Integrating Spatial and Frequency Information in the ... - CiteSeerX

Economic Geologtj Vol. 83, 1988, pp. 18-29

Integrating Spatialand FrequencyInformationin the Searchfor KurokoDepositsof the HokurokuDistrict, Japan DONALD

A. SINGER

U.S. GeologicalSurvey,345 Middlefield Road,Menlo Park, California 94025 AND RYOICHI

KOUDA

GeologicalSurveyof Japan,1-1-3 Higashi,Yatabe,Ibaraki-ken,305, Japan Abstract

A new method (FINDER) that usesthe area of influenceand Bayesianstatisticsto aid in selectionof target areason the basisof one or morevariablesandmultiple observations was testedwith drill hole data.A previouslydefinedbimodaldistributionof Na20 with the low sodiumgroupconfinedto a 1.5 X 3.0-km zonebeneaththe clusterof depositsat Fukazawa was used as a control area for one test of FINDER. Usingthe Na20 meansand standard deviationsfor the controlareaandminimumNa20 valuesfrom 174 drill holes,a probability mapof centersof sodiumdepletionis producedfor the Hokurokudistrict.High probability areascorrespondto the knowndepositsthat shouldhavebeen rediscoveredandto several areaswithout knowndeposits. Useof X-ray datafrom 165 drill holes,someof which alsohavechemicalanalyses,led to the identificationof two additionalvariables,sericiteandgypsumplusanhydrite,that allow moredrill holesto be usedandthat expandthe areasof influencearounddrill holes.Sericite is enrichedup to 2.15 km andgypsumplusanhydriteup to 3.5 km fromthe centroidof the controlareaFukazawadeposits.For the depositgroupswith X-ray datanearby,Fukazawa, Shakanai,andFurutobe,a patternof sericiteenrichment,kurokodeposits,andgypsumplus anhydrite enrichmentover 4 or 5 km is shown. With sodium,sericite, and gypsumplus anhydrite, FINDER's high probability areas includeeachof the four groupsof kurokodepositsthat shouldhavebeen rediscoveredand only one knowndepositthat is muchsmallerthan Fukazawais missed.Severallarge areas that are favorablecentersof undiscovereddepositsandotherareasthat are unlikelycenters of depositsare alsoidentified. Introduction

COMMONto different disciplinesinvolved in mineral explorationand resourceassessment is the difficulty of distinguishing anomaloussamples(that is very high or low values)that are related to the deposit type soughtfrom valuesrelated to other processes.A fundamentalproblemin explorationis to discriminatesamplesrelated to mineralizationfrom samplesrelatedto barrenareas.The approachtypically employedby geochemists relies on determining the frequencydistributionof one or more elements in a barren control area and defining all values more than two standard deviations above the

knowledge of the characteristicsof the variable near and away from the deposittype soughtand a meansto integrate the responsesand their spatial distributions.In this paper we present an application of a recently developed method, FINDER (Singer,1985), that canbe usedto aid in the selection of target areason the basisof one or more geologic, geochemical,or geophysicalvariables and any spatial distribution of samples.The method combinesclassicalstatisticswith Bayesianstatistics (Raiffa, 1968) and an area of influence procedure (Singer, 1976; Singerand Drew, 1976). A similar idearelyingon simulationwaspresentedby Rehder and van den Boom (1983) for geochemicalvariables. Following a discussion of how FINDER works,we presentthe resultsof a test of the system with kuroko depositsin the Hokuroku district of

meanasanomalousfor the studyarea.Use of information about the spatial distribution of "anomalous" samplesusuallydependson the interpretation by the geochemists, muchasthe geophysicist interprets magneticpatternsor the geologistinterprets Japan. alterationor lineamentpatterns.Recognitionof a How FINDER Works patternrequiresthe integrationof the spatialdistributions of data with the values observed. In order to identify an anomaloussample,it is How closethe samplesshouldbe and what pro- necessaryto have someidea about what a typical portionof them shouldbe abovesomelimit requires sampleis like. Geochemistsin somecasesuse the 0361-0128/88/767/18-1252.50

18

TARGETINGKUROKODEPOSITS,HOKUROKUDIST.,JAPAN

19

crustalabundanceof an elementfor a typicalbackground value and suggestthat valuesabove some multipleof crustalabundanceare anomalous. Without knowinghow frequentlydifferent valuesoccur, this approachcanproducevery misleadingresults. For example,two different frequencydistributions that havethe samemeancanhavemarkedlydifferent chancesof valuesoccurringabovetwo timesthe mean.Thus, there is a strongneed to obtaininformation not only about the typical value but also aboutthe frequencydistributionof the background

if it came from the backgroundpopulation and a very low probabilityof occurringif it camefrom the mineralizedpopulation;by examinationof the histogramsof Figure i it would appearto belongto the backgroundpopulation.Similarly, a samplewith a valueof 50 or more wouldby examinationof Figure i appearto belong to the mineralizedpopulation; sampleswith valuesbetween 20 and 40 couldhave come from either population.A samplethat had a value of 35 or more would have a smallprobability of occurringif it camefrom the backgroundpopulapopulation. tion and a muchhigher probabilityof occurringif it If the frequencydistributionof the background camefrom the mineralizedpopulation. population has been characterized and a sample The probability of being from the mineralized from the studyarea hasan exceptionallyhigh (or population,given one or more samples,can be callow) value,then the samplemightbe relatedto the culated by meansof Bayesrule (Raiffa, 1968) as mineraldepositsought.However, it is alsopossible follows: that the samplerepresentssomeextraneous process P(mineralizedI Xl, . .., Xn) not related to a deposit.Without informationabout the frequencydistributionof the variable in or near P•i=l]•IP(X,I mineralized) the deposit type of interest, it is not possibleto determine the chancethat samplesare from the (1) mineralizedpopulation.For example,the proporPm fi P(X,I mineralized) i=l tion of depositsof a particulartype and sizelocated at the intersectionof majorfaultsmightbe the same asthe proportionof depositsawayfrom faultsin the i=l backgroundpopulation. In order to showhow the methodspresentedin where P(mineralized[X1, ..., Xn) is the revised this paper work, we have first constructeda simple probabilityof belongingto the mineralizedpopulaartificial example;later we will examinea real ex- tion, given the observationsX1, . . . , Xn; Pm is the ample. In a well-studied control or training area prior probability of being from the mineralized there is a circular-shapedgeochemical pattern that population, typically a small number like 0.01 or hasa radiusR centeredo'l a mineraldeposit(Fig. 0.005 is used initially; II P(Xi[ mineralized) is the 1). The pattern can be re •resented in two dimen- productof the probabilitiesof eachsamplevalue or sions.Boththe backgrouncand mineralizedpopula- variable occurring given the mineralized populationshave been sampleds•lfi:icientlyto producethe tion, that is P(Xi[ mineralized); and H P(X•{ backrespectivefrequencydistributions(Fig. 1). If there ground)is the product of the probabilitiesof each are only two populations, )ackgroundand mineral- samplevalue or variableoccurringgiven the backized, then it is possibleto estimate the probability groundpopulation,that is P(Xi[background); andn for either populationthat ,nyparticularsamplein a is the number of samplesor variables. study area exceedsa particular value based on the The prior probability of belongingto the mineralrelative frequencyhistograms. From the observed ized population may be estimated from external relativefrequenciesin the controlarea,the proba- sourcesof informationsuchashistoricaldata.Typibility of observinga valu.• at least as great as Xi, cally, a smallnumber is usedbecauseeven in known giventhat a sampleis from the backgroundgroup,is mining districts,the depositscomprisea smallproP(Xil background); the p•obabilityof observinga portion of the total area that is favorable.Initially value at leastas great as)[i, given that a sampleis the smallprior probability is assignedto all of the from the mineralizedpopulation,is P(Xil mineral- studyarea and the informationfrom samplesis then ized). Modified forms of these probabilities are used to revise the probabilitiesnear the samples. called"a necessityindex," P(Xil mineralized),and Becausewe assumethat the general geologiccon"a sufficiencyindex," P(X I background),in PROS- ditions, frequency distributions, and associated PECTOR(Dudaet al., 1977). What is reallydesired anomalysizesfor the controlarea (Fig. 1) represent is to be able to calculatethe probabilityof being the conditionsin the studyarea(Fig. 2), we canmap from the mineralizedpop•dationgivena particular the probabilitiesof sample values occurringfrom sample,P(mineralizedI Xil, which is different from eachpopulationontothe studyarea.In the extreme the aboveprobabilities.A samplehavinga value of casewhere the probabilityof being from the miner10 or lesswould have a los, probabilityof occurring alizedpopulationis very closeto zero andthe prob-

+ [1- Pro] fi P(X•[ background)

20

D. A. SINGER AND R. KOUDA

given that they are from the mineralized population, and low probabilitiesof occurringgiven that they are from the backgroundpopulation(Fig. 1) andthe revisedprobabilityof beingfrom the mineralized populationshouldbe high for C and for D. Becausethe circlesabout C and D do not overlap (Fig. 2), we can saywith a high probabilitythat the center of a depositis located within each of these circles.

BACKGROUND CONTROL

P(XiI backgrøund)

10

20

AREA

P(Xilmineralized)

30

40

50

VALUE

FIG. 1. Upper part: Control area showingmineralizedarea within radiusR. Lower part: Frequencydistributionsfor samples taken within radius R and beyond radius R. Possiblesamples

For pointsnearsampleC in Figure 2, equation(1) canbe usedto estimatethat the revisedprobability of belongingto the mineralizedpopulation,P(mineralizedI Xc), equals0.808 basedon a prior probability (Pm)of 0.05, a probabilityof 0.40 that a value of 38 or more could occur given the mineralized population(P(Xcl mineralized)),and a probability of 0.005

that a value of 38 or more could occur

given the backgroundpopulation (P(Xcl background));for pointsnearsampleD, P(mineralizedI XD) equals0.929 basedon a probabilityof 0.25 of observinga valueof 41 or moregiventhat the sample camefrom the mineralizedpopulation(P(XDI mineralized)),and a probabilityof 0.001 of observing a value of 41 or more given the samplecame from the background population (P(X•I background)). In caseswhere there is overlap of the radii about the samplessuchassamplesC andE in Figure3, the

probabilities(P(Xil mineralized)and P(Xil background))associated with eachsampleare usedin equation(1) to calculatethe probabilityof belongability of belongingto the backgroundpopulationis ingto the mineralizedpopulationfor the part of the = A-E.

very closeto 1.0, we can map a circle of radiusR around the study area samplelocations,A and B (Fig. 1) and saythat the probabilitythat a mineralized targetis centeredwithin eachradiusis closeto zero (Fig. 2). Similarly,valuesof sampleslocatedat C and D have very high probabilitiesof occurring

study area where the overlap occurs (that is p --0.999 in Fig. 3). This is the key to the use of spatialinformationderived from the locationsof samplesin the studyarea;the mappingof the target sizeand shapefrom the controlareaallowsthis revisionof estimatedprior probabilities.

FIG. 3.

FIG. 2.

Probabilities of mineralization centered within radius

R givensamplelocations A-D in the studyarea.Probabilities (p) are fromFigure 1 andare modifiedby Bayesrule; no overlap.

Probabilities of mineralization

centered within radius

R givensamplelocationsA-C, E in the studyarea.Probabilities (p) arefromFigureI andaremodifiedby Bayesrule;overlapofC and E.

TARGETING KUROKO DEPOSITS, HOKUROKU DIST.,JAPAN

The probabilityof each samplevalue occurring, given the mineralizedpopulation,P(X•I mineralized) and the backgroundpopulation,P(Xil background),canbe estimatedfrom the observedrelative frequencies in the controlareaor it canbe calculated from probability distribution functions based on estimated parameters. In the program FINDER (Singer, 1985), the normal probability distributionfunctionis usedto estimatethe probabilities of samplevaluesoccurringgiven both the backgroundor barren,P(Xil background),and the mineralized,P(Xil mineralized),populations. In general:

P(xl,, =

,

(2)

where P(x[•, •r) = probabilityof at leastx, P(X•[ mineralized)or P(X•[background); x = an observation; z = (x - •)/a; • = populationmean;and a = populationstandarddeviation. From the control area, the estimatedpopulation meansand standarddeviationsof the background and of the mineralizedsamplesare calculatedand usedwith the normalprobabilitydistributionfunction, equation(2) (HoggandCraig, 1965), to calculate probabilities used in the Bayes rule (eq. 1). Bayesrule allows the effects of multiple samples andmultiplevariablesto be representedin the estimatedprobability.It is importantto note, however, that the variablesand samplesmust be independent. The independenceof variablescanbe tested by standardcorrelationmethods.The fact that sampleswithin the mineralizedpopulationor the backgroundpopulationtend to be high or low doesnot violate the independencerequirement. Thus, for properly transformed variables, a mechanismis providedfor integratingmultiple v•iables andsamples to make a probabilisticestimateof the likelihood that an area contains the center of a mineral-

ized target. The simple examples for circular targets presentedaboveshowthe logicof the methodsdeveloped here. In practice, the computer program, FINDER, dividesthe study area into a number of smallcellsandassigns the prior probabilityto each cell; the revised(posterior)probabilitiesare calculated for eachcell basedon the spatialarrangement of the samplesand the sizeand shapeof the target sought.The map plan patternsof many variables related to mineralizedareascan be approximated by circles,ellipses,annuluses,or annularellipses. The mappingof the target onto samplelocations allowsprobabilisticstatementsto be made about possiblecentersof anyof theseshapedtargetvariables.

21

For ellipticallyshapedtargetsthe samereasoning that is used for circlesis applied; points or cells farther away than the variable semimajoraxis (a) from a sample,representedby the larger circle in Figure4, are not modifiedby the informationfrom the sampleandpointscloserthanthe variablesemiminor axis(b) from a sample,representedby the smallercircle in Figure 4, are treatedin the same manner as circular variables discussed above. For

pointsbetweenthe semimajorand semiminoraxis lengthsawayfromthe sample,effectsof orientation mustbe considered.The central angleof possible orientationsaffected,4) in Figure 5, is calculated (Drew, 1966; SingerandDrew, 1976) asfollows:

4)=(2tan -1)b /(a2-d•)) fora>d>b,(3) • ,•/•-•_b• where a is the lengthof the semimajoraxisof the variableellipse,b isthe lengthof the semiminoraxis of the variable(Fig. 4), and d is the distancebetweenthe sampleandthe pointor cellbeingconsidered (Fig. 5). The angle4)can vary from 180ø for distances equalto the semiminoraxisto zero degrees for distancesequal to the semimajoraxis. Equations(1) and (2) are appliedto the possible orientationsaffectedto calculatethe probabilities for each orientation. If it is assumed that all orienta-

tions of the variable of interest are equally likely,

then the sumof the probabilitieswithin 4)divided by 180ø providesan estimateof the probabilityfor a cell. The FINDER programcan also deal with preferredorientationsby restrictingthe possible orientations.

In the FINDER program,a fine grid of cells is defined for the study area. Sequentially,the distancebetween cell centersand samplelocationsare comparedwith the radiusof the circularvariableor the lengthof the semimajoraxisof the variableellipse.For circularvariables,the cell'sprobabilityis calculateddirectlyfrom equations(1) and (2). For

FIG.4. Ellipticallyshaped variablewith semimajor axis(a)and semiminoraxis(b).

22

D. A. SINGER AND R. KOUDA

FIG. 5. Elliptically shapedvariable with the orientationsaffected (6) and the associatedintermediate distance(d).

the magneticpatternaroundsomeporphyrycopper depositsor the geochemicalhalos near some deposit types. For annular shapes,FINDER assumes that the inner part of the annulusbelongsto the same population as the zone beyond the annulus, that is, the backgroundpopulation.Thus for a sample that has a high probabilityof being from the mineralized population based on Bayes equation, FINDER will increasethe probabilitiesof all cells that are in an annuluscentered on the samplelocation. It is alsopossiblefor FINDER to estimatethe number of deposits,but this feature is not used in this report. Circles,ellipses,and annulusesare used in the test of the systemwith kurokodepositsin the Hokuroku district presentedbelow. Sodium and Kuroko Deposits

elliptical variables,equation (3) is used with the anglebetweenthe cell andsampleto determinethe affectedorientationsand equations(1) and (2) are

Kuroko depositsare massivesulfidescontaining copperand zinc, and locally, silver,lead, and gold. They are associated with felsicto intermediatevol-

used for each orientation.

canic rocks and are believed to have formed on the

All cellsandorientationsinitially are assignedthe prior probability,thusonlycellswithin a distanceof the variable circle radius or ellipse semimajoraxis of a samplelocationhave their prior probability modified by new information. If a sample value could have come from either the background or mineralizedpopulations with equallikelihood,then the prior probabilityisnot changed;the morelikely the sample came from either population, the greaterthe prior probabilityis modifiedby equa-

seafloor; the upper massiveparts containingsphalerite and galena are largely syngeneticand the lowerstringeror stockwork partscontainingchalcopyrite and pyrite are epigenetic.There are several

tion (1). Anotherway to look at the way FINDER worksis to assumethat geographictemplatesrepresenting, say,one smallelliptical variableand one larger circular variable are centered over each of the grid cells. If there are no sampleslocated under the

templates,then the prior probabilityfor that cell is not changed.If there is only one samplelocated underonlythe circulartemplate,thenthe probability associated with that sampleandthat variableis usedin equation(1) to modifythe prior probability for that cell. Two samplesunder the circular template would result in the probabilitiesof that variable associatedwith the two samplesto be used in equation(1) to modify the prior probabilityof the cell. A single sampleclose enough to the cell to haveboth the elliptical and circulartemplatescover

excellent summariesof kuroko deposits(Ishihara, 1974; Ohmoto and Skinner, 1983) and volcanic-as-

sociatedmassivesulfidesin general(Franklinet al., 1981).

The mostthroughlystudiedkurokoarea in the world, the Hokuroku district in northern Japan, is

the focusof our tests(Fig. 6). The Miocenekuroko depositsin the districtare underlainby up to a kilometer of submarine volcanic units which accumu-

lated duringOligoceneto Miocenetime. The volcanic units are mainly composedof andesiticand basaltic rocks overlain by the kuroko host rocks

composedof dacitic to rhyolitic lavas,lithic tuff breccias,and tuffs interbedded with minor amounts of basalt lavas and mudstones. The basement con-

sistsof Paleozoicand Mesozoicchert, phyllite, and slate.

In 1983, Date et al. presented evidence that a

largezoneof sodiumdepletionexistedin the footwall dacites beneath

the Fukazawa

kuroko and

Ezuri depositsin the Hokuroku district. Several papersin Japaneseprecededthe Englishpublication (Date andWatanabe,1979; Hashiguchiet al., the samplelocationwouldresultin the probabilities 1981). We decided to test the FINDER program of each variable associatedwith the sampleto be usingthe reported sodiumdepletionwith the reapplied in equation (1). Once all samplelocations suitsof 20 yearsof drilling in the Hokurokudistrict; covered by the templates are considered, the thisdrillingwassponsored by the Japanese national FINDER programwould move on to considerthe and local governments (Ministryof International Trade and Industry,1983). The data usedhere for sametemplatesover the next cell. Amongthe presentoptionsfor the FINDER pro- the sodium depletion and other tests consistof gramis the use of annular-and annularelliptical- chemistryfor about72 percentandX-ray analyses shapedtargetsthat couldbe used,for example,for for a partiallyoverlapping68 percentof 243 drill

TARGETING KUROKODEPOSITS, HOKUROKU DIST.,JAPAN

23

AINAI

[] % ucFl iNOTA !

•

FUKAZAWA ß

EZURI

KC•K I

• Kuroko Deposit []

Railroad

station

FIG. 6. Location of the Hokuroku district and its known kuroko deposits.

holesin the approximately 40 X 40-km2 Hokuroku The FINDER program,usingthe observedNasO district.Stratigraphyis availablefor all drill holes. valuesfromthe publisheddata(Ministryof InternaBased on 1,337 samples from 59 drill holes tionalTrade andIndustry,1983) andthe Fukazawa around the Fukazawadeposits,Date et al. (1983) depositsas a controlarea, not only showsthat Fudemonstrateda bimodal distribution of Na20. Each

of the subpopulations wasapproximatelylognormal and the low NasO group was confined to a 1.5 X 3.0-km zone in plan beneaththe 0.8 X 1.5-km cluster of kuroko deposits.Within the low NasO zone, every drill hole had at leastsomedacitethat wasNa depleted. Becausethere are onlya few drill holeswith publishedchemistrywithin the 1.5 X 3.0-km low NasO zone, we usedthe elliptical shapeand size (after conversion to semiminor and semimajor axes lengths)definedby Date et al. (1983). Due to the inconsistentstratigraphicnomenclatureand the rapid lateral variability in rock types, we choseto use the minimum NasO value in each drill hole; in

everyplacewherethe stratigraphy waswell studied (near deposits),the lowest Na20 value was in the footwall and the rock units were either mudstone or

of dacitic composition.Becausewe used the minimum NasO value, the means and standard deviationsusedhere are differentfrom thosereportedby Date et al. (1983). For example,an NasO value of 0.1 percent is 0.23 standarddeviationsabove the estimatedmean of the low sodiumpopulationand 2.2 standard deviations below the estimated

mean

of the backgroundsodiumpopulation.A plot of drill holes that have minimum Na20 values above and

below 0.1 percent NasO showsmany low sodium drill holesnear known deposits(Fig. 7).

kazawais the centerof Na20 depletionbut alsothat Ezuri, Shakanai-Matsumine, and Furutobe are (Fig. 8). Near Komakiand other areaswithin the region consideredin Figure 8 the white patternis usedto

representthe arbitraryprior probabilityof 0.001. Theseare placeswhere no informationis available to modifythe prior probability;the drill holeshave minimumNa20 valuesthat are either intermediate between the mineralizedand backgroundpopulations suchas near Komaki, or beyond the region considered,there are no drill holesnearby.Areasin Figure 8 that have the pattern associated with a probabilityof lessthan 0.001 have high minimum NasO values,suggesting sodiumenrichmentand, perhaps, unlikely sites for kuroko deposits.Depositsnear Hanaokaand Uchinotaicouldnot have been detectedbecausethey are too far from drill holeswith publishedchemistry.The southerndepositsin the Furutobe-Ainai group are not associatedwith a high probabilityof NasO depletion accordingto theseresults;the reasonfor this may be the apparentsynsedimentary transportand redepositionof someof thesedeposits.The only area that mighthavebeendetectedbut is clearlymissed is near the Komaki depositwhich is much smaller than the Fukazawacontrol deposit.In additionto the high probabilityareasnear depositsand some scattered drill holes, there are high probability areasextendingsouthfrom the Fukazawadeposits

24

D. A. SINGER AND R. KOUDA

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$

,

**

*

* ,•A' A

*

*

*RUTORE

**

*Na20 1.0

G

Gypsum + > 0.1

.

Other

[]

RR Station

'•G4•'•% 's

%ß FURUTOBE

s

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AINAI

• Kuroko Deposit

9 UCHINOTAI o

•

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EZURI

S ß

S

S

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TO•DA MINAMI

KOMAKI

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FIG. 10. SericiteandgypsumplusanhydritevaluesfromX-ray datain drill holes.

TARGETING KUROKO DEPOSITS, HOKUROKU DIST.,JAPAN

27 AI

,o

HT4

HT5

HT16

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?%N•O

H,058I HOKUROKU/CROSS-SEC TO• of Kuroko horlZo• ß (