geostatistical modeling of ore grade distribution from geomorphic

Geostatistical Modeling of Ore Grade Distribution fromGeomorphic Characterization in a Laterite Nickel Deposit

Asran Ilyas1 and Katsuaki Koike2,3

Received 11 July 2011; accepted 23 January 2012Published online: 15 February 2012

Due to growing consumption of nickel (Ni) in a range of industries, the demand for Ni hasincreased rapidly around the world. This trend requires a more precise estimation ofavailable Ni grade deposits and an identification of factors controlling the grade distribution.To achieve these requirements, this study applies geostatistical techniques to spatial mod-eling of the Ni grade in a laterite Ni deposit, with reference to geomorphic features such asslope gradient and the thickness of limonite and saprolite zones. The Sorowako area inSulawesi Island, Indonesia, was chosen as a case study area because it has a representativelaterite Ni deposit with large reserves. Chemical content data from drillhole cores at 294points were used for the analysis. The slope gradient was found to have a remarkablecorrelation with the thickness of the limonite zone, but there was no correlation between thethickness of the limonite and the saprolite zones above the bedrock. One important featurewas a general correlation between the thickness of the saprolite zone and the maximum Nigrade in this zone: the grade increases with the thickness of the zone. Co-kriging wasadopted to incorporate this correlation into estimating the maximum Ni grade in the sap-rolite zone. As a result, the maximum Ni grade in the saprolite zone tends to be high mainlyin areas of slight slope. The Ni accumulation at this topographic feature probably originatesfrom deep weathering by groundwater infiltrating through well-developed rock fractures.

KEY WORDS: Co-kriging, slope gradient, limonite zone, saprolite zone, nickel grade, Sulawesi.

INTRODUCTION

Nickel (Ni) exists as a silvery-white lustrousmetallic element that can withstand high tempera-tures. This characteristic is suitable for producingheat-resistant equipment such as aircraft engines. Inaddition, Ni has a stainless feature (USGS MineralCommodity Summaries 2011), and has been widelyused in alloys with other metals (Thompson 2000).Because of these two favorable metallic features, Nihas been used as a raw material for many kinds of

industrial products, including steel, chemicals, elec-trical equipment, fabricated metals, householdappliances, and machinery. Its major use is in stainlesssteel, which accounts for two-thirds of primary Niproduction. The widespread consumption of Ni, alongwith the growth in new developments in the elec-tronics and telecommunication industries, has seenthe demand for Ni increase rapidly since 2000. Thistrend requires on-going exploration and exploitationof Ni deposits around the world, while ensuring Nimining is sensitive to natural environments.

There are two types of Ni deposits with differentmechanisms of formation. They are laterite andmagmatic sulfide deposits. The principal ore mineralsare nickeliferous limonite (Fe, Ni)O(OH) and garni-erite (a hydrous nickel silicate) (Ni, Mg)3Si2O5(OH)4

of the laterite type and pentlandite (Ni, Fe)9S8 of themagmatic sulfide type. Laterite deposits are more

1Graduate School of Science and Technology, Kumamoto

University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan.2Department of Urban Management, Graduate School of Engi-

neering, Kyoto University, Katsura C1-2-215, Kyoto 615-8540,

Japan.3To whom correspondence should be addressed; e-mail:

[email protected]

177

1520-7439/12/0600-0177/0 � 2012 International Association for Mathematical Geology

Natural Resources Research, Vol. 21, No. 2, June 2012 (� 2012)

DOI: 10.1007/s11053-012-9170-8

important for land-based resources, because approx-imately 60% of Ni originates from laterite depositsout of a total of 130 million ton (Mt) (Gleeson et al.2003). Laterite Ni deposits have been discovereddominantly in the tropical and subtropical belts(Gleeson et al. 2003; Thorne et al. 2009), and aregenerated by intense weathering of ultramafic igne-ous rocks, with the resulting secondary concentrationsof Ni-bearing oxide and silicate minerals. This type ofdeposit is commonly derived from chemical weath-ering of olivine-rich cumulate rocks and their meta-morphic derivatives, which have primary initial Nicontents of 0.2–0.4% (Brand et al. 1998).

Indonesia is one of the major countries rich in Niresources and has world-famous large lateritedeposits. In 2009, world Ni production had reached1.43 Mt and approximately 13% of the productioncame from Indonesia. Indonesia is the second rankedcountry for Ni production (Price 2010; Sufriadin et al.2010). Large laterite deposits are concentrated onSulawesi Island, and Sorowako is a typical area con-taining a hydrous silicate deposit that has been

developed since 1968 by a mining company, PT.INCO Indonesia (Fig. 1). It is well known that anaccurate estimation of Ni reserves is difficult in lat-erite deposits because of the complexity of geologicalstructure, local changes in degree of weathering evenin the same lithology, strong heterogeneity of Nigrade distribution, differences in Ni concentrationpatterns such as vein or disseminated ore body, andthe influence of many factors controlling the Ni grade.

Based on the above background information, thisstudy is aimed at developing a method for precisespatial modeling of Ni grade in a laterite deposit. Ourmodeling process is implemented by identifying con-trol factors on the grade distribution and applyinggeostatistical techniques. Precise Ni grade modelingcan contribute to accurately assessing Ni reserves. TheSorowako area in Figure 1 is a representative lateriteNi deposit and considerable exploration data has beenaccumulated by PT. INCO Indonesia. Thus, the areawas selected as a suitable test site for grade modeling.Among the many possible factors, a geomorphic fac-tor is selected as the most dominant because it can

CELEBES SEA

North Sulawesi Trench

GORONTALO BASIN

MA

KA

SSA

R S

TR

AIT

BANDA SEA

MO

LU

CC

A S

EA

BUTON

BONE GULF

SULAWESI

East

San

gihe

Thru

st

Tolo Thrust

Sula Thrust

Sula Platform

Tukang BesiPlatform

Lawanoppo Fault

Matano Fault

PaluFault

Continental Fragments of Banggai-Sula, TukangBesi, and Buton

West Sulawesi Volcano-Plutonic Arc Belt

East SulawesiOphiolite Belt

Central SulawesiMetamorphic Belt

Study Area (PT. INCO, Indonesia, Sorowako)

Thrust Fault

High Angle Fault

2oN

0o

2oS

4oS

120oE 126oE124oE122oE

Nickel deposit

X

X

MA

KA

SSA

R S

TR

AIT

BUTON

SULAWESI

Sula Thrust

Lawanoppo Fault

Matano Fault

PaluFault

- ,

-

)

120 Eoo

X

X

Figure 1. Location of study area (mining area of PT. INCO Indonesia) in South Sulawesi Province, Sulawesi Island, Indonesia with a

geological map and four principal tectonic belts in Sulawesi Island (Mubroto et al. 1994).

178 Ilyas and Koike

strongly affect the rock-weathering rate, whichdetermines the thickness of the laterization zone.

GEOLOGY AND DATA FOR ANALYSIS

Geological Setting

The generation of the laterite Ni deposits in theSulawesi Island, Indonesia, is closely related to thesetting of this island, which is at the convergencezone of three tectonic plates, Eurasian, Pacific, andIndian-Australian plates. Because of high tectonicactivity, many active faults and extensional basinswere developed throughout the Cenozoic era(Macpherson and Hall 2002), which made the geo-logic structures very complicated. This activity pro-duced several huge ore deposits in a range ofmineralization and metallogenic provinces.

Sulawesi Island consists of four principal tectonicbelts (Fig. 1): the West Sulawesi Volcano-PlutonicArc Belt, the Central Sulawesi Metamorphic Belt, theEast Sulawesi Ophiolite Belt, and the ContinentalFragments of Banggai-Sula, Tukang Besi, and Buton(Mubroto et al. 1994). The tectonic setting and physi-ography of Sulawesi Island were formed during theNeogene orogenesis that generated chains of moun-tains with peaks over 3,000 m a.s.l. and mineraldeposits of laterite Ni, chromite, gold, and base metalsin the East Sulawesi Ophiolite Belt. Laterite Nideposits are mainly located in the complex of Creta-ceous ultramafic rocks in the eastern Sulawesi and inthe eastern coast zone (Fig. 1), which is composed oftwo Miocene rocks of subduction melange of approx-imately 10 Ma (Golightly 1979; Suratman 2000). Mostdeposits are formed in hills and low mountains, whichare deeply eroded and strongly weathered.

The geology of the Sorowako area and its sur-roundings can be divided mainly into three rock units:alluvial and sedimentary lacustrine rocks of Quater-nary, Tertiary ultramafic rocks such as Harzburgite,and Cretaceous sedimentary rocks (Golightly 1979;Suratman 2000). Laterite Ni deposits in this area weregenerated in the Tertiary ultramafic rocks, which area part of the serpentinized peridotite zone.

The study area is generally composed of unser-pentinized ultramafic rocks. Laterite Ni depositsaround the study area are classified as hydrous silicatedeposits with harzburgite and dunite in the bedrocks(Gleeson et al. 2003). The weathered strata above thebedrock could be classified simply into two zones fromthe ground surface: the limonite and the saprolite

zones, which were composed mainly of hematite andolivine, respectively. The average thicknesses of thelimonite and saprolite zones are almost the same, 11 m(PT. INCO Indonesia 2006). Fine grain soils with red,brown, and yellow colors generally comprise thelimonite zone. However, the saprolite zone is gener-ally a mixture of soils with unweathered host rocks thatretain their original texture and structure. Many frac-tures have developed in this zone due to weathering,with boulders forming between the fractures due togroundwater flowing through the fractures. Garnierite,which has a high Ni concentration, is usually found atthe rim of these boulders. Below the saprolite zone, thebedrocks consist of unweathered ultramafic rockswhose upper parts are well fractured with garnieriteand silicates present as filling minerals in the fractures.

Drillhole Data

Drillhole data at 294 sites were used for Ni grademodeling. The holes were drilled in a lattice patternin a 1.6 km (E–W) by 1.0 km (N–S) area with a50-m spacing between adjacent drillholes (Fig. 2).Drillholes were distributed along the ridges trendingNE–SW. Because Ni-bearing minerals were concen-trated in the weathered rocks, drillings were set topenetrate the weathered layer and reach the bedrock.The average depth of the 294 drillholes was 26.62 m.

The sample data collected at each site consistedof the concentrations (wt%) of four chemical com-ponents (Ni, Fe, SiO2, and MgO), rock type, and themain constituent mineral. These data were measuredfrom sub-cores of mostly 1-m length that were splitfrom the original core sample. Accordingly, the datawere collected at approximately 1-m depth intervalsalong the drillholes at each site. We initially examinedthe correlations between the Ni concentration and theother three components, but the correlations with Niwere all poor. Although the original sample data weremultivariate, only the Ni data were used in the anal-yses because of this lack of correlation. Table 1 showsa part of the sample data at one site located on a hill.

GEOSTATISTICAL METHODSAND RESULTS

Selection of Influence Factor

The spatial variability of ore grade in a depositis the most important feature for precise assessment

179Geostatistical Modeling of Ore Grade in Laterite Nickel Deposit

of ore reserves (Hartman 1992). Therefore, a properspatial modeling technique, which interpolates andextrapolates the sample data of ore grade for un-sampled points or blocks, is indispensable for thisassessment. The success of geostatistics has beendemonstrated in many case studies of ore gradeestimation (e.g., Koike et al. 1998; Srivastava 2005;Verly 2005; Emery 2006). In addition, the identifi-cation of geologic factors that control the formationof the ore body and the heterogeneity of ore gradedistribution is also significant (e.g., Koike andMatsuda 2006). Laterite Ni deposits, in general, arecomplicated in shape and chemical composition byseveral controlling factors related to climate, topo-graphic condition, tectonic setting, lithofacies,parent rock type, geologic structure, groundwater,

organic matter content, and rates of weathering(Brand et al. 1998; Gleeson et al. 2003). Dependingon the size of each laterite deposit, the geomorphicfactor may be the most predominant, because it canaffect other factors such as the groundwater system,weathering processes, and geological features, onthe layer thickness of the laterization zone (limoniteand saprolite zones) above bedrock.

Thus, the geomorphic factor was expressed inthis study of Ni grade modeling by classifying thetopography into five categories. These are: (1) steepslope (gradient ‡45�); (2) ridge (regions near the lineof a ridge with gradient <45�); (3) slope with inter-mediate gradient (gradient ‡20�); (4) slight slope(gradient ‡5�); and (5) flat slope with a gradient<5�,which is associated with a valley area, or cavity

A102276

A103965

A115118

A115319A115320

A115218

A115219

A115559

A104136

A102277A115460A103794

A104567A103787A104377 A115928 A104471A103786

A115557

A103785

A115929A115461

A104368

A104674 A104675

A104560

A103780

A115546A115920

A104470 A104379

A115449

14200

A103966

A103793A104385A104679

A115921

A115550

A104563A104562

A103791

A115925 A104569

A115926 A115559

A115548

A104380

A103795

A115547

A104669

A115558

A115549

A104665

A104666 A104378A103783

A115463

A104469

A103790

A104463

A104464

A104474B

A104573A104376

A104370

A104571

A104575

A115459 A115462

A115933 A104568

A104473

A115931

A104460A115932

A104461A115464 A104465

A104672

A104670

A104667

A115922A115934 A104671

A104668

A104476

A104475

A103789

A115556A104576

A104570

A115555

A115923

A104572

A104477

A115935

A115035 A115036A115936 A104466A115938 A115937 A115039 A115040

A104383

A104135

A104382

A103792

A104678

A103967

A104680

A104681

A115553A115552

A115561

A115930

A104381

A104677

A115560A115562

A115554

A104468A104467

A103788

A104673

A104684

A115450

A115458

A104676

A115927

A103784

A104472

A115551

A115451

A104564

A115456 A104574A103781

A104566

A104369 A115455

A104561

A104683

A115453

A104565

A115454

A103796A103782A115452

14000Nor

thin

g (m

)

A115041

A104744

A104743

A104960

A104740

A104738

A104737

A104685A104944

A104961

A104741A104739

A104577 A104943

A104935A115033

A104937

A104736

A104578

A104835A104579 A104478

A104371 A115037

A104834

A104837

A104843A104838

A104936

A115466

A104939

A115468

A104836

A104940

A115034

A104372

A104942

A104462

A104938

A115940 A115465

A104479

A115924A115467A115564

A115038

A104848

A104941A115563

A104373A104846

A115457

A115469

A115939

A104374

A104480

A104375

A104841

A103797

A104845

A104849A115047

A104847

A104842

A104482

A104839

A115470

A104746

A103798

A104844

A104840A115471

A115045

A104585

A115046

A115472

A104580

A104949A115473

A104950

A104481

A104953

A115941

A104958A104957A115567

A115565

A115944A115942

A115943 A115566A104483

A104581A104582A104583

A104384

A115043

A104682

A115042A104745

A104959

13600

13800

A115948

A104946A104947

A104945

A104742

A104948

A104388

A104750

A104753

A104748

A104751

A104747

A104754

A104850

A104752

A104749

A104952 A115044

A104851

A104951

A115568

A115053

A104954

A104852A104956

A104955

A104855

A115048

A104386A104686

A115049

A103799

A104854

A115052

A115050

A104853

A104587

A104584

A115051

A104586

A104387

A104687 A115946

A115945 A115947

13400

5200 5400 5600 5800 6000 6200 6400 6600

1: Steep slope area

2: Ridge area

250 m0 mEasting (m)

3: Slope with intermediate gradient area

4: Slight slope area

5:Flat slope associated with a valley area or cavity

Drillhole site

Figure 2. Drillhole distribution at 294 sites in the 1.6 km (E–W) and 1.0 km (N–S) area, superimposed upon the contour

lines of topography. The sites were classified into the five categories of topographic features (see Fig. 3). Location in the

study area is expressed using a plane rectangular local coordinate system in the mining area of PT. INCO Indonesia.

180 Ilyas and Koike

feature (Fig. 3). These five categories are consistentthe first proposal that considered topography for Nigrade characterization (Darijanto 1999) which sug-gested that the thickness of the laterization zonesand the resultant Ni grades were correlated withthese geomorphic features, and the terrain classifi-cation based on the slope angle by Van Zuidam(1985). Suitable threshold angles for the categorieswere defined in this study by considering the localminimums from the histograms of slope angles.

Slope gradient can control the infiltration rate ofsurface water into the ground, which further affectsweathering of rocks and the enrichment processes ofNi. In addition, slope gradient can characterizegeomorphology simply when the study area is small.Based on this criterion, the drillhole sites wereclassified into: steep slope (37 sites), ridge (56 sites),slope with intermediate gradient (57 sites), slightslope (105 sites), and flat slope (39 sites), as shown inFigure 2. This figure shows that the steep slope and

Table 1. Example of Drillhole Sample Data Composed of Four Chemical Concentrations, Rock Type, and Main Constituent Mineral

Drillhole

Number

Depth

Range (m)

Ni

(wt%)

Fe

(wt%)

SiO2

(wt%)

MgO

(wt%) Layer

Rock

Type

Primary

Mineral

A104378 0.20–1.00 1.16 47.20 7.00 1.20 lim hmt

A104378 1.00–2.00 0.33 6.60 36.00 42.50 lim hmt

A104378 2.00–3.00 1.21 43.40 9.00 1.30 lim hmt

A104378 3.00–4.00 1.53 44.50 7.70 1.50 lim hmt

A104378 4.00–5.00 1.32 44.40 7.10 1.40 lim hmt

A104378 5.00–6.00 1.32 43.60 7.80 1.40 lim hmt

A104378 6.00–7.00 1.32 34.80 24.50 5.00 lim hmt

A104378 7.00–8.00 1.46 44.10 9.90 1.50 lim hmt

A104378 8.00–9.00 1.21 28.20 26.80 5.10 sap hmt

A104378 9.00–10.00 1.81 9.58 39.54 27.19 sap hrz olv

A104378 10.00–10.55 2.03 10.65 39.30 26.22 sap hrz olv

A104378 10.55–11.00 0.52 8.30 41.20 48.50 sap hrz olv

A104378 11.00–12.00 0.20 7.00 73.20 0.30 sap hrz olv

A104378 12.00–12.40 2.13 11.40 40.60 28.70 sap hrz olv

A104378 12.40–13.00 0.26 6.40 39.00 48.50 sap hrz olv

A104378 13.00–13.55 1.59 10.70 31.90 24.70 sap hrz olv

The depth ranges of data at all sites were classified into three layers, limonite, saprolite, and bedrock.

lim limonite, sap saprolite, hrz harzburgite, hmt hematite, olv olivine.

Rock fractures

Ridge area

Steep slope

Slope with intermediate gradient

Slight slope 50 m

Steep slope

200 mFlat slope associated with a valley area or cavity

Figure 3. Schematic map of topographic features classified into five categories by slope gradient (steep

slope, ridge, slope with intermediate gradient, slight slope, and flat slope associated with valley area or

cavity).


ridge areas are situated on the northeast and thesouthwest sides; intermediate gradient areas arenear the northeastern and the southern edges; andthe slight slope and flat areas are in the central andnorthern parts of the study area.

Correlation Analysis

In general, there is a relationship between slopegradient and thickness of the laterization zone, whichwas caused by differences in weathering processesdepending on geomorphology (Ahmad 2001). Toconfirm this general relationship, the average thick-ness of the limonite zones was calculated at everycategory of topographic feature as shown in Figure 4.Clearly, the average thickness tends to increase with adecrease in slope gradient. This trend was furtherexamined by considering the topographic detailunder the following two specific conditions. Becausethe lithologies and rock properties in a laterite Nideposit are known to be highly heterogeneous (e.g.,Gleeson et al. 2003), we examined the trend moreprecisely using only neighboring data.

The first condition was to select the drillholeslocated close to each other at the same elevation inthe same category (Fig. 5a). Such data were consid-ered to be in the same geological environment. Forcategory 1, only three drillholes were at the sameelevation (390 m) and were used for calculating theaverage thickness of the limonite and saprolite zones.Their averages were 3.72 and 12.02 m, respectively

(Table 2). For category 2, four drillholes located on410 m were selected as shown in the table. The sec-ond condition for selecting the drillholes was thatthey should be located close to a straight line that wasin the direction of maximum gradient (Fig. 5b). Thisselection was intended to use the data that wereconsidered to be under the same weathering process.For category 1, four drillholes satisfying this condi-tion were at elevations of 460, 440, 410, and 380 m andthe results are shown in Table 2.

Results from Table 2 of the mean thicknesses ofthe limonite zones in the five categories are depictedin Figure 6. Both sets of results for these topo-graphic conditions show the characteristic that thethickness increased with a decrease in slope gradientis more precise than for the gross analysis inFigure 4. In general, limonite forms the top layer inlaterite deposit areas. Therefore, slope gradient isidentified as an important factor for controllingweathering depth of the limonite zone; flat topog-raphy causes a thicker weathering zone in the shal-low depth range, because of greater infiltration ofrain and surface water.

But, the thickness of the saprolite zone belowthe limonite zone has no correlation with thethickness of the limonite zone as shown in Figure 7a(coefficient of determination R2 = 0.01). This poorcorrelation is the same for the data at the sameelevation selected by the first condition (R2 = 0.03)(Fig. 7b). Therefore, mechanism and dominant fac-tors of weathering on the formation of the saprolitezones were different from the limonite zone. Plau-sible dominant factors on the formation of the sap-rolite zone are geological structure, drainagepattern, and the position of the water table. Thesefactors coupled with the maximum rates of leachingand drainage of the subsequent solution enhancedboth the residual concentration and the accumula-tion of Ni in the saprolite zone (Gleeson et al. 2003).

Changes in Ni grade with depth at each drill-hole site were characterized for every category oftopographic feature. Figure 8a, b, c, and d are thedata on slight slope, flat slope, ridge, and steep slopeareas, respectively. The limonite zones are relativelythick on the gently sloping areas (a and b), but thinat the steep areas (c and d). Common to the fourgraphs, the Ni grade increases from the limonite tosaprolite zones and reaches a maximum (enclosed bycircle) in the saprolite zones. The grades are low inthe bedrock zone. Figure 8 highlights the fact thatthe Ni grades change abruptly within the saprolitezone and their average values are similar among the

14.0

16.0

8.0

10.0

12.0

2.0

4.0

6.0

Mea

n th

ickn

ess

of li

mon

ite z

one

(m)

0.01 2 3 4 5

Category of topographic feature

Figure 4. Correlation between the category of topographic fea-

tures (first to fifth category depending on slope gradient as

defined in Fig. 2) and mean thickness of the limonite zones

in each category. Slope gradient decreases from first to fifth

category.

182 Ilyas and Koike

Table 2. Mean Thicknesses of Limonite and Saprolite Zones and the Maximum Ni Grade in the Saprolite Zone at Each Category of

Topographic Feature

Drillhole

Location

Category of

Topographic

Feature

Number

of Drillholes

Value

Mean Thickness (m)Mean of Maximum

Ni Grade in the

Saprolite Zone (wt%)

Limonite

Zone

Saprolite

Zone

Same elevation 1 3 3.72 12.02 1.88

2 4 8.33 11.45 1.88

3 3 11.85 2.03 1.56

4 7 14.80 13.80 3.55

5 4 13.30 9.75 2.11

Different elevations 1 4 2.75 11.76 2.19

2 5 7.06 11.03 2.52

3 5 9.49 5.86 2.00

4 7 17.25 13.16 3.03

5 6 13.06 11.87 2.95

Sample data were classified into two groups: the sites located at similar elevations and the other sites at different elevations by the two

methods in Figure 5.

Topographic surface

Drillhole

Contour line

Drillhole

Contour line

(b)

(a)

Figure 5. Two conditions for selecting the drillholes in the same category to identify relationships between

the slope gradient and the thickness of laterization zone, in particular limonite zone in detail, which are for

drillholes located (a) on the same elevation and (b) along a straight line in the direction of the maximum

gradient.


four categories. As an example, the averages of Nigrade data are similar over all drillhole sites andtherefore, the use of averages leads to ambiguouscorrelations between geomorphology and Ni grade,and to featureless mapping of Ni grade in the sap-rolite zone. The maximum Ni grade is variablyattributable to the degree of weathering, lithofacies,and topographic features such as the slope gradient.Moreover, the maximum Ni grade in the saprolitezone is significant for identifying the most promisinglocation of the Ni resource and developing a mineplan and design. Therefore, the saprolite zone is atarget for Ni mining and the maximum Ni grade inthis zone can be an indicator for predicting thelifetime of a mine. This is a compelling reason forusing the maximum Ni grade for spatial modeling.

It is noted that the thickness of the saprolitezone was generally well correlated with the maxi-mum Ni grade in this zone as shown in Figure 9.

Although the data were scattered around theregression lines, the maximum Ni grade tends toincrease with increasing layer thickness and thistrend is common to all five categories (the maximumR2 for category 2 was R2 = 0.23; and the minimumfor category 3 was R2 = 0.11) and to the overall data(R2 = 0.26). The saprolite zone is known to becomethick in a well-fractured area, because the ground-water easily infiltrates through rock fractures, caus-ing deep weathering. Ni grade tends to be high inthis circumstance, due to high levels of leaching andchemical reaction within fractured rocks, in partic-ular under tectonic uplift (Gleeson et al. 2003).

CO-KRIGING FOR NI GRADE MODELING

Co-kriging is a method for estimation thatminimizes the variance of the estimation error by

(b)(a)

18.016.0

18.0

14.0

10.0

12.0

16.0

14.0

10.0

12.0

Mea

n th

ickn

ess

of li

mon

ite z

one

(m)

Mea

n th

ickn

ess

of li

mon

ite z

one

(m)

6.0

8.0

4.0

2.0

6.08.0

4.0

0.0

2.0

Category of topographic featureCategory of topographic feature431 2 5431 2 5

Figure 6. Relationships between the categories of topographic feature and the average thicknesses of the

limonite zone using drillhole data located (a) on the same elevation and (b) along the maximum gradient

of slope selected by the two conditions in Figure 5.

35.0 30.0(b)(a)

20.0

25.0

30.0

15.0

20.0

25.0R2 = 0.03R2 = 0.01

5.0

10.0

15.0

5.0

10.0

Sapr

olite

zone

thic

knes

s (m

)

Sapr

olite

zone

thic

knes

s (m

)

0.00.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0

0.0

Limonite zone thickness (m) Limonite zone thickness (m)

Figure 7. Scattergrams between the thicknesses of limonite and saprolite zones using (a) all drillhole data

and (b) drillhole data at the same elevations selected by the method in Figure 5a.

184 Ilyas and Koike

exploiting the cross-correlation between severalvariables; the estimates are derived using supple-mentary variables, as well as the primary variable(Isaaks and Srivastava 1989). Co-kriging techniqueshave been applied widely to metal and nonmetalresource analyses on maps of ore grade, resourcequality, and reserve assessment (e.g., Dowd 1992;Koike and Matsuda 2006; Heriawan and Koike 2008;Juan et al. 2011). In the case of two variables only,the ordinary co-kriging estimate is a linear combi-nation of the values of the primary and secondaryvariables as:

w ¼Xn

j¼1

bj � wj þXm

i¼1

ai � vi

Xn

j¼1

bj ¼ 1;Xm

i¼1

ai ¼ 0

ð1Þ

where wj and vi are the primary and secondaryvariables at n and m nearby locations around thelocation to be estimated, respectively, w is the esti-mated value, and ai and bj are the co-kriging weightsthat can be obtained from the semivariogramand cross-semivariogram of the two variables. For

standardized ordinary co-kriging, the nonbiasedcondition is changed to:

Xn

j¼1

bj þXm

i¼1

ai ¼ 1 ð2Þ

Because of the general correlation between themaximum Ni grade in the saprolite zone, which wasdefined as the primary variable, and the thickness ofthe saprolite zone as the secondary variable, co-kriging was adopted for spatial modeling of theprimary variable. ArcGIS� Geostatistical Analyst(ver. 10) was used for the following variography andkriging calculations. Experimental semivariogramsof each variable and a cross-semivariogram of thetwo variables, c(h)s, were calculated in the hori-zontal direction using 50 m as the unit of lag dis-tance. As described above, the depths of thedrillholes were much shallower than the size of studyarea, and suitable c(h) values could not be obtainedin the vertical direction. Thus, we only consideredthe horizontal direction for the variography. Theresultant omnidirectional c(h)s could be fitted byspherical models as shown in Figure 10. The nuggeteffect on the c(h) of the maximum Ni grade in the

2.0

2.5

3.0

1.5

1.8

1.0

1.5

0.6

0.9

1.2N

i gra

de (

wt%

)N

i gra

de (

wt%

)

0.0

0.5

0.0 5.0 10.0 15.0 20.0 25.0 30.00.0

0.3

Depth (m)

Depth (m)

0.0 5.0 10.0 15.0 20.0 25.0 30.0

0.0 5.0 10.0 15.0 20.0 25.0

Depth (m)

Depth (m)

3.0

3.5

(a) (b)

(c) (d)

1.5

2.0

2.5

0.0

0.5

1.0

Ni g

rade

(w

t%)

Ni g

rade

(w

t%)

3.0

3.5

1.5

2.0

2.5

0.0

0.5

1.0

0.0 3.0 6.0 9.0 12.0 15.0

Limonite zone Saprolite zone Bedrock zone

Figure 8. Changes in the Ni grades with depth at four drillhole sites at (a) slight slope, (b) flat slope,

(c) ridge, and (d) steep slope areas. Open circle denotes the maximum Ni grade at each drillhole.


saprolite zone is the largest and the ranges of c(h)for each variable (110 and 90 m) are less than therange of c(h) of the two variables combined (145 m).This result demonstrates the effectiveness of com-bining the maximum Ni grade in the saprolite zonewith the thickness of the saprolite zone for thespatial modeling of Ni grade.

Co-kriging calculations on the distribution ofthe maximum Ni grade in the saprolite zone wereimplemented using a grid spacing of 10 m. The fol-lowing discussion is based on the standardizedordinary co-kriging result, which gave a better esti-mation than ordinary co-kriging. The estimateddistribution highlights clear anisotropy along NE–SW corresponding with the topography. The resultoverlaid topographic features (Fig. 11a), and a per-spective view of the topography (Fig. 11b) clarifiesthe finding that the maximum Ni grade tended to behigh mainly at the slight slope area, which may beattributable to the enrichment processes of Ni atthese topographic features. Deep and strong

weathering caused by rock fractures may haveoccurred in such groundwater-rich zones andaccordingly, the thick laterization zones that wereformed were conducive to the accumulation of Ni.Enlargement of the highest grade zone in Figure 11areveals large variability in the grades on a muchsmaller scale than the interval of two adjacentdrillhole sites (50 m). High and low grades wereestimated locally at sample sites. This characteristicproves the preciseness of the co-kriging.

Figure 12 represents a cross-validation betweenthe measured and the predicted co-kriging values ofthe maximum Ni grade. The coefficient of correla-tion between the two values (R) is 0.83 and the rootmean square (RMS) error is 0.80. The co-krigingresult was compared with the ordinary kriging resultusing a single variable (i.e., the maximum Ni gradein the saprolite zone). The maximum Ni grade dis-tribution determined by ordinary kriging, as shownin Figure 13a, is much smoother than the co-krigingmodel and featureless. This smoothing effect

5.0

5.0

6.0

5.0

6.0Category 3Category 1 Category 2

R2 = 0.11R2 = 0.21 R2 = 0.23

2.0

3.0

4.0

2.0

3.0

4.0

2.0

3.0

4.0

0.0

1.0

0.0 10.0 20.0 30.0 40.0 50.00.0

1.0

0.0 5.0 10.0 15.0 20.0 25.0 30.00.0

1.0

0.0 10.0 20.0 30.0 40.0

0.0 10.0 20.0 30.0 40.0

Saprolite zone thickness (m) Saprolite zone thickness (m) Saprolite zone thickness (m)

Saprolite zone thickness (m)Saprolite zone thickness (m)Saprolite zone thickness (m)

Max

imum

Ni g

rade

on

the

zone

(w

t%)

Max

imum

Ni g

rade

on

the

zone

(w

t%)

Max

imum

Ni g

rade

on

the

zone

(w

t%)

Max

imum

Ni g

rade

on

the

zone

(w

t%)

Max

imum

Ni g

rade

on

the

zone

(w

t%)

Max

imum

Ni g

rade

on

the

zone

(w

t%)

10.0

4.0

4.5

6.0

7.0Category 4 Category 5 All data

R2 = 0.17 R2 = 0.12 R2 = 0.26

4.0

6.0

8.0

1.52.0

2.53.0

3.5

3.0

4.0

5.0

0.0

2.0

0.0

0.51.0

0.0

1.0

2.0

0.0 10.0 20.0 30.0 40.0 50.00.0 10.0 20.0 30.0 40.0 50.0

Figure 9. Scattergrams between the saprolite zone thickness and the maximum Ni grade of the zone for every category of topographic

feature and for all drillhole data. See Figure 2 for the detail of the category.

186 Ilyas and Koike

appeared clearly in the cross-validation graph inFigure 13b, where the regression line is much gentlerthan for the co-kriging (Fig. 12) or the 45� line. TheRMS error for ordinary kriging is 1.11, which islarger than the co-kriging RMS value. The superi-ority of co-kriging over ordinary kriging is clearlyshown by these comparisons, and consequently, theco-kriging result can be regarded as providingsufficient accuracy.

To examine the relationships between thetopographic features and the formation of the sap-rolite zone, and the maximum Ni grade distribution,the mean and upper and lower quartile values of thethickness of the saprolite zones and the maximum Nigrades on the saprolite zones at the five topographicfeatures were calculated, as shown in Figure 13. Thisfigure clarifies that the thick saprolite zone and themaximum Ni grade are located generally at the slightslope area. Consequently, topography is confirmed tobe a strong factor determining Ni grade distribution.

DISCUSSION

In laterite Ni deposits, many rock fractures tendto be developed at slight slopes, steep slopes, andridge areas, because the rocks in such areas are

relatively hard with considerable resistance to ero-sion. As demonstrated in Figure 14, the saprolitezone is thick in the slight slope, steep slope, andridge areas. Therefore, the thick saprolite zone mayhave formed by the existence of many rock fracturesthat have functioned as a path for groundwaterbecause of high hydraulic conductivity. It is knownthat the infiltration of groundwater through thefractures causes rapid leaching of Ni in the uppersaprolite zone and also rapid deposition of Ni in thelower saprolite zone (Ahmad 2001). In fact, rockfractures are developed at every topographic featurein the study area, but the slight slope is the mostfractured, due to the reverse fault movements underthe regional tectonic stress field. Figure 15 showsexamples of rock fractures at slight slope, steepslope, and ridge areas, which confirm a dense dis-tribution of fractures almost all filled with garnierite.

High Ni grade at the slight slope area depictedin Figure 11 confirms that this topographic feature isa catchment capable of gathering much rain andsurface water, which in part becomes groundwater.Groundwater causes leaching and enrichment of Ni,as well as causing the fractured zones and deepweathering of both the limonite and the saprolitezones. As a result, both zones become thicker with ahigh Ni grade peaking on the slightly sloping areas.

9.2

12.3

6.1

2.1

2.7

1.6

1.1Se

miv

ario

gram

Sem

ivar

iogr

am

range

range

50 100 150 2000200 300 4001000

3.10.5

Separation distance (m)Separation distance (m)

2.5

2.0

1.5

Cro

ss-s

emiv

ario

gram

range

1.0

0.5

Separation distance (m)4003002001000

(a) (b)

(c)

Figure 10. Omnidirectional semivariograms of: (a) the maximum Ni grade in the saprolite zone; (b) the

thickness of zone; and (c) a cross-semivariogram combining these two variables. Spherical models were

used to fit all the semivariograms. Each dot represents the semivariances at each separation distance.


CONCLUSION

For precise spatial modeling of Ni grade in a lat-erite deposit, this study identified factors controllingthe grade distribution and then applied geostatisticaltechniques to a world-famous Ni deposit area inSulawesi Island, Indonesia. At first, geomorphiccharacteristics such as topographic features and thethickness of the laterization zone (limonite and sap-rolite zones above the bedrock) and the maximum Nigrade in the saprolite zone were used for the corre-lation analysis between every pair of sites in thedataset. The topographic features were classified intofive categories depending on the magnitude of slopegradient from steep to flat areas. The slope gradientwas shown to have a strong spatial correlation with the

N

0 m 500 m

Maximum Ni grade (wt%):

(a)

(b)

2:1:

Category of

topographic feature:

0.81 – 1.34

1 35 1 72

0.00 – 0.80

5:4:3:

1. – .

1.73 – 1.97

1.98 – 2.35

2.36 – 2.89

N

2.90 – 3.69

4.87 – 6.57

3.70 – 4.86

6.58 – 9.06

Figure 11. Distribution of the maximum Ni grade in the saprolite zone by co-kriging superimposed upon (a) the category of topographic

feature and (b) a perspective view of topography. Enlargement of the highest grade zone is included in (a).

7.0

4.0

5.0

6.0 RMS = 0.80

1.0

0.0

2.0

3.0

Pred

icte

d va

lue

(wt%

)

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0Measured value (wt%)

Figure 12. Scattergram for cross-validation of

co-kriging accuracy between measured and pre-

dicted co-kriging values of the maximum Ni

grade in the saprolite zone.

188 Ilyas and Koike

thickness of the limonite zone; the thickness of thelimonite zone increased with a decrease of the slopegradient. On the other hand, there were no correla-tions in the thickness between the saprolite and thelimonite zones, and between the slope gradient and thethickness of saprolite zone. The most important trendwas a general spatial correlation between the thicknessof the saprolite zone and the maximum Ni grade in thatzone; the maximum Ni grade in the saprolite zoneincreased with the thickness of the zone.

Because the maximum Ni grade in the saprolitezone is one of the foremost properties for mineplanning and description of a laterite Ni deposit, co-kriging was adopted to construct a distributionmodel of the grade with respect to the correlationwith the thickness of the saprolite zone. The resul-tant co-kriging model highlighted that the maximumNi grades in the saprolite zone were generally

highest at the slight slope area. Ni accumulation atthis area probably originates from deep weatheringcaused by the development of rock fractures andpassing of groundwater through the fractures fromsignificant water catchments.

ACKNOWLEDGMENTS

The authors express their sincere thanks to PT.INCO Indonesia for permission to use the data set.Sincere thanks must be extended to Absar, Sudarmin,Malik Hakim Sopi, Ade Kadarusman, RobbyRafianto, Mashury, Amir Mahmud, Arifin, Kamto,Yonas, Aliahni Djafar, Selvi Yuminti, and Asrianifor their constructive help in the field and in theoffice, and furthermore to anonymous two reviewers

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

0.81 – 1.34

1.35 – 1.72

1.73 – 1.97

1.98 – 2.35

2.36 – 2.89

2.90 – 3.69

6.58 – 9.06

4.87 – 6.57

3.70 – 4.86

0.00 – 0.80

Maximum Ni grade (wt%) (b)(a)

Measured value (wt%)

Pred

icte

d va

lue

(wt%

) RMS = 1.11

N

0 m 250 m

Figure 13. Distribution of the maximum Ni grade in the saprolite zone by ordinary kriging analysis (a) and a scattergram

showing the cross-validation of the ordinary kriging accuracy (b).

1 2 3 4 5

Sapr

olite

zon

e th

ickn

ess

(m)

Max

imum

Ni g

rade

in

the

sapr

olite

zon

e (w

t%)

(b)(a)4.0

1.0

0.0

3.0

2.08.0

4.0

0.0

16.0

12.0

20.0

Category of topographic feature1 2 3 4 5

Category of topographic feature

Figure 14. Relations of the mean (closed circle) and the upper and lower quartiles (top and bottom of

bar) of (a) the thickness of saprolite zone and (b) the maximum Ni grade in the zone to category of

topographic feature.


for the valuable comments and the detailed sugges-tions that helped improve the clarity of the manu-script.

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A115948

A102276A115319A115320 A115219

A103793A104385A104679

A115921

A115550

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A104937

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A104579 A104478

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A104840A115471

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5941

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A104958A104957567

565

A104851

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568

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A104852A104956

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A115048115049

A104854

A115052

104853

4587

4586

A104383

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A104567A103787A104377 A115928103786

A115553A115552

A115561 A104381A115560A115562

A1154

A115554

A104468A104467

03788

A104674

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A104684

A115450

A115

A115458

A104682

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A115920

A1044

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A115456 A104574A103781

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A104565

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A103796A103782A115452

5200 5400 5600 5800 6000 6200 6400 6600

13400

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AAAA103798 A115555471 A1045

59

55

5

555

1155505

10448

45

45

1037777786

0030 788

A102276A11555533319A115320 A115219

0.3 mRock fracture was filled

by garnierite mineral

0.4 m

Rock fracture was filled by garnierite mineral

0.15 m


Easting (m)

Nor

thin

g (m

)

0 m 500 m

x

xx

Steep slope area

Ridge area

Slope with intermediate gradient area

Slight slope area

Flat slope associated with a valley area or cavity

Drillhole site

x Sample location

0.1 m


Figure 15. Examples of rock fractures in the saprolite zone at ridge area (right), slight slope area (middle), and steep slope area (left).

Almost all fractures are filled with garnierite.

190 Ilyas and Koike

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geostatistical modeling of ore grade distribution from geomorphic

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