RAL DEPOSIT DENSITY—AN UPDATE—U.S. Geological Survey Professional Paper 1640–A

FOL

CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH
Mine photograph on cover. The Bingham Canyon porphyry copper-gold-molybdenum

mine in the Oquirrh Mountains, southwest of Salt Lake City, Utah, was opened in 1904 as

the first open-pit copper mine in the world. The pit is about 3 kilometers across and has

produced nearly 12 million tons of copper, an unequaled record. This report provides mineral deposit densities for 13 deposit types, including porphyry copper deposits like that at

Bingham Canyon. Photograph by Charles Cunningham, U.S. Geological Survey.

Satellite image on cover. View of North and South America from space. Image courtesy

of the National Aeronautics and Space Administration.
U.S. Department of the Interior

U.S. Geological Survey

Mineral Deposit Density—An Update

By Donald A. Singer, W. David Menzie, David M. Sutphin, 

Dan L. Mosier, and James D. Bliss

U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1640–A

A description of a method to estimate the numbers of 

undiscovered deposits and a compilation of 27 mineral 

deposit density estimates for 13 deposit types 

CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH

Edited by Klaus J. Schulz
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

CHARLES G. GROAT, Director

U.S. GEOLOGICAL SURVEY, RESTON, VIRGINIA : 2001

Version 1.0

Published in the Eastern Region, Reston, Va.

Manuscript approved for publication September 28, 2001.

Any use of trade, product, or firm names in this publication is for descriptive purposes only

and does not imply endorsement by the U.S. Government.

For sale by

U.S. Geological Survey

Information Services

Box 25286, Federal Center

Denver, CO 80225

or call the toll-free telephone number

1–888–ASK–USGS

This report is also available on the World Wide Web at 

http://pubs.usgs.gov/prof/p1640a

Library of Congress Cataloging in Publication Data

Mineral deposit density: an update / by Donald A. Singer . . . [et al.].

p. cm. — (U.S. Geological Survey professional paper ; 1640–A) (Contributions to global mineral resource 

assessment research)

1. Ore deposits—United States. 2. Mines and mineral resources—United States. I. Singer, D. A. II. Series. 

III. Geological Survey professional paper ; 1640–A.

QE75.P9 v. 1640–A

[TN23]

553’.0973—dc21 2001055704
III

EDITOR’S PREFACE

Global demand for mineral resources will continue to increase for the foreseeable

future because of the continuing increase in global population and the desire to improve

living standards worldwide. Although no global shortages of mineral resources are expected in the near future, the growing demand requires continued exploration for undiscovered

mineral deposits as identified resources are depleted. However, competing land uses and

growing concerns over the possible environmental degradation associated with mining are

increasingly affecting mineral exploration and development worldwide.

Informed planning and decisions about biological sustainability and resource development require a long-term perspective and an integrated approach to land-use, resource,

and environmental management. This approach needs unbiased information on the global

distribution of identified and especially undiscovered mineral resources; the economic,

social, and political factors influencing their development; and the environmental consequences of, and requirements for, their utilization. 

The U.S. Geological Survey (USGS) is authorized by Congress to collect, analyze,

and disseminate data on the domestic and international supply of and demand for minerals essential to the U.S. economy and national security. In response to the growing concern about global sustainability of mineral production and environmental quality, and the

simultaneous increase in demand for global mineral resource information, the USGS has

initiated a project to begin assessing selected mineral commodities globally. Along with

providing estimates of the quantity, quality, and regional distribution of undiscovered mineral resources, these global assessments will provide consistent, systematic data bases of

current geologic and mineral-resource information at continental and global scales. The

assessments will provide information necessary for evaluating the potential effects of

land-use, environmental, and resource-development decisions on global minerals supply

and sustainable development.

A vital component of the USGS global mineral resource assessment project is new

research to test and improve our data, geologic and mineral deposit models, and understanding of the fundamental processes of mineral formation, preservation, and environmental response. USGS Professional Paper 1640, “Contributions to Global Mineral

Resource Assessment Research,” presents significant results of this research to advance

the state-of-the-art in mineral deposit modeling and resource assessment.

Klaus J. Schulz

V

CONTENTS

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

Three-Part Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Mineral Deposit Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Placer Gold Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

Cyprus Massive Sulfide Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Kuroko Massive Sulfide Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

Porphyry Copper Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Climax Porphyry Molybdenum Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Wolframite Quartz Vein Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

A Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Scale Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

References Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

FIGURES

1. Plan view of known deposits in 12 hypothetical well-explored permissive

areas and histogram of derived deposit densities . . . . . . . . . . . . . . . . . . . . . . . . . A3

2. Histogram of the number of podiform chromite deposits per square kilometer

of ultramafic rock in 27 California counties and in 12 Oregon areas . . . . . . . . . . . 9

3. Graph of the number of podiform chromite deposits in 27 California counties

vs. area of ultramafic rock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

TABLE

1. Mineral deposit densities for 13 selected deposit types from this report

and previous publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A4
VI

CONVERSION FACTORS

Multiply By To obtain

meter (m) 3.281 foot

kilometer (km) 0.6214 mile

square kilometer (km2) 0.3861 square mile

CONTENTS
A1

ABSTRACT

A key function of many quantitative mineral resource

assessments is estimation of the number of undiscovered

deposits. Numerous techniques can be used directly or as

guidelines to make these estimates. Most robust of these

methods is a form of mineral deposit model wherein for a

deposit type, the numbers of deposits per unit area from

well-explored regions are counted and the resulting frequency distribution is used either directly for an estimate or

indirectly as a guideline in some other method. Ratios of the

number of deposits per unit area can be used in histograms

to show variation of deposit densities by type. In three-part

quantitative resource assessments, prevention of bias

requires that deposits of each type be defined the same way

as in delineation of permissive tracts and as in construction

of grade and tonnage models; these same definitions and

rules must also be applied to deposit density models.

This paper provides mineral deposit densities for 13

selected deposit types from previous publications and this

study. Many of the specially selected areas reported here

provide standards to identify what should be high estimates

of the number of undiscovered deposits in most situations.

Previously reported densities follow:

1. Low-sulfide gold quartz vein deposits in four regions

have deposit densities ranging from 0.0043 to 0.0054

deposit per square kilometer. 

2. Bedded barite deposits in Nevada have a deposit density

of 0.074 deposit per square kilometer.

3. Diamond kimberlite pipe deposits in southern Africa

have a deposit density of 0.000012 deposit per square

kilometer.

——————— 1U.S. Geological Survey, 345 Middlefield Road, Menlo Park, CA

94025, U.S.A. Please e-mail comments to singer@usgs.gov 2U.S. Geological Survey, 12201 Sunrise Valley Drive, Reston, VA

20192, U.S.A. 3U.S. Geological Survey, 520 N. Park Avenue, Tucson, AZ

85719, U.S.A.

4. Podiform chromite deposits in California have a

deposit density of 0.115 deposit per square kilometer.

5. Franciscan volcanogenic manganese deposits in California and Japan have deposit densities of 0.019 and

0.03 deposit per square kilometer, respectively.

6. Cuban volcanogenic manganese deposits in Cuba and

Fiji have deposit densities of 0.1 and 0.0066 deposit per

square kilometer, respectively.

7. Cyprus volcanogenic manganese deposits in Cyprus

have a deposit density of 0.046 deposit per square

kilometer.

Densities from this study follow:

1. Placer gold deposits in two locations in Alaska have

deposit densities of 0.0054 and 0.0061 deposit per

square kilometer.

2. Cyprus massive sulfide deposits in the Troodos ophiolite have a deposit density of 0.0082 deposit per square

kilometer.

3. Kuroko massive sulfide deposits in five localities have

deposit densities ranging from 0.0033 to 0.03 deposit

per square kilometer.

4. Porphyry copper deposits in Nevada and Arizona have

deposit densities of 0.00015 and 0.0012 deposit per

square kilometer, respectively.

5. Climax porphyry molybdenum deposits in New Mexico

and Colorado have deposit densities of 0.00031 and

0.00033, respectively.

6. Wolframite (tungsten) quartz vein deposits in

Xihuashan, China, have a deposit density of 0.04

deposit per square kilometer.

Frequency analysis of 39 podiform chromite deposit

densities demonstrates a highly skewed distribution, suggesting that mean estimates can be misleading; however,

probabilistic estimates are possible using log-transformed

data and the normal distribution. The same data show deposit

density varying with size of permissive area—a regression

equation is required to provide unbiased estimates of deposit

densities for all but median sized areas.

CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH

Mineral Deposit Density—An Update

By Donald A. Singer,1 W. David Menzie,2 David M. Sutphin,2

Dan L. Mosier,1 and James D. Bliss3
A2 CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH

INTRODUCTION

A key function of many forms of quantitative mineral

resource assessments (Singer and Mosier, 1981; Harris,

1984) is the estimation of the number of undiscovered

deposits. The first example of this kind of estimation is

probably Allais’ (1957) study in which the number of

deposits per square kilometer from several explored areas

was used with the Poisson distribution to estimate the number of deposits in a relatively unexplored area.

Most resource assessments based on the three-part

form of assessment (see the next section and Singer and

Cox, 1988; Singer, 1993) have used subjective methods to

estimate the number of deposits—estimates are presented

in a probabilistic form. Research in psychometrics has

raised questions about the ability to make unbiased subjective estimates (Tversky and Kahneman, 1974). However, in

meteorology, probabilistic forecasts made by subjective

methods show little evidence of problems suggested by the

psychometric results and have been quite reliable (Murphy

and Winkler, 1984). Subjective methods as used in meteorology outperformed multivariate methods, but they worked

best when preceded by numerical-statistical estimates

(Murphy and Winkler, 1984). Experiments by W.D. Menzie (an author of this paper) in 1986 show that many geologists can make unbiased estimates of the number of porphyry copper deposits. The results in meteorology suggest

that subjective estimates of the number of deposits might

be improved if they are preceded by numerical-statistical

estimates.

Ideally numerical-statistical estimates of the number of

deposits should rely on analogies with similar wellexplored areas in the same way that grades and tonnages of

well-explored deposits serve as analogs of the grades and

tonnages of undiscovered deposits. These numerical-statistical estimates or base rates are prepared from counts of

known deposits per unit area in explored regions. Some

research has been conducted on several deposit types so

that these base rates can be more widely used as a guide for

number-of-deposits estimates (Bliss and others, 1987;

Bliss, 1992; Root and others, 1992; Bliss and Menzie,

1993). Most of these studies provide point (that is single)

estimates of the number of deposits per unit area. In practice, these numerical-statistical estimates of the number of

deposits have been used in only a few cases (Cox, 1993;

Scott, 2000). 

In this paper, we summarize earlier work and extend

and update the work reported by Bliss and Menzie (1993)

by providing estimates of the number of deposits for the following settings:

• Two settings for placer gold deposits

• One setting for Cyprus massive sulfide deposits

• Five settings for kuroko massive sulfide deposits

• Two settings for porphyry copper deposits

• Two settings for Climax porphyry molybdenum

deposits

• One setting for wolframite (tungsten) quartz vein

deposits

To explain the strengths and uses of these estimates,

we first describe three–part mineral resource assessments.

This description is followed by a discussion of mineral

deposit densities, a review of some earlier studies, and

presentation of new deposit density results for the deposit

types listed in the previous paragraph. We end with a discussion of some complexities with numerical-statistical

estimates of the number of deposits, scale-related issues,

and conclusions.

ACKNOWLEDGMENTS

For the estimate of porphyry copper deposits in Arizona, D.P. Cox of the U.S. Geological Survey (USGS) suggested the use of Titley and Anthonys’ (1989) terrane, and

B. Moring (USGS) calculated areas of geologic units in this

terrane.

THREE–PART ASSESSMENTS

Considerable care must be exercised in quantitative

resource assessments to prevent the introduction of biased

estimates of undiscovered resources. In three-part assessments (Singer, 1993), (1) areas are delineated according to

the types of deposits permitted by the geology, (2) the

amount of metal and some ore characteristics are estimated

by means of grade and tonnage models, and (3) the number

of undiscovered deposits of each type is estimated.

Part 1.—In order to be consistent, areas are delineated

where geology permits the existence of deposits of one or

more specified types. These areas, called permissive tracts,

are based on geologic criteria derived from deposit models

that are based on studies of known deposits within and,

more commonly, outside the study area. Boundaries of permissive tracts are defined such that the probability of

deposits of the type specified occurring outside the boundary is negligible; that is, less than 1 in 100,000 to 1,000,000.

Part 2.—A critical part of the exploration for mineral

deposits and of quantitative mineral resource assessments is

the estimation of the sizes of undiscovered deposits. Typically, this problem is addressed by using grade and tonnage

models because a major source of variation in possible

deposit sizes can be accounted for by differences among

types of deposits (Singer and Kouda, 1999). In three-part

assessments, previously constructed grade and tonnage

models are typically used unless local deposits are significantly different from those in the general model. These

models have the form of frequency distributions of tonnages and average grades of well-explored deposits of each

type. They serve as models for grades and tonnages of

undiscovered deposits of the same type occurring in geo-
logically similar settings. By design, the target population is

the distribution of grades and tonnages of undiscovered

mineral deposits rather than mineral occurrences.

Part 3.—The third part is the estimate of the fixed, but

unknown, number of deposits of each type that exists in the

delineated tracts. Until the area being considered is thoroughly and extensively drilled, that fixed number of undiscovered deposits, which could be almost any number

(including zero), will not be known with certainty. In threepart assessments, estimates of the number of deposits

explicitly represent the probability (or degree of belief) that

some fixed but unknown number of undiscovered deposits

exists in the delineated tracts. These estimates reflect both

the uncertainty of what may exist and a measure of the

favorability of the existence of the deposit type. Uncertainty is shown by the spread of the number-of-deposits estimates associated with the 90- to the 10- or 1-percent quantiles—a large difference suggests great uncertainty. Favorability can be represented by the estimated number of

deposits associated with a given probability level or by the

expected number of deposits.

Consistency.—In these assessments, the estimates are

internally consistent when the delineated tracts are consistent with descriptive models, grade and tonnage models are

consistent with descriptive models, grade and tonnage models are consistent with known deposits in the area, and estimates of the number of deposits are consistent with the

grade and tonnage models. Biases can be introduced into

these estimates either by a flawed grade and tonnage model

or by lack of consistency of the number-of-deposits estimates with the grade and tonnage model. Grade and tonnage

models combined with estimates of number of deposits are

the fundamental means of translating resource assessments

by geologists into a language that economists can use. For

these reasons, determining a mineral deposit density

requires unambiguous definitions of what is a deposit and

what are the rules for delineation.

MINERAL DEPOSIT DENSITIES

There are no fixed methods for making estimates of the

number of undiscovered deposits. On the basis of experience and logic, however, there are a number of techniques

that can be used directly or as guidelines to make these estimates. Each method represents some form of analogy. Most

robust of these methods is a form of mineral deposit model

wherein for a deposit type, the numbers of deposits per unit

area from well-explored regions are counted and the resulting frequency distribution either is used directly for an estimate or is used indirectly as a guideline in some other

method.

In figure 1A, a hypothetical situation is presented where

for some deposit type, the number of discovered deposits is

counted in each of 12 well-explored permissive tracts, and

the areas of each tract are recorded. The ratios of number of

deposits per area can then be used to make a histogram (fig.

1B) to show how commonly different deposit densities

occur. It is not necessary that the base areas be explored

completely, but it is necessary that the number of deposits

found and the proportion of the area explored be estimated.

In some situations, it is possible to consider mineral

deposit density as the probability that a deposit of a given

type occurs within some standard measure of area such as a

square kilometer. We do not use that approach here because

it requires an assumption that there can be one and only one

deposit within the area.

Examples of mineral deposit densities are shown in

table 1. These examples are the main focus of this paper—

they represent estimates of mineral deposit densities from

various published sources and new estimates. The densities

for low-sulfide gold quartz veins were discussed by Bliss

and others (1987) and Bliss and Menzie (1993). These

mesothermal deposits were defined in the descriptive model

by Berger (1986) and are consistent with the grade and tonnage model by Bliss (1986). It is important to note that the

MINERAL DEPOSIT DENSITY—AN UPDATE A3

• • •

• •

• •

•

• •

• •

•

•

0.3/km2

0.4/km2

0.0/km2

0.31/km2

0.15/km2

0.25/km2

0.29/km2

0.45/km2

• 0.5/km2

• • 0.15/km2

0.1 0.2 0.3 0.4 0.5

NUMBER OF DEPOSITS PER SQUARE KILOMETER

FREQ

UEN

C

Y

0

• 0.24/km2

•

•

• 0.32/km2

A B

3

1

2

4

0

Figure 1. Plan view of known deposits (filled circles) in 12 hypothetical well-explored permissive areas (A) and histogram of derived

deposit densities (B).
A4 CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH

Table 1. Mineral deposit densities for 13 selected deposit types from this report and previous publications.

 Location Area Density Permissive rock type 

 (km 2) (deposits/km2)

Low-sulfide gold quartz vein deposit type (Bliss and others, 1987)

Sierra Nevada, California, U.S.A. --- 0.0046 Metavolcanic, metasedimentary, and ophiolitic 

 rocks, greenschist facies or lower.

Klamath Mountains, 

 California/Oregon, U.S.A. ...... --- 0.0043 Ditto. 

Meguma Group,

 Nova Scotia, Canada ............ --- 0.0054 Ditto. 

Bendigo, Victoria, Australia ...... --- 0.005 Ditto.

 

Placer gold deposit type (this report)

Wiseman, Alaska, U.S.A. ........ 2,760 0.0054 Greenschist-facies rocks.

Kenai, Alaska, U.S.A. ............ 3,260 0.0061 Low-grade metamorphic rocks.

Bedded barite deposit type (Orris and Bliss, 1989)

Nevada, U.S.A. .................... --- 0.074 Slaven Chert.

Diamond kimberlite pipes deposit type (Bliss, 1992)

Southern Africa .................... 1,560,000 0.000012 Stable cratonic rocks.

Cyprus massive sulfide deposit type (this report)

Cyprus ............................... 2,440 0.0082 Troodos ophiolite.

Cyprus ............................... 1,010 0.02 Extrusive rocks of Troodos ophiolite.

Kuroko massive sulfide deposit type (this report)

Snow Lake, Manitoba, Canada ... 268 0.03 Volcanic rocks in basin.

Hokuroku, Japan ................... 900 0.0088–0.013 Volcanic rocks in basin.

Western Tasmania, Australia ..... 1,500 0.0033 Volcanic rocks at Mount Read.

Sierran subtype:

 480 0.0083 Copper Hill Volcanics.

California, U.S.A. ...... 1,370 0.0059 Gopher Ridge Volcanics and a

 western volcanics unit.

Porphyry copper deposit type (this report)

Nevada, U.S.A. .................... 32,800 0.00015 Exposed plutons.

Arizona, U.S.A. ................... 34,000 0.00071 Exposed igneous rocks in southeastern Arizona

 that formed in the Laramide orogeny or earlier.

Arizona, U.S.A. ................... 16,700 0.0012 Ditto.

Climax porphyry molybdenum deposit type (this report)

Colorado, U.S.A. .................. 12,000 0.00033 Tertiary intrusions, central Colorado mineral belt.

New Mexico, U.S.A. ............. 3,200 0.00031 Tertiary intrusions, northern New Mexico.

California, U.S.A. ......
same proximity rule used to construct the grade and tonnage

model (workings within 1.6 km of each other are treated as

part of the same deposit) was used to define deposits for the

deposit densities. Control area boundaries of permissive

tracts, based on standards from the descriptive model,

enclose areas containing metavolcanic, metasedimentary,

and ophiolitic rocks of accreted terranes. Plutonic rocks

(within 40 km of veins) also intrude these areas, and the

metamorphic grade is greenschist facies or lower (Bliss and

others, 1987). Reported densities vary over a rather narrow

range from 0.0043 to 0.0054 deposit/km2. 

Mineral deposit densities (table 1) of bedded barite

deposits (Orris and Bliss, 1989), diamond kimberlite pipes

(Bliss, 1992), podiform chromite deposits (Singer, 1994),

and three types of volcanogenic manganese deposits

(Mosier and Page, 1988) are also based on deposits that are

consistent with their respective descriptive and grade and

tonnage models. The following new examples of mineral

deposit densities for placer gold, Cyprus massive sulfide,

kuroko massive sulfide, porphyry copper, Climax porphyry

molybdenum, and wolframite quartz vein deposits further

demonstrate the variability of estimates and some consequences of assumptions about permissive areas and extent

of exploration.

PLACER GOLD DEPOSITS

Two density estimates for placer gold deposits (table 1)

were based on data from the areas delineated as permissible

for gold placers in the mineral resource assessments of the

Wiseman 1° by 3° quadrangle, Brooks Range, Alaska

(Bliss, Brosgé, Dillon, Dutro, and others, 1988), and the

Kenai Peninsula planning unit, Chugach National Forest,

Alaska (Bliss, 1989). These regions were selected because

they have well-defined placers and the delineation criteria

used for both are comparable. Gold placer data from the

Wiseman quadrangle were compiled by Bliss, Brosgé, Dillon, Cathrall, and others (1988), and data from the Chugach

National Forest were compiled by Jansons and others

(1984). All gold placers exposed on the surface in the Wiseman quadrangle are probably included; however, buried

placer deposits may have been overlooked by early prospectors, who lacked the techniques and tools for finding them.

MINERAL DEPOSIT DENSITY—AN UPDATE A5

Table 1. Mineral deposit densities for 13 selected deposit types from this report and previous publications—Continued.

Location Area Density Permissive rock type 

(km2 ) (deposits/km2)

Podiform chromite deposit type (Singer, 1994)

California, U.S.A. ................ 6,980 0.115 Ultramafic rocks.

Franciscan volcanogenic manganese deposit type (Mosier and Page, 1988)

California, U.S.A. ................ 23,700 0.019 Franciscan Complex.

Japan ................................ 3,890 0.03 Sandstone, slate, and chert in the Kitakami

 Mountains.

Cuban volcanogenic manganese deposit type (Mosier and Page, 1988)

Cuba ................................. 1,200 0.1 Cobre Formation.

Fiji ................................... 2,720 0.0066 Deposit-bearing volcanic conglomerates, marl,

 lithic tuff, lava, and andesite pyroclastics at

 Viti, Levu.

Cyprus volcanogenic manganese deposit type (Mosier and Page, 1988)

Cyprus .............................. 1,960 0.046 Troodos ophiolite.

Wolframite quartz veins deposit type (this report)

China ................................ 140 0.04 Metasedimentary rocks above granite ridge,

 Xihuashan-Piotang.
These deposits were defined in the descriptive model by

Yeend (1986) and are consistent with the grade and tonnage

model by Orris and Bliss (1986). It is important to note that

the same proximity rule used to construct the grade and tonnage model (workings within 1.6 km of each other are treated as part of the same deposit) was used to determine the

number of deposits present in the area for the deposit density estimate.

The largest (2,760 km2) of three tracts for gold placers

delineated in the mineral resource assessment of the Wiseman quadrangle (Bliss, Brosgé, Dillon, Dutro, and others,

1988) was used as one of the areas for this estimate. It was

delineated on the basis of the presence of low-grade metamorphic rocks (greenschist facies or equivalent). The northern boundary was delineated by the absence of significant

metamorphism; the southern, by a major fault zone.

In the Kenai Peninsula planning unit, an area of lowgrade metamorphic rocks was used as the other permissive

area. The boundaries, however, were truncated to conform

to the boundary of the national forest. The Placer River fault

was used as the eastern boundary. Strictly speaking, this

area is a portion of a larger area of low-grade metamorphism that should be included; although missing part of the

area causes the estimate to be less robust than it might have

been, it does not introduce any bias into the estimate.

CYPRUS MASSIVE SULFIDE DEPOSITS

The Troodos massif on the island of Cyprus may be the

most complete and intact ophiolite exposure in the world.

The ophiolite sequence ranges downward from pillow lavas

through a sheeted-dike sequence and cumulate gabbros, and

from peridotites to tectonized harzburgite. Deposits here

have been mined for copper pyrite ore since the Bronze Age.

Extensive slag dumps, surface and underground workings,

and abundant artifacts are evidence of the magnitude of this

early mining industry.

In the ophiolite complex, there are 20 known Cyprus

volcanogenic massive sulfide deposits (Singer, 1986a) that

are defined in the same way as the deposits in the Cyprus

volcanogenic massive sulfide grade and tonnage model

(Singer and Mosier, 1986a); several of the deposits are components of the grade and tonnage model, and all 20 deposits

fit the grade and tonnage model. All known deposits are

located in the extrusive pillow lavas of the ophiolite complex; some mineralization occurs in the upper levels of the

Basal Group (Constantinou, 1976) of basalt lavas below the

pillow lavas. Large-scale copper mineralization is not found

in the diabase of the sheeted-dike complex. Most copper

occurrences outside of the extrusive rocks are small copper

veins and are not included in the deposit models; pyrite

deposits barren of copper are also not included.

The permissive region for Cyprus volcanogenic massive sulfide deposits is defined as the ophiolite complex part

of the island where extrusive ophiolite rocks are within 1

km of the surface. Within the permissive area, the rocks of

the Basal Group metabasalt, the Lower Pillow Lavas, and

the Upper Pillow Lavas are the permissive rock units. Exposures of those rock types are very well explored within the

permissive area; it is unlikely that any undiscovered Cyprus

volcanogenic massive sulfide deposits are exposed in these

rocks. Continued drilling programs may, however, locate

buried deposits. The exposed permissive rocks cover an

area of about 1,010 km2. The Basal Group metabasalt covers 512.6 km2, and the Lower Pillow Lavas and the Upper

Pillow Lavas cover 299.5 km2 and 198.7 km2, respectively.

By using descriptions of the deposits, the host rocks for

each of the deposits can be determined; however, many of

the deposits form at, or near, the contact between rock units.

No deposits are located in the Basal Group metabasalt, 10

deposits are hosted in the Lower Pillow Lavas, another 9

deposits are found in the Upper Pillow Lavas, and for 1

deposit, the specific host pillow lava unit could not be

determined.

Around the world, ophiolitic rocks may be less well

explored and less well exposed than the rocks of the Troodos massif, and so the rocks in these other areas may be

mapped as “ultramafic, undifferentiated” rather than as specific subunits of the ophiolite, such as mantle complex,

sheeted-dike complex, and extrusive rocks. For this reason,

the entire 2,440 km2 of the exposed part of the ophiolite has

been considered as if it were “ultramafic, undifferentiated,”

and a base rate of occurrence for such rocks has been calculated (table 1). We also include an estimate based on the

exposed extrusive rocks for situations where these rocks are

mapped.

KUROKO MASSIVE SULFIDE DEPOSITS

Snow Lake district, Manitoba, Canada.—In the Snow

Lake district in Manitoba, Canada, there are eight known

deposits (Chisel Lake, Lost Lake, Anderson Lake, Stall

Lake, Rod, Joanne, Pot Lake, Ghost Lake) defined in the

same way as deposits in the kuroko massive sulfide descriptive model (Singer, 1986b) and grade and tonnage model

(Singer and Mosier, 1986b). These deposits have been thoroughly drilled, and all mineralization within 500 m is treated as part of the same deposit in order to be consistent with

the rules used to construct the grade and tonnage model.

The permissive area is the basin containing felsic volcanic rocks, which occupies 268 km2 according to Wright

and Bonham-Carter (1996). If we assume that there are no

deposits to be discovered (that is, the basin is completely

explored), then the estimated mineral deposit density is

0.03 deposit/km2 (8 deposits/268 km2). If the definition of a

kuroko deposit is ignored and we include prospects, then

the deposit density almost doubles to 0.06 (15

“deposits”/268 km2); this broadened definition of a deposit

A6 CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH
would lead to biased estimates of the number of undiscovered kuroko deposits that are like those in the grade and

tonnage model. It should be noted that the estimate of 0.03

deposit/km2 (table 1) is based on a small area that is a wellstudied district noted for volcanic-rock-hosted massive

deposits (Sangster, 1980).

Hokuroku district, Japan.—The Hokuroku district in

northern Japan is probably the most thoroughly explored

and studied district for kuroko-type massive sulfide deposits

in the world (Singer and Kouda, 1988). Eight known

deposits (Ezuri, Fukazawa, Furutobe-Ainai, Hanaoka-Doyashiki, Hanaoka-Matsumine-Shakanai, Kosaka-Uchinotai,

Kosaka-Motoyama, and Nurukawa) are defined in the same

way as deposits in the kuroko grade and tonnage model

(Singer and Mosier, 1986b). They are thoroughly drilled: all

known mineralization within 500 m is treated as part of the

same deposit in order to be consistent with the rules used to

construct the grade and tonnage model. The permissive area

consists of the felsic volcanic rocks associated with deposits

in the middle Miocene basin, which is about 900 km2 in

extent. If we assume that no additional deposits are to be

discovered (that is, the basin is completely explored), then

the deposit density estimate is 8 deposits/900 km2 = 0.0088

deposit/km2. 

In the Hokuroku district, we have additional information

that could be used to refine this estimate. National and local

governments drilled 260 exploratory holes in the district, and

industry drilled a large number of holes, mostly near known

deposits. The average projected surface area extent of known

kuroko deposits in this district is about 0.45 km2. About 10

percent of the basin has the mineralized horizon exposed

(and thus, is thoroughly explored). If we assume that for the

unexposed part, only the immediate neighborhoods of government drill holes are completely explored, then an additional 13 percent of the basin can be considered explored

([260 holes × 0.45 km2 /hole]/900 km2). Thus, a more specific estimate of deposit density here would be 8 deposits/(900

km2 × 0.23 proportion explored) = 0.038 deposit/km2. If this

estimate is correct, then the expected number of undiscovered kuroko deposits in the Hokuroku district is 26, as indicated by 900 km2 × (1–0.23) × 0.038 deposit/km2. From this

estimated number, we can estimate that the probability that a

drill hole in the covered area would hit a deposit is 0.0169, as

indicated by (26 deposits × 0.45 km2/deposit)/(900 km2 ×

0.77 [proportion of area unexplored]).

None of the 260 drill holes found any of these estimated 26 undiscovered kuroko deposits; some holes did penetrate local mineralization. If we assume that the placement of

the drill holes was random (it wasn’t), then the probability

that at least one deposit would have been hit, given 260 holes

and 26 deposits, is 0.99 (1–[1–0.0169]260). Such a high probability with no deposits found is unlikely and suggests that

the estimated number of undiscovered deposits is too high.

Kouda and Singer (1992a,b) estimated that there is a 10

percent chance of at least four undiscovered kuroko deposits

in this district. This estimate leads to a deposit density estimate of 0.013 deposit/km2 (12 deposits/900 km2), and the

probability of hitting at least one deposit with 260 holes is a

more reasonable 0.49 (1–[1–0.0026]260). Thus, a reasonable

estimate of the density of kuroko deposits in the wellexplored Hokuroku district is between 0.0088 and 0.013

deposit/km2. 

Western Tasmania, Australia.—In Western Tasmania,

Australia, there are five massive sulfide deposits (Mt. Lyell,

Rosebery, Hercules, Que River, Hellyer) that are consistent

with the kuroko descriptive and grade and tonnage models.

They are all located in the Middle Cambrian volcanic rocks

of Mount Read (Reid and Meares, 1981; Collins and

Williams, 1986). The area, as defined by the central belt of

volcanic rocks, is 150 km by 5 to 15 km, or about 1,500

km2. If the area is completely explored, then the mineral

deposit density is 0.0033 deposit/km2.

Sierran subtype, California.—The deposit density of a

subtype of kuroko deposits called Sierran kuroko massive

sulfides has been estimated in California. Twelve deposits

that are consistent with the grade and tonnage model

(Singer, 1992) are known in the Jurassic volcanic and volcaniclastic rocks that extend about 300 km along the

foothills of the western Sierra Nevada Mountains. Primarily

on the basis of the geologic maps of Kemp (1982), the volcanic rocks are divided into the Copper Hill Volcanics and

the Gopher Ridge Volcanics plus a western volcanics unit.

The Copper Hill area (480 km2) has a mineral deposit density of 0.0083 deposit/km2, whereas the Gopher Ridge area

(1,370 km2) has a density of 0.0059 deposit/km2. Although

these rocks have been well explored on the surface, undiscovered deposits could exist at depth.

PORPHYRY COPPER DEPOSITS

Nevada.—Seven known deposits in Nevada (Yerington,

SFS [Luning], Macarthur, Bear, Ely, Ann Mason, and Copper Canyon) are defined in the same way as deposits in the

porphyry copper descriptive model (Cox, 1986) and the

grade and tonnage model (Singer, Mosier, and Cox, 1986).

The tract permissive for all pluton related deposits, including porphyry copper, is defined as an area extending 10 km

outward from the outcrop of a pluton, or, in cases where the

pluton has a geophysical expression, from the subsurface

boundary of the pluton inferred from its geophysical expression (Cox and others, 1996). The permissive tract occupies

about 117,300 km2, which is about 41 percent of the area of

the State. The exposed permissive rocks in Nevada cover an

area of about 32,800 km2, which is well explored. This terrane hosts five of the seven known porphyry copper

deposits. About 72 percent of the permissive tract (84,500

km2) is covered by 1 km or less of upper Tertiary and QuaMINERAL DEPOSIT DENSITY—AN UPDATE A7
ternary rocks and sedimentary deposits. Areas covered by

more than 1 km are excluded from consideration. Two of the

known porphyry copper deposits (Bear and Ann Mason) are

completely covered by younger materials and thus cannot

be considered to belong to the population of deposits that

are well explored and exposed.

If we assume that there are no additional porphyry

copper deposits to be discovered in the exposed plutons in

Nevada, then 5 deposits/32,800 km2 (exposed permissive

area) equals 0.00015 porphyry copper deposit/km2. We can

use this density of deposits to estimate the expected number of undiscovered porphyry copper deposits in Nevada.

Thus, 0.00015 porphyry copper deposit/km2 times 84,500

km2 of covered permissive area equals an expected 12.9

concealed deposits; subtracting the 2 discovered deposits

leaves 11 undiscovered concealed deposits that are defined

in the same way as the deposits in the porphyry copper

grade and tonnage model. For comparison purposes, the

subjective estimate of the number of undiscovered porphyry copper deposits in Nevada by Cox and others (1996)

is 8.7 deposits.

Arizona.—In Arizona, there are 36 known porphyry

copper deposits like those in the descriptive and grade and

tonnage models. The permissive area is the part of southeastern Arizona that may have igneous rocks that formed in

the Laramide orogeny. In the permissive area, exposed

rocks are very well explored: it is unlikely that undiscovered porphyry copper deposits are exposed. Deposits with

mineralized systems greater than 50 percent covered are

counted in the covered population. Thus, 12 of the 36

deposits are counted as part of the covered population, and

the remaining 24 deposits are from the exposed population.

If we assume that there are no additional porphyry copper

deposits in exposed rocks of the permissive area, then 24

deposits/34,000 km2 equals a mineral deposit density of

0.00071 porphyry copper deposit/km2.

A particularly favorable part of the permissive area is

defined in the southeastern corner of Arizona. This area,

called the Pinal-Paleozoic Terrane of Titley and Anthony

(1989), consists of 59,700 km2 of covered rocks and

16,700 km2 of exposed rocks. This favorable part hosts 32

known porphyry copper deposits, is characterized by Basin

and Range Province and Central Mountains landforms,

and contains most Paleozoic outcrops in the southern part

of Arizona (Reynolds, 1988). In this favorable area, 12 of

the 32 deposits are in the covered population, and 20 are

from the exposed population. If we assume that there are

no more porphyry copper deposits to be discovered in

exposed rocks of the favorable part of the permissive area,

then 20 deposits/16,700 km2 equals 0.0012 porphyry copper deposit/km2. The estimate of 0.0012 deposit/km2 is

about 50 percent higher than the estimate for all of the

permissive area.

CLIMAX PORPHYRY

MOLYBDENUM DEPOSITS

Delineating the boundaries of tracts that contain intrusion-related mineral deposits can be difficult because some

types of deposits are emplaced in the upper parts of intrusive complexes or in overlying rocks. Climax-type porphyry molybdenum deposits are related to high-silica

granites (Ludington, 1986). These granites are thought to

have formed by partial melting of lower crustal rocks due

to the emplacement of mafic to intermediate-composition

magmas following cessation of subduction and related

calc-alkaline magmatism (White and others, 1981). Melting of Precambrian crust that had been subjected to repeated crustal heating is thought to be an important regional

control for the generation of high-silica granites associated with Climax-type molybdenum deposits. However, the

nature of the lower crust is not a suitable operational criterion for delineating ground that might contain undiscovered mineral deposits. An operational criteria used for

estimating mineral deposit density of Climax-type porphyry molybdenum deposits is the distribution of Tertiary

intrusive rocks and thickened continental crust, as indicated by Bouguer gravity anomalies (see figure 35 in White

and others, 1981).

Colorado.—The area of Tertiary intrusive rocks in the

central Colorado mineral belt is approximately 12,000

km2. There are four known Climax-type porphyry molybdenum deposits in the tract (Climax, Henderson, Mount

Edmonds, and Redwell Basin) that are consistent with the

grade and tonnage model (Singer, Theodore, and Mosier,

1986). Thus, the mineral deposit density is 0.00033

deposit/km2.

New Mexico.—Another area of Tertiary subductionrelated calc-alkaline intrusions and later high-silica granites occurs around the Questa molybdenum deposit in

northern New Mexico. The area of Tertiary intrusive rocks

is 3,200 km2. The area contains one Climax-type porphyry

molybdenum deposit. Thus, the mineral deposit density is

0.00031 deposit/km2.

WOLFRAMITE QUARTZ VEIN DEPOSITS

Wolframite (tungsten) quartz vein deposits, described

as W vein deposits by Cox and Bagby (1986), are numerous

in South China. Kang Yongfu and others (1990) reported

that in the Zhuguang Mountains (Chongyi Dayu-Shangyou

region), 185 deposits occur in an area of 7,800 km2 (0.02

deposit/km2) and, in the Pangushan region, 111 deposits

occur in an area of 11,000 km2 (0.01 deposit/km2). Yang and

Lu (1982) reported more than 20 deposits occurring within

an area of 300 km2 (0.067 deposit/km2) in the XihuashanPiotang district. In these cases, the deposits are probably not

consistent with the grade and tonnage model (Jones and

Menzie, 1986).

A8 CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH
By using figures 1 and 3 from Yang and Lu (1982), it is

possible to calculate the area above the Xihuashan-Piotang

granite ridge. The area is broken into two parts, one northeast of a northwest-trending inferred fault southwest of

Piotang and the other southwest of the fault. The northeast

area is 30 km2, and the area to the southwest is 110 km2. The

host rocks are metasediments. Although many of the

deposits may be too small to be consistent with the grade

and tonnage model (Jones and Menzie, 1986), the whole

area (140 km2) contains up to 10 known deposits:

Xihuashan, Dangping, Luokeng, Shenlongkou, Xialuogushan, Niuzishi, Muziyuan, Dalongshan, Piotang, and

Zongshukeng. At least 4 of the deposits (Xihuashan, Dangping, Muziyuan, and Piotang) are believed to fit existing

grade and tonnage models (Jones and Menzie, 1986); 2

more (Dalongshan and Zongshukeng) are thought likely to

fit the models; and all 10 deposits might fit the models.

These numbers of deposits would yield estimated deposit

densities of 0.03, 0.04, and 0.08 deposit/km2, respectively;

the middle estimate seems most robust and is provided in

table 1. The area can be considered well explored.

A COMPLEXITY

In an assessment of Alaska (MacKevett and others,

1978), some of the estimates for the number of undiscovered podiform chromite deposits (Albers, 1986) were based

on a regression of the area of ultramafic rock on the number

of known podiform chromite deposits (Singer and Page,

1986) in well-explored California and Oregon. The same

regression was used to estimate the number of chromite

deposits in Costa Rica (Singer and others, 1987) and in

wilderness areas of the U.S. Pacific mountain system (Drew

and others, 1986).

Singer (1994) presented the regression of the area of

ultramafic rock on the number of known podiform chromite

deposits referred to above and compared this form of estimation with deposit density estimates derived from the

same areas. Podiform chromite deposits occur in the ultramafic parts of ophiolite assemblages. Although lithologic

variations of ultramafic rocks are useful in estimating the

number of deposits (N.J Page, USGS, oral commun., 1983),

most geologic maps simply report undifferentiated ultramafic rocks; this study is therefore restricted to undifferentiated ultramafic rocks. The area of ultramafic rock in each

county of California was estimated by point counting using

an effective grid spacing of 1 mile (1.6 km) on 1:250,000-

scale maps (Singer, 1971). In southwestern Oregon, Page

and Johnson (1977) estimated the areal extent of ultramafic

rock for 12 subareas based on geologic boundaries. The

areas of 12 ultramafic masses in Oregon, the areas of ultramafic rock in each of the 27 counties of California that contain podiform chromite deposits, and their associated number of deposits represent the samples in this analysis.

It is important to note that the chromite deposits reported reflect very thorough exploration of the surface, but

deposits not exposed were rarely discovered. Thus, the statistics presented here apply to the surface only and are not

reliable for three-dimensional estimates (see Menzie and

Singer, 1980). A second point of consideration is the use of

county data for California and subareas for Oregon, which

leads to a grouping of individual ultramafic bodies that has

the effect of an undetermined, but probably small, reduction

in the variability of estimates. A common way to estimate the

deposit density of occurrence is to average the number of

deposits per permissive area over a number of permissive

areas. Calculated with these data, the base rate of occurrence,

averaged over the 39 sample areas, is 0.2248 podiform

chromite deposit per square kilometer of ultramafic rock.

This estimate is of questionable value, however, because the

frequency distribution of the untransformed variable

(deposits/area) is significantly skewed and peaked (fig. 2).

Thus, a few high values have a very large influence on the

estimate, and probabilistic estimates of the number of undiscovered deposits are very difficult to calculate.

A reasonable way to make probabilistic estimates in this

situation would be to use the mean and standard deviation of

the transformed data and the normal distribution. The frequency distributions of the logarithms of the area of ultramafic rock,

the number of podiform chromite deposits, and the number of

podiform deposits per square kilometer of ultramafic rock are

not significantly different from normal distributions. It is more

appropriate to model the distribution of the number of deposits

with a discrete distribution such as the negative binomial

(Agterberg, 1977). As pointed out by Agterberg (1984), the

continuous lognormal distribution is equivalent to the discrete

negative binomial distribution, but use of the lognormal distribution can lead to discrepancies for small frequencies.

MINERAL DEPOSIT DENSITY—AN UPDATE A9

0

5

10

15

20

25

0 .2 .4 .6 .8 1 1.2 1.4 1.6 1.8 2

N

U

MBER OF C

O

U

N

TIE

S A

N

D AREA

S

NUMBER OF DEPOSITS PER SQUARE KILOMETER

Figure 2. The number of podiform chromite deposits per square

kilometer of ultramafic rock in 27 California counties and in 12

Oregon areas (from Singer, 1994).
Based on the lognormal distribution and the values, in

90 percent of the cases, the base rate would be 0.0238

deposit or more per square kilometer, in 50 percent of the

cases, it would be 0.1152 deposit or more per square kilometer, and in 10 percent of the cases, it would be 0.5581

deposit or more per square kilometer. The median estimate

of 0.1152 deposit/km2 is almost exactly the same as an estimate made by dividing the total number of deposits (805) by

the total area of ultramafic rock (6,982 km2); that is, 0.1153

deposit/km2. This result suggests that the usual method of

calculating the base rate of occurrence with untransformed

data probably yields reliable estimates of the median density when the permissive area is quite large. However, unless

many areas are used, there is no way to estimate variability

and, consequently, no way to make probabilistic estimates

of the number of deposits without some other information.

A further improvement in the estimates can be made by

examining the relation between the area of ultramafic rocks

and the number of podiform chromite deposits.

A plot of the area of ultramafic rock versus the number

of podiform chromite deposits in 27 California counties

shows a clear positive relation in figure 3. The linear regression line and the 80-percent-confidence limits to the regression estimates are also provided in figure 3. Estimates of the

number of podiform chromite deposits can be made from

figure 3 by using the logarithm of ultramafic rock area on

the x axis projected to the lower confidence limit for the 90-

percent estimate of the number of deposits, to the regression

line for the 50-percent estimate, and to the upper confidence

limit for the 10-percent estimate.

Although the correlation coefficient is not particularly

high (r=0.49), it and the associated regression slope are significantly different from zero at the 1-percent level. The

slope of the regression line (b=0.5768) is also significantly

different from 1.0. A slope of 1.0 would mean that a doubling of permissive area would result in a doubling of the

estimated number of deposits; that is, the ratio of the number of deposits to the size of the permissive area would be

independent of the size of the permissive area. Thus, if the

slope equaled 1.0, then the ratio of the number of deposits

to the size of the permissive area would provide an unbiased

estimate for any sized area. The fact that the slope is significantly lower than 1.0 means that the ratio of the number of

deposits to the size of the permissive area is a biased estimator in many cases. This conclusion is reinforced by the

observation that the correlation between deposits per area

of ultramafic rock and area of ultramafic rock (r=–0.38) is

significant at the 5-percent level; that is, the base rate of

occurrence decreases as the size of the permissive area

increases. 

The observed frequencies of the area of ultramafic

rock, the number of podiform chromite deposits in ultramafic areas or groups of areas (counties), and the rate of

occurrence of podiform chromite deposits (deposits per

permissive area) are all represented better by lognormal

distributions than by normal distributions. Because the frequency distribution of each variable is highly skewed, use

of the mean of the untransformed data is of questionable

value. The normal distribution with the mean and standard

deviation of the log-transformed rate of occurrence is recA10 CONTRIBUTIONS TO GLOBAL MINERAL RESOURCE ASSESSMENT RESEARCH

y = – 0.1038 + 0.5768 x r = 0.49

N

U

MBER OF DEPOSITS

 Log10 AREA OF ULTRAMAFIC ROCK IN SQUARE KILOMETERS

AREA OF ULTRAMAFIC ROCK IN SQUARE KILOMETERS 

N

U

MBER OF DEPOSITS

80% confidence limit

1

2

0

3

200 500 1300 3200

0.5 1.5 2.5 3.5

1

10

100

1000

4

40

400

Log10

0.7 0.9 1.1 1.3 1.7 2.7 1.9 2.9 2.1 2.3 3.1 3.3

5 13 32 79

Figure 3. Number of podiform chromite deposits in 27 California counties versus area of

ultramafic rock with regression line and 80-percent confidence limits for individual points

(from Singer, 1994). 
ommended over the simple rate of occurrence for probabilistic estimates. Because of the significant correlation

between the number of deposits and the area of ultramafic

rock, even this improvement is useful only for ultramafic

bodies that are near the median area of 93 km2. The fact

that the base rate of occurrence for podiform chromite

deposits is dependent on the size of the permissive area

suggests that more research is needed to see if this relation

exists for other mineral deposit types. Unbiased estimates

of the number of podiform chromite deposits can be made

by using the regression and 80-percent confidence limits

represented in figure 3.

SCALE ISSUES

When we take samples that represent small areas, such

as the two well-explored kuroko massive sulfide districts

discussed in this paper (Snow Lake district, Canada, and

Hokuroku district, Japan), we expect that there will be large

differences in deposit density from sample to sample based

on sampling theory. If we had a number of well-explored

regions that each represented a large area, we would expect

much lower variability in the estimates of deposit density.

Thus, even in situations where we do not have the complexity observed for podiform chromite deposits, the scale

of the observations affects the variability of mineral deposit

densities. For example, if samples representing larger areas

had been used to make the histogram of deposit densities in

figure 1, we would expect that there would be fewer observations at the higher and lower densities because there

would be less variability of the estimates.

The relation of sample size affecting deposit densities

was recognized by Agterberg (1977) in his studies of the

volcanogenic massive sulfide deposits of the Abitibi region

of Canada and was extensively discussed by Bliss and

Menzie (1993) in terms of the distributions and spatial correlations of several deposit types. These studies of frequency distributions and spatial correlations are typically concerned with variability within mineral deposit districts,

whereas the present study is concerned with variability

among districts or other larger areas.

Consideration of the effects of scale on the variability

of deposit densities is meaningful only where the samples

are a random selection of all possible (that is, permissive)

areas. The two well-explored kuroko massive sulfide districts discussed here are not random selections, but purposeful selections of some of the best-endowed districts in

the world. The same could be said of the estimates of the

density of porphyry copper deposits in Arizona, of Climax

porphyry molybdenum deposits in Colorado, and of wolframite veins from Xihuashan, China. The proper use of

each of these estimates is as a guide to what might be considered a very good density of deposits. If a kuroko massive

sulfide deposit density estimate made for some region is as

high as those in table 1, then an exceptionally good district

is being predicted; commonly, this prediction would

require some explanation. Thus, these specially selected

areas provide standards to identify what might be unreasonably high estimates of the number of undiscovered

deposits in most situations.

CONCLUSIONS

A key function of many forms of quantitative mineral

resource assessments is the estimation of the number of

undiscovered deposits. Numerous techniques can be used

directly or as guidelines to make these estimates. Most

robust of these methods is a form of mineral deposit model

wherein for a deposit type, the numbers of deposits per unit

area from well-explored regions are counted and the resulting frequency distribution is used either directly for an estimate or indirectly as a guideline in some other method.

Ratios of the number of deposits per unit area can be used

in histograms to show variation of deposit densities by

type. In three-part quantitative resource assessments, prevention of bias requires that deposits of each type be

defined the same way as in delineation of permissive tracts

and as in construction of grade and tonnage models; these

same definitions and rules must also be applied to deposit

density models.

The 27 mineral deposit density estimates reported here

representing 13 different deposit types should be considered only a start at compiling the estimates necessary to

guide assessments. In addition, many of the specially

selected areas reported here provide standards to identify

what should be high estimates of the number of undiscovered deposits in most situations. Many of the issues that

should be addressed in developing mineral deposit density

estimates are identified. Not only should care be used in

defining mineral deposits and their permissive areas, but

skewed distributions of densities and possible correlations

between densities and areas should be considered.

REFERENCES CITED

Agterberg, F.P., 1977, Frequency distributions and spatial variability of geological variables, in Ramani, R.V., ed., Application

of computer methods in the mineral industry: New York,

American Institute of Mining, Metallurgical and Petroleum

Engineers, Society of Mining Engineers, p. 287–298.

Agterberg, F.P., 1984, Discrete probability distributions for mineral deposits in cells: International Geological Congress, 27th,

Proceedings, v. 20, p. 205–225. (Published by VNU Science

Press, Utrecht, Netherlands.)

Albers, J.P., 1986, Descriptive model of podiform chromite, in

Cox, D.P., and Singer, D.A., eds., Mineral deposit models:

U.S. Geological Survey Bulletin 1693, p. 34.

Allais, M., 1957, Method of appraising economic prospects of

mining exploration over large territories—Algerian Sahara

case study: Management Science, v. 3, p. 285–345.

MINERAL DEPOSIT DENSITY—AN UPDATE A11
Berger, B.R., 1986, Descriptive model of low-sulfide Au-quartz

veins, in Cox, D.P., and Singer, D.A., eds., Mineral deposit

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MINERAL DEPOSIT DENSITY—AN UPDATE A13