

    k2o CaO

    Granite

    Average o f rhyolitedikes associated with

    5.75 0.31 should read

    the Stronghold Granite

    4.95 0.36

  • THE UNIVERSITY OF ARIZONA

    GRADUATE COLLEGE

    I hereby recommend that this dissertation prepared under my

    direction by Charles M, Bock___________________________________

    entitled The distribution of some selected alkali metals and alkaline

    earths in the Stronghold Granite, Cochise County, Arizona_______

    be accepted as fulfilling the dissertation requirement of the

    degree of Doctor of Philosophy_______________________________

    After inspection of the dissertation, the following members

    of the Final Examination Committee concur in its approval and

    recommend its acceptance:*

    *This approval and acceptance is contingent on the candidate's adequate performance and defense of this dissertation at the final oral examination. The inclusion of this sheet bound into the library copy of the dissertation is evidence of satisfactory performance at the final examination.

    Date / z

  • STATEMENT BY AUTHOR

    This thesis has been submitted in p artia l fulfillment of req u ire m ents for an advanced degree at The University of Arizona and is deposited in The University L ibrary to be made available to borrow ers under ru le s of the L ibrary .

    B rief quotations from this thesis a re allowable without special perm ission, provided that accurate acknowledgment of source is made. Requests for perm ission for extended quotation from or reproduction of th is m anuscript in whole or in p art may be granted by the head of the m ajor departm ent or the Dean of the Graduate College when in their judgment the proposed use of the m ateria l is in the in te rests of scholarship. In all other instances, however, perm ission m ust be obtained from the author.

  • THE DISTRIBUTION OF SOME SELECTED ALKALI METALS AND ALKALINE EARTHS IN THE STRONGHOLD

    GRANITE, COCHISE COUNTY, ARIZONA

    by

    C harles M. Bock

    ABSTRACT

    X -ray fluorescent spectrographic analyses show the Stronghold

    G ranite to be im poverished in Sr with respec t to other analyzed granites

    of sim ilar Ca content and higher in the ratio . C a/S r. Rb and K/Rb values

    for the Stronghold G ranite a re sim ilar to values obtained for other bio-

    tite granites. Trend surface analysis techniques applied to the v a ri

    ables m easured show that definite compositional trends exist in the

    m assif. High order trend surfaces for Sr and Ca show negative cor

    relation with the high order trend surface for the ra tio C a/S r. The

    high order surfaces for C a/S r and K/Rb show negative correlation with

    each other indicating that la te stage igneous events a re m ore dominant

    in the northeast than in other p a r ts of the pluton.

    ii

  • TABLE OF CONTENTS

    Page

    GLOSSARY ..................... ........................................................................... 1

    INTRODUCTION ....................................................... ............... .............. 3

    PROCEDURE........................... 7

    GEOLOGICAL SETTING OF THE STRONGHOLD GRANITE . . . . 15

    Country Rocks .................................................. 15Contact M etamorphism ............................................................... 17Rhyolite and Aplite Dikes A ssociated with the Stronghold

    G ranite ....................... 18Xenoliths ..................... 19Petrography of the Stronghold G r a n i te ................ 19

    M ajor M inerals ................................... 20A ccessory M inerals ............................. 20

    RESULTS OF ANALYSES ..................................................................... 22

    K and Ca Analyses ......................................................... .. 22Sr Analyses ................................... 27Rb Analyses ................................. 27

    TREND SURFACES .............................................. 30

    Assumptions .......................................... 30Sampling ..................................................... 31Computation .................................................. 32Discussion of Trend S u rfa c e s ...................................... ............... 34Significance of Trend Surfaces ............... ............................... .. 38

    DEVIATION MAPS .................................................. 55

    SUMB4ARY AND CONCLUSIONS . . . . . . . . . . . . . . o . . . . . . . . . . . . . 83

    iii

  • Page

    APPENDIX I—-TABULATION OF ANALYSES OF STRONGHOLD GRANITE SAMPLES EXCLUDING LOCATIONS .............................. 64

    APPENDIX H— TABULATION OF ANALYSES OF RHYOLITE AND APLITE DIKES ASSOCIATED WITH THE STRONGHOLD GRANITE................ 74

    APPENDIX HI— COEFFICIENTS FOR TREND SURFACE EQUATIONS ...................................... ........................................................ 77

    APPENDIX IV— TABULATION OF U-V LOCATIONS AND ANALYSES OF STRONGHOLD GRANITE SAMPLES ...................... 80

    APPENDIX V— SUMMATIONS OF COMPUTED AND OBSERVED VARIABLES, SUMS OF DEVIATIONS, SUMS OF SQUARES OF COMPUTED AND OBSERVED VARIABLES,AND SUMS OF SQUARES OF DEVIATIONS ASSOCIATEDWITH THE TREND SURFACES ............................. 86

    SELECTED BIBLIOGRAPHY............................. 90

    LIST OF FIGURES

    Figure Page

    1. Index map showing the location of the DragoonMountains ............................... 4

    2. Topographic map of the central Dragoon Mountains . . . . . . 9

    3. Example m easurem ent and calculation for Sr and Rbusing G -l as a standard ...................................................... 12

    4. Geologic map of the central Dragoon M ountains................... 16

    5. Frequency distributions for percent K and percent Ca inthe Stronghold G ra n i te ................ 23

    6. Frequency distributions for ppm Rb and ppm Sr in theStronghold G ranite ........................... 24

    iv

  • Figure Page

    7. Frequency distributions for the ra tio s K/Rb and C a/Srin the Stronghold Granite ............................................ 25

    8. Outline of the Stronghold Granite showing samplelocations and U-V coordinate s y s te m ............................ .... 33

    9. Linear trend surface for ppm Sr in the StrongholdG ran ite ............. .............. ....................................................... .... 36

    10. Linear trend surface for the ra tio C a/Sr in theStronghold Granite ............................................... .......... .. 37

    11. Scatter plot of percen t Ca vs. ppm Sr in theStronghold Granite • ................. .......... .................................. .. 39

    12. L + Q trend surface for percen t Ca in theStronghold Granite .......................................... 41

    13. L + Q trend surface for ppm Sr in theStronghold Granite ................................ ................ .............. .. 42

    14. L + Q + C trend surface for percent Ca in theStronghold Granite ....................... 43

    15. L + Q + C trend surface for ppm Sr in theStronghold G ra n ite ............ ...................................................... 44

    16. L + Q trend surface for the ra tio C a/Sr in theStronghold G ranite .......................................... 45

    17. L + Q + C trend surface for the ra tio C a/Sr in theStronghold G ranite ..................... 46

    18. L + Q trend surface for percent K in the StrongholdG ran ite ........................................................... 47

    19. L + Q + C trend surface for percent K in theStronghold G ranite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    20. L + Q trend surface for ppm Rb in the StrongholdG ranite .................................... ....................... .. 50

    v

  • Page

    21. L + Q + C trend surface for ppm Rb in the StrongholdG ra n ite ................. . ................. .................. ............................... 51

    22. L + Q trend surface for the ra tio K/Rb in the StrongholdG ra n ite ............................................................................................. 52

    23. L + Q + C trend surface for the ra tio K/Rb in theStronghold G ranite ....................................................... .. 53 *

    24. Map for deviations from the linear trend surface forpercen t K in the Stronghold G ra n ite .................................... 56

    25. Map for deviations from the linear trend surface forpercen t Ca in the Stronghold G ra n ite .................................. 57

    26. Map for deviations from the linear trend surface forppm Rb in the Stronghold Granite ...................................... 58

    27. Map for deviations from the linear trend surface for ,ppm Sr in the Stronghold G ranite .......................................... 59

    28. Map for deviations from the linear trend surface forthe ra tio K/Rb in the Stronghold Granite .......................... 60

    29. Map for deviations from the linear trend surface forthe ratio C a/Sr in the Stronghold G ra n ite .............................. 61

    LIST OF TABLES

    Table Page

    1. Instrum ental analysis d a ta ................................................. 10

    2. P recision and accuracy of analyses ..................... .............. .. 13

    3. Isotope dilution analyses and X -ray fluorescentanalyses ................................................ ................................. .... 14

    4. Comparison of CaO and KgO contents of Nockolds’average biotite granite and the Stronghold Granite . . . . . 26

    Figure

    vi

  • Table Page

    5„ Comparison of CaO and KoO contents of averagealkali rhyolite and rhyoute-obsidian with rh y o lite s" associated with the Stronghold G ra n ite ........... .. o . . . 27

    6. Comparison of Sr contents and C a/S r ra tio s of lowCa granites and the Stronghold Granite ......... .. 28

    7. Comparison of Sr contents and C a/Sr ra tio s of lowCa rhyolites and rhyolites associated with theStronghold G ran ite ................................................................ 28

    8. Comparison of Rb contents and K/Rb ra tio s of 16South African biotite granites and the StrongholdG r a n i t e ........... ........................... ......................................... .. 29

    9. Percentages of total sum s of squares associated withthe trend surfaces ............................................................. .... 35

    10. Radii of the elem ents studied in the Stronghold G ranite . . 49

    vii

  • GLOSSARY

    DEVIATION TERMS. The algebraic difference between trend surface

    values and values actually m easured a t data locations.

    DIADOCHY. The substitution of one element for another element in a

    given site in a crysta l structure .

    G -l. A granite sam ple distributed by the U. S. Geological Survey for

    which the chem ical composition is known precisely .

    LINEAR SURFACE. A plane surface; a surface whose equation has no

    te rm s higher, than f irs t degree.

    LINEAR PLUS QUADRATIC SURFACE. A surface whose equation con

    tains second degree te rm s plus f irs t degree te rm s.

    LINEAR PLUS QUADRATIC PLUS CUBIC SURFACE. A surface whose

    equation contains f irs t, second, and th ird degree te rm s.

    NEGATIVE CORRELATION. R efers to a relationship between two v a ri

    ables that causes one variable to increase while the other de

    creases .

    POSITIVE CORRELATION. R efers to a relationship between two v a r i

    ables that causes one to increase when the other inc reases or

    to decrease when the other decreases.

  • 2

    REGRESSION ANALYSIS. In this study, a m athem atical treatm ent of

    the locations and magnitudes of a se t of variables to determ ine

    an equation which best describes the magnitude of the variables

    as a function of location.

    TREND SURFACE. In this study, a surface which describes a variable

    as a function of location.

    X-RAY FLUORESCENT SPECTROGRAMHY. A spectrographic technique

    in which X -rays a re used to excite fluorescent X -radiation

    which is characte ris tic for each element.

  • INTRODUCTION

    This paper is an attem pt to make a rea lis tic estim ate of the

    p artia l composition of the Stronghold Granite and to investigate the

    quantitative a rea l variations of K, Ca, Rb, Sr, K/Rb, and C a/S r using

    trend surface analysis techniques. The elem ents selected for analysis

    in this study were chosen because they a re readily amenable to quanti

    tative analysis by X -ray fluorescent spectrography and they a re of geo

    chem ical and petrologic moment.

    The Stronghold Granite is located in the Dragoon Mountains of

    Cochise County, Arizona (see Fig. 1).

    The Stronghold Granite was chosen for study for the following

    reasons:

    1. The Stronghold G ranite is clearly in trusive to the surround

    ing country rocks; i t can, therefore, be compared to other igneous

    bodies.

    2. The m assif is well exposed and only m oderately weathered.

    3. Reliable geological work, e. g . , outcrop mapping, had a l

    ready been accomplished.

    4. F ine-grained texture of the granite sim plified sampling

    and sam ple preparation because inadvertent inclusions of xenolithic

    3

  • Figure 1. —Index map showing the location of the

    Dragoon Mountains.

  • ARI ZONA

    INDEXMAP

  • 5

    m ateria l or phenocrysts in hand specim ens was not a problem . That is,

    a few cubic centim eters of a given hand specimen is as likely to be rep

    resen tative of that hand specimen as any other sm all portion of that

    hand specimen.

    The Dragoon Mountains a re a has been mapped as a p a rt of a

    la rg e r regional study by Gilluly (1956). Gilluly’s work included petro

    graphic descriptions of the Stronghold Granite as well as two chemical

    analyses of the intrusion. C ederstrom (1946) described the structu ra l

    geology of a sm all portion of the Stronghold Granite. Whitten (1959)

    has dem onstrated that quantitative m ineralogic variation in granitic

    bodies can be investigated successfully using trend surface analysis

    techniques.

    The w riter gratefully acknowledges technical support from Dr.

    R. W. G. Wyckoff of the Physics Departm ent of the U niversity of

    Arizona. X -ray fluorescent spectrographic analyses w ere ca rried out

    using equipment made available to Dr. Wyckoff for other re sea rch

    purposes under National Science Foundation Grant number 9760, and

    National Institute of Health Grant number DE 01183. The w riter also

    wishes to thank P ro fesso rs John W. Anthony and Spencer R. Titley for

    many helpful suggestions during the course of the study. M r. R ichard

    A. Bideaux operated the computer for the author, and wrote auxiliary

    routines which aided the w riter m aterially . The Num erical Analysis

    Laboratory of the U niversity of Arizona allowed the w riter use of their

  • equipment.

  • PROCEDURE

    Early in the course of th is study the w riter established several

    c r ite r ia which any granitic body would have to m eet to be successfully

    studied with X -ray fluorescent spectrography combined with trend su r

    face techniques. F irs t, the granite m ust be unequivocally in trusive so

    that trends of trace element distribution observed in other igneous bodies

    could be assum ed to be operative here. Second, the granite m ust be

    well exposed with as little weathering a s possible. Third, the texture

    m ust be fine enough so that 2 or 3 cubic centim eters of the rock would

    be represen tative of any hand specimen, and further, each hand speci

    men m ust be represen tative of the outcrop from which i t was taken.

    The Stronghold Granite sa tisfied a ll of these requirem ents.

    The location of sam pled s ites in th is study is best term ed

    "haphazard” in the s ta tis tica l sense. At the inception of the study the

    idea of collecting sam ples on a grid system was rejected because of the

    extrem ely rugged topography. The sam ples a re biased as to ease of

    accessib ility of outcrop and sta te of weathering. A sampling goal of 10

    sam ples per square m ile was used a rb itra rily , and the w riter tr ied to

    cover each square m ile as uniform ly as possible. Because of natural

    obstacles a uniform coverage is lacking in some a reas .

    7

  • 8

    Sample locations w ere m arked on a 1/62, 500 scale topographic

    map made of p a rts of the U. S. Geological Survey St. David and P earce

    15-minute quadrangles. Granite boundaries were traced from G illuly 's

    geological map of central Cochise County on the newer topographic

    se rie s and were corrected for location on the new map. No serious

    relocation of the granite boundaries was necessary in tran sferrin g the

    geology to the new map (see Fig. 2).

    Samples were chipped from outcrops with a ham m er and m oil,

    and rep resen t the fre sh est rock apparent to the worker at that location.

    Dike rocks were sam pled a rb itra r ily whenever a dike was within approx

    im ately 30 feet of a sample site and accessible. Approximately 3 cubic

    cen tim eters of rock were chipped off each hand specimen and ground in

    a P ica Blender m ill. The sam ple was reduced in the m ill for 1 minute,

    and the pulverized and thoroughly mixed sample was then placed in a

    p lastic "Caplug" and sealed with a l /4 -m il m ylar sheet held in place by

    a drapery ring. Sieve analysis showed that in treating the sam ples in

    th is manner over 80 percen t of the rock was reduced to -300 mesh.

    Samples w ere irrad ia ted in specially constructed sam ple cups so that

    the sam e a rea would be exposed to the exciting radiation for each sam ple.

    A Norelco X -ray vacuum spectrograph with standard control

    panel was used for analysis. Instrum ental analysis data is given in

    Table 1. All peak height m easurem ents w ere made with the chart

    reco rd e r. Signal intensity on the chart reco rd er was adjusted to give

  • Figure 2. —Topographic map of the central

    Dragoon Mountains.

  • 9

    TOPOGRAPHIC MAP OF THECENTRAL DRAGOON MOUNTAINS

    Composite mop of St. David and Peorce 15' Quod MopsScale

    1 0 1 2 Miles

  • 10

    TABLE 1. INSTRUMENTAL ANALYSIS DATA*

    Elem ents Rb and Sr K and Ca

    Tungsten tube potential: 50 K.V. 30 K. V.

    Tube current: 20 M. A. 25 M. A.

    Analyzing crysta l: L iF EDDT

    Radiation detector: Scintillation counter Flow proportional counterwith P-10 gas

    Potential of rad ia tion monitor: 700 V. 1, 800 V.

    Two-theta scan range: 24-28° C a ............... 43. 7-45. 5°

    K ............. .. 48 ;7-50.7°

    Two-theta position for background m easurem ent: A rb itrary C a ............... 43.7°

    K ......... ......... 48.7°

    ♦All m easurem ents w ere made with base level discrim ination se t a t 20 volts. K and Ca m easurem ents were made in a vacuum of le ss than 500 m icrons m ercury p ressu re . Sr and Rb analyses w ere made in an a ir path. Scanning speed for a ll analyses was 1° tw o-theta per minute and the chart reco rd er speed was se t a t half an inch per minute. Tim e constant was se t at four.

  • 11

    optimum deflection from the baseline for the standard.

    G -l, the U. S. Geological Survey standard granite, was used

    a s the standard for a ll analyses by assum ing a linear relationship be

    tween K-alpha X -ray peak height and composition for the sam ples. G -l

    was run at least every tenth sam ple and at the beginning and end of each

    se rie s of analyses. Ca and K peak heights were m easured from back

    ground to the top of the g rea test deflection above background, and a

    d irec t proportion was assum ed for the relation of peak intensity of the

    unknown and the known G -l.

    Sr and Rb contents w ere determ ined by constructing an a rb itra ry

    baseline (see Fig. 3) and assum ing the ra tio of peak height to background

    to be linear with variation in composition. The precision and accuracy

    of these methods can be seen in Table 2. Sr and Rb analyses a re here

    reported to the n ea rest 10 ppm (parts per million). Analyses on the

    U. S. Bureau of Standards rocks were made by including them in day-

    to-day runs and a re , therefore, an acceptable m easure of the accuracy

    and precision which can be associated with analyses on the Stronghold

    G ranite and associated rocks. Values used for G -l a re the values

    recom m ended in U. 8. Geological Survey Bulletin 1113.

    An independent check on the accuracy of the technique used for

    Rb and Sr analyses was made by M r. Donald E. Livingston using isotope

    dilution techniques. The re su lts of the isotope dilution analyses and

    X -ray fluorescence techniques used in th is study appear in Table 3.

  • * 12 k.CO

    X

    degrees 2 0(LiF)

    arbitrary background

    chart baseline

    Peak to background ratios(PBR)BCBA = 2L = 0-345 Rb:

    3452 2 0 ,

    P B R ^ ̂ppm Rbx

    EF — =DE

    §0 = 199 0-402,

    ^PBR for standards + PBR for unknown sample peaks ** unknown

    Sr: P B R i2502 ppm Srx

    1 ppm Rb ir, G-!2 ppm Sr in G-l

    Figure 3.Example measurement and calculation for Sr and Rb

    using G-l as a standard.

  • TABLE 2. PRECISION AND ACCURACY OF ANALYSES

    13

    P ercen t K P ercen t Ca ppm Rb ppm Sr

    Chelm sford Granite (U .S .B .S . # 4979)

    U. S.B . S. 4. 61 0.54

    This study 4. 6640.08* 0.59+0.05* 328+13+ 47+12+

    Turekian and C arr (1961) 65

    M ilford Granite (U .S .B .S . # 4983)

    U. 8. B. S. 3.32 0.40

    This study 3.4140.06* 0.42+0.03* 60+13+ 131+10+

    Turekian and C arr (1961) 125

    G raniteville Granite (U .S .B .S . # 4981)

    U. S .B .S . 3.82 0.46

    This study 3.84+0.02* 0. 6840.06* 432+16+ 11+3+

    Turekian and C arr (1961) 20

    Recommended values for G -l (Stevens, 1960) 4. 51 0.97 220 250

    ♦R esu lts of 9 runs.

    +R esults of 10 runs,

  • 14

    TABLE 3; ISOTOPE DILUTION* ANALYSES AND X-RAY FLUORESCENT ANALYSES

    (Livingston, 1962)

    Rb SrSample I. D.* X-Ray I. D.* X-Ray

    Ruin Granite 279 330 158 150

    Red Rock Rhyolite 205 260 226 220

    Rhyolite (DEL-5-62) 173 200 250 230

  • GEOLOGICAL SETTING OF THE STRONGHOLD GRANITE

    Country Rocks

    The following is a b rief description of the rocks which surround

    the Stronghold Granite. A detailed rep o rt on the region has been pub

    lished as U. S. Geological Survey Professional Paper 281 by Jam es

    Gilluly. The reader is re fe rre d to that paper for detailed stratigraphic

    and struc tu ra l information.

    The oldest unit exposed in contact with the granite is the P re -

    cam brian Pinal Schist. Exposures of the sch ist along the central septum

    (see Fig. 4) which divides the granite into two lobes a re characterized

    by biotite, muscovite, quartz, and a little hornblende. A second type

    of P inal Schist exposed along the eastern boundary of the pluton is

    characterized by muscovite and occasional porphyroblasts of andalusite

    averaging 5 mm in length.

    Paleozoic rocks lie unconformably on the P recam brian Pinal

    Schist and consist of the basal Cam brian Bolsa Q uartzite overlain by a

    Devonian through Perm ian lim estone sequence in terrupted by occasional

    shaly partings. The lim estone has suffered varying degrees of contact

    m etam orphism , but seem s to have been predominantly unreactive to the

    Stronghold Granite.15

  • Figure 4. —Geologic map of the central

    Dragoon Mountains.

  • 110*00'

    j #

    GEOLOGIC M A P % t _

    % %

    6 #r-j

    EXPLANATION

    V^V-:-y-J Quoternory ‘..‘dal..* alluvium

    ii

    f t

    #

    1 Tertiaryhr | Ts9 Stronghold

    " " "

    IvV-.VV-.V* --------- FormationC r ^ Trioesic or

    W p . . w(.•:* Quartz

    Monzonite%# ! H

    j # '' :V.*:*•"•*;\V: Precombrion

    OF THE CENTRAL

    DRAGOON MOUNTAINS Modified from Gilluly(I956)

  • 17

    T riass ic or Ju rass ic Cochise Peak Q uartz Monzonite cuts the

    Paleozoic rocks and is characterized by the presence of large well-

    aligned m icrocline phenocrysts in a q u artz -rich m atrix . The author

    observed an a rea north of the Stronghold Canyon Picnic A rea where the

    quartz monzonite was sheared and apparently rem obilized at the tim e

    of the Stronghold Granite emplacement.

    The Cretaceous Bisbee Form ation overlies the Cochise Peak

    Quartz Monzonite in depositional contact and consists dominantly of

    e lastics with le sse r lim estone. The Bisbee Form ation does not have

    an extensive exposed contact relationship with the Stronghold Granite

    (see Fig. 4).

    Contact M etamorphism

    Contact m etam orphic activity is variable around the periphery

    of the Stronghold Granite. At m ost contacts examined there appears to

    have been a m ere "baking" of the country rocks with little reaction be

    tween the granite and its host. However, there a re a few places where

    lim estones have reac ted with the granite to produce dense hornblende

    hornfels. Reaction was energetic enough to generate at least two pyro-

    m etasom atic o re deposits (Wilson, 1951).

    If one assum es the hornblende hornfels adjacent to the granite

    as an indicator of maximum contact tem perature and p ressu re , the

    granite probably intruded at a tem perature not higher than 700°C, and

  • 18

    with a partia l water p ressu re not g rea ter than 6 kilobars (cf. Fig. 107,

    Fyfe, Turner, and Verhoogen, 1958). However, hornblende hornfels

    zones a re not common, and the granite as a whole was probably cooler

    o r, at least, le ss reactive than indicated by the hornblende hornfels at

    the tim e of emplacement.

    Rhyolite and Aplite Dikes Associated With the Stronghold G ranite"

    Rhyolite dikes a re ubiquitous throughout the Stronghold Granite

    m assif and show well-developed flow lines with m arked chilling a t their

    bo rders. The rhyolite dikes a re usually 2 to 5 feet thick, but locally

    may be as much as 50 feet thick.

    Aplites occur as dikes cutting the granite and as zones within

    the granite which appear to be segregations. Rhyolite dikes intrude

    both granite and aplite and rep resen t the youngest igneous activity a s

    sociated with the granite. Aplite dikes do not appear to be as numerous

    as the rhyolites. They a re , however, especially well displayed half a

    m ile north of Slavin Gulch (see Fig. 2) on the west side of the m assif.

    A large podlike aplite m ass is exposed on the sheer cliffs

    north of the entrance to the Stronghold Picnic A rea, but its boundaries

    could not be determ ined because of inaccessibility of the te rra in .

    M iarolitic cavities displaying euhedral quartz and m icrocline a re

    especially abundant in th is aplitic m ass. Such cavities a re common

  • 19

    also in the granite north of West Stronghold Canyon. In some places

    m icrocline and quartz have completely filled the voids yielding sm all

    pegm atitic pods ranging from a few inches to several feet in diam eter.

    Xenoliths

    P laty b io tite -rich xenoliths 2 to 3 inches in diam eter w ere ob

    served in a roadcut approximately halfway up Slavin Gulch. These

    xenoliths a re probably rem nant products of reaction of the granite with

    blocks of Pinal Schist which were observed to be ro tated out of position

    along the w estern contact of the cen tra l septum.

    Petrography of the Stronghold Granite

    Thin sections of 15 specim ens of the Stronghold G ranite were

    studied with a petrographic m icroscope. No effort was made to get uni

    form coverage of the pluton with thin sections. The specim ens examined

    a re characterized by their cataclastic texture and late growth of m icro

    cline.

    Average estim ated volume percentages a re : 50-60 percent

    quartz, 30-40 percent K- spar, 10-20 percent plagioclase, and 0 to 3

    percen t biotite. M ineralogically the Stronghold G ranite corresponds

    to an alaskitic biotite granite (cf. Gilluly, 1956, p. 107).

  • 20

    M ajor M inerals

    K -spar is represen ted as perth itic m icrocline in euhedral to

    subhedral c ry sta ls 1 to 5 mm long which a re commonly observed re -

    sorbing plagioclase cry sta ls . Large m icrocline c ry sta ls a re m ost

    commonly poikiloblastic with quartz blebs which appear to have been

    partia lly replaced by K -spar. Some of the large crysta ls also show

    growth rings which m ay be outlined by quartz blebs or K -spar with a

    slightly different optical orientation.

    Subhedral to anhedral lath-shaped crysta ls of plagioclase range

    from l / 4 to 2 mm long, and in m ost of the specim ens studied the c ry s

    ta ls have been replaced to a g rea te r or le sse r degree by K -spar. An-

    orth ite molecule percentage, a s determ ined by the M ichel-Levy method,

    with a universal stage ranges from An^g to Angg. Values of An^g to

    An^g a re m ost common.

    Quartz c ry sta ls range from 1/4 to 5 mm in diam eter in an

    hedral, commonly strained grains. Small blebs of quartz a re often a r

    ranged in inclusion zones in K -spar and quartz also often has in te rs titia l

    appearance to large K -spar c ry sta ls .

    A ccessory M inerals

    L ight-green to yellow and yellow-brown laths of biotite range

    from l /8 to 3 mm long and a re not uncommonly being replaced by

  • 21

    m uscovite or K -spar. Opaques a re often in close proxim ity to the bio-

    tite being replaced and a re probably reaction products of the rep lace-X

    ment. Shreds of se ric ite were observed replacing plagioclase occa

    sionally, and le ss commonly as a replacem ent of K -spar. Muscovite

    usually occurs as a replacem ent of biotite, but a few isolated laths a re

    found without associated opaques. A few irreg u la r peripheral patches

    of chlorite, probably pennine, were observed replacing biotite. Euhedral

    to subhedral c ry sta ls of zircon w ere observed as inclusions in biotite.

    Haloes a re found around some zircon cry sta ls , but a re not characte r

    is tic . Anhedral to euhedral c ry sta ls of fluorite a re commonly associ

    ated with biotite and le ss commonly as apparent void fillings.

    Other accessory m inera ls include epidote, apatite, opaques,

    and clays. Epidote occurs as vein fillings in a few locations, but is not

    quantitatively im portant as an accessory m ineral in the granite. A few

    apatite cry sta ls a re occasionally associated with opaques. Magnetite,

    ilm enite, and hem atite observed in the Stronghold Granite appear to be

    associated with the breakdown of biotite. Clay m inera ls were observed

    as occasional alteration products of both K -spar and plagioclase.

  • RESULTS OF ANALYSES

    The re su lts of 243 X -ray fluorescent spectrographic analyses

    on the Stronghold Granite a re tabulated in Appendix I. For convenience

    of com parison with other data, oxide as well as elem ental percentages

    a re lis ted for K and Ca. Frequency distributions of the variables w ere

    made and appear in F igures 5, 6, and 7. C lass in tervals in the f re

    quency distributions were selected a rb itra rily , but in all cases exceed

    the rela tive standard deviation of analysis for the variable involved.

    Analyses of aplites and rhyolite dikes associated with the granite a re

    tabulated in Appendix IL

    K and Ca Analyses

    The KgO and CaO content of the Stronghold Granite do not ap

    pear to be significantly different from Nockolds’ averages for sim ilar

    granitic rocks (Nockolds, 1954; Table 4). However, i t has been pointed

    out that Nockolds* averages a re represen tative only for the hand speci

    m ens which w ere analyzed, and a re not necessarily represen tative of

    the composition of the plutons from which the sam ples were taken. This

    c ritic ism may apply to a ll averaged rock analytical data until m ore r e

    a listic estim ates of the composition of rock units a re available.

    22

  • Arithmetic mean = 4 11% Standard deviation = 0 41

    Frequency distribution for %K

    Figure 5. Frequency distributions for Stronghold Granite.

    Arithmetic mean - 0 42 % Standard deviation = 0-13

    Frequency distribution for % Co

    %K and % Ca in the

    3

  • 6 0.. Arithmetic mean = 3 9 0 PPm Geometric m eon = 375 ppm Standard deviation = 120

    5 0..

    4 0 1

    3 0..

    2 0 ..

    f !|om1oCM

    — 1. I - i. .4- 4—1- -1—1__I__l _ 4 _ 4 - L i . n n 4-4 -4-4—4. 1-4- 4Frequency distribution for ppm Rb

    Figure 6. Frequency distributions forStronghold Granite.

    Arithmetic mean = 30 ppm Geometric mean = 2 0 ppm Standard deviation = 2 0

    Frequency distribution for ppm Srppm Rb and ppm Sr in the

  • 6 0

    5 0

    4 0

    30

    20

    10

    Arithmetic mean = 110 Geometric mean = HO Standard deviation = 25

    4 0 IArithmetic mean = 2 6 0 Geometric mean = 2 0 0Standard deviations 2 0 0

    2 0

    io

    oGO

    1 JA i . m - i

    requency distribution for K/Rb Frequency distribution for Ca/Sr> 7. Frequency distributions for K/Rb and Ca/Sr in the Stronghold Granite.

  • TABLE 4. COMPARISON OF CaO AND K20 CONTENTS OF NOCKOLDS' AVERAGE BIOTITE GRANITE AND

    THE STRONGHOLD GRANITE

    26

    k 2o(percent)

    CaO(percent)

    Nockolds* average biotitegranite (Nockolds, 1954) 5.01 0.56

    Stronghold G ranite average 5.75 0.50

    Whitten (1962b) has proposed a new method for determ ination

    of the average composition of a granitic m assif based on trend surface

    analysis. This method will be applied to the Stronghold G ranite at a

    la te r date.

    The rhyolite dikes intruding the granite a re m ore potassic and

    le s s calcic than Nockolds* (1954) averages for alkali rhyolite and

    rhyolite-obsidian, as seen in Table 5.

    Three rhyolite dikes have sufficiently higher K content to

    w arrant further study, that is, samples Sgd 16, 17, and 24 (see Appen

    dix Ha).

    Too few aplites were analyzed in th is study to make any mean

    ingful com parisons with other data (see Appendix Bb).

  • 27

    TABLE 5. COMPARISON OF CaO AND K2O CONTENTS OF AVERAGE ALKALI RHYOLITE AND RHYOLITE-

    OBSIDIAN WITH RHYOLITES ASSOCIATED WITH THE STRONGHOLD GRANITE

    k 2o(percent)

    CaO(percent)

    Nockolds1 average alkali rhyolite and rhyolite- obsidian (Nockolds, 1954) 4. 73 0.61

    Average of rhyolite dikes associated with the Stronghold G ranite 5. 75 0.31

    Sr Analyses

    The Sr content of the granite appears to be significantly lower

    than the average given by Turekian and Kulp (1956) for granites in the

    0 .1 -1 . 0 percent Ca range (see Table 6). The lower Sr content also

    affects the C a/S r ra tio causing that param eter to be higher than the

    average C a/S r ra tio for rocks of sim ila r composition. Rhyolite dikes

    associated with the granite also run low in Sr when com pared with other

    data (see Table 7). The C a/Sr ra tio for the rhyolites is also higher

    than the average for rocks of sim ila r Ca content (see Table 7).

    Rb Analyses

    Rb values appear to be in good agreem ent with data obtained

  • TABLE 6. COMPARISON OF Sr CONTENTS AND C a/Sr RATIOS OF LOW Ca GRANITES AND THE

    STRONGHOLD GRANITE

    28

    Sr(ppm) C a/Sr

    Average for granitic rocks with 0 .1 -1 .0 percent Ca (Turekian and Kiulp, 1956) 100 60 (re

    ported %s Sr X 10 V Ca)

    Average for the StrongholdG ranite 30 260

    TABLE 7. COMPARISON OF Sr CONTENTS AND C a/Sr RATIOS OF LOW C a RHYOLITES AND RHYOLITES

    ASSOCIATED WITH THE STRONGHOLD GRANITE

    Sr(ppm) Ca/Sr

    Average for rhyolites with le ss than 1 .0 percen t Ca (Turekian and Kulp, 1956) 178 19.6

    (reported as Sr X 103/Ca)

    Average for rhyolites a s sociated with the Stronghold Granite 30 160

  • 29

    from other granites. Ahrens, Pinson, and Kearns (1952) investigated

    the Rb-K relationship in rocks, but did not identify the dark m inerals

    in the granites so that valid com parison is not p ractical. Butler,

    Bowden, and Smith (1962) have made a study of a se rie s of South African

    granites and their data for K/Rb and Rb in biotite granites agree well

    with data gathered in th is study (see Table 8).

    Frequency distributions for Ca and K show the expected norm al

    distributions (cf. Ahrens, 1954a) for m ajor elements (see Fig. 5). Sr

    and C a/S r show apparent lognorm al distributions (see Figs. 6 and 7).

    The distribution for Rb is not clearly norm al or lognormal, but the

    distribution for K/Rb is apparently norm al (see Fig. 7).

    TABLES. COMPARISON OF Rb CONTENTS AND K/Rb RATIOS OF 16 SOUTH AFRICAN BIOTITE

    GRANITES AND THE STRONGHOLDGRANITE

    Rb(ppm) K/Rb

    Average for 16 South African biotite granites (Butler, Bowden, and Smith, 1962) 400 116

    Average for the Stronghold G ranite 390 110

  • TREND SURFACES

    Assumptions

    Whitten (1959) has outlined the assum ptions necessary to a

    study of this nature, but i t seem s advantageous to review then here.

    F irs t , i t is assum ed that a hand specimen is represen tative of a broad

    a re a of rocks around it. Second, i t is assum ed that the laboratory anal

    yses a re tru ly represen tative of the composition of the rocks in question;

    and third, it is assum ed that there is a rational, m easurable trend in

    the granitic body. The f ir s t assum ption is perhaps the weakest of the

    th ree and, as far a s is known, no attem pt has been made to rigorously

    establish the relationship. Sampling plans have been proposed which

    allow equal chance for each outcrop to be sampled, but the w riter does

    not know of any attem pt to dem onstrate that a hand specimen is re p re

    sentative of a rock outcrop.

    The confidence that can be placed in the laboratory work is

    high, since the several analyses of the U. S. Bureau of Standards rocks

    com pare favorably for the known components. The w riter satisfied

    him self early in the study that a few chips from a hand specimen were

    rep resen tative of the hand specim en by making duplicate analyses of

    30

  • 31

    the sam e specimen. In th is respect, however, perhaps m ore confidence

    can be placed in the ra tio s of elem ents than in the absolute quantities.

    The ra tio s may be m ore re liab le because inadvertent inclusion of a

    sam ple rich e r in quartz than the hand specimen would cause the absolute

    amount of K, Ca, Rb, and Sr to be low, but the ra tio s of K/Rb and

    C a/S r should be unchanged, assum ing that the ra tio s a re constant for

    any given hand specimen.

    The assumption that th e re is a rational trend in the Stronghold

    G ranite and that it can actually be portrayed by trend surface can only

    be supported by the fact that trend surface analyses dem onstrate that

    trends do exist for the param ete rs m easured.

    Sampling

    Trend surface analyses have been critic ized because sam ples

    w ere not collected randomly in a rigorous sta tistica l sense (Link and

    Koch, 1962). Sampling models have been proposed based on a rec tan

    gular grid and random number scheme. However, the end re su lt of

    such schem es is that the worker m ust make a subjective decision con

    cerning the accessib ility of the sam ple site, weathering, and other r e l

    evant details. One m ajor problem that is commonly overlooked by

    designers of such plans is the identification of a sam ple site in the field

    from a grid intersection on a topograjiic map or ae ria l photo. In th is

    study a grid sampling procedure was re jected because of rugged

  • 32

    topography. Every effort was made to obtain uniform coverage on the

    outcrop of the pluton, and the w riter feels that the sampling is re p re

    sentative of the Stronghold Granite, even though it may not be s ta tis tica l

    ly valid in a rigorous sense (see Fig. 8). For detailed argum ents on

    sampling see Link and Koch (1962) and Whitten (1962a).

    Computation

    Trend surfaces were generated using an IBM 650 computer

    with a program (IBM file No. 8.3.001) described by Krumbein (1959).

    Information requ ired by the computer includes the location of each data

    point in te rm s of an a rb itra ry U-V coordinate system and data from that

    location. From reg ression analyses coefficients for general equations

    w ere generated for linear (L), linear plus quadratic (L + Q), and linear

    plus quadratic plus cubic (L + Q + C) surfaces. General equations

    (Krumbein and Faulkner, p. 6) for trend surfaces have the form

    XL - A + BU + CV (L)

    Xq = Aq + Bq U + CQ + D2QU + Eq UV + Fq V2 (L + Q)

    Xq - Aq + BCU + CCV + DCU2 + ECUV + F CV2 + GCU3 +

    H c u V + J CUV2 + Kq V3 (L + Q + C)

    where X is the computed value a t a location given by U and V, and A,

    B, C, etc. a re coefficients for the respective surfaces. Coefficients

    for the surfaces generated in th is study a re listed in Appendix ILL The

    U-V location of each sample and the raw data are lis ted in Appendix IV.

  • Figure 8= —Outline of the Stronghold Granite showing

    sample locations (.) and U-V coordinate

    system .

  • A23C K 2 4 E

    T.ii s.

    COCO

  • 34

    "Raw data" were converted to ra tio s and oxide percentages by an auxil

    ia ry computer program .

    Computed values were com pared with m easured values at each

    data point to yield deviation termso

    Trend surface and deviation m aps were contoured by inspec

    tion after computed values were manually plotted against U-V coordi

    nates.

    Discussion of Trend Surfaces

    The linear surfaces for K, Ca, Rb, and K/Rb all a re essen tial

    ly horizontal surfaces, that is , the differences in the variables ac ross

    the surfaces is le ss than the expected analytical e rro r of any individual

    analysis. F rom the percentages of sum s of squares accounted for by

    these surfaces, i t appears that the data fitted by the linear surfaces

    a re noisy (see Table 9). "Noise" may be attributed to analytical e rro r

    or to natural variations within the granite.

    The percentage of the totaled sum of squares accounted for by

    any surface is one appraisal of a surface (Dawson and Whitten, S62).

    This param eter is actually a m easure of "goodness of f i t , " that is ,

    when a high percentage of the sum of squares is accounted for by a su r

    face, the surface p asses through a large number of data points. The

    percentage of total sum of squares accounted for by a surface was

    calculated from the equation given by Dawson and Whitten (1962):

  • 35

    TABLE 9. PERCENTAGES OF TOTAL SUMS OF SQUARES ASSOCIATED WITH THE TREND SURFACES

    ComponentK

    (percent)Ca

    (percent)Rb

    (ppm)Sr

    (ppm) K/Rb C a/Sr

    L inear 0 .5 0.1 6.6 9.0 4.6 8.4

    L inear plusquadratic 9.25 3.19 24.7 16.2 21.5 17.6

    Quadratic alone (8.75) (2.09) (18.1) (7.2) (16.9) (9.2)

    L inear plus quadratic pluscubic 11.8 7.30 42.0 20.3 33.6 25.3

    Cubic alone (2.65) (4.11) (17.3) (13.9) (12.1) (7.7)

    100 (Sum of computed- (Sum X computed) V n)9 9(Sum observed-(Sum X observed) /N)

    This number is norm ally calculated as a p a r t of the computer program ,

    but for some unknown reason, the computer recorded absurd values for

    Sum X observed. Since th is number is used in the above calculation,

    the percentage was calculated by hand after an auxiliary program deter

    mined the tru e value for Sum X^ observed (see Appendix V).

    The linear surfaces for Sr and C a/Sr do show appreciable dif

    ferences in variab les ac ro ss the surfaces (see F igs. 9 and 10).

    L inear plus quadratic p artia l trend surfaces show appreciable

  • Figure 9. —Linear trend surface for ppm Sr in the

    Stronghold Granite.

  • ppm Sr line

    GOoa

  • Figure 10. —Linear trend surface for the ra tio C a/S r

    in the Stronghold Granite.

  • 38

    gains in percentages of sum s of squares (see Table 9), but a re essen

    tially no better at approximating the average variable than the f irs t su r

    face (see Appendix VI). The f ir s t approximation of the average of the

    variable is improved with higher o rder trend surfaces, but i t is doubt

    ful that improvem ent past the f i r s t th ree decimal p laces has any d irec t

    geological significance. Strike and dip symbols showing the attitude of

    the linear trend surface a re shown on the linear plus quadratic surfaces

    for com parison of trend. In all cases except K, the s trik e sense for

    the linear plus quadratic surface is sim ilar to the s trik e of the linear

    surface suggesting that the attitude of the linear surface is significant.

    L inear plus quadratic plus cubic trend surfaces show appreci

    able gains in sum s of squares, but for a ll surfaces except the percent

    Ca surface the gain is le ss than the gain from linear to linear plus

    quadratic. Further, the linear plus quadratic plus cubic surface re ta in s

    the sam e sense of dip and strik e a s that of the linear plus quadratic su r

    face.

    Significance of T rend Surfaces

    Turekian and Kulp (1956, Fig. 10) have established a positive

    correlation between Ca and Sr in rocks, and a sim ilar correla tion is

    suggested in the Stronghold G ranite, although a lim ited range of Ca

    values tends to m ask th is interdependence in a sca tte r plot (see Fig.

    11). Heier and Taylor (1959b, p. 297) note that Sr proxies for K as

  • I 3 0

    120 -

    I 10 -

    100 ’

    /

    •90

    •80

    •70

    •60

    ;30oo

    •4055

    •30

    •20

    •10

    tir-!4 ':

    Is•e

    • • •

    4

    4

    3

    5 10 20 30 40 50 6 0 70 80 90ppm S r ------ =""»

    Figure II. Scatter plot of % Co vs. ppm

    100 150

    Sr in the Stronghold Granite.W*

  • 40

    well as Ca and diadochy of th is so rt would also tend to obscure co rre la

    tion of Sr with Ca. The substitution of Sr++ for K* is a capture mech

    anism resulting from the sm aller divalent Sr ion (see Table 10) being

    included instead of the monovalent K ion.

    Trend surface analysis suggests a crude positive correlation

    between Ca and Sr, but the sim ilarity is only slight for the L + Q + C

    surfaces and even m ore obscure for the L + Q surfaces (see F igs. 12-

    15). The ra tio C a/Sr is apparently strongly controlled by the gradients

    of the Ca and Sr trends. The C a/S r ra tio trend surface shows a strong

    negative correlation with trend surfaces for the absolute amounts of Ca

    and Sr (see Figs. 14, 15, 16, and 17). This negative correlation be

    tween the ra tio C a/Sr and Ca and Sr had been noted previously by

    Turekian and Kulp (1956) and Heier and Taylor (1959).

    An increasing ra tio of C a/S r is considered an index of in c reas

    ing differentiation in igneous rocks (Heier and Taylor, 1959, p. 298).

    If the L + Q + C trend surface for C a/S r tru ly rep resen ts a trend in the

    Stronghold G ranite, then la te stage igneous events p rog ressed toward

    the northeastern p a rt of the pluton (see Fig. 17).

    The distribution of K throughout the pluton is apparently uni

    form because all the trend surfaces for absolute amount of K have a

    highly sym m etric relation to the outline of the intrusion (see F igs. 18

    and 19). By contrast, the Rb distribution is uniform for the linear su r

    face, but the second and th ird degree surfaces show pronounced r is e s

  • Figure 12. —L + Q trend surface for percen t Ca in the

    Stronghold Granite.

  • 0 4 0

    % C a I t q

  • Figure 13. —L + Q trend surface for ppm Sr in the

    Stronghold Granite.

  • Figure 14. —L + Q + C trend surface for percent Ca in the

    Stronghold Granite.

  • Figure 15. —L + Q + C trend surface for ppm Sr in the

    Stronghold Granite.

  • ppm Sr l + q + c

    +

  • Figure 16. —L + Q trend surface for the ra tio C a/Sr in the

    Stronghold Granite.

  • 5 0 0

    f t

  • Figure 17. —L + Q + C trend surface for the ra tio C a/S r

    in the Stronghold Granite.

  • CD

  • Figure 18, —L + Q trend surface for percen t K in the

    Stronghold Granite.

  • 4 0 0

  • Figure 19. —L + Q + C trend surface for percent K in the

    Stronghold Granite.

  • z z

    3 80

    %K l+q + c

    +00

  • TABLE 10. RADII OF THE ELEMENTS STUDIED IN THE STRONGHOLD GRANITE

    4 9

    Cation . K* • Ca++ • Rb+ Sr++

    o o o oRadius (Green, 1.42 A 1.03 A 1.57 A 1.16 A

    1959)

    in Rb values to the northeast (see Figs. 20 and 21).

    Rb values apparently strongly control the trend of the K/Rb

    ra tio for both L + Q and L + Q + C surfaces (see Figs. 22 and 23). As

    Rb values increase , K values decrease, so that the K/Rb ra tio s de

    c rease rapidly. The strong trend of lower values for the ra tio toward

    the northeast p a rt of the m assif is striking, and since the param eter of

    K/Rb is also considered as a differentiation index (Butler, Bowden, and

    Smith, 1962, p. 93), the idea that late stage igneous events p rogressed

    toward the northeast is reinforced.

    In noting that late stage igneous events p rogressed toward the

    northeast in the Stronghold Granite, the w riter does not mean that dif

    ferentiation in the granite p rog ressed la terally . Consideration of v e rti

    cal position of sampled sites in trend surface analyses would alm ost

    certainly a lter the configuration of the trend surfaces so that vertical

    trends may be distinguished. Further, from rela tions with the country

    rocks the w riter gained the im pression that the pluton is unroofed only

  • Figure 20. —L + Q trend surface for ppm Rb in the

    Stronghold Granite.

  • Figure 21. —L + Q + C trend surface for ppm Rb in the

    Stronghold Granite.

  • 5 0

    400450ppm Rb l + q + c

  • Figure 22, —L + Q trend surface for the ra tio K/Rb in the

    Stronghold Granite.

  • Figure 23„ —L + Q + C trend surface for the ra tio K/Rb

    in the Stronghold Granite.

  • !

    120

    K/Rb l+q+c

  • /

    54

    to a shallow depth. Thus, the weathering surface of the pluton in places

    may be very close to the original in terface between the m assif and the

    country rocks. P erterbating influences of reactions between the granite,

    country rocks, and la te stage differentiates will becloud the p ic tu re of

    the granite* s history until m ore is learned about the geology of the in

    trusion.

  • DEVIATION MAPS

    Deviations from calculated linear values w ere plotted and con

    toured (see F igs. 24-29). Deviations from higher o rder surfaces were

    not trea ted because higher o rder te rm s account for m ore and m ore

    sum s of squares thereby reducing deviations,, Im plicit in th is study is

    the assum ption that a linear trend surface is an adequate representation

    of any regional trend, while higher order trend surfaces may m ask im

    portant anom alies removing them from deviation te rm s. Deviations a re

    probably not significant unless they a re m ore than one standard deviation

    away from the surface, where the standard deviation is computed from

    frequency distributions of the variables. Significant deviations may

    also be surrounded by deviations of the sam e sign and of a le sse r or

    g rea ter magnitude.

    In th is study deviations from the regional trend (linear trend

    surface) apparently have no sim ple relationship to the surrounding

    country rocks. Since lack of reaction of the granite with the country

    rocks seem s to be characte ristic , lack of correla tion of the deviations

    with contiguous country rocks is not su rprising (cf. Fig. 4 with F igs.

    24-29). The Paleozoic rocks surrounding the m assif a re largely lim e

    stones, and one might expect positive Ca anom alies a t contacts of the

    55

  • Figure 24. —Map for deviations from the linear trend

    surface for percent K in the Stronghold

    Granite.

  • m m

    SB

  • Figure 25. —Map for deviations from the linear trend

    surface for percent Ca in the Stronghold

    Granite.

  • DEVIATIONSE X P L A N A T I O N

    P o s i t i v e N e g a t i v e

  • Figure 26. —Map for deviations from the linear trend

    surface for ppm Rb in the

    Stronghold Granite.

  • '' ’•X’X-Xv!

    Rb LINEAR DEVIATIONS

    E X P L A N A T I O NP o s i t i v e

    o x 0-200

    CJI00

  • Figure 27, —Map for deviations from the linear trend

    surface for ppm Sr in theK *

    . Stronghold Granite.

  • CJi

  • Figure 28. —Map for deviations from the linear trend

    surface for the ra tio K/Rb in the

    Stronghold Granite.

  • Figure 29, —Map for deviations from the linear trend

    surface for the ra tio C a/Sr in the

    Stronghold Granite,

  • Ca/Sr LINEA

    DEVIATIONSE X P L A N A T I O N

    N e g a t i v e

    B ,

  • 62

    granite and the Paleozoic country rocks, but no such sim ple re la tion

    ship is apparent in the deviation m aps.

    Speculations concerning deviation m aps m ust await processing

    of complimentary petrographic data by trend surface analysis.

  • SUMMARY AND CONCLUSIONS

    1. X -ray fluorescent spectrographic analysis is a re liab le

    method for p a rtia l analysis of granitic rocks, and it is especially

    amenable to the analyses of elem ents such as Sr and Rb which a re dif

    ficult to tre a t using norm al chem ical techniques.

    2. Trend surface analysis can be used to establish chemical

    trends in granitic bodies where such trends a re not otherw ise clear in

    raw data. Such trends can be used to establish a rea s within a granite

    pluton which are characterized by la te stage igneous activity.

    3. The Stronghold G ranite is an alkali granite im poverished

    in Sr and higher in the ra tio C a/S r with respec t to other analyzed

    granites of sim ilar Ca content. Rb and K/Rb values of the Stronghold

    G ranite a re not s ignificantly different from sim ilar rocks. Reported

    negative correlation between Ca and Sr, and the ra tio C a/Sr is co r

    roborated. C a/S r and K/Rb trend surfaces show negative correlation

    and indicate that la te stage igneous activity p rogressed toward the

    northeast in the Stronghold G ranite pluton.

    6 3

  • APPENDIX I

    TABULATION OF ANALYSES OF STRONGHOLD GRANITE SAMPLES EXCLUDING LOCATIONS

    NOTE: All data a re listed here in p a rts per million, that is ,

    to read percentages count four p laces over from the right.

    EXAMPLE: Read 0000044800 as 4.48 percent. Read

    0000000010 as 10 ppm.

    F or purposes of computation, Sr values originally recorded as

    le ss than 10 ppm a re reported as 5 ppm. Oxide percentages and ra tio s

    of the elem ents were computed by mi auxiliary program on the IBM 650

    computer.

    6 4

  • 65

  • Sample No.

    0000000001

    0000000002

    0 0 0 0 0 0 0 0 0 3

    0 0 0 0 0 0 0 0 0 4

    0 0 0 0 0 0 0 0 0 5

    0 0 0 0 0 0 0 0 0 6

    0 0 0 0 0 0 0 0 0 7

    0 0 0 0 0 0 0 0 0 8

    0 0 0 0 0 0 0 0 0 9

    0000000010

    0000000011

    0000000012

    0 0 0 0 0 0 0 0 1 3

    0 0 0 0 0 0 0 0 1 4

    0 0 0 0 0 0 0 0 1 5

    0 0 0 0 0 0 0 0 1 6

    0 0 0 0 0 0 0 0 1 7

    0 0 0 0 0 0 0 0 1 8

    000000001Q

    0000000020

    0000000021

    0000000022

    0 0 0 0 0 0 0 0 2 3

    0 0 0 0 0 0 0 0 2 4

    0 0 0 0 0 0 0 0 2 5

    0 0 0 0 0 0 0 0 2 6

    0 0 0 0 0 0 0 0 2 7

    0 0 0 0 0 0 0 0 2 8

    % K

    0 0 0 0 0 4 4 8 0 0

    0 0 0 0 0 4 3 6 0 0

    0 0 0 0 0 4 2 4 0 0

    0 0 0 0 0 3 9 2 0 0

    0 0 0 0 0 4 0 7 0 0

    0 0 0 0 0 4 4 2 0 0

    0 0 0 0 0 4 4 8 0 0

    0 0 0 0 4 0 0 0 0

    0 0 0 0 0 4 2 7 0 0

    0 0 0 0 0 3 8 9 0 0

    0 0 0 0 0 3 2 8 0 0

    0 0 0 0 0 4 3 0 0 0

    0 0 0 0 0 3 8 9 0 0

    0 0 0 0 0 3 9 8 0 0

    0 0 0 0 0 4 3 0 0 0

    0 0 0 0 0 3 3 3 0 0

    0 0 0 0 0 4 5 7 0 0

    0 0 0 0 0 4 3 4 0 0

    0 0 0 0 0 4 6 7 0 0

    0 0 0 0 4 0 0 0 0

    0 0 0 0 0 4 3 7 0 0

    0 0 0 0 0 4 2 7 0 0

    0 0 0 0 0 4 2 0 0 0

    0 0 0 0 0 3 7 3 0 0

    0 0 0 0 4 0 0 0 0

    0 0 0 0 0 3 7 7 0 0

    0 0 0 0 0 3 5 6 0 0

    0 0 0 0 0 4 1 4 0 0

    % k 2o

    0 0 0 0 0 5 3 9 7 0

    0 0 0 0 0 5 2 5 2 0

    0 0 0 0 0 5 1 0 8 0

    0 0 0 0 0 4 7 2 2 0

    0 0 0 0 0 4 9 0 3 0

    0 0 0 0 0 5 3 2 4 0

    0 0 0 0 0 5 3 9 7 0

    0 0 0 0 0 4 8 1 8 0

    0 0 0 0 0 5 1 4 4 0

    0 0 0 0 0 4 6 8 6 0

    0 0 0 0 0 3 9 5 1 0

    0 0 0 0 0 5 1 8 0 0

    0 0 0 0 0 4 6 8 6 0

    0 0 0 0 0 4 7 9 4 0

    0 0 0 0 0 5 1 8 0 0

    0 0 0 0 0 4 0 1 1 0

    0 0 0 0 0 5 5 0 5 0

    0 0 0 0 0 5 1 0 8 0

    0 0 0 0 0 5 6 2 5 0

    0 0 0 0 0 4 8 1 8 0

    0 0 0 0 0 5 2 6 4 0

    0 0 0 0 0 5 1 4 4 0

    0 0 0 0 0 5 0 5 9 0

    0 0 0 0 0 4 4 9 3 0

    0 0 0 0 0 4 8 1 8 0

    0 0 0 0 0 4 5 4 1 0

    0 0 0 0 0 4 2 8 8 0

    0 0 0 0 0 4 9 8 7 0

    % Ca

    0 0 0 0 0 0 4 7 0 0

    0 0 0 0 0 0 4 4 0 0

    0 0 0 0 0 0 6 4 0 0

    0 0 0 0 0 0 4 9 0 0

    0 0 0 0 0 0 4 2 0 0

    0 0 0 0 0 0 7 6 0 0

    0 0 0 0 0 0 3 2 0 0

    0 0 0 0 0 0 7 0 0 0

    0 0 0 0 0 0 5 1 0 0

    0 0 0 0 0 0 4 2 0 0

    0 0 0 0 0 0 4 4 0 0

    0 0 0 0 0 0 4 0 0 0

    0 0 0 0 0 0 4 4 0 0

    0 0 0 0 0 0 4 5 0 0

    0 0 0 0 0 0 5 7 0 0

    0 0 0 0 0 0 7 7 0 0

    0 0 0 0 0 0 5 0 0 0

    0 0 0 0 0 0 6 6 0 0

    0 0 0 0 0 0 3 3 0 0

    0 0 0 0 0 0 4 8 0 0

    0 0 0 0 0 0 4 5 0 0

    0 0 0 0 0 0 4 7 0 0

    0 0 0 0 0 0 4 2 0 0

    0 0 0 0 0 0 4 9 0 0

    0 0 0 0 0 0 3 4 0 0

    0 0 0 0 0 0 5 6 0 0

    0 0 0 0 0 0 5 2 0 0

    0 0 0 0 0 0 4 7 0 0

    % CaC

    0 0 0 0 0 0 6 5 8 0

    0 0 0 0 0 0 6 1 6 0

    0 0 0 0 0 0 8 9 5 0

    0 0 0 0 0 0 6 8 6 0

    0 0 0 0 0 0 5 8 8 0

    0 0 0 0 0 1 0 6 3 0

    0 0 0 0 0 0 4 4 8 0

    0 0 0 0 0 0 9 7 9 0

    0 0 0 0 0 0 7 1 4 0

    0 0 0 0 0 0 5 8 8 0

    0000006160

    0 0 0 0 0 0 5 6 0 0

    0 0 0 0 0 0 6 1 6 0

    0 0 0 0 0 0 6 3 0 0

    0 0 0 0 0 0 7 9 8 0

    0 0 0 0 0 1 0 7 7 0

    0 0 ^ 0 0 0 7 0 0 0

    0 0 0 0 0 0 9 2 3 0

    0 0 0 0 0 0 4 6 2 0

    0 0 0 0 0 0 6 7 2 0

    0 0 0 0 0 0 6 3 0 0

    0 0 0 0 0 0 6 5 8 0

    0 0 0 0 0 0 5 8 8 0

    0 0 0 0 0 0 6 8 6 0

    0 0 0 0 0 0 4 7 6 0

    0 0 0 0 0 0 7 8 4 0

    0 0 0 0 0 0 7 2 8 0

    0 0 0 0 0 0 6 5 8 0

    ppm Rb

    0 0 0 0 0 0 0 3 5 0

    0 0 0 0 0 0 0 3 4 0

    0 0 0 0 0 0 0 3 2 0

    0 0 0 0 0 0 0 4 2 0

    0 0 0 0 0 0 0 3 9 0

    0 0 0 0 0 0 0 6 5 0

    0 0 0 0 0 0 0 3 5 0

    0 0 0 0 0 0 0 3 0 0

    0 0 0 0 0 0 0 3 6 0

    0 0 0 0 0 0 0 3 4 0

    0 0 0 0 0 0 0 3 0 0

    0 0 0 0 0 0 0 3 4 0

    0 0 0 0 0 0 0 3 6 0

    0 0 0 0 0 0 0 4 2 0

    0 0 0 0 0 0 0 3 4 0

    0 0 0 0 0 0 0 2 4 0

    0 0 0 0 0 0 ^ 3 5 0

    0 0 0 0 0 0 0 3 4 0

    0 0 0 0 0 0 0 4 1 0

    0 0 0 0 0 0 0 4 7 0

    0 0 0 0 0 0 0 3 7 0

    0 0 0 0 0 0 0 3 8 0

    0 0 0 0 0 0 0 3 8 0

    0 0 0 0 0 0 0 3 0 0

    0 0 0 0 0 0 0 4 6 0

    0 0 0 0 0 0 0 3 5 0

    0 0 0 0 0 0 0 2 8 0

    0 0 0 0 0 0 0 3 6 0

    ppm Sr

    o o n o o o o o i o

    0000000020

    0 0 0 0 0 0 0 0 3 0

    0000000010

    0000000010

    0000000010

    0000000010

    0 0 0 0 0 0 0 0 6 0

    0 0 0 0 0 0 0 0 3 0

    0000000020

    0 0 0 0 0 0 0 0 3 0

    0 0 0 0 0 0 0 0 3 0

    0000000010

    0000000010

    0000000010

    0 0 0 0 0 0 0 0 4 0

    0000000010

    0 0 0 0 0 0 0 0 6 0

    0000000010

    0 0 0 0 0 0 0 0 0 5

    0000000010

    0 0 0 0 0 0 0 0 3 0

    0000000010

    0 0 0 0 0 0 0 0 5 0

    0000000010

    0 0 0 0 0 0 0 0 6 0

    0 0 0 0 0 0 0 0 5 0

    0000000020

    K/Rb

    0 0 0 1 2 8 0 0 0 0

    0 0 0 1 2 8 2 0 0 0

    0 0 0 1 3 2 5 0 0 0

    0 0 0 0 9 3 3 0 0 0

    0 0 0 1 0 4 4 0 0 0

    0 0 0 0 6 8 0 0 0 0

    0 0 0 1 2 8 0 0 0 0

    0 0 0 1 3 3 3 0 0 0

    0 0 0 1 1 8 6 0 0 0

    0 0 0 1 1 4 4 0 0 0

    0 0 0 1 0 9 3 0 0 0

    0 0 0 1 2 6 5 0 0 0

    0 0 0 1 0 8 1 0 0 0

    0 0 0 0 9 4 8 0 0 0

    0 0 0 1 2 6 5 0 0 0

    0 0 0 1 3 8 8 0 0 0

    0 0 0 1 3 0 6 0 0 0

    0 0 0 1 2 4 7 0 0 0

    0 0 0 1 1 3 9 0 0 0

    0 0 0 0 8 5 1 0 0 0

    0 0 0 1 1 8 1 0 0 0

    0 0 0 1 1 2 4 0 0 0

    0 0 0 1 1 0 5 0 0 0

    0 0 0 1 2 4 3 0 0 0

    0 0 0 0 8 7 0 0 0 0

    0 0 0 1 0 7 7 0 0 0

    0 0 0 1 2 7 1 0 0 0

    0 0 0 1 1 5 0 0 0 0

    Ca/Sr

    0 0 0 4 7 0 0 0 0 0

    0002200000

    0 0 0 2 1 3 3 0 0 0

    0 0 0 4 9 0 0 0 0 0

    0 0 0 4 2 0 0 0 0 0

    0 0 0 7 6 0 0 0 0 0

    0 0 0 3 2 0 0 0 0 0

    0 0 0 1 1 6 7 0 0 0

    0 0 0 1 7 0 0 0 0 0

    0002100000

    0 0 0 1 4 6 7 0 0 0

    0 0 0 1 3 3 3 0 0 0

    0 0 0 4 4 0 0 0 0 0

    0 0 0 4 5 0 0 0 0 0

    0 0 0 5 7 0 0 0 0 0

    0 0 0 1 9 2 5 0 0 0

    0 0 0 5 0 0 0 0 0 0

    0001100000

    0 0 0 3 3 0 0 0 0 0

    0 0 0 9 6 0 0 0 0 0

    0 0 0 4 5 0 0 0 0 0

    0 0 0 1 5 6 7 0 0 0

    0 0 0 4 2 0 0 0 0 0

    0 0 0 0 9 8 0 0 0 0

    0 0 0 3 4 0 0 0 0 0

    0 0 0 0 9 3 3 0 0 0

    0 0 0 1 0 4 0 0 0 0

    0 0 0 2 3 5 0 0 0 0

  • 66

  • 0 0 0 0 0 0 0 0 5 7

    0 0 0 0 0 0 0 0 5 8

    0 0 0 0 0 0 0 0 5 9

    0 0 0 0 0 0 0 0 6 0

    0 0 0 0 0 0 0 0 6 1

    0 0 0 0 0 0 0 0 6 ?

    0 0 0 0 0 0 0 0 6 3

    0 0 0 0 0 0 0 0 6 4

    0 0 0 0 0 0 0 0 6 5

    0 0 0 0 0 0 0 0 6 6

    0 0 0 0 0 0 0 0 6 7

    0 0 0 0 0 0 0 0 6 8

    0 0 0 0 0 0 0 0 6 9

    0 0 0 0 0 0 0 0 7 0

    0 0 0 0 0 0 0 0 7 1

    0 0 0 0 0 0 0 0 7 2

    0 0 0 0 0 0 0 0 7 3

    0 0 0 0 0 0 0 0 7 4

    0 0 0 0 0 0 0 0 7 5

    0 0 0 0 0 0 0 7 6

    0 0 0 0 0 0 0 0 7 7

    0 0 0 0 0 0 0 0 7 8

    0 0 0 0 0 0 0 0 7 9

    0 0 0 0 0 0 0 0 8 0

    0 0 0 0 0 0 0 0 8 1

    0 0 0 0 0 0 0 0 8 2

    0 0 0 0 0 0 0 0 8 3

    0 0 0 0 0 0 0 0 8 4

    0 0 0 0 0 4 1 3 0 0

    0 0 0 0 0 3 8 4 0 0

    0 0 0 0 0 4 9 0 0 0

    0 0 0 0 0 4 2 6 0 0

    0 0 0 0 0 4 3 7 0 0

    0 0 0 0 0 4 ? 3 0 0

    0 0 0 0 0 4 3 0 0 0

    0 0 0 0 0 3 7 3 0 0

    0 0 0 0 0 4 4 4 0 0

    0 0 0 0 0 4 5 6 0 0

    0 0 0 0 0 4 1 5 0 0

    0 0 0 0 0 4 3 8 0 0

    0 0 0 0 0 3 8 1 0 0

    0 0 0 0 0 3 7 6 0 0

    0 0 0 0 0 4 1 8 0 0

    0 0 0 0 0 3 6 6 0 0

    0 0 0 0 0 3 9 7 0 0

    0 0 0 0 0 4 3 3 0 0

    0 0 0 0 0 4 0 4 0 0

    0 0 0 0 0 4 6 7 0 0

    0 0 0 0 0 3 4 3 0 0

    0 0 0 0 . 3 0 0 0 0

    0 0 0 0 0 3 7 5 0 0

    0 0 0 0 0 3 9 8 0 0

    0 0 0 0 0 4 5 6 0 0

    0 0 0 0 0 4 1 8 0 0

    0 0 0 0 0 3 9 9 0 0

    0 0 0 0 0 4 1 0 0 0

    0 0 0 0 0 4 9 7 5 0

    0 0 0 0 0 4 6 2 6 0

    0 0 0 0 0 5 9 0 3 0

    0 0 0 0 0 5 1 3 2 0

    0 0 0 0 0 5 2 6 4 0

    0 0 0 0 0 5 0 9 5 0

    0 0 0 0 0 5 1 8 0 0

    0 0 0 0 0 4 4 9 3 0

    0 0 0 0 0 5 3 4 8 0

    0 0 0 0 0 5 4 9 3 0

    0 0 0 0 0 4 9 9 9 0

    0 0 0 0 0 5 2 7 6 0

    0 0 0 0 0 4 5 9 0 0

    0 0 0 0 0 4 5 2 9 0

    0 0 0 0 0 5 0 3 5 0

    0 0 0 0 0 4 4 0 9 0

    0 0 0 0 0 4 7 8 2 0

    0 0 0 0 0 5 2 1 6 0

    0 0 0 0 0 4 8 6 7 0

    0 0 0 0 0 5 6 2 5 0

    0 0 0 0 0 4 1 3 2 0

    0 0 0 0 0 3 6 1 4 0

    0 0 0 0 0 4 5 1 7 0

    0 0 0 0 0 4 7 9 4 0

    0 0 0 0 0 5 4 9 3 0

    0 0 0 0 0 5 0 3 5 0

    0 0 0 0 0 4 8 0 6 0

    0 0 0 0 0 4 9 3 9 0

    0 0 0 0 0 0 3 7 0 0

    0 0 0 0 0 0 4 1 0 0

    0 0 0 0 0 0 4 2 0 0

    0 0 0 0 0 0 4 0 0 0

    0 0 0 0 0 0 4 0 0 0

    0 0 0 0 0 0 3 9 0 0

    0 0 0 0 0 0 4 8 0 0

    0 0 0 0 0 0 4 9 0 0

    0 0 0 0 0 0 4 2 0 0

    0 0 0 0 0 0 4 4 0 0

    0 0 0 0 0 0 4 9 0 0

    0 0 0 0 0 0 5 0 0 0

    0 0 0 0 0 0 4 8 0 0

    0 0 0 0 0 0 3 9 0 0

    0 0 0 0 0 0 3 1 0 0

    0 0 0 0 0 0 4 3 0 0

    0 0 0 0 0 0 5 3 0 0

    0 0 0 0 0 0 4 8 0 0

    0 0 0 0 0 0 5 2 0 0

    0 0 0 0 0 0 3 6 0 0

    0000002000

    0 0 0 0 0 0 1 4 0 0

    0 0 0 0 0 0 3 0 0 0

    0 0 0 0 0 0 6 1 0 0

    0 0 0 0 0 0 3 6 0 0

    0 0 0 0 0 0 5 0 0 0

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    0 0 0 0 0 0 3 3 0 0

    0 0 0 0 0 0 5 1 8 0

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    0 0 0 0 0 0 5 8 8 0

    0 0 0 0 0 0 5 6 0 0

    0 0 0 0 0 0 5 6 0 0

    0 0 0 0 0 0 5 4 6 0

    0 0 0 0 0 0 6 7 2 0

    0000006860

    0 0 0 0 0 0 5 8 8 0

    0 0 0 0 0 0 6 1 6 0

    0 0 0 0 0 0 6 8 6 0

    0 0 0 0 0 0 7 0 0 0

    0 0 0 0 0 0 6 7 2 0

    0 0 0 0 0 0 5 4 6 0

    0 0 0 0 0 0 4 3 4 0

    0 0 0 0 0 0 6 0 2 0

    0 0 0 0 0 0 7 4 2 0

    0 0 0 0 0 0 6 7 2 0

    0 0 0 0 0 0 7 2 8 0

    0 0 0 0 0 0 5 0 4 0

    0 0 0 0 0 0 2 8 0 0

    0 0 0 0 0 0 1 9 6 0

    0 0 0 0 0 0 4 2 0 0

    0 0 0 0 0 0 8 5 4 0

    0 0 0 0 0 0 5 0 4 0

    ^ 0 0 0 0 0 7 0 0 0

    0 0 0 0 0 0 2 5 2 0

    0 0 0 0 0 0 4 6 2 0

    0 0 0 0 0 0 0 4 3 0

    0 0 0 0 0 0 0 4 1 0

    0 0 0 0 0 0 0 4 7 0

    0 0 0 0 0 0 0 3 9 0

    0 0 0 0 0 0 0 3 5 0

    0 0 0 0 0 0 0 4 5 0

    0 0 0 0 0 0 0 4 6 0

    0 0 0 0 0 0 0 4 1 0

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    0 0 0 0 0 0 0 3 2 0

    0 0 0 0 0 0 0 3 7 0

    0 0 0 0 0 0 0 3 4 0

    0 0 0 0 0 0 0 4 1 0

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    0 0 0 0 0 0 0 4 7 0

    0 0 0 0 0 0 0 4 2 0

    0 0 0 0 0 0 0 3 5 0

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    0 0 0 0 0 0 0 3 2 0

    0 0 0 0 0 0 0 4 8 0

    0 0 0 0 0 0 0 2 7 0

    0 0 0 0 0 0 0 2 8 0

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    0 0 0 0 0 0 0 3 2 0

    0 0 0 0 0 0 0 3 9 0

    0 0 0 0 0 0 0 3 2 0

    0 0 0 0 0 0 0 7 3 0

    0 0 0 0 0 0 0 3 2 0

    0000000020

    0000000020

    0000000020

    0000000010

    0000000020

    0000000010

    0000000010

    0000000010

    0000000020

    0 0 0 0 0 0 0 0 1 0

    0000000010

    0000000010

    0000000010

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    0 0 0 0 0 0 0 0 4 0

    0 0 0 0 0 0 0 0 1 0

    0 0 0 0 0 0 0 0 2 0

    0000000010

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    0000000010

    0000000020

    0000000010

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    0 0 0 0 0 0 0 0 3 0

    0000000020

    0000000020

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    0000000010

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    0 0 0 1 0 4 3 0 0 0

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    0 0 0 1 2 4 9 0 0 0

    0 0 0 0 9 4 0 0 0 0

    0 0 0 0 9 3 5 0 0 0

    0 0 0 0 9 1 0 0 0 0

    0001110000

    0 0 0 1 4 2 5 0 0 0

    0001122000

    0 0 0 1 2 8 8 0 0 0

    0 0 0 0 9 2 9 0 0 0

    0 0 0 0 9 6 4 0 0 0

    0 0 0 0 8 8 9 0 0 0

    0 0 0 0 8 7 1 0 0 0

    0 0 0 1 1 3 4 0 0 0

    0 0 0 1 3 1 2 0 0 0

    0 0 0 1 2 6 3 0 0 0

    0 0 0 0 9 7 3 0 H O

    0 0 0 1 2 7 0 0 0 0

    0 0 0 1 0 7 1 0 0 0

    0 0 0 1 2 5 0 0 0 0

    0 0 0 1 2 4 4 0 0 0

    0 0 0 1 1 6 9 0 0 0

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    0 0 0 2 0 5 0 0 0 0

    0002100000

    0 0 0 4 0 0 0 0 0 0

    0002000000

    0 0 0 3 9 0 0 0 0 0

    0 0 0 4 8 0 0 0 0 0

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    0002100000

    0 0 0 4 4 0 0 0 0 0

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    0001000000

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  • 6 7

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    0 0 0 0 0 0 0 0 6 5 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 5 3 4 8 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 5 8 8 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 1 0 0 0 0 0 0 0 2 1 0 0 0 0 0

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