Scherkenbach and Noble-1984

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    Economic GeologyVol. 79, 1984, pp. 565-572

    POTASSIUM AND RUBIDIUM METASOMATISM AT THE ]ULCANI DISTRICT, PERU

    DARYL A. SCHERKENBACH

    Noranda Exploration, nc., 139 East 51st Avenue, Anchorage, laska 99503

    AND DONALD C. NOBLE

    Department of Geological ciences, ackay School f Mines, University f Nevada-Reno, eno, Nevada 89557

    Introduction

    The Julcani district, central Peru, is a major silver-producing district hosting zoned polymeta]lic einsystems hat contain etrahedrite and enargite as theprinciple economic minerals. Results of numerousstudies t Julcani have added o our understandingof this deposit and the reader s referred to Petersenet al. (1977), Goodell and Petersen 1974), and Nobleand Silberman in press) or more detailed discussionsof the geology, geochronology, nd hydrothermalevolution of the center. The purpose of the presentstudy s o determine whether base nd precious metalmineralization n altered dacites and rhyodacites tJulcani s associated ith regular patterns f potassiumand rubidium metasomatism on both a district-widescale nd at close roximity o veins and vein systems.In addition, t is mportant o evaluate he applicationof such patterns s guides o the exploration nd de-velopment of additional areas of mineralization.

    This communication resents he results of a de-tailed study of the changes n concentrations f po-tassium, rubidium, and strontium in dacites from the

    Julcani district during hydrothermal lteration andmineralization Scherkenbach, 978). The Julcanidistrict s well suited o a study of potassium meta-somatism elated to base and precious metal miner-alization because: 1) the dacites hat host he min-eralization have similar original extures and com-positions, 2) the presence f unaltered dacites utsidethe area of alteration and mineralization facilitatesthe determination f accurate ackground alues, nd(3) extensive nderground orkings ermit system-atic sampling n areas of major mineralization ormalto selected eins and vein systems.

    Methods of StudyOver 500 rock samples were collected, about half

    from he surface nd half rom underground ocations,to provide a systematic overage of altered and un-altered areas. he subsurface amples ere collectedat measured ntervals along selected raverses ori-ented approximately erpendicular o veins. Most ofthese raverses re n the actively mined area of Her-minia; three traverses are in the Tentadora area. Sur-face samples ere collected o obtain a comprehen-sive coverage of about 20 km 2 of the altered andunaltered acites. he central, ydrothermally ltered

    area was sampled extensively o evaluate quantita-tively the intensity of alteration, but veins were pur-posely avoided during he collection of surface sam-pies. This was done to evaluate he pattern of per-vasive metasomatism rather than the more intensealteration near veins.

    Samples, composed of four to six selected rockfragments weighing a total of 250 to 400 g, werecrushed n a small aw crusher, and about two-thirds

    to three-fourths f this material was ground succes-sively n a disc-type ock pulverizer and a rotary mor-tar. Pressed owder pellets of this material were an-alyzed by X-ray fluorescence methods. Potassium asdetermined using Cr radiation in a helium atmo-sphere. Rubidium and strontium were determinedusing Mo radiation. The intensity of the Comptonscattered primary peak was used to correct for massabsorption ffects and nstrument drift in the Rb andSr analyses Powell et al., 1969). Corrections wereapplied or background urvature and peak overlap.X-ray diffraction and petrographic tudies were per-formed on many samples.

    Mineralogy and Chemical Changesof the Altered Rocks

    Unaltered dacites ontain abundant henocrysts fandesine, uartz, and biotite accompanied y minorapatite, Fe-Ti oxides, and, in some cases, pyroxeneand/or hornblende set in a fine-grained or glassygroundmass. ost of the altered rocks n the districtexhibit typical propylitic mineral assemblages, n-cluding epidote, chlorite, calcite, pyrite, smectite,quartz, sericite, albite, and/or K-feldspar. X-ray dif-fraction and petrographic tudies eveal hat in mostof the rocks near veins the added K and Rb is con-tained in adularia (disordered secondary otassiumfeldspar) and to a lesser extent in muscovite, llite,or mixed ayer illite-smectite phases Scherkenbach,1978; Wilson, 1979). Adularia in some cases s ac-companied y, or partially altered to, sericite or ka-olinite. A small number of specimens ound in theTentadora area on the surface, or in some cases oc-curring directly adjacent o veins and vein systemsunderground, are composed primarily of kaolinite,quartz, and pyrite, and in some cases ontain aluniteor pyrophillite.

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    566 SCIENTIFIC COMMUNICATIONS

    The validity of any geochemical alteration studyis dependent on establishing he composition f therocks prior to alteration. At Julcani his was accom-plished by analyzing ocks rom outside he area ofmineralization nd alteration which display no signsof alteration. total of 21 rock samples ere collected

    beyond he boundaries f the alteration map Fig. 1),including nine to the north and northwest, eight tothe south, two to the east, and two to the west. Allthese rocks and some additional unaltered sampleswere used to establish background values and theoriginal K/Rb ratio.

    The range of concentrations etermined for theserocks are 3.1 to 3.8 wt percent K20, 100 to 180 ppmRb, and 650 to 1,600 ppm Sr. The original Sr contentsshow a larger range of values than do K20 or Rb.This variation, found in many igneous ock suites,reflects he geochemical omplexity of Sr. Unaltered

    rocks rom the southwest orner of the Julcani districthave higher Sr contents, 800 to more than 1,500ppm, than do unaltered rocks from the south andnorthwest parts of the district (700-935 ppm). Thisvariation reduces he usefulness f Sr in evaluatingalteration.

    74'/*5'

    12'55'

    I [

    FIG. 1. Map of the Julcani istrict showing urface ein patterns nd boundary f alteration tudy.Irregular boundary ndicates area of dacite lava outcrop (after Petersen et al., 1977).

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    SCIENTIFIC COMMUNICATIONS 567

    &

    &

    I ;::'

    I I I I I

    A

    Surface samples

    Subsurface samples

    I I I I I I I

    3 4 5 6 7 8 9

    KO (wt%)FIC. 2. Plot ofRb vs. K20 for altered dacites rom he surface nd underground raverses. Outlined

    area corresponds o the range of composition rom unaltered ocks not plotted).

    Most of the intensely altered dacites have under-gone significant hemical change, with the K and Rbcontents of these rocks having been increased sub-stantially; some contain as much as 9.0 wt percent

    K20 and 600 ppm Rb. More Rb has been added rel-ative to the original rock concentration han K, re-suiting n a K/Rb enrichment atio in the added ma-terial of about 110. Thus, altered dacites have lower

    5

    i i I

    surface samples

    subsurface samplesunaltered samples

    ' o o o o

    I I I I I I I I I I I I I a I I800 tOO0 t200 t400

    200 400 600 Sr ppm)FIG. 3. Plot of K20 vs. Sr for surface and subsurface acites showing he marked depletion of Sr

    and accompanying ncrease n K20. Note the wide variation n original Sr content but nearly constantK20 values.

    1600

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    568 SCIENTIFIC COMMUNICATIONS

    K/Rb ratios K/Rb ratio ranging rom 210-130) thanthose of the unaltered ocks about 215; Fig. 2). Sig-nificant amounts of Sr have been lost from many ofthe dacites hat have gained arge amounts of K andRb (Fig. 3). Rocks composed of kaolin + quartz_+alunite _+pyrophyllite are leached of K and Rb andcommonly enriched in Sr. Spatial and parageneticrelationships elate eaching of these samples o min-eralization. Such eaching may ndicate areas of highfluid flow or strongly cid solutions, nd results romhydrolysis f host ocks hat may accompany r pre-date ore deposition.

    Surface patterns of K and RbTo facilitate visual evaluation of the variation in

    the patterns of K and Rb metasomatism, he analyseshave been grouped nto a few compositional ntervals

    and contoured sing he SYMAP program Fig. 4).The boundary eparating ltered and unaltered ocksis well defined on the south, southeast, nd northwestedges of the district. Most of the rocks n the central,altered part of the district show an increase n KOand Rb and a decrease n Sr. Strong enrichment ofK20 and Rb is found primarily n three areas: Mimosa,Herminia, and east of Acchilla Fig. 4A and B). Theseareas include most of the surface rocks that containmore han 5.0 wt percent K20 and 250 ppm Rb. Theyare separated rom each other by rocks hat containmarkedly ower amounts of KO and Rb.

    Highly altered rocks occur throughout Herminiaand extend to the southwest and north. The area un-derlain by moderately o highly altered rocks cor-responds well with the area of productive veins andintense luid movement Goodell and Petersen, 1974;

    o 500

    METERS

    KO (wt.%)o

    5.6 5.0- 5.6

    4.4 - 5.0

    5.8 - 4.4- 5.1 -5.8

    E OlOO0 x E 700 E 12000 E 13000

    FIO. 4. Maps A and B show the distribution of K20 and Rb contents, espectively, n surfacesamples f altered and unaltered dacite. Note strong enrichment n the productive Hermina andMimosa areas. Rocks re depleted n the Tentadora egion, an area of vertical luid movement. Contoursare at 4.4., 5.0, and 5.6 wt percent K20 and 200, 250, and 300 ppm Rb. Note similar patterns ofboth A and B. Small ight angles outlining ectangle near Tentadora nd Herminia n part A indicatethe location of the underground raverses hown n Figure 5.

    N 10500-

    N 9500-

    N 8500-

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    SCIENTIFIC COMMUNICATIONS 569

    Fig. 1). Furthermore, the termination of metaso-matism east of Herminia correlates well with the ter-

    mination of mineralization underground.Mimosa and the area between Mimosa and Ten-

    tadora, where economic mineralization has recentlybeen proven, has undergone strong enrichment ofK20 and Rb. Here, the alteration pattern is similarto that of Herminia, coinciding with underlying areasof economically mportant mineralization. The di-rection of fluid movement in Mimosa, and in Her-minia, shows a correlation with the location of alteredareas on the surface, notably oward he west and hesoutheast.

    In contrast o Herminia and Mimosa, the Tentadoraarea, which hosts Pb-Zn mineralization Goodell andPetersen, 1974) as well as veins containing ungstenand gold, shows different chemical pattern. Here,the rocks are moderately o strongly hydrothermallyaltered but have K and Rb contents hat are largely

    at or below background. he low values re reflected

    in the mineralogy f the altered rocks; most containalbite and some variable percentages f alunite.

    Another area of strong K and Rb enrichment slocated east of Achilla. This area acks significant einstructures n the surface, and many of the rocks ofthe area are not as pervasively altered, as seen in

    hand specimens nd thin sections, s rocks of theMimosa and Herminia areas. Furthermore, there areno underground orkings o allow evaluation f pos-sible hidden vein structures or to determine fluidmovement from metal ratio data. In addition, rockscollected from the southern, eastern, and northernmargins f the area are characterized y high K andRb contents but are from localities outside of areascontaining nown mineralization nd/or vein struc-tures.

    The two areas of major mineralization, pervasivewall-rock alteration, and strong K and Rb metaso-matism re separated y areas of lower K20 and Rbcontents. This corroborates the conclusion reached

    1

    x

    x i x i i

    0 0( ' i. I

    TERS xx x

    x

    ,%ooo

    Rb (ppm)o < I00 > 300

    250-300

    200 - 250

    180 - 200

    :, IOO - 180

    x

    x

    x

    x

    x

    x

    x

    E ,000

    N I0 500-

    N 9500-

    x

    x

    N 8500

    FIG. 4. (Continued).

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    o-- -o -...o ,', , o_o.OoXO -*-'-*.

    I000

    o.-

    0 Level 0Or.1 - -- %'' ...... -

    _2

    I000 0

    500_

    ..... ..... i...IOOO

    ...... , ,,,/' 500,

    Level 540 Cr 2_08 ' o ,-o 0

    8

    J: vein6

    K20 ( wt % )

    2 Rb (ppm x 10 2

    Sr(ppm)

    --/i SCALESections- 'E-E'nlyt , J I meters/o /o, o- /- 2900ppm

    X / / ,, Oo o ..-'.... ............................ ..

    ' ' -' .................... . ,V ....... ooo

    0 , , pm ,, 500_o... . ..o ____ ___o__ ___o_ o_ ... _ o. _ i o- o- oo - ' - -o ....... Level 580 Cr 67 - o- - - .... _. O_

    0 I000 Y,

    o - - - - o_ _ 500

    - - ...... ...... o- -o. _ _ . _o. . - .o. - ___ o- -. - - - ..... oo Level 420 Cr 233E o- / O.

    Lo / / .... %o/ ,/./,- -,, ,,.,, ..... o-/ ..... ,..,' ......... - %. ....2 '' * .... / .' / ''''-. I ... * ....... , ............................... * _ 2

    I0 ' '

    ' , . -. ' 8' o

    meters6 6

    ,,,.., oO frectured

    4 ,;/;i oOo ', _,_ . . 4

    .. .- -- , -.,-II .... .,

    p-. .... ............... --/ , ,o.. I 00 ' -o.. . / - o ... -_._____o 'o-. _ o - -o'] ' - o-. _- . ,

    0 Level 0 Cr 201 E

    KOo 5o ioo

    wt%) o o Rb(ppm x 0 2) ........... Sr(Dpm) ........ I , I Imeters

    FIG. 5. Diagram ofKO, Rb, and Sr contents f rock samples lotted vs. distance long undergroundtraverses. ein locations re represented y vertical arrows; ein systems re represented y arrowsconnected with a line. Rocks rom traverses how definite, yet in many cases rregular, enrichmentas veins are approached. evel 540: Cr (crosscut) 17 and 208 provide good examples of enrichmenttrends next to veins. Cr 208 shows substantial ervasive potassium metasomatism t its termination

    57O

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    SCIENTIFIC COMMUNICATIONS 571

    by Goodell and Petersen 1974) from metal atio data,that mineralization t Julcani was produced y severaldistinct hydrothermal systems. t also supports heinterpretation hat the greatest amount of chemicalchange s associated ith abundant luid movementand or fracturing, which is discontinuous ithin thedistrict.

    Subsurface and Rb changesThe chemical changes associated with selected

    veins n underground mine workings have been stud-ied n detail and are presented n Figure 5. Subsurfacesamples ere collected as close o the vein as possiblewithout actually sampling he mineralized portion ofthe vein, at 5-m intervals from the vein and at ad-ditional 10- to 25-m intervals. n some cases amplingintervals of greater han 25 m were used because ofrock homogeneity. his control allows one to observeenrichment patterns and to compare he relationshipof K and Rb metasomatism on the surface to min-

    eralization. Nearly all of the underground samplesare enriched n K and Rb, except a few samples hatare remote from the actively mined area and outsideof the area of alteration recognized on the surface(Fig. 5). Along some raverses nearly all the samplesare substantially bove background n K20 and Rb.

    Rb and K20 are enriched and depleted in a sym-pathetic manner and Sr follows an inverse relation-ship. As a vein or vein system s approached, KeOand Rb increase markedly, even if rocks along theentire traverse have KeO and Rb contents abovebackground. he highest KeO and Rb contents alongany traverse are typically found within 10 or 15 mof a vein. This increase s in some cases egular f thehost rocks are not highly fractured and altered andvery irregular n areas of intense racturing, high veindensity, and intense hydrothermal alteration.

    The termination of metasomatism in the southeast

    corner of the district s well defined and abrupt bothon the surface and underground n the 420 and 580levels. However, in the eastern portion of the 580level, the last occurrence of K and Rb metasomatismis located 100 m farther east than in the 420 level,suggesting reater ateral fluid movement at depth.Metal ratio data at Julcani (Goodell and Petersen,1974) support his suggestion, s do data on fluid

    movement n geothermal fields (Browne and Ellis,1970).

    Discussion

    Rubidium and potassium an be useful ndicatorsof mineralization because hey are commonly con-centrated in rocks near orebodies. These two elements

    are geochemically similar, having the same chargeand comparable tomic radii, so that Rb substitutesfor K instead of forming ts own mineral. n addition,hydrothermal luids become enriched n Rb relativeto K, resulting n a lowered K/Rb ratio (O'Neil et al.,1973; Goguel, 1983).

    Strontium, an element that behaves in a mannersimilar to calcium (Turekian and Kulp, 1956), is aless reliable indicator of alteration than Rb or K.

    Strontium and Ca are depleted n areas of potassiummetasomatism ecause minerals hat do not readilyaccept Ca and Sr are stable, which is the case forrocks n which plagioclase s replaced by K-feldspar.At Julcani his s shown by the plots of undergroundtraverses, which show Sr depletion with increasingRb and KzO (Fig. 5).

    Many fresh calc-alkalic volcanic rocks of conti-nental regions commonly have K/Rb ratios of from200 to 400 (Volkov and Savinova, 1961). Studies ofK, Rb, and Sr as guides o ore (Oyarzun, 1975; Arm-brust et al., 1977) have shown hat both the Rb con-tent and he Rb/K ratio of rocks ncrease n the alteredrocks related to ore. Even though enrichment n Kand Rb is a common eature of wall rocks rom epi-thermal precious metal deposits O'Neil et al., 1973;Bonham and Garside, 1979), such relationships recommonly complex. This metasomatism s not onlyassociated with potassium ilicate alteration but alsoaccompanies ropylitic alteration. At Wairakei andBroadlands, an increase in K and Rb results from theformation of adularia and illitc. In addition, theseminerals can equilibrate with solutions rom depththat have high concentrations f heavy alkalies andlow K/Rb ratios, resulting n decreased K/Rb ratiosin the altered rocks (Goguel, 1983). However, ingeneral not all alteration ypes or events hat affectalkali concentrations are associated with mineraliza-

    tion. n districts where more han one period of strongalteration has occurred, studies such as his may have

    on the right toward the center of the district. Level 580: Cr 67 located under the central Tentadoraregion shows high background long he traverse and added enrichment near the veins on the leftbut leaching of K and Rb at the vein on the right. Level 420: Cr 233E shows a similar pattern ofincreasing K20 and Rb enrichment oward the left. The first area of K-Rb enrichment marks hebeginning of the altered rocks n Cr 233E and s correlative with the abrupt surface boundary on theeast side of Herminia (Fig. 4A and B). K and Rb contents n rocks along Cr 233E decrease o backgroundvalues eyond he initial area of alteration ut increase oward he vein system ncountered t Herminia.Beyond he vein system, KzO and Rb contents eturn to background alues. Level 580: Cr 201 showsa gradual ncrease n K20 and Rb to the left away from the unaltered zone. The traverse n Cr 201intersects wo mineralized veins, one showing K=O-Rb enrichment and the other total leaching ofthese elements but an increase n Sr. Location of the traverses s given by Scherkenbach 1978).

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    572 SCIENTIFIC COMMUNICATIONS

    limited usefulness xcept o delineate unaltered areasor call attention o areas hat require closer nspection.

    Unaltered dacites rom he Julcani istrict have K/Rb ratios of about 215, whereas lightly ltered ocksaverage 210 and strongly K- and Rb-enriched ocksaverage bout 130. These atios eflect Rb enrichment

    in the mineralizing olutions rom depth which esultin a significant eduction n the K/Rb ratio of thealtered rocks. Lack of noticeable change rom dif-ferent parts of the district ndicates hat the alteringfluids partitioned Rb and K into wall rocks at the sameratio (about 110). At Julcani most areas underlain ysignificant ineralization, nd particularly hose reasnear veins as shown y underground raverses, xhibitmarked enrichment of K and Rb. Here, addition ofK and Rb may have taken place not only before thedeposition f ore (Noble and Silberman, n press) utalso fterward, uring he inal stages fhydrothermalactivity. Furthermore, acid and alunite- and kaolinite-

    stable solutions esponsible or alkali eaching earvein structures were present prior to, or during, oredeposition. imilar elationships re found at Butte(Brimhall and Ghiorso, 1983). Absence of thesechemical changes suggests lack of alteration andassociated conomic mineralization. his relationshipcan be of importance on two scales. On a district-wide scale, he intensity nd distribution f alterationmay be evaluated. On a smaller scale, he intensityof the K and Rb enrichment may help to locate n-dividual veins, since the alteration halo about veinsand vein systems resents much arger arget hanthe vein tself. This relationship ould be useful both

    when exploring ew areas and when attempting olocate displaced veins or continuations f locallypinched-out veins.

    Conclusions

    Dacite lavas n the central portion of the Julcanidistrict were altered differentially y hydrothermalfluids; most became enriched n K20 and Rb and de-pleted n Sr. Resurgence f magma t depth producedfractures which channeled olutions hrough muchof the rock. Strong enrichment of K20 and Rb is re-lated to fractures and mineralization, and rocks con-taining he highest amounts f KO and Rb (as muchas 8.0 wt % and 700 ppm, respectively) re foundwithin 10 to 15 m of veins or on the surface, nearthe areas that contain substantial mineralization. Thealtered ocks ave ower K/Rb ratios about 30) thanthe unaltered ocks rom the district (about 215),which ndicates nrichment f Rb n the mineralizingsolutions.

    Using K and Rb as guides o ore, t may be possibleto determine favorable sites for mineralization bothon a regional basis and on a smaller scale near pro-ductive veins. n addition, by defining he limits ofchemical hange, nproductive xploration may bereduced.

    AcknowledgmentsThe authors ratefully acknowledge inancial nd

    logistic upport or this research rom Compafiia eMinas Buenaventura, S. A., a Domestic Mining andMineral Fuel Conservation ellowship, nd a NationalScience Foundation Grant. Special thanks are ex-

    tended o Alberto Benavides nd J. O. Kalliokoski orenthusiastic upport hroughout he study. Thanksare also extended o Jake Dann, George Bennett, andMarc Wilson for help in acquiring X-ray diffractiondata, and o members f the staff of Mina Julcani orassistance uring he field portion of this study. Fi-nally, we are indebted o H. A. Wollenberg, whosereconnaissance gamma spectrometry measurementsoriginally suggested ajor areal variations n potas-sium content within the Julcani district.July 2, November 28, 1983

    REFERENCES

    Armbrust, G. A., Oyarz6n, J., and Arias, J., 1977, Rubidium asa guide to ore in Chilean porphyry copper deposits: ECON.GEOL., v. 72, p. 1086-1100.

    Bonham, H. F., Jr., and Garside, L. J., 1979, Geology of theTonopah, Lone Mountain, Klondike, and Northern Mud Lakequadrangles, Nevada: Nevada Bur. Mines Geology Bull. 92,142 p.

    Brimhall, G. H, Jr., and Ghiorso, M. S., 1983, Origin and ore-forming onsequences f the advanced rgillic alteration rocessin hypogene environments y magmatic gas contamination fmeteoric fluids: ECON. GEOL., v. 78, p. 73-90.

    Browne, P. R. L., and Ellis, A. J., 1970, The Ohaki-Broadlandshydrothermal rea, New Zealand: Mineralogy nd elated geo-chemistry: Am. Jour. Sci., v. 269, p. 97-131.

    Goguel, R., 1983, The rare alkalies n hydrothermal alterationat Wairakei and Broadlands, eothermal ields, N.Z.: Geochim.

    et Cosmochim. Acta, v. 47, p. 429-437.Goodell, P. C., and Petersen, U., 1974, Julcani mining district,Peru: A study of metal ratios: ECON. GEOL., v. 69, p. 347-361.

    Noble, D. C., and Silberman, M. L., Volcanic and hydrothermalevolution and K-Ar chronology of the Julcani district, Peru:ECON. GEOL., in press.

    O'Neil, J. R., Silberman, M. L., Fabbi, B. P., and Chesterman,C. W., 1973, Stable sotope and chemical elations during min-eralization n the Bodie mining district, Mono County, Cali-fornia: ECON. GEOL., v. 68, p. 765-784.

    Oyarzun, J. M., 1975, Rubidium and strontium s guides o coppermineralization emplaced n some Chilean andesitic ocks: Devel.Econ. Geology, v. 1, p. 333-338.

    Petersen, U., Noble, D.C., Arenas, M. J., and Goodell, P. C.,1977, Geology of the Julcani mining district, Peru: ECON.GEOL.,v. 72, p. 931-949.

    Powell, J. L., Skinner, W. R., and Walker, D., 1969, Whole-rockRb-Sr age of metasedimentary ocks below the Stillwater Com-plex, Montana: Geol. Soc. America Bull., v. 80, p. 1605-1612.

    Scherkenbach, D. A., 1978, Potassium and rubidium metaso-matism related to mineralization at the Julcani district, Peru:Unpub. M.S. thesis, Michigan Tech. Univ., 68 p.

    Turekian, K. L., and Kulp, J. L., 1956, The geochemistry f stron-tium: Geochim. et Cosmochim. Acta, v. 10, p. 245-296.

    Volkov, V. P., and Savinova, E. N., 1961, Variation in the po-tassium-rubidium atio during the evolution of calc-alkalic andalkalic magmas: Geochemistry nternat., v. 12, p. 1227-1236.

    Wilson, M. L., 1979, Some mineralogical relations in hydro-thermally altered dacites, Julcani Peru: Unpub. M. S. thesis,Michigan Tech. Univ., 60 p.