MODAL VARIATIONS WITHIN GRANITIC OUTCROPS D. O. EruBnsoN, Department of Geology, Uni'ttersity of C alif ornia, Dattis, C ali'f orni,a'

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1 THE AMERICAN MINERALOGIST, VOL. 49, SEPTEMBER-OCTOBER' 1964 MODAL VARIATIONS WITHIN GRANITIC OUTCROPS D. O. EruBnsoN, Deprtment of Geology, Uni'ttersity of C lif orni, Dttis, C li'f orni,' Aestnr The soure n mgnitue of the mol vritions etermine y point ounting thin setions from single outrops of grniti rok were stuie to etermine the most effiient mens of smpling. The rok is equigrnulr with n verge grin size of 2 mm n n LC. numer of 32. The,,verge" stnr evition of single thin setion moes from n outrop is of the whole for the mjor minerls ompre to the expete vrine ("error") for rnom smples of 1600 points from homogeneous popultion ol l.20/6' The "verge" stnr evition for the mjor minerls etermine from multiple thin setions ut from single hn smples is /s while repete ounts of single setion "verge" only l'3/6' Anlysis of vrine of the moes of four thin setions from eh of four hn smples ollete only five feet prt from n mellite outrop showe tht the qurtz ontent of the hn smples ws signifintly ifierent even though the totl stnr evition of the qurtz etermintions ws lrge (T. Beuse these vritions re lrge ompre to the ifierenes often sought in stuies of plutoni roks, sttistil methos of nlysis re neee to esign the smpling pln n i in the interprettion of the results. For exmple, to etermine qurtz in the mellite, it is 2 35 times more effiient to point ount one setion from eh of four hn smples thn to ount four setions from one hn smple. Thus, y proper esign, smller vritions n e etete withoug itionl ost of time or money. Ir.trnOoUrrOw A onsierle mount of work hs een one on the vriility of thin setion moe etermintions of the finer-grine grniti roks from the levels of opertor vritions n single thin setion reprouiility to the vriility of n entire grnite mss (Chyes, 1952, 1956). The results of previous work re n inition of the vriility to e expete in mol nlysis of similr roks. However' to properly interpret mol informtion it is neessry to etermine the vritions of eh rok type stuie. Mol ompositions use in the stuy of over 120 squre miles of grniti rok of the Inyo tholith, liforni-nev, were estimtes from one thin setion for eh squre mile. Signifint ifferenes etween the mjor rok types oul e foun with no more thn ten setions from eh unit (Emerson, 1959). Vritions within outrops were foun to ontin mjor prt of the pluton vrition. This within-outrop vrition n e split into severl levels n two of these (setions within hn smples, hn smples within outrops) were stuie. Volume perentges of the minerls present in the vrious rok t)-pes were estimte y miro point ounting. The Amerin Optil Com- 1224

2 MODAL VARIATIONS IN GRANITE 1225 pny point ounting stge with n est-west point sping of millimeter ws use with mirosope mgnifition of fifty times. Cellophne tpe ws ple on eh en of the thin setion to provie stright ege for the re smple n to voi is from the roken ege of the rok setion. The re smple from eh setion ws nerly onstnt n verge 750 squre millimeters. Sixteen 100 point trverses were spe to smple the entire thin setion re. Results of previous stuies (Lrsen n Miller, 1935, p. 723; Chyes, 1956, p.40) guie the writer in estlishing the numer of trverses n the totl numer of points use in these mol nlyses. Eight lsses, qtrtz, stine potsh felspr (for stining tehnique see Rosenlum, 1956), plgiolse, nonopque essories, iotite, hlorite, mphiole n opque essories were ounte. Fine-grine ltertion prouts of the felsprs were ounte s felspr. Although the lite of some of the perthites ws reognizle t the mgnifition use, it ws ounte s potsh felspr. HNr Slrpr,B VenrerroN Single setions from hn smples spe out five feet prt within n outrop of the Sgehen mellite, the Leiy mellite n two outrops of the Brroft grnoiorite were point ounte. These roks re equigrnulr, hve n verge grin size of two millimeters n n ientity hnge numer (the numer of mjor minerl ientity hnges long 25 mm trverse-chyes, 1964) of 32. Tle 1 summrizes the mol t. Any one stnr evition from Tle 1 is sujet to rther lrge error euse it is se on only four thin setions. A metho of omining the estimtes of vrition is neee to otin etter estimte of this vrition. After isussing the ssumptions involve, Chyes (1956, p. 67) lulte the squre root of the verge vrine (n,,verge" stnr evition) of minerls of pproximtely the sme unne. This omines the vritions of seprte minerls n provies etter estimte of the vrition. "Averge" stnr evitions lulte in this wy for the mol etermintions re shown in Tle 2. To i in interprettion, minerl vritions isusse will lwys e se on per ent of the whole n not of the mount present. These "verges" ontin vritions ue to the tehnique of estimtion s well s the tul minerl ontent vritions. As will e shown lter, the within-outrop vritions re epenent on the minerl etermine s well s the minerl unne. To unerstn the totl vrition the vrition t the ifierent levels of smpling must e etermine. To estimte the mgnitue of the vri-

3 D. O. ]JMERSON Telr,n 1. TnrN SstroN Moors lnou SrNr,r Ournops Set. I o, lr-,lu. l"t*..q*. I ei". I l'r. ]-pr.. lop"o"" Sgehen mellite 14 I II III IV t.o o.7 t.6 t.2 J.I l.j r.9 24 o Ave SD ) Leiy mellite 118 I II III IV /.t o.7 08 t.9 IJ O O l.j Brroft grnoiorite 11A I II III IV l t t1 9 tl.l 10 t.j I.J 135 1A Brroft grnoiorite 132 I II III IV t4.o zj.z t2.7 J/ 11.5 rr tz,j J/.6 25 o II J z.j tion etween thin setions from the sme hn smple, four setions were ut from eh of four smples tken from the outrops of Tle 1. When the stnr evitions of these moes (Tle 3) re "verge" (Tle 2) they re seen to ontin mjor prt of the totl vrition.

4 MODAL VARIATIONS IN GRANITE 1227 To estimte the preision otine from thin setion, four ounts of the sme setion were me (Tle 4). Beuse of the metho of trverse seletion, whih for eh ount smples 16 of possile 200 trverses, repete trverses of the sme pth re rre even when uplite ounts re me of the sme setion. Eh ount is essentilly rnom smple of prllel trverses within the sme re. These smples, whih re selete without replement from finite trverse popultion, will 1-iei vrines somewht lolver thn woul e otine y smpling with replement. The "verge" stnr evition of replite ounting of thin se- 'Illr 2. "Avrn.n" Srl,ro.tno Drvr.ruoNs or SrNr,n TurN Sp:rron Monus Level of Vrition Minerl unne 50 to 201" 20 to 5/6 5 to lt I to 0o/1; Outrop (Tle 1) Hn Smple (Tle 3) Thin Setion (Tle 4) "Error" (t mximum minerl unne) z,l O tr..l n,) tion (Tle 2) is of the sme mgnitue s the expete vrine (,,error") for rnom smpies of 1600 points from homogeneous popultions of pproprite ompositions (Chyes 1956, p. 39). More points must e ounte in orer to improve the estimte of the minerls tht onstitute less thn fi.ve per ent of the rok. There were suffiient numer of points ounte to shorv tht the more unnt minerls hve more vrition thn n e ttriute to single thin setion. In ition, it ppers tht one hn smple oes not equtely represent n outrop of grniti rok. Axrysrs of VARTANCE To estimte more preisely the mgnitue of the vrition etween thin setions from one hn smple n etween hn smples from single outrop, four smples out five feet prt were oilete from one outrop of the Sgehen mellite. F-our thin setions from eh smple were point ounte (Tle 5).It is interesting to note tht the mximum nlytil error in the point ount etermintion of the mjor ompo-

5 1228 D, O. DMERSON Tllln 3. TurN StroN Moors rnou SrNr,r HeNn S,lrrrpr-os Sgehen mellite Hn smple l4(i) t94 20.r s r l r.3 08 J.I J 208 I.J z , Leiy mellite Hn smple 118(I) s l o.4 t t,.l 06 o l.j t7 05 Brroft grnoiorite Hn smple 11A(I) 2r.4 tl -l t5.2 7n ro tl t.4 t2 Brroft grnoiorite Hn smple 132(I) t s o o r07 /.o t.t. /

6 MODAL VARIATIONS IN GRANITD 1229 Tlrr,n 4. Quonurr,rlm PorNr CouNrs FRoM STNGLE Tnrr Sruoxs ount 0,,. r-sp.. Ipl". I A. ". Sgehen mellite #4 (I) I nt. I,.pt. loouo.," (1) (2) (3) (4) t o t5. I l JI o l..t zo.j I Sgehen mellite 16 (1) (2) (3) (4) t r.o 2.7 t A1 A Brroft grnoiorite 11A (III) (1) (2) (3) (4) rr O rt lo? 9.5 1l 2.0 Brroft grnoiorite #32 (l) (1) (2) (3) (4) r J/.O o. / 11.5 r 10. I r J/.J t.2 o z,j nents is not more thn the /6 preite y Chyes (1956, p. 83) for setions of this re n grin size. For omprison with the grn totl stnr evition, the lst line of Tle 5 is the "error expete for rnom smples of 1600 points from homogeneous popultions."

7 1230 D. O. L,MERSON T.tnr,r 5. HeNo SelprB TnrN Serrom Molrs lnou ONr Ournop ol tur Sounlt Aourr-rttn Set. I 0,,. I r-,ou, "t*.,t... Bio. I r'r. I -or'. ]oouo,," Hn smple 14 (I) t I.J U.J 2 t l.t 3.9 U.J Hn smple 14 (II) 2 22.O At t t 09 nt zj.l M Hn smple #4 (III) A I O Hn smple 14 (IV) 1< A A1 I AA J 104 t2 (,. -') J.J 3.1 t.9.a A 2.9 r J,t 42.6,)) 3.3 Grn totl Expete "Error" na o.2

8 MODAL VARIATIONS IN GRANITE l23l When n is lrge n the prout np, the numer of points within smpie (n) times the proportion of the minerl in the smple (p), it lrger thn 10 the inomii istriution is very lose to norml istriution n nlysis of vrine is pproprite without trnsformtion of the t. The t (Tle 5) were trete y rnom effets moel of the nll'sis of vrine (Sneeor, 1956, p. 259). Qurlz is foun to e signifintll' ifferent etrveen hn smples (Tle t5). This ifferene ppers to e ue to smple l4(i) whih ver- TenlB 6. Awer,vsrs ol V,lm,lNe or. WrrnrN Ournop V.lnr,qrroN Srunv (Der,l lnolr Trr, 5) Qurtz Potsh felspr Plgiolse Nonopque essorres F. M.S s Biotite Chlorite Amphiole Opque essorles o.t Signifint t the 5 per ent level. ges lmost four per ent less qurtz thn the other three smples. The other minerls show no signifint ifferenes etween hn smples. The ost, in time n monev, of mking n point ounting thin setions is high. To e most effrient, it is importnt to otin the mximum mount of informtion from the minimum numer of thin setions. The nlysis of vrine provies the informtion neessry to etermine the mgnitue of the vritions t vrious levels in the nlysis. From this informtion the est smpling pln n e esigne. Among the mjor minerls of this stuy, qtrtz shows the gretest vrition. The following pln is se on its etermintion. If the mgnitue of the vrition sought is known, you n etermine the numer of thin setions neee. However, in petrology' the limiting ftor is often the numer of thin setions tht n e stuie in the time

9 1232 D. O. EMERSON ville. AIso, the mgnitue of the vrition is selom known. If fixe numer of thin setions (r.s.q re to e use t eh outrop, the prolem is to etermine wht setions shoui e me n ounte. From the nlysis of vrine, the setion men squre (3.50 for qurtz in Tle 6) is n estimte of the omponent of vrine ue to vritions etween thin setions from hn smple. This estimte is esignte s2. The smple men squre (15.04) is n estimte of the setion men squre plus four times the omponent of vrine ue to vritions etween hn smples (s2{4ss2). For qurtz, the estimte of the omponent of vrine ue to hn smples, (ss2): ( )/4:8. Sneeor (1956, p. 261) shows tht the men squre of the hn smple men, s112: [s2f (snt)]/n; where : numer of hn smples n n: numer of setions per hn smple. To e most effrient, sf shoul e minimize. Ii one hn smple is use, :1, n:4 n s112:3.76. It, on the other hn, four hn smples re use with onll'one setion from eh one, :4, n:1 n s112:0. The seon pln when ompre to the first is si to e 2.35 times or 235/6 more effiient. By the sme resoning, two thin setions from eh of two hn smples woul e 4 times or more effiient thn tking four setions from one smple. Surrlr-q.nY One of the iggest prolems in quntittive petrology is otining the t neessry to properly esign smpling pln. This stuy gives some ie of the mgnitue n lotion of the vritions foun y point ounting plutoni roks. Eh minerl from eh rok type presents seprte smpling prolem. If the flutution or "error" of the mol nlyses use in speifi prolem re of the sme orer of mgnitue s the ifferenes sought, then etile sttistii methos of nlysis re neee to esign effiient smpling plns n interpret the resulting informtion. In this exmple, the etween-thin-setion results show tht irge prt of the totl vrition is t this level. More or lrger setions re neee to etet ifferenes etween outrops. The etween-hn-smple vrition is lerly lrge enough tht more thn one smple shoul e tken from eh outrop to etet ifferenes etween outrops. To etermine within-pluton vritions of the Inyo grniti roks more thn one setion n more thn one hn smple shoul e use. Both of these onitions n est e met y exmining thin setion from two or more hn smples tken from eh outrop stuie. ArNowr-nuEMENT The writer is inete to Professor J. C. Griffiths of the Pennsylni Stte ljniversity n L. E. Borgmn of the University of Cliforni,

10 MODAL VARIATIONS IN GRANITE 1233 Dvis Cmpus, for vlule vie n ritiism. AIso, s lerly shown y the frequent ittions, the pulishe works of Felix Chyes hve een essentil to this stuy. Rulon.BNrs Cnvrs, F. (1952) The finer-grine llkline grnites of New Engln : four. Geol. 6O, 207, (1956) Petrogrphi Motr Anlysis. John Wiley & Sons, In., N. Y. --- (1964) per sonl ommunition. EuensoN, D. O. (1959) Grniti roks of the northern portion of the Inyo tholith. Ph.D. Thesis, Pennsylvni Stte University. LesnN, E. S. No F. S. Mrr.lnn (1935) The Rosiwl metho n the mol etermintion of roks. Am. Minerl.20, RosrNnr.uu, S. (1956) Improve tehnique for stining potsh felsprs. Am. Mi.nerl. 4r SNenron, G W (1956) Sttistiel Meths. forv Stte College Press, Ames, Iow. Monusri;l reeie., June 28, 1953; eepte Jor puliotion, June 1, 1964.