geostatistical modeling of ore grade distribution from geomorphic
TRANSCRIPT
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:
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).
181Geostatistical Modeling of Ore Grade in Laterite Nickel Deposit
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.
183Geostatistical Modeling of Ore Grade in Laterite Nickel Deposit
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.
185Geostatistical Modeling of Ore Grade in Laterite Nickel Deposit
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.
187Geostatistical Modeling of Ore Grade in Laterite Nickel Deposit
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.
189Geostatistical Modeling of Ore Grade in Laterite Nickel Deposit
for the valuable comments and the detailed sugges-tions that helped improve the clarity of the manu-script.
REFERENCES
Ahmad, W. (2001). Chemistry, mineralogy and formation of Nilaterites (pp. 41–54). Sorowako: PT. INCO Indonesia.
Brand, N. W., Butt, C. R. M., & Elias, M. (1998). Nickel laterites:Classification and features. Australian Geology and Geo-physics, 17(4), 83–88.
Darijanto, T. (1999). The influence of morphology to the forma-tion and distribution of laterite nickel deposits. In Proceed-ings of 8th Indonesian association of mining experts (pp. 1–18). Bandung, Indonesia.
Dowd, P. A. (1992). Geostatistical ore reserves estimation: A casestudy in a disseminated nickel deposit. Geological Society ofLondon Special Publications, 63, 243–255.
Emery, X. (2006). Two ordinary kriging approaches to predictingblock grade distributions. Mathematical Geology, 38(7), 801–819.
Gleeson, S. A., Butt, C. R. M., & Elias, M. (2003). Nickel laterites: Areview. Society of Economic Geologists Newsletter, 54, 9–16.
Golightly, J. P. (1979). Geology of Soroako nickeliferous lateritedeposit. Ontario, Canada: INCO Metals Company.
Hartman, H. L. (1992). Mining engineering handbook (Vol. 1,pp. 344–347). Denver, CO: Society for Mining, Metallurgyand Exploration, Inc.
Heriawan, M. N., & Koike, K. (2008). Uncertainty assessment ofcoal tonnage by spatial modeling of seam distribution andcoal quality. International Journal of Coal Geology, 76, 217–226.
Isaaks, E. H., & Srivastava, R. M. (1989). An introduction toapplied geostatistics (pp. 400–416). Oxford: Oxford UniversityPress, Inc.
Juan, P., Mateu, J., Jordan, M. M., Mataix-Solera, J., Malendez-Pastor, I., & Navarro-Pedreno, J. (2011). Geostatisticalmethods to identify and map spatial variations of soil salinity.Geochemical Exploration, 108(1), 62–72.
Koike, K., Gu, B., & Ohmi, M. (1998). Three-dimensional dis-tribution analysis of phosphorus content of limestone througha combination of geostatistics and artificial neural network.Nonrenewable Resources, 7(3), 197–210.
Koike, K., & Matsuda, S. (2006). New indices for characterizingspatial models of ore deposits by the use of a sensitivityvector and an influence factor. Mathematical Geology, 38(5),541–564.
Macpherson, C. G., & Hall, R. (2002). Timing and tectonic con-trols in the evolving orogen of SE Asia and the westernPacific and some implications for ore generation. GeologicalSociety of London Special Publications, XXX, 1–19.
Mubroto, B., Briden, J. C., McClelland, E., & Hall, R. (1994).Paleomagnetism of the Balantak ophiolite, Sulawesi. Earthand Planetary Science Letters, 125, 193–209.
A115948
A102276A115319A115320 A115219
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A115921
A115550
A104563
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5941
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565
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568
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A115048115049
A104854
A115052
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4587
4586
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A104382
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A115553A115552
A115561 A104381A115560A115562
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A115554
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03788
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A103796A103782A115452
5200 5400 5600 5800 6000 6200 6400 6600
13400
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14200
AAAA103798 A115555471 A1045
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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
Rock fracture was filled by garnierite mineral
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
Rock fracture was filled by garnierite mineral
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
Price, J. G. (2010). The world is changing, View I. Society ofEconomic Geologists Newsletter, 82, 12–14.
PT. INCO Indonesia. (2006). Inventory of mineral resources andmineral reserves, Unpublished report (in Bahasa Indonesia).
Srivastava, R. M. (2005). Probabilistic modeling of ore lensgeometry: An alternative to deterministic wireframes.Mathematical Geology, 37(5), 513–544.
Sufriadin, Idrus, A., Pramumijoyo, S., Warmada, I. W., Yonezu, K., &Imai, A. (2010). Characterization and leaching behavior ofminerals by sulphuric acid in the Sorowako nickeliferous ores,Sulawesi, Indonesia. In Proceedings of international symposiumon earth science and technology, Fukuoka, Japan (pp. 421–425).
Suratman. (2000). Geology of laterite nickel deposit in Sorowakoarea, South Sulawesi Province. In Proceedings of 29th Indone-sian association of geologists, Bandung, Indonesia (pp. 37–43).
Thompson, S. A. (2000). An overview of nickel-titanium alloysused in dentistry. International Endodontic Journal, 33, 297–310.
Thorne, R., Herrington, R., & Roberts, S. (2009). Compositionand origin of the Caldag oxide nickel laterite, W. Turkey.Mineralium Deposita, 44, 581–595.
USGS. (2011). Nickel: Mineral commodity summaries (pp. 108–109). Reston, VA: U.S. Geological Survey.
Van Zuidam, R. A. (1985). Terrain analysis and classificationusing aerial photographs. In ITC-Textbook (2nd ed., VII-6).International Institute for Aerial Survey and Earth Sciences,Enschede, Netherland.
Verly, G. (2005). Grade control classification of ore and waste, acritical review of estimation and simulation based proce-dures. Mathematical Geology, 37(5), 451–475.
191Geostatistical Modeling of Ore Grade in Laterite Nickel Deposit