The Distributions and Relationships of 

Grade and Tonnage Among 

Some Nickel Deposits

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1 16
The Distributions and Relationships of 

Grade and Tonnage Among 

Some Nickel Deposits

By M. P. FOOSE, W. D. MENZIE, D. A. SINGER and J. T. HANLEY 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 1160

An analysis of the relationships of 

grade and tonnage among 

several types of nickel deposits

UNITED STATES GOVERNMENT PRINTING OFFICE, W ASH I N GT O N : 1 980
UNITED STATES DEPARTMENT OF THE INTERIOR 

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY 

H. William Menard, Director

Library of Congress Catalog-card No. 8Q-6QQ14Q

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402
CONTENTS

Page rage

Abstract ______________________________ 1 General geologic and economic considerations concerning

Introduction ____________________________ 1 controls on deposit grade and tonnage ____________ 4

Acknowledgments _________________________ 2 Grade and tonnage analysis ____________________ 6

Sulfide deposits __________________________ 2 Nickel sulfides associated with komatiitic rocks ______ 6

Deposits in stable tectonic settings _____________ 2 Nickel sulfides associated with small intrusions ______ 9

Deposits in areas that have been tectonically active ____ 2 Comparison of nickel sulfide deposits in small intrusions

Komatiites _________________________ 2 with those associated with komatiitic rocks ______ 10

Small intrusions _____________________ 3 Nickel-laterite deposits ____________________ 11

General characteristics ____________________ 3 Summary and conclusions _____________________ 12

Nickel-laterite deposits _____________________ 3 References cited _________________________ 13

ILLUSTRATIONS

FIGURES 1-8. Graphs showing:

1. Several hypothetical grade and tonnage relationships _____________——————————————————— 5 

2, 3. Grade and tonnage of:

2. Nickel sulfide deposits associated with komatiitic rocks _____________—__————————————— 7

3. Nickel sulfide deposits in komatiitic rocks from four regions ________——————————————————— 8 

4. Quality control of tonnage and grade for nickel sulfide deposits in komatiitic rocks from four regions ———————— 9 

5-8. Grade and tonnage of:

5. Nickel sulfide deposits associated with small intrusions __________———————————————————— 10

6. Two types of nickel sulfide deposits _____________________—————————————————— 11

7. Nickel-laterite deposits _______________________________——_——————————————— 12

8. Oxide nickel-laterite deposits _________________________________———————————— 13

TABLES

TABLES 1-6. Summary statistics for grade and tonnage of:

1. Fifty-two nickel sulfide deposits associated with komatiitic rocks __________________——_——————— 7

2. Nickel sulfide deposits in komatiitic rocks from each of four regions and from the regions as a pooled group ————— 9

3. Nickel sulfide deposits associated with small intrusions _____________________————————————— 10

4. Nickel sulfide deposits ________________________________________———_———————— 11

5. Nickel-laterite deposits _________________________________————_——————————————— 11

6. Oxide nickel-laterite deposits _______________________——_——————————————————————— 12

in
CONVERSION FACTORS

Metric unit Inch-Pound equivalent

Length

millimeter (mm) 

meter (m) 

kilometer (km)

= 0.03937 inch (in) 

= 3.28 feet (ft) 

= .62 mile (mi)

Area

square meter (m2 ) 

square kilometer (km2 ) 

hectare (ha)

= 10.76 square feet (ft2 ) 

= .386 square mile (mi2 ) 

= 2.47 acres

Volume

cubic centimeter (cm3 ) 

liter (L) 

cubic meter (m3 ) 

cubic meter 

cubic hectometer (hm3 ) 

liter 

liter 

liter 

cubic meter

cubic meter

= 0.061 cubic inch (in3 ) 

= 6,1.03 cubic inches 

= 35.31 cubic feet (ft3 ) — .00081 acre-foot (acre-ft) 

= 810.7 acre-feet 

= 2.113 pints (pt) 

= 1.06 quarts (qt) 

= .26 gallon (gal) 

= .00026 million gallons (Mgal or 

106 gal) 

= 6.290 barrels (bbl) (1 bbl = 42 gal)

Weight

gram (g) 

gram 

metric tons (t) 

metric tons

= 0.035 ounce, avoirdupois (oz avdp) 

= .0022 pound, avoirdupois (Ib avdp) 

= 1.102 tons, short (2,000 Ib) 

= 0.9842 ton, long (2,240 Ib)

Specific combinations

kilogram per square 

centimeter (kg/cm2 ) 

kilogram per square 

centimeter 

cubic meter per second 

(mVs)

— 0.96 atmosphere (atm)

— .98 bar (0.&869 atm) 

= 35.3 cubic feet per second (ftf/s)

Metric unit

Specific

liter per second (L/s) 

cubic meter per second 

per square kilometer 

[(m3/s)/km2 ] 

meter per day (m/d)

meter per kilometer 

(m/km) 

kilometer per hour 

(km/h) 

meter per second (m/s) 

meter squared per day 

(mVd) 

cubic meter per second 

(mp/s) 

cubic meter per minute 

(m3/min) 

liter per second (L/s) 

]iter per second per 

meter [(L/s)/m] 

kilometer per hour 

(km/h) 

meter per second (m/s) 

gram per cubic 

centimeter (g/cm3 ) 

gram per square 

centimeter (g/cm2 ) 

gram per square 

centimeter

Inch-Pound equivalent

combinations — Continued

= .0353 cubic foot per second 

= 91.47 cubic feet per second per 

square mile [(fts/s)/ml2]

= 3.28 feet per day (hydraulic 

conductivity) (ft/d) 

= 5.28 feet per mile (ft/ml)

— .9113 foot per second (ft/s)

— 3.28 feet per second

= 10.764 feet squared per day (ft2/d) 

(transmissivity) 

= 22.826 million gallons per day 

(Mgal/d) 

= 264.2 gallons per minute (gal/min)

= 15.85 gallons per minute

= 4.83 gallons per minute per foot 

[(gal/min) /ft]

— .62 mile per hour (mi/h)

= 612.43 pounds per cubic foot (lb/fts) 

= 2.048 pounds per square foot (lb/ft2 ) 

= .0142 pound per square inch (lb/in2 )

Temperature

degree Celsius (°C) 

degrees Celsius 

(temperature)

= 1.8 degrees Fahrenheit (°F) 

= [(1.8x°C)+32] degrees Fahrenheit
THE DISTRIBUTIONS AND RELATIONSHIPS OF GRADE AND TONNAGE

AMONG SOME NICKEL DEPOSITS

By M. P. FOOSE, W. D. MENZIE, D. A. SINGER, and J. T. HANLEY

ABSTRACT

Frequency distributions and relationships of tonnage and average 

grade among three types of nickel deposits were investigated as 

models for regional resource assessment: sulfide deposits associated 

with komatiitic rocks, sulfide deposits associated with small intrusions 

of diverse types, and laterite deposits. In laterite deposits, the geologic 

factors that influence deposit tonnage are mostly distinct from those 

that control deposit grade; no correlation of deposit tonnage and grade 

should be expected. However, in sulfide deposits, the geologic factors 

that influence grade and tonnage are too complex to suggest the type 

of relationship between tonnage and grade.

Both tonnage and grade of sulfide deposits associated with 

komatiitic rocks follow lognormal distributions. These deposits have a 

median nickel grade of 1.24 percent and a median tonnage of 9.49 x 106 

metric tons. Deposit grade and tonnage have a significant inverse correlation. Analysis of komatiitic deposits from four regions revealed 

significant differences in grade and tonnage between regions.

The tonnage and grade of a second type of sulfide deposit, which is 

associated with small orogenic intrusions, were also found to be lognormally distributed. The median nickel grade of these deposits is 0.60 

percent, and their median tonnage is 1.27xl06 metric tons; these 

variables are statistically independent.

The tonnage, but not the grade, of laterite deposits follows a lognormal distribution. However, when the effect introduced by including 

high-grade silicate laterite ores was eliminated, both tonnage and 

grade of deposits composed primarily of oxide ore were found to follow 

lognormal distributions; oxide deposits have a median nickel grade of 

1.36 percent and a median tonnage of 45xl06 metric tons. These 

variables were found to be statistically independent.

INTRODUCTION

Regional mineral-resource assessments are essential 

in making land-use decisions and in determining national and international availability of minerals. 

Although these assessments can be made by several 

techniques, one of the most straightforward is to use the 

frequency distributions and relationships of important 

variables among known deposits as models of how these 

variables will behave among undiscovered deposits. 

Grades and tonnages are the most important variables.

Once models of these variables have been constructed, 

the problem of regional resource appraisal largely

becomes that of delineating favorable areas for each 

type of mineral deposit and estimating the number of 

deposits in each area. This latter task is by no means 

easy, but its success in part relies on having first 

established a basic understanding of grade and tonnage 

relationships and distributions. These relationships are 

useful for long-term analysis of resources because they 

provide important information on how the quantity of 

resources changes as average grades of deposits worked 

decline.

This discussion is concerned with grade and tonnage 

frequency distributions and relationships for certain 

types of nickel deposits. Nickel is found in a wide variety 

of ores that are formed by different geologic processes, 

but most deposits may be placed in one of four broad 

geologic classes. Most important are sulfide deposits, 

most of which form when nickel sulfides concentrate 

within mafic or ultramafic magmas. Sulfide deposits 

contain approximately 20 percent of the world's nickel 

reserves and currently supply nearly 65 percent of the 

nickel mined each year (Lawrence, 1974). Nickel-rich 

lateritic soils are a second important deposit type. 

Formed mainly by chemical weathering of ultramafic 

rocks, these nickel-bearing soils are estimated to contain 

80 percent of the world's nickel reserves. A third deposit 

type consists of small and relatively unimportant concentrations of nickel sulfides and arsenides deposited 

from hydrothermal solutions. Finally, large expanses of 

nickel-bearing manganese nodules have been identified 

on the ocean floor and may represent an important 

source of nickel in the future.

In this study, the grade and tonnage of several 

subgroups of the important sulfide and laterite deposit 

classes are examined. First, some of the geological 

features of nickel deposits in general and of these 

specific deposit types in particular are described. Then 

grade and tonnage distributions within each of the 

chosen deposit types are presented and compared with 

theoretical statistical models.
DISTRIBUTIONS, RELATIONSHIPS OF GRADE AND TONNAGE AMONG SOME NICKEL DEPOSITS

ACKNOWLEDGMENTS

The assistance of Gus Goudarzi and Glen Shaffer of 

the U.S. Geological Survey in the initial stages of data 

gathering and the critical comments of N.J. Page , R. B. 

McCammon, and C. E. Brown, also of the U.S. Geological Survey, are gratefully acknowledged.

SULFIDE DEPOSITS

Sulfide deposits in mafic and ultramafic rocks have 

supplied most of the world's nickel, even though they 

represent less than one quarter of the world's nickel 

reserves. These important deposits may be divided into 

two broad classes (Naldrett, 1973; Naldrett and Cabri, 

1976). The first class of deposits, those in stable cratonic 

areas, has traditionally been the largest nickel producer. 

However, as a result of discoveries during the last 15 

years in Canada and Australia, a second class of 

deposits, those in settings that have been tectonically active, is assuming greater importance. Geologic features 

of both classes of deposits are described in the following 

paragraphs; however, the data needed to statistically 

test the grade and tonnage relationships are available 

only for two subgroups of deposits belonging to the second class.

DEPOSITS IN STABLE TECTONIC SETTINGS

Large, differentiated, layered igneous complexes in 

stable cratonic areas have long been considered ideal 

targets for nickel prospecting. Largely, this has been 

due to the numerous nickel sulfide deposits located and 

mined in the Sudbury intrusion in Canada. Other intrusions similar to Sudbury are the Stillwater (Montana), 

Bushveld (South Africa), Muskox (Canada), Skaergaard 

(Greenland), and Dufek (Antarctica). Although large 

amounts of nickel are found in some of these intrusions, 

all the deposits are low grade, and either the deposits 

are subeconomic or nickel is not the principal mineral 

mined. In addition, much of the nickel may be in silicate 

rather than sulfide minerals. For these reasons, relatively little data have been made available about these nickel 

occurrences.

Although the Sudbury intrusion has many similarities 

to other large differentiated igneous complexes, important differences exist and may indicate that it is unique. 

Of particular interest is the evidence concerning the 

origin of the intrusion that has resulted in two differing 

interpretations. Proponents for a "conventional" origin 

suggest that normal magmatic processes were responsible for the body, whereas others argue that the body 

resulted from a meteor impact, which formed a large 

crater and activated deep-level magmatic processes. 

Since its proposal by Dietz (1964), this latter hypothesis 

has acquired increasing, but not universal, acceptance.

If correct, an impact origin for the Sudbury intrusion 

may have significant implications for finding additional 

similar deposits. The combination of events, including 

meteor impact, needed to generate a Sudbury-type intrusion may be so uncommon as to make the formation 

of similar deposits unlikely. Other deposits of this type 

may be scarce or even nonexistent, and thus analysis of 

tonnage and grade of the Sudbury nickel deposits would 

have little significance outside of the Sudbury region.

The Norilsk-Talnakh complex in the Arctic area of 

northwest Siberia (U.S.S.R.) is the only other major 

nickel-producing area in a stable tectonic setting. It is 

markedly different from Sudbury in that nickel-rich 

sulfides have accumulated within tholeiitic sills that 

have been contaminated by sulfur-bearing country rock 

(Gorbackev and Grinenko, 1973). No deposit data are 

available for this district. Except for the apparently 

geologically unique Sudbury intrusion, a general lack of 

data exists for deposits in stable tectonic settings. Thus, 

no grade and tonnage analysis for this group was attempted.

DEPOSITS IN AREAS THAT HAVE BEEN TECTONICALLY 

ACTIVE

If the Sudbury intrusion is discounted, deposits in 

areas that have been tectonically active host most of the 

world's nickel sulfide reserves. Differences among these 

deposits make their division into numerous subclasses 

possible. However, for the broader purposes of regional 

resources assessment, only two general subclasses are 

considered here.

KOMATIITES

By far, the most important subclass of deposits is 

associated with a relatively recently identified suite of 

mafic and ultramafic rocks called komatiites. The 

deposits in Botswana, Rhodesia, and western Australia 

and in the Thompson, Abitibi, and Ungava districts of 

Canada belong to this subclass. Some characteristic 

features of this magmatic suite are listed as follows 

(more complete discussions of the character and origin 

of this magma type are presented by Viljoen and Viljoen, 1969; Pyke and others, 1973; Brooks and Hart, 

1974; Naldrett and Cabri, 1976; Arndt and others, 

1979):

1. Komatiites commonly have a distinctive chemistry (a 

low FeO/FeO + MgO ratio, a low Ti02 concentration, and a CaO/Al203 ratio of nearly 1) and a 

unique quench texture called spinefex, which is 

formed by skeletal blades and plates of olivine and 

pyroxene.

2. The apparent restriction of these nickel deposits to 

rocks older than 1.7xl09 years suggests that the 

magmatic processes responsible for these deposits 

are no longer operating.
SULFIDE DEPOSITS

3. Experimental evidence (Green and others, 1975) indicates that these ultramafic flows were extruded 

at temperatures from 1,400-1,600° C. These 

temperatures imply that the geothermal gradients 

controlling komatiite formation were much steeper 

than those presently existing (Green, 1975).

4. Nickel deposits are associated with only the most 

magnesium-rich members of the komatiitic suite 

(Naldrett and Arndt, 1976).

Highly successful exploration models have been devised using the nickel sulfide-komatiite association. Exploration has been directed toward shield areas in which 

ancient erogenic belts and magnesium-rich ultramafic 

rocks exist. Particular attention is given to the basal 

contact where immiscible sulfides would most likely accumulate. Since discovery of the Kambalda (Australia) 

deposits in 1966, this model has been used to find many 

other deposits throughout western Australia. Deposits 

associated with komatiites are now known from the 

shield areas of Canada, Africa, and Australia. Additional deposits in these areas surely exist. Further, large 

shield areas, such as those in Greenland, Brazil, India, 

the U.S.A., and the U.S.S.R., have favorable rock types 

in which few or no nickel deposits have yet been 

discovered. Promising exploration targets are surely 

present in these areas. The wide geographic distribution 

of these deposits and the availability of grade and tonnage data make this deposit subclass particularly 

suitable for grade and tonnage analysis.

SMALL INTRUSIONS

The second subclass (small intrusions) for which 

statistical analysis of grade and tonnage was attempted 

contains several diverse types of deposits. Although 

division of these deposits into several smaller groups is 

possible, placing them together in a broad subclass 

makes a large and homogeneous population that is 

amenable to statistical analysis and use in regional 

resource assessments. The deposits are mostly small 

and low grade; thus they have not been significant producers of nickel, and little has been written about their 

geologic character. Most are in small- to medium-size, 

predominantly mafic intrusions that range in age from 

Precambrian to Tertiary. Their relatively large copperto-nickel ratio (generally greater than one copper to five 

nickel) reflects their mafic composition and is particularly useful in distinguishing these deposits from those 

associated with the more ultramafic komatiites 

(Naldrett and Cabri, 1976). The Great Lake, Lynn Lake, 

and Giant Nickel deposits of Canada are examples of 

this subclass.

GENERAL CHARACTERISTICS

Although different in many details, different types of 

sulfide deposits are strikingly similar. Largely, this 

results from basically similar mechanisms of formation. 

Most nickel deposits associated with igneous rocks are 

believed to have been formed by separation of an immiscible sulfide phase within a crystallizing silicate melt. 

Because of the strong affinity of sulfur for metals, dense 

droplets of immiscible sulfides combine with metallic 

elements in the melt and settle toward the bottom of the 

magma. Commonly, massive metallic-sulfide deposits 

form in topographic or structural depressions at the 

magma-chamber base. Successively overlying the 

massive-sulfide ores are a zone of disseminated sulfides 

and a zone of barren silicates. Sulfide minerals within 

deposits commonly are pyrrhotite, pentlandite, 

chalcopyrite, and minor pyrite. In addition to nickel, 

many deposits contain significant amounts of copper 

and minor, but locally recoverable, amounts of cobalt, 

platinum-group elements, and selenium. Later deformation, metamorphism, or hydrothermal alteration may 

mobilize the sulfides and obscure the deposit's initial 

magmatic character.

Tonnage of nickel sulfide varies greatly and is influenced by many factors. Perhaps most important are 

(1) the size of the igneous complex (as size of the igneous 

complex increases, the potential for forming larger tonnage deposits generally also increases), (2) the nickel 

and sulnir content of the magma (the potential for 

larger tonnages increases as the nickel and sulfur content of the magma increases), (3) the size of the trap in 

which sulfides accumulate, (4) the nature of the magma 

circulation, and (5) postore deformation.

The grade of nickel sulfide deposits also varies, but it 

appears to be controlled principally by the crystallization history of the magma, which in turn is closely tied to 

the magma's primary sulnir and metal content. If the 

magma were saturated with sulfur before many silicates 

had crystallized, then an almost pure immiscible nickel 

sulfide phase could separate and concentrate to form a 

high-grade deposit. If, however, sulnir saturation were 

delayed, the immiscible sulfide phase would be intermixed with silicate crystals and lower grade sulfide deposits 

would form. Other factors locally important in determining grade involve the circulation system of the magma 

chamber, wallrock reactions, postmineralization 

mobilization of ore, and supergene alteration.

NICKEL-LATERITE DEPOSITS

The contribution of nickel-laterite deposits to the 

world nickel supply has been variable. In the late 1800's, 

production from New Caledonia deposits supplied most 

of the world's nickel. However, with the development of
DISTRIBUTIONS, RELATIONSHIPS OF GRADE AND TONNAGE AMONG SOME NICKEL DEPOSITS

more easily processed sulfide ores from Sudbury, 

Canada, the contribution of laterite deposits declined. 

Today, nickel from laterite deposits represents about 20 

percent of the world's production but more than 80 percent of identified world nickel reserves. With improved 

extraction technology and increasing demand for nickel, 

laterite deposits are assuming greater importance as a 

source of nickel.

Nickel laterite is soil formed in warm humid climates 

by chemical breakdown of ultramafic rocks. Two different ore types-oxide and silicate-are formed depending on the nature of the chemical alteration. Oxide ores 

contain approximately 0.8-1.5 percent nickel, which is 

in iron oxide (mostly goethite). These ores are the most 

common and represent the bulk of material currently being mined in Cuba, the Dominican Republic, and the 

Philippines. Nickel silicate ores are generally of higher 

grade (2-4 percent nickel). In these ores nickel is included in poorly defined hydrous magnesium silicate, commonly termed garnierite. Deposits of this type are currently being mined at Riddle, Oreg., and in New 

Caledonia. Both ore types are frequently found within 

the same deposit.

The formation of nickel laterite begins with the 

chemical weathering of ultramafic rocks. When immiscible sulfides are absent in a magma, nickel's strongest affinity is for the olivine and pyroxene crystal structure, 

and rocks composed largely of these minerals frequently 

have a relatively high primary nickel content (commonly 

0.2-0.4 percent nickel). When exposed to a tropical 

climate, the ultramafic rocks break down through a 

series of complex hydrolysis reactions. Iron in solution 

readily oxidizes and precipitates to form a hard crust at 

the top of the weathering profile. Nickel, magnesium, 

and silica are more mobile and tend to be leached from 

the surface zone. Magnesium and silica concentrate 

toward the base of the soil profile or are carried away in 

solution while the downward moving ground water effects a less complete separation of the less soluble nickel 

from the iron-rich layer. If extensive separation of 

nickel is not achieved, as is common, then most of the 

nickel occurs with iron. Oxide laterite is formed. Upon 

more complete separation, nickel precipitates with 

magnesium and silica at the base of the weathering profile, and accumulations of hydrous silicate ore 

(garneirite) form (Golightly, 1979). Because of 

mineralogic differences, silicate ore tends to be richer in 

nickel than is oxide ore. Within most laterite, both ore 

types are generally present in varying amounts, and 

thus the classification of a deposit as oxide or silicate is 

somewhat arbitrary.

The factors that most directly affect tonnage of 

laterite deposits are

1. the size of the underlying ultramafic body;

2. the duration and intensity of the weathering process;

3. the size of the "trap" that may pond nickel-bearing 

ground-water solutions; and

4. the physical erosion and dissection of the

deposit. 

Grade of nickel laterite is principally controlled by

1. the concentration of nickel in the parent 

ultramafic rock;

2. the mineralogy of the parent rock; and

3. the duration and intensity of the weathering process.

GENERAL GEOLOGIC AND ECONOMIC

CONSIDERATIONS CONCERNING CONTROLS

ON DEPOSIT GRADE AND TONNAGE

The geologic factors that control the relationship of 

deposit tonnage to grade may be very complex. When 

each deposit is examined individually, it becomes evident that many factors affect either grade alone or tonnage alone. Some factors, however, influence both 

grade and tonnage. A simplified example, involving only 

one factor, may be used to illustrate this. If an oreforming system is closed, then the total amount of metal 

available to form a deposit is fixed. Therefore, a relationship between the potential grade and tonnage within 

that deposit is established because the deposit grade 

equals the value for the amount of metal in a deposit 

divided by that for deposit tonnage. Potential values of 

grade and tonnage define a negative sloping line (fig. 

L4); the actual grade and tonnage of the deposit makes 

a point on this line. The relationship of potential grade 

to potential tonnage within deposits is, of course, much 

more complex. The important point is that within any 

given ore-forming system, the factors determining an 

individual deposit's grade may not be entirely independent of those controlling a deposit's tonnage.

However, attempts to extrapolate potential grade and 

tonnage relationships in individual deposits to those for 

a regional or global population of similar deposits may 

encounter serious problems. Usually each ore deposit is 

formed in a geologic system that is isolated from 

systems forming other similar deposits. Thus, the tonnage and grade of a deposit in one system will be unaffected by that in other systems. They will, therefore, 

tend to be independent. This independence of systems is 

illustrated in figure IB, where four similar but isolated 

and different-sized ore systems are shown (a, small, to d, 

large); among these deposits no grade and tonnage relationship exists or should be expected.

From the foregoing, it is apparent that no simple 

generalizations can be made for the presence or absence 

of grade and tonnage relationships within ore deposits. 

For some deposit types, independent geologic factors
GENERAL GEOLOGIC AND ECONOMIC CONSIDERATIONS

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FIGURE 1.-Log-log plots illustrating several hypothetical tonnage and grade relationships. A, Closed ore system. The 

dashed line shows the potential values for deposit grade and tonnage; the dot represents the actual deposit grade 

and tonnage. B, Four separate ore systems similar to that in A. Because each system is isolated from the other, 

grade and tonnage among the actual deposits (a,b,c,d) are independent; no correlation exists. C, Deposit type in 

which chemical and physical factors (such as mineralogy) place limits on deposit tonnage and grade and thus tend to 

restrict the part of the plot in which deposits fall (dots). Depending on the envelope (dashed line) produced by the 

restrictions, a grade-tonnage correlation may be induced. D, Two different deposit types (dots and crosses) tend to 

occupy discrete areas of the grade-tonnage plot. Although tonnage and grade are independent within each deposit 

type, an inverse grade and tonnage correlation exists when the two deposit types are considered together.
DISTRIBUTIONS, RELATIONSHIPS OF GRADE AND TONNAGE AMONG SOME NICKEL DEPOSITS

quite obviously affect only grade or tonnage and thus 

tend to make these two variables independent. For example, in laterite deposits the starting size of the 

ultramafic parent rock and subsequent physical erosion 

are particularly important factors affecting tonnage, 

but these factors do not significantly influence grade, 

which is largely controlled by chemical weathering. 

Thus, within lateritic deposits, one might reasonably expect a general independence of grade and tonnage.

In sulfide deposits, however, the relation appears to be 

more complex. The interaction between ore-forming and 

concentrating processes is poorly known. For example, 

the primary concentration of sulfur and nickel in the 

magma may influence both the tonnage and grade 

within an individual deposit. Among a group of deposits, 

the chemical and physical constraints on the emplacement of intrusions and the subsequent formation of 

sulfides may place limits on the grade and tonnage a 

deposit may have. Sulfide mineralogy, for example, controls the maximum grade of a deposit. Depending on the 

nature of the restrictions, deposits may be confined to a 

part of the grade and tonnage plot and an inverse gradetonnage relationship might form (fig. 1C).

Two general comments should be made concerning 

the foregoing. First, it is necessary to compare only 

deposits of the same type. Because deposit mineralogy, 

mode of formation, and other variables may restrict the 

grade and tonnage values of a given deposit, mixing of 

two or more deposit types in the data may induce an artificial grade and tonnage correlation (fig. ID). This mixing of different deposit types can often be detected 

statistically, although it may be difficult to identify and 

separate different types of deposits. Second, a variety of 

economic and operational factors generate uncertainties 

in the grade and tonnage data; some factors that may 

tend to impose an inverse grade and tonnage correlation 

are listed as follows:

1. Very low-grade, small deposits are not profitable to 

mine and consequently may not be examined or 

reported.

2. Because it is economically more profitable, a large 

deposit may be studied, reported on, and mined 

before a smaller deposit of the same grade is.

3. For small deposits, reserves are commonly developed 

for only 5 to 10 years, and thus the resultant tonnage estimate is biased downward. For larger 

deposits, the scale of operation requires more complete estimates of grade and tonnage.

4. Some reported grade and tonnage may include all of 

the mineralized rock, whereas other estimates are 

restricted by artificially established cutoff grades. 

Frequently, no clear distinction between mineralized and barren rock exists. An accurate assessment

of what each reported value means is usually not

possible.

These factors are related in that they bias the sampling of what actually exists. Particularly, the lack of data 

on low-grade small deposits tends to produce an apparent inverse correlation. Despite these problems and 

uncertainties, the tonnage and grade relationships obtained may still provide a predictive base for resource 

estimates if one can expect that the basic nongeologic 

factors that influence grade and tonnage relationships 

among deposits today will also be influencing the relationships among deposits found in the future.

GRADE AND TONNAGE ANALYSIS

Statistical analysis was carried out on three specific 

nickel-deposit types: deposits associated with komatiitic 

rocks, nickel sulfide deposits in small intrusions, and 

nickel-laterite deposits. Data from each type were first 

analyzed by fitting frequency distributions to both 

deposit grade and deposit tonnage. This was necessary 

to (1) insure that the population was homogeneous, (2) 

provide empirically tested theoretical distributions that 

can be used in regional resource assessments, and (3) insure that the assumptions required for testing the correlations among grade and tonnage can be met. After 

investigating the frequency distributions separately for 

grade and tonnage, tests were made to see if the two 

variables were independent.

The adequacy of lognormal distributions as models of 

grade and tonnage was tested by fitting theoretical normal distributions to the logarithms of the data and then 

testing the beta statistics (moments) of the observed 

distributions, V&i (asymmetry) and bz (skewness), 

, against expected values of V/3^0.0 and /32 = 3.0. Once 

Hhe distributions of grade and tonnage were investigated, the correlation coefficient (r) of the variables 

was calculated and used to test the hypothesis that 

grade and tonnage were independent (r=0). All tests 

were made at the 5-percent probability level.

NICKEL SULFIDES ASSOCIATED WITH KOMATIITIC ROCKS

Data on average nickel grade and tonnage were collected for 52 nickel sulfide deposits associated with 

komatiitic rocks (fig. 2.). The data include deposits from 

three continents (Africa, Australia, North America). 

Comparison of the observed distributions of grade and 

tonnage of these deposits with theoretical lognormal 

frequency distributions indicates that, at the 5-percent 

probability level, lognormal distributions adequately 

model the deposit grade and tonnage. Table 1 presents 

the means, median, and standard deviation of the 

observed distributions and the beta statistics. In the 

previous section, economic factors that tend to impose
GRADE AND TONNAGE ANALYSIS

0.32

0.60

1.00

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3.16 10.0 31.6 100 316

cc 

(D

0.40

0.20

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LOG 10 TONNAGE (METRIC)

FIGURE 2.-Grade and tonnage of nickel sulfide deposits associated with komatiitic rocks.

8.5 9.0

0.16

TABLE I.-Summary statistics for grade and tonnage of nickel sulfide 

deposits associated with komatiitic rocks

Arithmetic

Number of 

Variable deposits Median Mean 

(n)

Tonnage, 

metric ___ 52 8.49 xlO2 6.93

Nickel grade, 

percent __ 52 1.24 .09

Logarithmic data (base 10)

Standard Vftj 62 Correladevia- (assym- (skew- tion cotion metry) ness) efficient (r)

0.86 0.49 2.31 -0.62

.27 -.29 2.65 -0.62

an inverse relationship on reported grade and tonnage 

were discussed. Often these economic effects are revealed by truncation of data for low grade and tonnage in 

observed distributions and by skewness of the observed 

distributions in the direction of higher grade and tonnage, even though the variables have been transformed 

by taking logarithms. Examination of figure 2 suggests 

that economic bias probably has resulted in the truncation of data from some low-tonnage deposits.

Because the observed distributions of tonnage and 

average grade are not significantly different from 

lognormal distributions, a test can be made to see if the 

two variables are independent. The Pearson product 

moment correlation coefficient (r; table 1) was found to 

be significantly different from zero, indicating that a 

negative correlation exists between the two variables; 

as deposit grade increases, deposit tonnage decreases.

Thus, the lognormal distribution's fit to deposit 

average grade and tonnage, together with the correlation coefficient (r), seem to provide an adequate model 

of komatiitic nickel deposits. However, as demonstrated 

by Singer and others (1975), some deposit types show 

regional differences in average grade and tonnage. Such 

differences may be an important consideration for 

regional assessment of mineral resources.

The 52 deposits used in the model are in nine different 

regions; of this group, 41 of the deposits are in four
DISTRIBUTIONS, RELATIONSHIPS OF GRADE AND TONNAGE AMONG SOME NICKEL DEPOSITS

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FIGURE 3.-Grade and tonnage of nickel sulfide deposits in komatiitic rocks from four regions.

regions. Because the five remaining regions contain at 

most four deposits each, they were excluded from an 

analysis of regional differences. The average nickel 

grade and tonnage of deposits from the four regions are 

plotted in figure 3, and summary statistics for the 

observed distributions of both variables for each region 

and for all regions combined are presented in table 2.

The beta statistics for four regions are not significantly different from values expected from theoretical 

lognormal distributions. However, the average nickel 

grade of the four groups together is significantly skewed. Thus, the data from the four regions meet one of the 

requirements of most statistical methods (such as 

analysis of variance) for testing for population (regional) 

differences. Another requirement of most methods is 

that variances (and covariances) of the regions be approximately equal. Standard deviations (the square root 

of variance) of average grade and tonnage within each 

region (table 2) vary by about an order of magnitude. 

The large differences in the standard deviations plus the 

relatively small sample size of each region suggest that 

the data probably do not meet the requirements of 

techniques such as the analysis of variance. In such 

situations a quality-control chart, showing grade and 

tonnage, can aid in the interpretation of differences of 

the means of variances.

Figure 4 presents the means of average grade and 

tonnage and the means plus and minus two standard errors of the means for the deposits in the four regions. 

Figure 4 reveals that differences between regions can be 

quite large. Given that large regional differences exist in 

the average grade and tonnage of deposits, the question
GRADE AND TONNAGE ANALYSIS

TABLE 2. -Summary statistics for grade and tonnage of nickel sulfide deposits in komatiitic rocks from each of four regions and from the regions

as a pooled group

[All data except "«" are expressed as logarithms. Vft , asymmetry; 62 , skewness]

Region

Abitibi

Ungava

West Australia

Four regions

Number o: 

deposits 

(n)

7

19

8

14

41

f Mean of 

log Ni 

grade

-0.0795

.0642

.2867

.2117

.1334

Standard 

deviation

0.1224

.0600

.0288

.0678

.0781

A

0.5995

-.0152

- .5290

- .2937

„

1.9764

1 9694

2.2301

1 9770

3.0858

Mean of 

log tonnage

6.7858

7.5433

6.3590

6.8007

6.9293

Standard 

deviation

1.7681

.5539

.1622

.6932

.8587

*

0.8285

-.1045

-.1050

.4256

.5050

"

1.8589

2.2541

1.9799

2.080

2.1266

Correlation coefficient (r)

0.9166

.6116

- .2989

- .6417

-.6633

• Significant at 5-percent level

arises: Are the correlation coefficients of average grade 

and the tonnage of deposits within regions significantly 

different? The correlation coefficients (table 2) of the 

variables for the regions were tested to see if they were 

different; the test could not establish significant differences among the correlation coefficients for the four 

regions. These results suggest that although the regions 

differ in the average grade and tonnage of deposits, the 

overall process that related the two variables may be the 

same. Thus, statistical results are consistent with the inference that basically the same geological processes 

formed the deposits in the four regions.

NICKEL SULFIDES ASSOCIATED WITH SMALL INTRUSIONS

Nickel sulfide deposits associated with komatiitic 

rocks present one type of deposit found in orogenic 

belts; another type of deposit is associated with a variety 

of small to medium-sized intrusions of predominantly 

mafic composition. In many places, these deposits are 

associated with a diverse group of intrusions that in8.0

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FIGURE 4. -Quality-control chart (a plot of means and standard errors) of tonnage and grade for nickel sulfide deposits in komatiitic rocks. Data 

are from four regions, plotted both as a group and as separate areas. X represents the means; bar extensions indicate plus and minus 2 stand 

ard errors. A, For tonnage. B, For grade.
10 DISTRIBUTIONS, RELATIONSHIPS OF GRADE AND TONNAGE AMONG SOME NICKEL DEPOSITS

TABLE 3. -Summary statistics for grade and tonnage of nickel sulfide 

deposits associated with small intrusions

Variable

Tonnage, 

metric

Nickel 

grade, 

percent _

Arithmetic

Number of 

deposits Median 

(n)

50 1.27 xlO6

50 .60

Logarithmic data (base 10)

Standard 

Mean deviation

6.10 0.51 

- .22 .23

^ (assymmetry)

0.15 

-.23

b2 Correla- 

(skew- tion coness) efficient (r)

3.33 -0.09 

3.00 -0.09

elude differentiated sills, zoned intrusions, and breccia 

pipes. Data on average nickel grade and tonnage were 

collected for 50 such deposits (fig. 5), most of which are 

in Canada. Summary statistics (table 3) of the observed 

frequency distributions of average grade and tonnage 

are not significantly different from values expected for 

samples from theoretical lognormal distributions. A test 

of the correlation coefficient (r) indicates that the 

observed variables may be regarded as independent. 

Thus statistical tests suggest that values for average 

grade and tonnage of nickel sulfide deposits associated

with small intrusions are independent variables that fit 

theoretical lognormal distributions.

COMPARISON OF NICKEL SULFIDE DEPOSITS IN SMALL

INTRUSIONS WITH THOSE ASSOCIATED WITH

KOMATIITIC ROCKS

The two types of nickel sulfide deposits were defined 

largely by their geologic characteristics. A plot of 

average grade and tonnage of deposits of both types 

(fig. 6) demonstrates several points:

1. A marked difference exists in average grade and tonnage of the two deposit types. A median nickel 

grade of the deposits associated with komatiitic 

rocks (1.24 percent) is about twice that of the 

deposits associated with small intrusions (0.60 percent). The median tonnage of the deposits 

associated with komatiitic rocks (8.49xl06 metric 

tons) is about 6V2 times that of the deposits 

associated with small intrusions (1.27xl06 metric 

tons).

2. A difference exists in correlation coefficients of the 

variables in the two groups.

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FIGURE 5.-Grade and tonnage of nickel sulfide deposits associated with small intrusions.

7.5
GRADE AND TONNAGE ANALYSIS 11

ORE, IN MILLIONS OF METRIC TONS

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FIGURE 6. - Grade and tonnage of two types of nickel-sulfide deposits. Deposits associated with komatiitic rocks are represented by a dot (•), and

those associated with small mafic intrusions are represented by a cross (+).

Summary statistics for sulfide deposits of both types 

considered together (table 4) show a significant 

skewness of deposit-tonnage data. This skewness can be 

interpreted as indicating that the data set is 

heterogeneous-that is, geologically different deposit 

types have been mixed. Absence of skewness where 

each subgroup is considered separately lends statistical 

support to the geologic distinction between these two 

deposit types.

TABLE 5. -Summary statistics for grade and tonnage ofnickel-laterite

deposits

Arithmetic

Number of

Variable

Tonnage,

metric

Nickel

grade,

percent

deposits

(n)

64

64

Median

40.48 xlO6

1.41

Mean

7.61

.15

Logarithmic data (base 10)

Standard

deviation

0.60

.10

,Vfc,

(assymmetry)

-0.05

'.69

&2

(skewness)

3.42

3.72

Correlation coefficient (r)

-0.211

-0.211

TABLE 4. -Summary statistics for grade and tonnage of nickel sulfide \

deposits

Arithmetic

Number of

Variable

Tonnage,

metric

Nickel

grade,

percent

deposits

(n)

102

102

Median

3.34 xlO6

.87

Mean

6.52

-.06

Logarithmic data (base 10)

Standard

deviation

0.82

.30

Vft

(assymmetry)

10.80

-.03

62

(skewness)

3.43

2.62

Correlation coefficient (r)

-0.0531

-0.0531

Significant at the 1-percent level

NICKEL-LATERITE DEPOSITS

Average nickel grade and tonnage data for 64 nickellaterite deposits from six continents were collected. The

1 Significant at the 5-percent level.

data are plotted in figure 7, and summary statistics for 

the observed distributions of average nickel grade and 

tonnage of the laterite deposits are presented in table 5. 

Beta statistics indicate that the observed distribution of 

average grades is significantly skewed toward deposits 

having high average grades. Whereas the observed frequency distribution of tonnage can be adequately modeled by a lognormal distribution, the observed frequency 

distribution of grade cannot.

Skewness of average grades of nickel-laterite deposits 

could have several sources. First, it may result from 

economic factors. Much of the data have come from 

deposits in remote locations, and higher operating costs
12 DISTRIBUTIONS, RELATIONSHIPS OF GRADE AND TONNAGE AMONG SOME NICKEL DEPOSITS

ORE, IN MILLIONS OF METRIC TONS

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FIGURE 7.-Grade and tonnage of nickel-laterite deposits.

TABLE 6. -Summary statistics for grade and tonnage of oxide nickellaterite deposits

Arithmetic Logarithmic data (base 10)

Number of Standard V^ 62 CorrelaVariable deposits Median Mean devia- (assym- (skew- tion co-

(n) tion metry) ness) efficient (r)

Tonnage,

metric

Nickel

grade,

percent

54

54

45.18xl06

1.36

7.65

.13

0.63

.08

-0.21

.19

3.35

3.59

-0.13

-0.13

for such deposits might force higher cutoff grades than 

for less remote deposits that have lower operating costs. 

This would tend to raise the average grade and reduce 

the tonnage of these deposits. Second, the skewness in 

average grade can result from mixing of more than one 

type of laterite deposit. As previously mentioned, nickellaterite deposits can be geologically divided into two 

end-member groups on the basis of mineralogy. These 

are silicate deposits, which have garnierite as the principal nickel mineral, and oxide deposits, in which nickel 

is with iron oxides. Although these two types grade into 

one another, the ore formation represents different 

degrees of physical and chemical interactions. Thus, the 

skewness in average grade can be caused by mixing 

deposits of silicate and oxide ores.

In figure 8, only deposits that do not contain significant amounts of silicate ore (garnierite) are plotted; 

summary statistics are shown in table 6. Beta statistics 

for the observed distributions of average grade and tonnage of the deposits are not significantly different from 

values expected from theoretical lognormal distributions. The correlation coefficient of average grade and 

tonnage for the oxide nickel-laterite deposits is not 

significantly different from zero. Thus, average grade 

and tonnage of nonsilicate nickel-laterite deposits follow 

theoretical lognormal distributions and act as independent variables.

SUMMARY AND CONCLUSIONS

In this study we have investigated the distribution of 

and relationships among average grades and tonnage of 

nickel deposits belonging to several geologically defined 

deposit types. Consideration of the geologic factors influencing grade and tonnage suggests that for nickelbearing laterite deposits no relationship between the 

two variables should be expected. For sulfide deposits, 

the factors are too complex to determine the correlation 

between tonnage and grade.
REFERENCES CITED 13

ORE, IN MILLIONS OF METRIC TONS

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LU

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FIGURE 8. - Grade and tonnage of oxide nickel-laterite deposits.

Two types of sulfide deposits were defined on the basis 

of associated host rocks. Within deposits associated with 

komatiitic rocks and those associated with small 

orogenic intrusions, the lognormal distribution was 

found to be an adequate model for average grade and 

tonnage of deposits. However, the relationships between grade and tonnage in both deposit types are quite 

different. For deposits associated with komatiites, 

deposit grade correlates inversely with tonnage. Among 

deposits in small orogenic intrusions, grade and tonnage 

are independent. Further analysis of the komatiite 

association reveals that regional differences exist for 

average grade and tonnage of deposits but that no 

significant regional difference exists in the correlation 

coefficients that relate tonnage to grade. Regional differences of this type have important implications concerning the overall geologic controls that determined 

the formation of ore deposits and concerning the 

distribution of undiscovered ore deposits that might be 

predicted while making regional land assessments.

Initially, the lognormal distribution model was rejected for laterite deposits because of the skewness of 

deposit grades. Possible causes of this skewness were

'economic bias against low-grade deposits and mixing 

the data for two different deposit types. The latter 

possibility was examined by removing data for deposits 

in which significant amounts of silicate ore (garnierite) 

were present. Analysis of the low-garnierite deposits indicates that lognormal distributions are adequate 

models of both grade and tonnage and that lateritedeposit grade is independent of deposit tonnage. 

Statistical analysis confirmed this independence of 

grade and tonnage that was inferred from an assessment of the geological factors controlling deposit tonnage and grade.

REFERENCES CITED

Arndt, N. T., Francis, Donald, and Hynes, A. J., 1979, The field 

characteristics and petrology of Archean and Proterozic 

komatiites: Canadian Minerologist, v. 17, no. 2, p. 143-163.

Brooks, C., and Hart, S. R., 1974, On the significance of komatiite: 

Geology: v. 2, no. 2, p. 107-110.

Dietz, R. S., 1964, Sudbury structure as an astrobleme: Journal of 

Geology, v. 72, no. 4, p. 412-434.

Golightly, J. P., 1979, Nickeliferous laterites-A general description, 

in Evans, D. J. I., and others, eds., International Laterite Symposium: New York, American Institute of Mining, Metallurgical, 

and Petroleum Engineers, p. 3-23.
14 DISTRIBUTIONS, RELATIONSHIPS OF GRADE AND TONNAGE AMONG SOME NICKEL DEPOSITS

Gorbachev, N. S., and Grinenko, L. N., 1973, Origin of the October 

sulfide-ore deposit, Noril'sk region, in the light of sulfide and 

sulfate sulfur isotope compositions: Geochemistry International, 

v. 10, no. 4, p. 843-851.

Green, D. H., 1975, Genesis of archean peridotitic magmas and constraints on Archean geothermal gradients and tectonics: 

Geology, v. 3, no. 1, p. 15-18.

Green D. H., Nicholls, I. A., Viljoen, M. J., and Viljoen, R. P., 1975, 

Experimental demonstrations of the existence of peridotitic liquids in earliest Archean magmatism: Geology, v. 3, no. 1, p. 

11-14.

Lawrence, M. J., 1974, Supergene nickel deposits; origin and features: 

Australasian Institute _of uMiiiing and Metallurgy Conference 

Series, no. 3,°p. 523-542.

Naldrett, A. J., 1973, Nickel sulfide deposits; their classification and 

genesis, with special emphasis on deposits of volcanic association: Canadian Mining and Metallurgical Bulletin, v. 66, no. 739, 

p. 45-63.

Naldrett, A. J., and Arndt, N. T., 1976, Volcanogenic nickel deposits

with some guides for exploration: Society of Mining Engineers

Transactions, v. 260, p. 13-15. 

Naldrett, A. J. and Cabri, L. J., 1976, Ultramafic and related mafic

rocks: their classification and genesis with special reference to

the concentration of nickel sulfides and platinum-group elements:

Economic Geology, v. 71, no. 7, p. 1131-1158. 

Pyke, P. R., Naldrett, A. J., and Eckstrand, 0. R., 1973, Archean

ultramafic flows in Munro Township, Ontario: Geological Society

of America Bulletin v. 84, no. 3, p. 955-977. 

Singer, D. A., Cox, D. P., and Drew, L. J., 1975, Grade and tonnage

relationships among copper deposits: U.S. Geological Survey

Professional Paper 907-A, 11 pp.

Viljoen, M. J. and Viljoen, R. P., 1969, Evidence for the existence of a 

mobile extrusive peridotitic magma from the Komati Formation 

of the Onverwacht Group: Geological Society of South Africa, 

Special Publication 2, p. 87-112.

•h U.S. GOVERNMENT PRINTING OFFICE: 1980 O— 311-344/164