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A quantitative analysis of some vein-type mineral deposits in southern British Columbia Goldsmith, Locke B. 1984

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A QUANTITATIVE ANALYSIS OF SOME VEIN-TYPE MINERAL DEPOSITS IN SOUTHERN BRITISH COLUMBIA by LOCKE B. GOLDSMITH B.Sc. (Honours), Michigan Technological University A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of Geological Sciences We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1984 © Locke B. Goldsmith, 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department o r by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Geology  The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date May 9, 1984 DE-6 (2/79} ii ABSTRACT Production and location data for polymetallic vein deposits in four mining camps in southern British Columbia (Ainsworth, Slocan, Slocan City and Trout Lake camps) illustrate the potential of such data for comparing mining camps in a rigorous manner and as a basis for developing quantitative exploration models. Spatial densities of mineral deposit occurrences serve both to define clusters of deposits and to demarcate mining camps. This latter application results in a reproducible, rigorous approach to comparing metal endowment of several mining camps. Detailed analysis of production and location data for the Trout Lake camp demonstrate the importance of size and grade in developing a quantitative exploration model for the camp. Production tonnages define two different size populations of deposits. Average silver grades of veins indicate four separate groupings that correspond clearly with specific geological characteristics of the groups. A correlation and regression study demonstrates the importance of the procedure in evaluating size potential of deposits and, in particular, illustrates the importance of gold grades in determining size potential of prospects in the camp. A review of multiple regression applied to quantitative modelling of deposit size potential in five vein camps in southern British Columbia shows the method to have practical application in vein deposit evaluation during progressive exploration of a deposit. ^ iii TABLE OF CONTENTS CHAPTER 1 - Introduction 1 Acknowledgments 2 CHAPTER 2 - Spatial Density of Silver-Lead-Zinc-Gold Vein Deposits in Four Mining Camps in Southeastern British Columbia 4 Abstract 4 Introduction 4 Methodology , 8 Measurement of Spatial Density Variability 8 Examples of Spatial Density Maps 11 Outlining Mining Camps 11 Systematic Variations in Spatial Densities 15 Ainsworth Camp 16 Slocan City Camp 18 Slocan Camp 19 Trout Lake Camp 19 Discussion 22 Conclusions 24 Acknowledgments 24 References 25 CHAPTER 3 - An Evaluation of Average Grades and Production Tonnages, Trout Lake Mining Area, Southern British Columbia 26 Abstract 26 Introduction 27 Data Evaluation Procedure 29 Spatial Density 30 Probability Plot of Ore Production Tonnage 39 Probility Plots of Metal Grades 42 Metal Content vs Production Tonnage 43 Triangular Graphs 46 Simple Correlation of Metal Grades and P r o d u c t i o n Tonnage 49 iv Table of Contents (continued) Multiple Regression Applied to Forecasting Deposit Size 52 Deposits Without Recorded Production 54 Conclusions 55 Acknowledgments 57 References 57 CHAPTER 4 - Multiple Regression, A Useful Quantitative Approach in Evaluating Production Data from Vein-Type Mining Camps, Southern B .C 60 Abstract 60 Introduction 61 Procedure . 63 Slocan (Sandon). Camp 64 Ainsworth Camp 67 Slocan City Camp 69 Trout Lake Camp 71 Zeballos Camp 72 Discussion 73 Conclusions 75 Acknowledgments 75 References 76 CHAPTER 5 - CONCLUSIONS 78 APPENDIX - Triangular Graphs as an Aid to Metallogenic Studies of Polymetallic Vein Deposits 81 V LIST OF TABLES Table 2-1 Area Measurement Statistics, Ainsworth Mining Camp 7 2-II Area Measurement Statistics, Slocan Mining Camp 7 2-III Area Measurement Statistics, Slocan City Mining Camp 10 2- IV Average Spatial Densities for Some Southern British Columbia Mining Camps 15 3- 1 Stratigraphic Column, Trout Lake Mining Camp 28 3-II Ore-Tonnage Producer Data, Trout Lake Camp (to 1976) 31 3-III Metal Endowment/km2, Ainsworth, Slocan, Slocan City, and Trout Lake Mining Camps 35 3- IV Correlation Matrix for Logarithmic Values of Production Data from 43 Producers, Trout Lake Mining Camp 50 4- 1 Slocan (Sandon) Regression Models ................... — 65 4-II Ainsworth Regression Models .................................... 68 4-1II Slocan City Regression Models ................................. 70 vi LIST OF FIGURES Figure 2-1 Generalized locations of Ainsworth, Slocan City, Slocan, and Trout Lake mining camps, south-eastern British Columbia 6 2-2 Machine-contoured spatial density contours for vein deposits (number of veins per 4 square kilometres) in and near the northern end of the Nelson batholith 13 2-3 Machine-contoured spatial density contours for vein deposits (number of veins per 1 square kilometre) in and near the northern end of the Nelson batholith 1 4 2-4 Hand-contoured spatial density map, Ainsworth camp 17 2-5 Redraughted machine-contoured map of spatial densities of mineral occurrences in Slocan mining camp based on 1 square kilometre counting cell with 50 percent overlap of adjacent cells 20 2- 6 Manually produced spatial density contours (number of occurrences per 2 by 2-kilometre cell) for vein deposits in the Trout Lake area. 21 3- 1 Location of high and low tonnage silver producers in the Trout Lake camp, with grades of silver and strike of deposits. Inset is a probability graph of mean silver grades in ounces/short ton 37 3-2 Location of high and low tonnage gold producers in the Trout Lake camp, with grades of gold and elevation in metres. Inset is a probability graph of mean gold grades in ounces/short ton 38 3-3 Probability graphs, Trout Lake camp. Number of deposits (ND) = number of deposits cumulated from largest to smallest. Cumulative tonnage (CT) = tonnage cumulated from largest to smallest 40 3-4 Probability graphs for mean Pb grades and mean Zn grades for past producing veins, Trout Lake mining camp 44 vii List of Figures (continued) Figure 3-5 Metal content versus production tonnage, Trout Lake camp. Diagonal line accentuates two groups of deposits with distinct grades of silver. 45 3-6 Triangular graphs, Trout Lake camp .................... 47 3-7 Correlation diagram showing tons to be most strongly, but inversely, related to precious metals, Trout Lake camp 51 4-1 Observed versus calculated tonnages using a multiple regression equation, Slocan camp 66 1 CHAPTER 1 INTRODUCTION Studies of mining camps characterized by vein deposits have provided a wealth of empirical data regarding mineral associations and spatial disposition of both ore and gangue minerals. Such information has provided important constraints in the development of mineral zonation models (Hosking, 1951), our understanding of physical-chemical conditions of mineral deposit formation, the implications of textures and mineral associations with respect to paragenesis (Stanton, 1972), and numerous other aspects of ore genesis. Many of these studies depend on the recognition of individual minerals or mineral assemblages, as is commonly the case in the documentation of systematic patterns (zoning) to the distributions of ore and/or gangue minerals. One type of data that appears to have found only limited use in the past is the quantitative production data that exist for many mining camps. In places, these data are only fragmentary and therefore perhaps far from representative. However, elsewhere such as in British Columbia, high quality production records have been maintained almost since the inception of mining in the late Nineteenth Century, with the result that a substantial partial chemical record is available for hundreds of individual mineral deposits, in some cases from quite restricted areas. The potential of these data in providing a quantitative basis both for metal-logenic studies and as a guide to mineral exploration has been investigated to a limited extent by Orr and Sinclair (1971), Sinclair (1974, 1979), and Goldsmith and Sinclair (1983) . These studies indicated clearly that sub-stantial benefit in developing guidelines for mineral exploration exists in 2 a rigorous evaluation of deposit location data and average deposit grades based on ore produced. This present study is designed to develop further some of the suggestions made by Sinclair (ibid.) and Orr and Sinclair (1971) regarding the evaluation of quantitative data for vein mining camps in southern British Columbia. The data base consists of two computer files, one developed by Orr and Sinclair (1971) for about 340 vein deposits in the Slocan, Slocan City and Ainsworth Mining Camps and the other developed by Read (1976) and extensively edited by the writer, for about 200 mineral occurrences in the Trout Lake Mining Camp (Figure 1). The study has three specific aspects as follows: (1) a systematic evaluation of the use of spatial densities of veins as a means of delimiting vein camps and providing a basis for comparing various camps. (2) a comprehensive study of quantitative data for the Trout Lake camp as a means of developing a rigorous approach to metallogeny and exploration in the camp. (3) a general evaluation of multiple regression as a basis for estimating vein potential using average grade information for a number of vein camps in southern British Columbia. ACKNOWLEDGMENTS This research was initiated with funding from the Geological Survey of Canada and completed with financial assistance from the British Columbia Minis-try of Energy, Mines and Petroleum Resources, and a British Columbia Science Council grant to A.J. Sinclair, who as Supervisor provided assistance and direction for the study. 3 The early contribution of the Trout Lake data file was made by P.B. Read. A posthumous acknowledgment is made to J.F.W. Orr for his prodigious effort in developing one of the early mineral deposit data files that was used as a basis for rigorous evaluation and development of exploration models. Technical assistance of A. Bentzen in obtaining computer output, N. Stacey for much of the drafting, and L. Lightheart for typing and proofing of the manuscript, is appreciated. 4 CHAPTER 2 SPATIAL DENSITY OF SILVER-LEAD-ZINC-GOLD VEIN DEPOSITS IN FOUR MINING CAMPS IN SOUTHEASTERN BRITISH COLUMBIA ABSTRACT Clusters of vein deposits are examined in two dimensions both by evalua-tion of patterns of spatial density within a mining camp and by comparison between camps of gross spatial density outlines. Selection of the counting cell size is critical to camp area estimates. In some cases the largevaluable deposits occur within high-density contours. Exploration may be aided by noting the location of a deposit with respect to the surrounding density of occurrences and the corresponding metal endowment per square unit of area. INTRODUCTION Spatial density appears to have several practical applications important in resource assessment, viz.: (1) defining limits to mining camps, (2) providing a systematic basis for comparing mining camps in terms of average deposit density or average metal concentration, and (3) recognition of systematic variations in spatial density of mineral occur-rences within individual mining camps. The potential uses of spatial density applied to clusters of vein deposits are examined herein. Sinclair (1979) suggested that contoured spatial density maps of location data (centroids) of mineral deposits might provide a consistent if empirical means of defining boundaries to certain types of mining camps or mineralized 5 centres. In particular, he recommended that a moving average method be used as a basis for contouring "number of veins per square kilometre" and that the 0.5 density contour be used to define the empirical limits to the Ainsworth vein camp in southeastern British Columbia. The method appears applicable to two-dimensional problems and, of course, suffers the limitation that the 0.5 spatial density contour does not exist as a real entity. Exact locations of some depos-its are not always readily attainable from available literature but this problem is restricted largely to small deposits actively explored and/or exploited during the nineteenth century. Uncertain locations in general do not appear to repre-sent problems in contouring spatial density because the uncertainty is generally small relative to the scale of a mining camp. This study extends the early work by Sinclair (1979) to include four vein camps, Ainsworth, Slocan, Slocan City, and Trout Lake (Lardeau), in south-eastern British Columbia (Fig. 2-1) in an attempt to generalize the approach in relation to vein camps. The data base for three of the mining camps is an updated version of a computer-based producer file established by Orr and Sinclair (1971). Data for the Lardeau (Trout Lake) camp are an edited version of a file established originally by P.B. Read (Read, 1976; Goldsmith, this study, Chapter 3). The former file (Slocan, Slocan City, and Ainsworth) contains information only for deposits with a recorded production of at least one short ton or ore. The original file for Trout Lake camp contains locations of all publicly recorded deposits irrespective of whether or not they have produced ore. 6 Figure 2-1. Generalized locations of Ainsworth, Slocan City, Slocan:, and Trout Lake mining camps, southeastern British Columbia. (Z, Zeballos.) TABLE 2-1 AREA MEASUREMENT STATISTICS, AINSWORTH MINING CAMP 25Z OVERLAP 0.5 DEPOSIT/CELL 1.0 DEPOSIT/CELL Window e < — Number of Mi l e s 2 Av Av Number of Mi l e s 2 Av Av Deposits (4 measurements) Miles 2 km2 Deposits (4 measur ements) Miles 2 km2 4 ton x 4km 81 77.70 78.00 77 86 201.67 81 63.66 63.84 63.83 165 31 77.88 77.88 63.96 63.84 2km x 2km 80 63.54 36.36 36 35 94 13 80 28.26 27.96 28.08 72 73 36.18 36.30 28.08 28.02 1km x 1km 72 13.68 13.00 13 74 35 58 71 10.80 10.80 10.80 27 97 13.68 13.80 10.80 10.80 50X OVERLAP 0.5 DEPOSIT/CELL 1.0 DEPOSIT/CELL 4km x 4km 81 68.10 68.28 68 15 176 50 81 56.22 56.22 56.18 145 49 67.98 68.22 56.28 55.98 2km x 2km 75 30.36 30.24 30.30 78 48 75 23.28 23.22 23.24 60 18 30.24 30.36 23.40 23.04 1km x 1km 72 13.20 13.26 13 19 34 15 71 10.68 10.74 10.76 27 86 13.14 13.14 10.62 10.98 75Z OVERLAP 0.5 DEPOSIT/CELL 1.0 DEPOSIT/CELL 4km x 4km 81 82.20 81.78 81 95 212 24 80 66.60 67.32 67.1C 173 78 81.84 81.96 67.26 67.20 2km x 2km 74 24.60 24.54 24 59 63 68 72 19.56 .19.08 19.31 50 00 24.60 24.60 19.56 19.08 1km x 1km 71 11.70 11.76 11 75 30 42 71 . 9.48 9.42 9.44 24 44 1.1.70 11.82 9.43 9.36 TABLE 2-II AREA MEASUREMENT STATISTICS, SLOCAN MINING CAMP 25% OVERLAP 0.S DEPOSIT/CELL 1.0 DEPOSIT/CELL Sis e Number of Miles 2 Av Av Number of Miles 2 Av Av Deposits (4 measurements) Miles 2 km2 Deposits (4 measurements) Miles 2 km2 4km x 4 km 176 160.50 160.98 160 S3 415 77 176 140.46 140.04 140 36 363 51 160.32 160.32 140.40 140.52 2km X 2km 176 108.00 107.46 107. 67 278 86 169 73.14 73.20 73 11 189 35 107.64 107.58 73.08 73.02 1km X 1km 121 28.65 28.47 28 58 74 02 116 20.37 . 20.43 20 40 ' 52 84 28. S3 28.6S 20.37 20.43 50% OVERLAP O.S DEPOSIT/CELL 1.0 DEPOSIT/CELL 4km X 4 km 176 1S7.08 156.78 156 59 40S 56 175 137.40 137.76 137 75 356.76 156.24 156.24 137.40 138.42 2km X 2 km 176 102.12 102.36 102 03 264 26 172 72.18 72.06 72 11 186 75 102.18 101.46 72.12 72.06 1km X 1km 124 30.60 30.42 30 51 79.02 121 19.50 19.50 19 46 SO 39 30.60 30.42 19.50 19.32 75% OVERLAP 0.5 DEPOSIT/CELL 1.0 DEPOSIT/CELL 4km X 4 km 176 158.10 158.16 158 02 409 23 175 139.26 138.54 138 75 359.36 1S7.74 1S8.10 139.02 138.18 2 km X 2km 171 90.42 90.00 90 00 233 1 165 54.78 54.66 54 74 141 76 89.94 89.64 54.66 54.89 1km X 1km 101 20.10 20.10 20 19 52 79 99 15.18 15.48 IS 33 39 77 20.10 20.46 15.18 15.48 8 METHODOLOGY Consider the problem of depicting spatial density of mineral occurrences to be two-dimensional. An interpolation technique is required to provide spatial density estimates on a regular grid superimposed upon a district con-taining numerous irregularly located occurrences and/or deposits. The spatial density values for each cell of the grid then can be contoured by simple linear interpolation, either by hand or machine. One procedure used here is to move a (square) window over the field of interest in a regular, periodic fashion, count the number of deposits in the window at each position, and assign each count to the centre of the square for which the count was obtained. Three parameters can be varied in this procedure: (1) the window shape, (2) the window area, and (3) the proportion of overlap (if any) of adjoining counting cells. The level of variability in spatial density data that results from these sources must be quantified if spatial density is to be used in a meaningful fashion. MEASUREMENT OF SPATIAL DENSITY VARIABILITY Several sources of variability are evaluated in obtaining spatial density estimates for vein mining camps. In particular the following effects are examine d: (1) varying size of counting window, that is, 1 by 1 kilometre, 2 by 2 kilo-metres, and 4 by 4 kilometres, (2) defining camp area by two different spatial density contours, that is, 0.5 deposit per cell and 1.0 deposit per cell, and (3) testing actual reproducibility of camp area estimates by planimeter. 9 Data from tests for three mining camps are summarized in Tables 2-1, 2-II and 2—III from which several conclusions seem evident. The most obvious feature of the tabulated data is that planimetric measurements in camp areas vary much less than 1 per cent of the area; these errors are negligible. Estimated camp areas increase dramatically as the size of the counting cell increases, regardless of extent of overlap. This results largely from an ever-increasing zone of no deposits that is included within the camp boundaries as the cell size increases. This effect can be minimized by using a 1.0 rather than a 0.5 deposit-per-cell contour. Nevertheless, window size is a large source of variability in mining camp areas by the method outlined. To counter-act this problem a mining camp is defined somewhat subjectively on the basis of the smallest window size that results in a high proportion (more than 90 per cent) of known occurrences being contained within a reference contour (for example, 0.5 deposit per cell). Extent of overlap of adjoining counting windows does not appear to be an important source of variability for smallest cell sizes that produce a cohesive rather than a disaggregated camp outline. For example, for Slocan camp the 2 by 2 km 2 window produces areas of 121, 117, and 111 square kilometres for overlaps of 25, 50, and 75 per cent respectively. Subjective evaluation of these data and the many maps which were viewed (one for each line of information in each table) has led to the conclusion that areas of mining camps can be defined usefully and reproducibly, if empirically and subjectively, as follows: (1) use a 0.5 deposit per cell as the margin contour to define the outer extremity of a mining camp, (2) use 50 per cent overlap of square counting cells, and 10 TABLE 2-III AREA MEASUREMENT STATISTICS, SLOCAN CITY MINING CAMP 25\ OVERLAP O.S DEPOSIT/CELL 1.0 DEPOSIT/CELL Size Number of Miles 2 Av Av Number of Miles 2 Av Av Deposits (4 measurements) Miles 2 km2 Deposits (4 measurements) Mile s 2 km2 4km x 4 km 60 111.90 111.30 111.60 289. 04 58 82.20 81.95 82.165 212.81 111.30 111.90 82.32 82.20 2km x 2 km 57 46.62 46.68 45.68 120. 90 55 39.00 39.18 39. 05 101.13 46.74 46.68 39.00 39.00 1km x 1km 57 19.50 19.56 19.55 50. 62 37 6.84 6.84 6. 84 17.72 19.50 19.62 6.84 6.84 S0% OVERLAP 0.5 DEPOSIT/CELL 1.0 DEPOSIT/CELL 4 km x 4km 59 89.52 89.52 89.48 231. 74 59 77.94 77.70 77. 78 201.44 88.45 89.40 77.88 77.58 2km x 2 km 57 44.44 45.18 45.07 116. 74 55 37.56 37.20 37. 43 96.93 45.06 45.12 37.50 37.44 1km x 1km 57 20.34 20.16 20.28 52. S3 50 10.17 10.18 10. 17 27.38 20.16 20.46 10.17 10.16 7S% OVERLAP O.S DEPOSIT/CELL 1.0 DEPOSIT/CELL 4km x 4km 59 61.74 62.10 62.07 160.76 57 50.94 51.00 SI. 02 132.13 62.10 62.34 51.18 50.94 2km x 2km 57 42.78 43.00 42.87 111.02 55 35.50 34.32 34. 43 89.16 42.90 42.78 34.38 34.50 1km x 1km S7 17.16 17.40 17.28 44. 75 43 7.26 7.26 7. 26 18.90 17.16 17.40 7.26 7.26 11 (3) cell size must be selected by trial and error to be that smallest size which retains the large majority of deposits of a subjectively recognized mining camp within the marginal contour. EXAMPLES OF SPATIAL DENSITY MAPS Two extreme cases of the application of spatial density procedures applied to mineral deposit location data are: to define boundaries of clusters of vein deposits, and to examine patterns of spatial density contours of mineral deposits within a mining camp. OUTLINING MINING CAMPS In a large region containing several mining camps one might wish to develop a reproducible procedure which can define boundaries to mining camps and determine an estimate of their individual geographic limits. Such informa-tion would be useful for purposes of quantifying the distribution of mineral occurrences in a camp in terms of average spatial density. Similarly the amount of various metals concentrated into veins per unit area in a mining camp could be examined and displayed. The foregoing objectives require that the total number of deposits in a camp and the geographic limits of the camp be known. Of course a newly found deposit in an old camp or one outside the existing camp limits will bias the parameter we are estimating. As long as these sources of errors are recognized they need not represent serious problems, and, in fact, are likely minimal in many old, thoroughly explored camps. 12 Figure 2-2 is a moving average spatial density contour map for an area including the northern end of the Nelson batholith. A window of 2 by 2 kilo-metres was used with 50 per cent overlap in the two principal grid directions. Note that in such a case a single deposit will occur in four cells whose centres are in a square with sides half the cell dimension. The 0.5 deposit per 4-square-kilometre contour around an isolated deposit is therefore the same size as the basic counting cell. In a few cases where deposit locations are exactly on the boundary of a counting cell, isolated deposits are surrounded by a rectangular contour with area less than the basic cell area. After some ex-perimentation the artificial contour 0.5 deposit per 4-square-kilometres was selected arbitrarily as setting the outer limit of vein concentrations defining mining camps in the area. Once an acceptable limit is defined for a mining camp we can calculate average spatial density and average known metal endowment. Our present study is concerned primarily with spatial density of mineral deposits, although the methodology can be extended easily to the presentation of metal endowment using known metal production. Average spatial densities are summarized in Table 2-IV for Slocan, Slocan City, and Ainsworth mining camps. It is impor-tant to realize that the figures quoted in Table 2-IV are derived only from those deposits lying within the 0.5 deposit per 4-square-kilometre contour. The data of Table 2-IV are based on the same counting criteria for the entire area. Such a procedure is probably desirable for reasons of practicabil-ity. However, different counting criteria may be optimal for different camps. Our experience has shown that counting cell size is particularly critical (see Tables 2-1, -II, -III) to camp area estimates. A subjective evaluation of the Ainsworth camp, a tightly clustered group of veins in a relatively small area, 540 530 520 510 Figure 2 - 2 . Machine contoured spatial density contours for vein deposits (number of veins per 4 square kilometres), in and near the northern end, of the Nelson batholith. High spatial densities centre on Ainsworth (A), Slocan (S), and Slocan City (SC) mining camps. Contours obtained for a square counting window with 50 percent overlap of adjacent cells. Individual vein deposits are shown as closed triangles. Marginal numbers are UTM co-ordinates in kilometres. 5 4 0 r 5 3 0 r 5 2 0 r510 4 7 0 4 8 0 4 9 0 5 0 0 510 S & -S - 0 % , R •J.-** 4 7 0 4 8 0 4 9 0 5 0 0 510 5 4 0 5 3 0 J 5 2 0 510 Figure 2-3. Machine contoured spatial density contours for vein deposits (number of veins per 1 square kilometre) in and near the northern end of the Nelson batholith. Clusters of high spatial densities centre on Ainsworth (A), Slocan (S), and Slocan City (SC) mining camps. Contours obtained for a square counting window with 50 percent overlap of adjacent cells. Individual vein deposits are shown as closed triangles. Marginal numbers are UTM co-ordinates in kilometres. 15 suggests that a 1 by 1-kilometre counting cell is more appropriate than the 2 by 2-kilometre counting cell used for Figure 2-2. Spatial contours using a 1 by 1-kilometre counting cell for the equivalent area of Figure 2-2 are shown on Figure 2-3. This latter plot also demonstrates how disaggregated a camp appears if too small a counting cell is used as in the case of Slocan and Slocan City camps. TABLE 2-IV AVERAGE SPATIAL DENSITIES FOR SOME SOUTHEASTERN BRITISH COLUMBIA MINING CAMPS (BASED ON 2 x 2 km COUNTING CELLS WITH 50 PER CENT OVERLAP) Camp Area No. of Deposits (km 2) Deposits per km 2 Ainsworth 78.5 75 1.0 Slocan 264.3 172 0.7 Slocan City 116.7 57 0.5 SYSTEMATIC VARIATIONS IN SPATIAL DENSITIES Spatial density maps of mining camps also are important as a means of exam-ining systematic patterns to deposit clustering within individual mining camps.. For such a purpose we are faced with the same problem as in defining camp boundaries, that to select an appropriate contouring approach for examining variations in spatial density in a camp is to use a square cell with sides approx-imately the inverse of the deposit densities of Table 2-IV. Thus, Ainsworth camp can be examined with a 1 by 1-kilometre counting window, Slocan City camp with a 2 by 2-kilometre counting window, and Slocan camp midway between the two. Four separate mining camps are described in detail. 16 AINSWORTH CAMP Spatial densities for Ainsworth camp (Sinclair, 1979) are shown on Figure 2-4. Here it is apparent that the camp is well defined as a cohesive unit with only a single nearby outlier, yet local concentrations are apparent within the camp. It is also apparent that a single contouring grid will serve both purposes, that is, define general camp limits and average spatial densities, as well as showing local structure to the spatial densities. Average spatial densi-ties calculated in this case for a square contouring grid cell of 1 by 1 kilometre provide an average density of 2.0 deposits per-square-kilometre. This compares with an average density of 1.0 deposits per-square-kilometre deter-mined in an earlier section, and provides an indication of the variability of mean spatial density estimates relative to size of contouring grid. As expected, the smaller the grid, the smaller the "camp area" and, if number of deposits remains constant, the higher will be the average spatial density. In this particular case it appears that choosing the smallest contouring cell that provides a cohesive camp outline is the optimal empirical approach. Such a procedure, although subjective, provides potential for reproducibility by different operators. It is interesting to speculate about the importance of the five highs shown in the detailed spatial density contours for Ainsworth camp. A plot of the five largest deposits in the camp shows that all are within the four southernmost spatial density highs. Even without further information one might speculate that the northernmost high, that consists only of small deposits, is an area that warrants investigation. The writer's interpretation for the camp is that "bedded" veins represent syngehetic deposition in Cambrian time and that some of these bodies were partly mobilized during and/or after emplacement of 0 0 Figure 2-4. Hand-contoured spatial density map, Ainsworth camp. Counting cell used is 1 by 1 kilometre with 50 percent overlap. Contours are number of past producers per 1 square kilometre. Modified.from Sinclair (1979). 18 the Nelson batholith to form numerous small "transverse" veins. This model is consistent with observed distribution patterns of small (mostly transverse) deposits, relative to large (mostly bedded) deposits. It provides some geologi-cal basis for conducting further exploration in the northern spatial density high. SLOCAN CITY CAMP Visual examination of the distribution of deposits in Slocan City camp shows that the distribution is asymmetric with a small area of relatively high density and a much larger area, mainly to the east, of much lower density (Fig. 2-2). A grid serving for one part may not serve for the other. However, a grid size controlled by the less dense area will serve, generally at least, for the denser areas. The contoured results of Figure 2-2 for Slocan City camp based on a 2 by 2-kilometre contouring grid cell cannot be improved significant-ly by the use of a smaller cell size (Fig. 2-3). High spatial densities form a horseshoe-shaped zone with low values both in the core and surrounding the "horseshoe". Considering the "structural" nature of the camp and known zonal patterns, the "horseshoe" probably reflects a fundamental attribute of the camp. For example, near-circular fracture patterns on this scale (approximate-ly 4 kilometres diameter) might be produced during emplacement of an underlying hypabyssal intrusion. If such is the case, the "opening" in the horseshoe may represent an area of exploration interest because a circular pattern could be expected. 19 SLOCAN CAMP In Slocan camp it is advantageous to examine spatial densities at two differ-ent scales of contouring grids. A large contouring grid cell defines a simple density high along a north-northwest direction and allows for clear definition of the camp. However, the camp contains a very large number of deposits and the possibility of determining some detailed structure to spatial densities exists. An example shown on Figure 2-5 is based on a counting window cell size of 1 by 1 kilometre and shows clearly separate groups or clusters of past produc-ers. As in other examples, a considerable subjectivity exists in attempting to interpret the spatial density patterns. TROUT LAKE CAMP Trout Lake camp represents somewhat different data than do the other three camps considered to this point. Only a small portion of the approximately 200 deposits reported in the camp have produced. Instead of contouring spatial densities of past producers, spatial densities of all recorded veins are contoured and compared to the positions of 43 known producers with the result-ing pattern. The results, based on a contouring grid cell of 2 by 2 kilometres, are shown on Figure 2-6. Clearly, several separate major clusters of deposits are evident. Within each of these clusters are well-defined highs. Plotted positions of producers lie within the high contours. As with the Ainsworth camp, an explanation is not obvious, particularly since here we do not appear to have the possibility of two separate genetic models. Furthermore, there is the possibility that intense exploration in the: immediate vicinity of a large deposit will give rise to more small discoveries. In other words, the: association of past producers with areas of high spatial densities is self-generating. 470 480 490 500 540 530 540 530 470 Figure 2-5. 480 490 500 Redraughted machine-contoured map of spatial densities of mineral occurrences in Slocan mining camp based on 1 square kilometre counting cell with 50 percent overlap of adjacent cells. Filled triangles are deposit locations; marginal figures are UTM co-ordinates in kilometres. Contour values are number of deposits per square kilometre. ND on the western part of the diagram is centred on New Denver. ure 2-6. Manually produced spatial density contours (number of occurrences per 2 by 2 kilometre cell) for vein deposits in the Trout Lake area. Contours obtained with square counting window and 50 percent cell overlap. Filled triangles are known vein occurrences in the camp. Numbers in circles refer to past producers for which geological and production information is tabulated by Read (1976). 22 This latter explanation may be true in part, but it does not appear to provide a total explanation in old camps that have been thoroughly explored over a period of 70 or 80 years. Spatial density contours clearly define three separate clusters of camps within the Trout Lake area. These separate clusters represent a quantification of previously recognized mineral belts. Because of the very narrow widths of the mineral belts relative to their lengths, it is not possible to see any structure in the spatial density contours apart from the association of past producers with spatial density highs. DISCUSSION Spatial densities of mineral deposits present problems relating to basic data and interpretation. One such problem is illustrated by the case of a major lode along which several different deposits are known — at what point does an ore shoot along a lode become a separate entity for contouring purposes? This question has been ignored by accepting individual mining properties as individ-ual deposits. Conversely, two separate veins from a single property may have their production data combined, in which case spatial density contours will produce an overly smoothed pattern. Newly found deposits affect spatial density contours derived from a data base of known deposits. Of course, spatial densities become underestimates if new deposits are found within the borders of a camp. It is possible that new deposits will be found outside the margins of a camp and add to the area of a camp. In this latter case it is unlikely that average spatial densities will change greatly. Overall, spatial densities are biased on the low side of reality. In long established camps that have undergone exploration for many decades, 23 such as are studied here, this bias is likely to be slight in terms of mineral occurrences but could be substantial, at loeast locally, to metal distribution contours. Average metal endowments of several mining camps can be compared. For example, average silver endowment in Slocan City camp, based on known pro-duction and the camp limits shown on Figure 2-2, is about 1,325,000 grams silver per square kilometre. The comparable figure for Ainsworth camp, based on the camp limits of Figure 2-4, is about 2,457,000 grams per square kilometre. The use of metal spatial density contours appears a practical means of generalizing resource (metal) productivity in mining camps where production and/or resources are not concentrated in a few deposits. Even where many deposits exist, metal productivity can change dramatically over short distances and logarithmic values for contours are desirable. Most deposits were found over a few years in the early history of the camps considered here. Modern exploration concepts and methods applied to these camps have not yet resulted in a marked improvement (increase) in the number of finds, as might be expected if existing spatial densities are highly biased. This is an interesting conclusion to emerge from an evaluation of spatial density maps, and some indication of the importance of rates of discovery becomes apparent, as does the need to evaluate recent or new discoveries in the light of their positions relative to known spatial densities. 24 CONCLUSIONS (1) Average spatial densities of deposit location and metal endowment data, although biased, represent useful means of comparing vein camps. (2) In some cases spatial densities have internal patterns that may provide some insight to specific small areas warranting additional exploration or in providing an additional framework for conceptual models of mineraliza-tion . (3) In many cases the large, valuable deposits in a vein camp occur in clusters with many small deposits. It appears that these associations may arise through complicated genetic histories, such as early formed deposits being mobilized to produce younger deposits. In other cases the clustering of large deposits with many smaller ones may be purely a question of clusters of structures, all mineralized at more or less the same time. (4) The suggestion that spatial densities are highly biased seems unreason-able in the camps examined here. The implication of this statement is that relatively few veins remain to be found within the camps themselves. ACKNOWLEDGMENTS This work has developed intermittently over several years with the financial assistance of the Geological Survey of Canada, the B.C. Ministry of Energy, Mines and Petroleum Resources, and the Science Council of British Columbia. The technical assistance of Asger Bentzen in producing large numbers of contoured spatial density maps is appreciated. 25 REFERENCES Goldsmith, L.B., Sinclair, A.J., and Read, P.B. (in preparation), An evalua-tion of average grades and production tonnages, Trout Lake mining area, southern British Columbia. Orr, J.F.W., and Sinclair, A.J., 1971, A computer-processable file for mineral deposits in the Slocan and Slocan City Areas of British Columbia; Western Miner, Vol. 44, pp. 22-34. Read, P.B., 1976, Lardeau west-half; Geol. Surv., Canada, Open File Rept. 464. Sinclair, A.J., 1979, Preliminary evaluation of summary production statistics and location data for vein deposits, Slocan, Ainsworth and Slocan City camps, southern British Columbia; in Current Research, Pt. B., Geol. Surv., Canada, Paper 79-IB, pp. 173-178. 26 CHAPTER 3 AN EVALUATION OF AVERAGE GRADES AND PRODUCTION TONNAGES, TROUT LAKE MINING AREA, SOUTHERN BRITISH COLUMBIA ABSTRACT Ore tonnage production data from 43 former producers in the Trout Lake mining camp are examined by plots of spatial density of deposits and statistical methods. Outlines of mineral belts are established from spatial density with the 0.5 deposit per 4 km 2 contour. Probability plots of pre tonnages distinguish two lognormal populations of deposits. Probability plots of metal grades show four lognormal populations of silver and two of gold. A metal content versus ore tonnage graph draws attention to the similarity in proportions of metals produced from high tonnage, and medium + low tonnage deposits. Triangular graphs of metal contents emphasize the direct relationship between silver and lead; metal ratios suggest some relationships which may be dependent upon host rocks. Linear correlation coefficients of tonnage and metal content show an inverse relationship between tonnage and precious metals, and a direct relation-ship between silver and lead. Multiple regression models established between production tonnages and average grades can estimate deposit size within one order of magnitude. Systematic evaluation of quantitative production and location data can aug-ment exploration decisions. 27 INTRODUCTION Trout Lake mining camp is in southeastern British Columbia, about midway between Revelstoke and the north end of Kootenay Lake (Figure 2-1). In broad outline the boundaries of the camp measure 52 km northwesterly by 26 km north-easterly (32 x 16 mi), covering an area of approximately 1350 km 2 (510 mi 2). Within this area three principal mineral belts (districts) are defined (Figures 2-6, 3-1, 3-2). History, general geology, and property descriptions are sum-marized by Emmens (1914), Walker, Bancroft and Gunning (1929), and Fyles and Eastwood (1962). Discoveries of lode deposits of silver and gold were made in the early 1890's and sporadic exploration and production have continued to the present. The most recent exploration success is the Trout Lake porphyry molybdenum deposit in the Southwest Mineral Belt (Macauley, 1979). Precious-metal vein deposits are contained chiefly in the Lardeau Group, a Lower Paleozoic, predominantly sedimentary assemblage, which includes Cambri-an Badshot limestone at its base and extends to mid-Devonian Broadview schists, pyroclastic rocks, and grits. A generalized stratigraphic section for the Trout Lake area is provided in Table 3-Lwhere probable ages and refer-ences are also indicated. Regional strikes are northwesterly, approximately parallel to the elongation of mineral belts (Figure 3-1). Folding of at least three phases has produced a complex fold pattern (Fyles and Eastwood, 1962; Ross, 1968). Southwestern limbs of anticlines are overturned in places, as is the case along the southern edge of the Central Mineral Belt (Figure 3-1) where the Broadview metavolcanic member is folded recumbently producing dips oriented stepply to gently northeasterly. Veins and lodes are open-fissure fillings sub-parallel or parallel to bedding but replacement of wallrock has also occurred where gold-bearing quartz veins TABLE 3-1 GENERALIZED STRATIGRAPHIC SECTION OF THE TROUT LAKE MINING CAMP Age Group Formation Lithology Jurassic (?) . Mafic intrusives. Diorite. Penn sylvan ian to Permian (?). Milford. Slate, argillite, chert, limestone, and pebble conglomer-ate. Stratigraphic relationship not established within the map-area. Cambrian to Mid-Devonian. Lardeau. Broadview. Grey and green grit and phyllite; minor pebble conglom-erate and pyroclastic rocks. Jowett. Mafic lavas, pyroclastic rocks, argillite, minor limestone. Sharon Creek. Dark-grey to balck siliceous argillite; slate, phyllite, and minor grit. Ajax. Massive grey quartzite. Triune. Grey to black siliceous argillite. Index. Dark-grey and green phyllite; dark-grey argillite; minor limestone and volcanic rocks; includes Molly Mac limestone: Probable conformity - relationship uncertain in map-area. Badshot. Grey limestone. (Lade Peak.) (Grey limestone and argillaceous limestone.) Apparent conformity - relationship uncertain in map-area. Late Proterozoic Hamill. Mohican. Dark-grey and green phyllite; minor limestone. to Cambrian Marsh-Adams. Grey, brown, and white quartzite; micaceous quartzite; (?). minor phyllite. Mount Gainer. White to pinkish quartzite. Base not exposed. 29 and silver-lead-zinc veins are in carbonate units in or near chlorite schists and metavolcanic rocks. Quartz is the main vein gangue mineral with subordinate carbonate, largely ankerite. Pyrite, galena, and sphalerite are the dominant vein sulphides; tetrahedrite, chalcopyrite, and locally pyrrhotite occur in some deposits. A generalized paragenetic sequence from oldest to youngest is quartz-carbonate-pyrite-(gold)-sphalerite-tetrahedrite-chalcopyrite-galena. Tetrahedrite and chalcopyrite are locally contemporaneous or reversed in order, and quartz deposition apparently continued intermittently to the final stages of mineralization. In the northwestern end of the Central Mineral Belt a silver-galena fissure vein cuts and offsets an auriferous pyrite-quartz vein, indicating successive stages to mineralization. Silver-base metal concentrations are distributed erratically along lodes, ore shoots commonly having one dispro-portionately long dimension. Replacement deposits in limestone contain galena with a relatively low silver content (1 oz Ag/ton and 5% Pb), commonly in lenses of siderite in fold crests (Fyles and Eastwood, 1962), p. 55). Veins in limestone have higher silver-lead values in small, harrow shoots. The Trout Lake porphyry-molybdenum deposit (Macauley, 1979) is not included in this study. DATA EVALUATION PROCEDURE MINDEP computer files* for NTS map area 82 K NW prepared originally by Read (1976) contain much of the numerical and geological data on which this study was undertaken. This initial computer file was thoroughly edited and *These computer-based mineral deposit files are available, in large part; on magnetic tape and computer listings under the name MINFILE, from the Mineral Resources Division, Ministry of Energy, Mines and Petroleum Resources, Victoria, B .C . 30 augmented to provide the final data base for evaluation. The resulting file contains information on 43 past producers and 180 additional vein prospects. Geological information for the file was also collected from various reports, bulletins, and maps. Geological Survey of Canada Open File Map 462 (Read, 1976) should be examined in conjunction with this evaluation. A summary of production data is given in Table .3-11. Evaluation procedures considered are largely those of Sinclair (1979) and Orr and Sinclair (1971). These include cumulative percentage probability plots, and machine-contoured plots of vein orientation and spatial density of deposits (Goldsmith and Sinclair, 1983). A graph of metal content versus production tonnage, triangular graphs of metal-lic elements, and multiple regression techniques are also used. Spatial plots of deposit locations and various geological characteristics were machine-generated at a scale of 1:125,000 for the map area (NTS Sheet 82 K NW). Each map was produced with one set of numerical information printed per deposit location. Maps with identification numbers, elevations, production tonnages, all metal grades, and all metal contents were generated and examined in relationship to available geological information. The most sig-nificant of these maps are compiled into Figures 2-6, 3-1, and 3-2. Spatial Density Figure 2-6 is a hand-contoured spatial density map of all known vein deposits and occurrences in the Trout Lake camp (i.e. 223 separate reported occurrences and producers). Deposits that have produced one or more short tons of ore are shown individually by numbers keyed to Table 3-II. For contouring purposes, a grid of 2 x 2 km 2 with a 50% overlap was used. Number of deposits per counting cell was assigned to the cell centre and the resulting regular grid was hand-contoured at intervals of 0.5, 2, 4, and 6 of mineral T A B L E 3-II ORE-TONNAGE PRODUCER DATA (TO 1976) RECORDED AVERAGE METAL GRADES HOST ROCK READ NO. NAME PRODUCTION (short tons) Ag oz/ton Au oz/ton Pb % Zn % Formation Rock Type 9 Ritchie Group (Teddy Glacier) 6 12.330 .0.667 15.70 24.82 Index Ls. 13 Lead Star 13 47.770 0.077 26.32 10.71 Broadview Chi. Schist 25 Mammoth 83 187.337 0.101 30.77 5.82 Index Ls. (Chi. Schist) 28 Kootenay Chief 21 50.000 0.0 68.05 0.0 Badshot Ls. 30 Camborne 1450 0.124 0.463 0.0 0.0 Broadview Chi. Schist ( P h y l l i t e ) 34 Eva 31656 0.097 0.219 0.0 0.0 •I 11 36 Meridian 56086 0.067 0.148 0.0 0.0 ii II 37 Oyster 10102 0.059 0.160 0.0 0.0 H II 45 Spider 141169 12.180 0.084 8.47 9.00 Jowett (Broadview?) Chi. Schist 49 Mohawk 9 48.220 0.0 16.63 20.81 Broadview Phyl1i te 54 GiIman 1 2.600 2.040 2.90 3.10 TABLE 3-II (CONTINUED) RECORDED AVERAGE METAL GRADES HOST ROCK READ NO. NAME PRODUCTION (short tons) Ag oz/ton Au oz/ton Pb % Zn % Formation Rock Type 71 Metropolitan 6 202.670 0.167 16.47 0.0 Index Ls. (Chi. Schist) 79 L i t t l e Robert 3 114.000 0.0 24.00 0.0 ii Ls. (Schist) 85 S i l v e r Queen & Sil v e r King 26 50.000 0.0 40.00 0.0 Badshot Ls. 86 Old Gold 28 90.530 0.0 18.29 0.0 Index Phyl1i te 89 Badshot 50 146.259 0.0 48.84 4.60 Badshot Ls. 95 Mike 2 12.500 0.0 10.75 36.20 Below Index (Mllford?) P h y l l i t e (Quartzite?) 96 Beatrice 585 77.620 0.102 30.72 0.0 Broadview Chi. Schist ( P h y l l i t e ) 97 St. Elmo 206 80.058 0.092 26.41 9.07 II Phyl1i te 99 Blue Bell 66 46.470 0.150 29.95 8.92 II II 101 True Fissure 5077 6.450 0.039 5.25 2.98 II 102 Broadview 275 36.080 0.070 34.51 16.66 Broadview P h y l l i t e 112 Nettie L 12820 36.389 0.061 5.11 28.24 Sharon Cr., Ajax P h y l l i t e , Quartzite 114 Ajax 539 35.070 0.028 51.27 0.0 Sharon Cr., Ajax Phyl1i te, Quartzi te TABLE 3-II (CONTINUED) AVERAGE METAL GRADES HOST ROCK READ NO. NAME PRODUCTION (short tons) Ag oz/ton Au oz/ton Pb % Zn % Formation Rock Type 115 Raven 4 42.750 0.0 36.65 6.25 Ajax Quartzite 130 Lade 13 0.0 1.000 0.0 0.0 Index Chi. Schist ( P h y l l i t e ) 136 Mohecan 9 55.000 0.010 27.19 0.0 P h y l l i t e (Schist) 137 Black Prince 30 154.770 0.0 14.22 0.0 Badshot Ls. 146 High Grade (Ruffled Grouse) 14 171.780 0.0 11.94 0.0 Below Index P h y l l i t e 147 Copper Chief 14 138.285 0.0 9.54 14.52 n II II 148 Lucky Boy 421 206.306 0.008 25.80 0.0 •I H II 153 Ethel 76 121.720 0.0 8.33 0.0 H H Ls. 159 Winslow 1788 0.172 0.333 0.02 0.001 Broadview Chi. Schist ( P h y l l i t e ) 160 Towser 25 56.000 0.200 40.23 0.0 Triune P h y l l i t e 164 S i l v e r Cup 23091 62.110 0.220 12.52 2.26 Triune, Index P h y l l i t e , Tuff 167 Triune 653 221.940 0.529 37.89 6.68 P h y l l i t e TABLE 3-II (CONTINUED) RECORDED AVERAGE METAL GRADES HOST ROCK READ NO. NAME PRODUCTION (short tons) Ag oz/ton Au oz/ton Pb % Zn % Formation Rock Type 169 Foggy Day 9 13.880 4.333 4.60 0.0 Broadview P h y l l i t e (Schist) 173 Cromwell 15 14.867 4.267 0.22 0.32 Triune P h y l l i t e 174 IXL Fraction 7 55.710 1.143 26.98 0.0 Index P h y l l i t e (Schist) 176 Noble Five 11 72.184 0.273 17.53 6.83 Triune Phyl1 i t s & Ls. 180 Si l v e r Belt 1 33.000 1.000 76.85 0.0 Index Ls. & Chi. Schist 187 American 14 63.710 0.0 64.84 0.0 II P h y l l i t e 198 Fi d e l i t y 44 65.159 0.718 27.48 0.0 Broadview P h y l l i t e & Schist TOTAL: 43 Deposits Zero = No data ( ) = Host rock to subordinate amount of ore TABLE 3-III METAL ENDOWMENT/km2, AINSWORTH, SLOCAN, SLOCAN CITY, AND TROUT LAKE MINING CAMPS (2 x 2 km COUNTING CELL) Mineral Belt No. of Deposits A rea Deposits with Production /km J Total Short Tons of Ore Total Short Tons of Ore Total Metal Endowment Metal Endowment/km 2 Producers Occurrences km 2 Produced Produced/km 2 A g , oz P b , tons A g , oz Pb , tons Ainsworth 75 78.5 1.0 770,398 9,814 5,689,392 60,775 72,476 774 Slocan 172 264.3 0.7 3,935,879 14,891 58,348, 596 239, 762 220,766 907 Slocan City 72* 116.7 0.6 86,689 742 4,940,380 3,893 42,334 33 Trout Lake: CO cn Lime Dyke 10 3 83.0 0.1 269 3 34,442 88 415 1 Molly Mac 0 7 108.0 e e 0 0 0 0 0 Central 28 -t 13 197.2 0.1 283,804 1,439 3,468,663 16,587 17,589 84 South-western 5 0 56.2 0.1 527 9 100,471 118 1,787 2 *From Orr (1971) 36 occurrences that correspond with three long-established "mineral belts" which are, from east to west, Lime Dyke, Central,.and Southwestern mineral belts. The western part of the Lime Dyke belt on Figure 2-6 is referred to as the Mollie Mac belt. The principal advantages of contouring spatial densities of deposit loca-tions are that arbitrary boundaries to mining districts can be determined and various aspects of the "structure" of deposit locations within individual belts can be examined (Goldsmith and Sinclair, 1983). In this case, it is apparent that nearly all past producers are located near highs of the spatial density contours. The advantage of an empirical approach to determining areal extent of mining camps is that quantitative comparisons among camps then become possible. Limits to various mineral belts are defined arbitrarily with the 0.5 deposit per 4 km 2 contour (Sinclair, 1979; Goldsmith and Sinclair, 1983) and, on this basis, various features of the three belts of Figures 2-6, 3-1 and 3-2 are compared in Table .3-111. Note the uniformity in spatial density of mineral occurrences. Productivity as measured by mean spatial density of producing deposits, and mean spatial density of tonnage produced (tons/km 2), however, varies considerably (see Table 3-III). The geographic distribution of mean silver grades of past producers and the strike or strikes of individual veins are shown in Figure 3-1. In general, silver grades are highest in the Lime Dyke and Southwest mineral belts, with one high value in the southeastern part of the Central Mineral Belt. The highest silver values in the Southwest and Central mineral belts are associated spatially with diorite or granodiorite dykes (read, 1976). High-tonnage silver deposits occur in the northwestern and central portions of the Central Mineral Belt. Strikes of productive veins tend to be parallelor sub-parallel to strike LEGEND ii LOW-TONNAGE SILVER PRODUCERS » ORE TONNAGE PRODUCER LOCATION WITH GRADE OF SILVER IN OZ./SHORT TON. HEAVY LINE DEPICTS STRIKE OF DEPOSIT. O 2 4 6 8 O MILES 16 k m Figure 3-1. Location of high and low tonnage silver producers in the Trout Lake camp, with grades of silver and strike of deposits. Inset is a probability graph of mean silver grades in ounces /short ton. S I * 51" Figure 3-2. Location of high and low tonnage gold producers in the Trout Lake camp, with grades of gold and elevation in metres. Inset is a probability graph of mean gold grades in ounces /short ton. 39 of the host rocks; divergences appear to be caused by local variations in fold attitudes or to represent small transverse fissures extending outward from concordant or subconcordant veins. Figure 3-2 shows gold grades of ore-tonnage producers and the elevations of surface outcroppings. The Central Mineral Belt contains all of the deposits which have significant gold content and significant production. Four of five high-tonnage orebodies (more than 99,000 tons of the 101,000 tons total production) cluster in the northwestern end of the belt. Deposits with gold as the primary metal seem to occur at lower elevations than do deposits with silver as the primary metal. Probability Plot of Ore Production Tonnage Extracted ore tonnages are biased measures of sizes, and relative values of deposits (Sinclair, 1974, 1979). Consequently, the probability density func-tion of production tonnages is of interest for use as an exploration parameter. The histogram for vein "sizes" in a single camp commonly can be approximated by lognormal populations or mixtures of lognormal populations (Sinclair, 1974, 1979). Figure 3-3 is a probability graph of production tonnages cumulated individually (from high to low tonnage) as suggested by Sinclair (1976) for small data sets (n=43 in this case). The ND curve (cumulated number of deposits) shows the presence of two lognormal-size populations. A threshold of approxi-mately 600 short tons separates the populations into large and small categories. The thirteen largest producers (30% of total) are included in the upper popula-tion and approximately 70% of all past.producers are contained in the low-tonnage group. It is appreciated that some of the small past producers may have high-tonnage potential that has not been explored adequately, but the 40 Figure 3-3. Probability graphs, Trout Lake camp. Number of deposits (ND) = number of deposits cumulated from largest to smallest. Cumulative tonnage (CT) = tonnage cumulated from largest to smallest. 41 segregation into two classes focuses attention on the large deposits and their characteristics. The CT curve of Figure 3-3 is also constructed for individual deposits but depicts cumulative tonnage as a function of decreasing size of a deposit (Sinclair, 1979). For comparison purposes at a size corresponding to the smallest ore-producer in the high-tonnage population (13th cumulated deposit - Lucky Boy - 421 tons produced) it may be seen that the 13 largest deposits account for more than 99% of the total tonnage produced in the camp. Cumula-tive metal curves (not shown) were constructed in a manner analogous to the CT curve of Figure 3-3 and showed similar features as the CT curve. The advantage of the CT curve is that production tonnage is a single relative value measure for individual deposits, whereas individual cumulative graphs would be required for each of the four metals for which production data are available (cf. Sinclair, 1979). To illustrate the application of probability curves to exploration, assume that a conceptual ore target for the district is set at a minimum of 50,000 tons. The probability plot allows a rapid determination that 2 of 43 deposits (approxi-mately 5%) exceed this lower limit. A new prospect, therefore, has about a 5% chance that it will contain a minimum of 50,000 tons. However, if the deposit can be identified as belonging to the high-tonnage population, a determination can be made from the partitioning of the probability plot that there is a 20% chance the deposit will have a minimum of 50,000 tons. If a deposit can be identified as belonging to population L it will have a negligible probability of meeting the arbitrary size criterion and additional exploration should probably be limited. Implications for exploration decisionmaking and cost-saving are obvious. 42 Probability Plots of Metal Grades Silver: Deposits appear to cluster in four principal grade categories. Four lognormal populations approximate these categories in Figure 3-1 (inset). Geo-metric parameters of the populations are as follows: Population % Parameters (oz Ag/ton) Mean (b) b ,+ s T b - s T Li LI I 27 160 210 124 II 45 52 68 40 III: 16 13.1 15.0 11.8 IV 12 0.108 0.181 0.062 These populations correlate closely with geological type of deposit. Popu-lation IV is a group of gold deposits from the north end of the Central Mineral Belt, whereas population III represents replacement deposits in carbonate. The two high-grade populations (I and II) represent the Pb-Zn-Ag veins character-istic of the camp and correspond fairly closely to the two size categories deduced from Figure 3-5. Gold: Figure 3-2 (inset) is a probability plot of gold production grades from 30 deposits, cumulated individually. Two indistinct lognormal populations are partitioned with parameters: Population % Parameters (oz Au/ton) Geom. Mean (b) b + . b - S L H (high Au) 21 1.750 3.850 0.690 L (low Au) 79 0.140 0.420 0.047 High gold values have only. 2% of the population below 0.250 6z/ton. This grade fits well with the upper grade of the high-tonnage gold ore producers. 43 The low-grade gold population may contain two or more additional populations; a second threshold was selected at 0.050 oz/ton to bracket a medium-grade population between 0.050 and 0.250 bz/ton. An inverse relationship between gold grade and tonnage is indicated. Lead and Zinc: Figure 3-4 combines probability plots of lead and zinc. Two populations seem to be represented in each curve, possibly one normal and one lognormal. In both cases the data base is too small to permit meaningful partitioning of the populations. Metal Content vs Production Tonnage Metal content is calculated as grade times tonnage to yield total metal pro-duced (ounces for precious metals, short tons for lead and zinc). Figure 3-5 is divided at 670 tons to focus attention upon the high-tonnage and medium + low tonnage groups. An additional segregation could be made between high-tonnage silver ore deposits and high-tonnage gold ore deposits by drawing a diagonal line from the lower left corner; the five deposits which contain low silver values are the high-tonnage gold deposits in the camp. Near-linear dispersions of metal content vs production tonnage show that high-tonnage and medium + low-tonnage deposits have produced on the average similar proportions of each commodity. Because total content of metals is a measure of the value of a deposit, the associated tonnage may therefore be used as a single measure of the; relative worth of a deposit, obviating the need to sum several metal contents of a polymetallic deposit through the medium of fluctuat-ing dollar values and metal prices (cf. Sinclair, 1979). Consideration of total metal content rather than grades may also smooth some of the bias introduced by hand-sorting of ore, particularly common for production from deposits of less than 1000 tons. 44 Figure 3-4. Probability graphs: for mean Pb grades and mean Zn grades for past producing veins, Trout Lake mining camp. 45 U 3 0 0 O o UJ 2 | c — o tq CONTENT | o a Au CONTENT 1 • 1 0 * R> CONTENT 1 • • Zn CONTENT o . MEDIUM + LOW-TONNAGE DEPOSITS HIGH-TONNAGE DEPOSITS o ° i o o 1 1 1 r 0 0 | 0 1 a o Ol a « o • o 3 1 0 o a 0 ' o ° o • o » * a o 1 o A . A o A | o 0 0 ° o 1 • — A 1 o 1 • a A °t • J • • a a O A * 1 • A 9 a 1 A a | • • • m i l l . • i>i n m O , — i • • • 1 1 1 » - i - i - l l l i too ipoo PRODUCTION TONNAGE 10,000 ure 3-5. Metal content versus production tonnage, Trout Lake camp. Diagonal line accentuates two groups of deposits with distinct grades of silver. 46 Variations in metal content combine variabilities arising from both size and grade. Consequently, metal content can be a complex variable to interpret. Nevertheless, metal content appears to be extremely useful as a classification scheme for Lardeau vein deposits. Figure 3-5 also is of interest as regards silver, which plots in two separate linear groupings of data which can be approximated by two sub-parallel lines. The lower group represents low-grade silver deposits; the upper group represents higher-grade deposits. The two groups overlap substantially in terms of tonnage but their separation is facili-tated because of the second dimension (grade vs metal content) present in the classification scheme. These data also support the suggestion by Sinclair (1979) that tonnage is a reasonable value measure for vein deposits although in this case an added complication exists in the form of two linear trends of tonnage versus silver content. Triangular Graphs Triangular plots are a useful way of examining clustering of deposits in terms of three elements. However, it is important to realize that absolute abundances are lost for data plotted on such diagrams where three elements that form a small percentage of the whole are being considered, as is the case with average ore grades from the Trout Lake camp. For purposes of clarity, silver and gold are maintained as oz/ton and lead and zinc as percent metal in constructing the triangular plots shown in Figure 3-6. The advantage of this procedure is that lines from a vertex to the opposite side of the triangle can be labelled directly in terms of commonly used metal ratios such as Ag (oz)/Pb (%), Au (oz)/Zn (%), Pb/Zn, and Ag/Au. 47 Oz. Ag/ton Figure 3-6. Triangular graphs, Trout Lake camp. 48 Distinctive symbols are used for high-tonnage silver ore producers, high-tonnage gold ore producers, and low-tonnage producers. Figure 3-6(a), the silver-lead-zinc plot, shows (1) that zinc is generally subordinate to lead, and (2) thatthe silver-lead ratio (oz/%) is highly, variable but only rarely is less than one. Note that in Figure 3-6(a) a line drawn from the zinc vertex to the opposite side of the triangle defines a constant Ag/Pb ratio in this case in ounces of silver per percent of lead. For example, the line from zinc to the 50 percent position represents a ratio of 1 oz Ag for each percent of lead. Both high- and low-tonnage silver deposits plot in comparable fields; both are rela-tively high in silver. The two low zinc deposits with lowest proportions of silver to lead are contained in the Broadview formation (grits) whereas the other deposits with higher proportions of silver to lead are largely in the Sharon Creek-Ajax and Triune-Index formations (slate-phyllite). Only one high-tonnage gold ore deposit has recorded lead and zinc values for production, and average lead and especially zinc grades are extremely low. The remainder of the deposits where gold is the primary metal product have a comparable low base metal content; consequently, they would cluster on the silver-lead line near the silver vertex. Figure 3-6(b), silver-gold-lead, depicts the relationship of silver and lead more forcefully. There are not gold-lead deposits without appreciable silver content. High-tonnage silver ore deposits lie near the silver-lead line. Gold is invariably present but its share of the total metal content is small. The pair of large-tonnage silver ore deposits with ratios that plot midway between silver, gold and lead occur in the Broadview formation as noted previously, whereas deposits with higher proportions of silver to lead are contained in older forma-tions. High-tonnage gold ore deposits plot on the silver-gold line where the proportions of silver:gold are approximately 25:75. 49 Figure 3-6(e), silver-gold-zinc, shows a similar pattern to the silver-gold-lead graph with the exception that one of the large-tonnage silver deposits in rocks older than the Broadview formation has a slightly lower silver:zinc ratio than do the Broadview-hosted deposits. Besides the group of high-tonnage gold ore producers which cluster near silver:gold proportions of 25:75, there appears to be a group of low-tonnage silver ore deposits which have a very low gold content. Two populations of silver-gold deposits therefore may be indicat-ed, one with low quantities (less than 0.500 bz/ton) of both silver and gold, and the other with high quantities of silver (greater than 15 oz/ton) and low quantities of gold (less than 0.500 oz/ton). An overprinting of one population upon the other could explain the several deposits where either silver or gold grades could have made the property economic. There are no gold-zinc deposits without recorded silver content. In summary, triangular diagrams provide a useful means of examining groupings or classifications of deposits in Trout Lake mining camp on the basis of metal ratios. High-tonnage gold deposits stand out as a distinctive cluster based exclusively on the Au:Ag ratio (circa 75: 25). High- and low-tonnage Ag deposits are all relatively rich in Ag (Ag/Pb oz/% >1) and plot in more or less coincident fields. Note that low silver, lead-zinc replacements in limestone have not been considered in discussion of these diagrams because of the scarcity of multi-element production data. Simple Correlation of Metal Grades and Production Tonnage Probability graphs presented in Figures 2-6, 3-1,-2, -3 and -4 show that grade and tonnage variables for Trout Lake camp have complex frequency dis-tributions that can be interpreted as mixtures of two or more logriormal populations. Consequently, simple correlation coefficients can be viewed only in 50 a semi-quantitative manner as regards interpreting their statistical significance. Nevertheless, these coefficients can be used as an indication of the relative goodness to which two variables are clearly related. Simple linear correlation coefficients for Trout Lake mean grades and production tonnages are provided in Table 3-.IV for log-transformed data. Table••3-.IV.. Corelation matrix* for logarithmic values of production data from 43 producers, Trout Lake mining camp. Tons Ag Au Pb Zn Tons 1.00 Ag -0.49 1.00 Au -0.41 -0.18 1.00 Pb -0.20 0.72 -0.33 1.00 Zn -0.07 0.13 -0.58 0.56 1.00 ^Absolute values above 0.4 are underlined. These data are shown in a correlation diagram in Figure 3-7 where deposit relative value (as depicted by production tons) is seen to be inversely correlat-ed to precious metals and uncorrelated to average base metal grades. From these data, the best single estimator of potential size is log(Ag grade) although it is apparent that silver grade does not provide a particularly good estimator of potential deposit size. These results nevertheless indicate the possibility that some more complex function of grades may provide a better estimator of potential deposit size. The strongest linear relationship indicated in the correlation matrix is Pb vs Ag (r=0.72) for which a linear relationship explains 52 percent of the vari-51 Correlation diagram showing tons to be most strongly, but inversely related to precious metals. 52 ability. This linear relationship quantifies the close association of silver and lead that is characteristic of many deposits throughout the Kootenay arc. The best linear relationship for the entire data file that involves produc-tion tonnages and metal grades is Ag vs tons (r = -0.49), a relationship that explains 24 percent of the variability. One of the aspects of production data that we are concerned with is the possibility that grades vary in a regular way as a function of deposit size. It is apparent that the best individual element (Ag) to use as a basis for estimating deposit size by production tonnage will suffer from a very large error. To improve this situation the interrelation of all elements with tonnage will be examined through the application of multiple regression techniques. Multiple Regression Applied to Forecasting Deposit Size Multiple regression techniques have been used in a few cases (Orr and Sinclair, 1971; Sinclair, 1982) to develop quantitative models that determine a value measure of polymetallic vein deposits as a function of known mean grades. The general methodology is based on the empirical relationship suggested by Sinclair (1979): logio (metal content) = K logio(production tons) ± e where K is a constant and e is a random error. Both K and e differ for each metal in a particular mining camp, but in general e is small relative to the range of production tonnages (about 6 orders of magnitude) for a given vein camp. Production tonnages of past producers therefore define a single continuous relative value measure for polymetallic vein deposits. The approximate linear relationship of log (metal content) to log (production tonnages) is demonstrated clearly in Figure 3-5 for Trout Lake camp leading to the possibility of establish-53 ing a quantitative model for lvalue" of a vein deposit in the camp in terms of known average grades. The advantages of such a model are at least two-fold. First, individual deposits that are outliers from the model are "anomalous" and warrant examination in detail. Thus, the model approach results in specific targets being isolated for detailed examination. Second, average grades based on sampling of newly found deposits can be substituted in a camp model to provide insight into resource potential. For Trout Lake camp past producers form three groups: (i) Ag-Pb-Zn deposits, (ii) Au deposits low in Pb and Zn, and (iii) a combination of the two foregoing groups where type (i) apparently has been superimposed on type (ii). In general, the Ag-Pb-Zn deposits have been small producers whereas Au deposits have been relatively large producers (see Table 3-II). Average production grades for four metals are available for 14 separate deposits in Trout Lake camp. An additional 4 deposits have known average Au and Ag grades and extremely low Pb and Zn grades that were not measured. Grades of 0.1% for both Pb and Zn in these deposits have been substituted because it is not possible to take logarithms of zeros. These 18 deposits serve as the basis for a multiple regression analysis with production tons as the dependent variable and average production grades as independent variables. The model obtained is: logioi(tons) = 1.917 - 1.995 log(Au) - 0.907 log(Pb) ± 1.089 with R 2 =0.57.' In other words, the potential size of a deposit can be estimated within a standard error of about an order of magnitude using only the average Au and Pb grades. Moreover, low grades of both Au and Pb indicate relatively large tonnages. Of these two variables Au is correlated most highly with tons (for log Au and log tons r = -0.50). Thus, Au grade alone is a relatively good indicator of potential size. 54 Models of this sort are empirical and while they can be used to interpolate it is unwise to extrapolate with a model beyond the limits of data on which it is based. Consequently, the model quoted above would be considered unrealistic if estimated tonnages approached or exceeded one million tons. An alternative approach to the use of two mineral deposit types which are assumed to be two extremes of a continuum in the preceding example is to develop a multiple regression model within a single deposit type. This has been attempted for the Ag-Pb-Zn vein category, that being the only group for which sufficient data are available. Data exist for 12 deposits and lead to the follow-ing model: log(tons) = 1.128 - 1.239 log Au ± 0.955 with R2 = 0.44. The variables Pb, Zn and Ag have dropped out of the equation because their coefficients were found to be not distinguishable from zero at the 0.05 level. A striking feature of this result is that Au is the most important "value" estimator in a deposit-type in which the Au content is of little economic importance relative to the much more abundant metals (Ag, Pb, and Zn). Deposits Without Recorded Production A search of the available literature did not locate grade data for well sampled mineral deposits from which no production exists. Several channel samples over a length of at least 4 feet were considered a minimum upon which to characterize metal grades for use in multiple regression models. Should this information be available in private files for specific deposits, the multiple regression models derived from production records might be applied as an eval-uation procedure. Assay data for all four metals (Ag-Pb-Zn-Au) should be 55 collected during future evaluations in the Trout Lake area for use in the most satisfactory of the multiple regression models. CONCLUSIONS A rigorous, systematic evaluation of quantitative production and location data for Ag-Au-Zn-Pb veins in the three mineral belts of the Trout Lake mining camp, British Columbia, provides useful insight to a variety of mineral explor-ation decisions as follows: 1) Comparative exploration success rates as indicated by past productivity show the Central Mineral Belt to be the most productive per unit area. Assuming equal intensity of exploration among mineral belts and repre-sentative success rates in all cases, highest productivity may imply highest potential for exploration. 2) High concentrations of small mineral occurrences are favoured sites for the location of relatively large Ag-Au-Zn-Pb vein deposits in Trout Lake camp. 3) Probability graphs demonstrate that two principal size categories of vein producers exist in Trout Lake camp where size is indicated by production tonnages of ore, and is structurally controlled. Detailed field studies of structural control are required to characterize the two populations. 4) Probability graphs indicate the likely existence of four fundamentally diff-erent categories of average silver grades. These grade categories correspond to i) low-tonnage high-grade silver ore deposits; ii) large-tonnage high-grade silver ore deposits; iii) large-tonnage medium-grade silver-gold ore deposits; iv) large-tonnage gold deposits with very low silver grade. 56 5) Production tonnage is demonstrated to be an adequate single value estimator of relative value of a Ag-Au-Zn-Pb deposit in Trout Lake camp. Consequently, production tonnage will serve as a dependent variable representing deposit value in mathematical modelling. 6) Triangular graphs emphasize the relationship between silver and lead and the apparent independence of gold from other metals. Large-tonnage silver ore deposits with low silver-to-lead ratios may occur in the Broad-view formation; deposits with higher proportions of silver to lead are contained in older formations. 7) A matrix of simple correlation coefficients shows that average precious metal contents (especially silver) are more closely related (inversely) to deposit size (production tonnage) than are base metal average grades. 8) A multiple regression model for production tons in terms of four average production grades (Ag, Au, Zn, Pb) forecasts tonnage with a standard error of about one order of magnitude. Such a model applied to average grades may forecast deposit size early in the exploration of a newly found deposit. Practical applications of the multiple regression model might be based on either or both of diamond drill or channel (surface and under-ground) samples. 57 ACKNOWLEDGMENTS This study was initiated with funding from the Geological Survey of Canada and completed with financial assistance from the British Columbia Ministry of Energy, Mines and Petroleum Resources, and an NSERC operating grant to A.J. Sinclair. The initial Trout Lake data file was compiled by P.B. Read. REFERENCES Edwards, H.C., 1934, Report on mineralogy of Red Horse and Oyster-Criterion claims, Meridian Mining Company, Camborne, B.C.; unpublished report, Dept. of Geological Sciences, University of British Columbia. Emmens, N.W., 1915, Lardeau Mining Division, Annual Report of the B.C. Minister of Mines for the year 1914, pp. 245-273. Emmens, N.W., 1915, Trout Lake Mining Division, Annual Report of the B .C. Minister of Mines for the year 1914, pp. 291-325. Fyles, J.T., and Eastwood, G.E.P., 1962, Geology of the Ferguson Area; B.C. Dept. of Mines Bulletin 45. Goldsmith, L.B., and Sinclair, A.J., 1983, Spatial density of silver-lead-zinc-gold vein deposits in four mining camps in southeastern British Columbia; B.C. Ministry of Energy, Mines and Petroleum Resources, Paper 1982-1, pp. 251-265. Hosking, K.F.G., 1951, Primary ore deposition in Cornwall. Roy. Geol. Soc. Cornwall Trans., Vol. 18, pp. 309-356. Krumbein, W.C., and Graybill, F.A., 1965, An Introduction to Statistical Models in Geology; McGraw-Hill, New York, 475 pp. 58 Macauley, T.N., 1979, Trout Lake molybdenum deposit, southeastern British Columbia. Evolution of the Cratonic Margin and related mineral deposits; Cordilleran Section GAC Meeting, February 9-10, 1979. Abstract. Muraro, T.W., 1966, Metamorphism of zinc-lead deposits in southeastern British Columbia; in C.I.M.M. Special Volume 8, Symposium on the Tectonic History and Mineral Deposits of the Western Cordillera, pp. 239-247. Orr, J.F.W., 1971, Mineralogy and computer-oriented study of mineral deposits in Slocan City Camp, Nelson Mining Division, British Columbia; M.Sc. Thesis, University of British Columbia. Orr, J.F.W., and Sinclair, A.J., 1971, A computer-processible file for mineral deposits in the Slocan and Slocan City areas of British Columbia; Western Mines Reprint, February 1971. Orr, J.F.W.., and Sinclair, A.J., 1971, Computer evaluation of Slocan mining camp, B.C.; unpublished report. Read, P.B., 1976, Lardeau west-half. G.S.C. Open File Map 462, 1:125,000, and Open File Rept. 464. Read, P.B., 1973, Petrology and structure of Poplar Creek map area, B.C.; G.S.C. Bulletin 193. Ross, J.V. , 1968, Structural relations at the eastern margin of the Shuswap Complex, near Revelstoke, southeastern British Columbia; Can. Jour. Earth Sciences vol. 5, pp. 831-849. Sinclair, A.J., 1982, Multivariate models for relative mineral potential, Slocan silver-lead-zinc camp; B.C. Ministry of Energy, Mines and Petroleum Resources, Paper 1982-1, pp. 167-175. Sinclair, A.J., 1979, Preliminary evaluation of summary production statistics and location data for vein deposits, Slocan, Ainsworth, and Slocan City 59 camps, southern B.C.; in Current Research, Pt. B., Geol. Surv.,Canada, Paper 79-IB, pp. 173-178. Sinclair, A.J., 1976, Applications of probability graphs in mineral exploration; Special Volume No. 4, Association of Exploration Geochemists, Richmond, B.C., 95 pp. Sinclair, A.J. , 1974, Probability graphs of ore tonnages in mining camps -a guide to exploration; Bull. Canadian Inst. Min. Metall., V. 67, pp. 71-75. Sinclair, A.J., 1972, Some statistical applications to problems in mineral explora-tion; B.C. Professional Engineer, March 1972. Sinclair, A.J., and Goldsmith, L.B., 1980, Metallogeny of Ag-rich Pb-Zn veins, central Kootenay Arc, southeastern British Columbia (Abstract); Can. Inst. Min. Metall. Bull. vol. 73, no. 821, p. 74. Stanton, R.L., 1972, Ore Petrology. McGraw-Hill, New York, 713 pp. Walker, J.F. , Bancroft, M.F., and Gunning, H.C., 1929, Lardeau map area, British Columbia; G.S.C. Memoir 161. Zuwaylif, F.H., 1972, General Applied Statistics. Addison-Wesley, Don Mills, Ontario, 311 pp. 60 CHAPTER 4 MULTIPLE REGRESSION, A USEFUL QUANTITATIVE APPROACH IN EVALUATING PRODUCTION DATA FROM VEIN-TYPE MINING CAMPS, SOUTHERN B.C. ABSTRACT Production data from five mining camps in Southern British Columbia demonstrate the use of multiple regression as a potent technique in establishing quantitative exploration models for polymetallic vein deposits. Mined tonnage serves as a useful size (relative value) measure and is the dependent variable: used in developing quantitative models. Average deposit grade figures deter-mined from all recorded production are used as independent variables. Regression using log transformed data commonly results in models with standard errors for estimated size of deposits of less than one, that is less than one order of magnitude - not unreasonable considering that the dependent variable itself can span six or seven orders of magnitude in a single mining camp. Practical importance of the models is (1) recognition of deposits with low past productivity that might have substantial remaining potential, and (2) evaluaiton of the potential of newly found deposits after a relatively short sampling and exploration campaign. 61 INTRODUCTION Relatively little has been published on the development of quantitative mineral resource models of direct use in mineral exploration and evaluation. Nevertheless, an interesting array of literature pertaining to British Columbia has appeared since the late 1960's. An early study by Kelly and Sheriff (1969) was concerned with estimating the economic mineral potential of 20 x 20 mi 2 cells over the entire province in terms of gross dollar value of all contained mineral deposits. A comparable methodology was applied on a different scale and with more detailed geological information ( 4 x 4 mi 2 cells) in the Terrace area by Sinclair and Woodsworth (1970). Most recently this "cell" approach was applied by Godwin and Sinclair (1979) in an evaluation of a single porphyry-type deposit, the Casino Cu-Mo deposit in Yukon Territory, based on a 400 x 400 f t 2 cell size. All these studies related some measure of cell value (the dependent variable) to a variety of geological and other attributes of the cells (independent variables) by a multiple regression relationship. Multiple regression has also been applied to the development of quantita-tive models for the relative worth of individual deposits within a mining camp (Orr, 197.1; Orr and Sinclair, 1971; Sinclair, 1979; Sinclair and Goldsmith, 1982; Sinclair, 1982). Models derived from these latter studies have a relative value measure for deposits (e.g., log of production tonnage) as the dependent variable and logarithm of average grade figures for several metals (e.g., Ag, Pb, Zn, Au) as independent variables. The most extensive test to date by Sinclair (1982) for the Slocan Ag-Pb-Zn-Au camp suggests several important applications of the method, viz.: 62 (1) Newly located deposits can be sampled and the average grades used to estimate potential size (value), thus providing a quantified target for further exploration. (2) A statistical model will isolate those deposits not fitting the general model. In particular, deposits with low recorded production that have grade characteristics of large deposits would appear to warrant further detailed examination. (3) In some mining camps it may be useful to contour "values" calculated according to a multiple regression model as one means of examining systematic variations in potential and delimiting areas for detailed explor-ation . 63 PROCEDURE A necessary precursor to the multiple regression approach to model devel-opment is the availability of appropriate production information. For this purpose, computer files, developed or improved, were used as follows: Slocan, Slocan City and Ainsworth camps - Orr and Sinclair (1971) and Orr (1971); Zeballos camp - Sinclair and Hansen (1983); Trout Lake camp - Read (1976) and Goldsmith (in prep.). Locations of five of the camps are shown in Figure 2-1. The multiple regression method involves selection of a value measure for each deposit for which production data are available. Logio production tonnage was selected as a satisfactory relative value measure based on results by Sinclair (1979). Similarly, dependent variables were mostly logarithms of average deposit grades (Ag, Pb, Zn, Au) derived from total recorded produc-tion. The general form of the model is log(tons) = B 0 + Z [B. log M.] + e i where the: M. represents Au, Zn, Ag, Cu, and Pb. Logarithmic transformations are necessary to produce near-normal probability density functions. These data were treated by TRP regression packages, available through the U.B.C. Computing Centre. In particular, the backwards stepwise option was used, which rejects variables whose regression coefficients cannot be distinguished from zero at a specified level of significance (a = 0.05'.,' in this case). 64 SLOCAN (SANDON)CAMP Slocan mining camp has been an important silver producing region since the Nineteenth Century. More than 200 individual Ag-Pb-Zn-Au veins are known from which some produciton has been obtained (Orr and Sinclair, 1971). These deposits have been divided into two groups for purposes of quantitative modelling (Sinclair, 1982). The: western two-thirds of the camp provided a training set (138 deposits) with which quantitative models were established as summarized in Table 4-1. These models were then used to estimate potential of deposits in the eastern group for which production tonnages were known. An example is shown plotted in Figure 4-1 from Sinclair (1982), where the scatter is comparable to the standard error of the model. Such a result provides validity for the general approach. Unfortunately, calculated tonnage by the 4-variable model could be compared with only 19 known production tonnages because gold contents were not recorded for most of the 65 deposits in the eastern group. Obviously, gold is an important component in such a model (compare standard errors of the two models in Table 4-1). The number of deposits on which to base a model increases dramatically if only three independent variables are considered and Au is the one omitted. However, the resulting model (model B, Table 4-1) is very unsatisfactory from a practical point of yeiw because of the large standard error and the very low coefficient of variation. It is evident that Au data are highly:desirable in such models for Slocan (Sandon) camp. Perhaps the most significant contribution of this study is the recognition of the importance of Au assays in evaluating vein deposits in Slocan camp. 65 TABLE 4-1 SLOCAN (SANDON) REGRESSION MODELS A : Log (tons) = 1.3789 - 1.1459 log (Au) R 2 = 0.59 S e = 0.8608 0.5544 log (Pb) n = 62 B: Log (tons) 5.4172 - 1.3907 log (Ag) - 0.3786 log (Zn) R 2 = 0.22 S e = 1.2490 n =95 66 Log 1 0 (obs. tons) Figure 4-1. Observed versus calculated tonnages using a multiple regression equation, Slocan camp. AINSWORTH CAMP Of the: more than 90 Pb-Zn-Ag-Au deposits in Ainsworth camp with record-ed production, only 13 have average grade information for all 4 variables/These "complete" sets of assay data have been used to develop regression model A of Table .4-11. The multiple regression model has reduced to a simple regression model in this case because Pb is a linear combination of other variables and Ag and Zn were both rejected as not contributing (at the 0.05 level) to explaining variability in tons. Clearly Au is an important variable for estimating size potential, but unfortunately is available for so few deposits. A much larger data base existed upon which to base a regression modelif Au were not included. With this larger data base only Pb was rejected as not contributing to an explan-ation of the variability of tons. The remaining model (B in Table 4-II), although statistically meaningful, is of little practical use because of the low coefficient of variation. 68 TABLE 4-II AINSWORTH REGRESSION MODELS A: Log (tons) = 1.5268 - 0.8068 log (Au) R 2 = 0.68 S a = 0.6949 e n = 13 B: Log (tons) = 3.4067 - 0.5770 log (Ag) - 0.8011 log (Zn) R 2 = 0.21 S Q = 1.1270 e n = 49 69 SLOCAN CITY CAMP Slocan City camp contains 74 small polymetallic vein deposits for which production information is available (Orr and Sinclair, 1971). These deposits are scattered throughout an area of about 115 km 2. Of these, only 17 have complete production information for tonnage mined and average grades of Ag, Pb, Zn and Au. Data for these 17 deposits were used to develop regression model A of Table .4-111. The model is mediocre at best, but at that, is substantially better than modelB (Table 4-III) obtained when Au is omitted. 70 TABLE 4-III SLOCAN CITY REGRESSION MODELS A: Log (tons) = 1.5878 - 0.6085 log (Au) - 0.5177 log (Zn) R 2 = 0.37 S = 1.0700 e n = 17 B: Log (tons) = 2.0867 - 0.4508 log (Zn) R 2 = 0.14 S '. .= 1.1290 e n = 33 71 TROUT LAKE CAMP Four grade variables and production tonnages are available for 18 past producer Au-Ag-Pb-Zn veins. These data were used to establish the following multiple regression model: log (tons) = 1.917 - 1.995 log Au - 0.907 log Pb R 2 = 0.57 S = 1.089 e Only two grade variables have a significant contribution to the: reduction of variance in the model, although Au is the single most important variable. Production data span more than five orders of magnitude; consequently, a model that estimates size with an absolute error of one order of magnitude would appear to have potential in evaluating well sampled deposits in the camp. Prac-tical application of the model at the moment is limited because for many deposits production data were not recorded for all four metals; zinc data in particular are deficient. A second approach developed for Ag-Pb-Zn veins, for which data are available from 12 deposits, gives the following model: log (tons) = 1.128 - 1.239 log Au R 2 = 0.44 S = 0.955 e The variable Au is the most important estimator in this class of deposits where Au is of minor economic importance relative to Ag-Pb-Zn. 72 ZEBALLOS CAMP Production data for 11 vein deposits from the Zeballos gold camp, Vancouver Island (Hansen and Sinclair, 1984), were used to derive the follow-ing model: logio (tons mined) = 3.09 - 0.97 logio (Ag) - 1.67 logio (Cu) R =0.98 S = 0.41 where tons mined is short tons of recorded production, and Ag and Cu are average grades of recorded production in ounces per short ton and percent respectively. The backwards stepwise procedure removed two potential grade variables from the model at the 0.05 level, viz. Au and Pb. 73 DISCUSSION The five examples cited here demonstrate a procedure for developing useful quantitative (regression) models to evaluate size or relative value of poly-metallic vein deposits. Each of the examples involves four independent grade variables. Experience with one, two, or three independent variables is that the resulting models have substantially larger standard errors than is the case with four independent variables. In four cases the calculated models involve Ag-Au-Pb-Zn deposits. At the fifth camp the metals are Au-Ag-Pb-Cu. The models differ dramatically from one camp to another, a difference that is accented by considering the most important single variable in reducing variance in the model. At Zeballos the important element, copper, is correlated negatively with tonnage. In Slocan (Sandon), Ainsworth and Trout Lake camps, gold is by far the most significant independent variable and is also negatively correlated with tons. The regression model approach suggests a variety of practical applications. 1) The small number of deposits in a camp that depart most from the model may be anomalous. Of particular interest are those deposits with low observed tonnages and very much higher calculated tonnages. Such deposits may fit the model and have relatively large undiscovered tonnages. 2) In each camp there are a large number of past-producers for which fewer than four metal grades were recorded. In some cases resampling of old workings might be possible and such samples, analysed for four variables, could be evaluated by the regression model. Such a program would appear especially viable in the: case of Slocan (Sandon) camp where about 270 past-producers are known, only:89 of which have data for all four independent variables of the regression model. 74 3) Newly found deposits evaluated by drilling, surface and/or underground sampling may have sufficient data so that weighted mean grades can be substituted in the model for rough estimates of size potential. Of course, past-producers also can be re-evaluated in this way as additional data become available. The principal difficulty with the method lies in the substantial amount of information necessary to establish the models. Even in camps with many deposits and a long history of production, much of the production may have been analysed for insufficient variables or inappropriate variables to provide an acceptable model. These investigations demonstrate that different variables are important in different camps. Furthermore, the most important variable for purposes of estimating tonnage may be of relatively minor economic importance with the result that little or no attention is paid to measuring the variable. This is true of Cu in Zeballos deposits and Au in deposits of Slocan (Sandon) and Ainsworth camps. 75 CONCLUSIONS Multiple regression models relating production tonnages to average grades of production for deposits from polymetallic vein camps appear to have potential as a deposit evaluation technique. In the five camps studied here the models provide tonnage estimates with an error of about one order of magnitude or less, in some cases much less. This error is large, but in the context of range of deposit sizes (commonly over five to seven orders of magnitude) the models can discriminate between small tonnage and large tonnage extremes. In addition, the models provide a basis for a probabilistic approach concerning the chances a deposit has of exceeding a "minimum conceptual target". Despite limitations of the availability of data, the regression method appears to have potential in evaluating new finds in established mining camps and in re-evaluating known deposits for which more comprehensive assay infor-mation becomes available. ACKNOWLEDGMENTS This project began with the efforts of J.F.W. Orr (deceased) in establish-ing comprehensive mineral deposit files for Ainsworth, Slocan (Sandon) and Slocan City mining camps. M. Hansen did the same for Zeballos camp, as did P.B. Read for the Trout Lake camp. Assistance in computer file editing was provided by A. Bentzen, who also supplied a prodigious amount of computer output. 76 REFERENCES Davidson, R.A., 1972, A computer oriented analysis of metal production from Ainsworth mining camp, southeastern B .C .; B.A.Sc. Thesis, Dept. Geol. Sciences, Univ. of British Columbia. Godwin, C.I., and Sinclair, A.J., 1979, Application of multiple regression analysis to drill target selection, Casino porphyry copper-molybdenum deposit, Yukon, Canada; Trans. Inst. Min. Metall. Sec. B, v. 88, pp.B93-B106. Goldsmith, L.B., arid Sinclair, A. J., 1984, Triangular graphs as an aid to metallogenic studies of polymetallic vein deposits; B .C. Ministry of Energy, Mines and Petroleum Resources, Paper 1984-1, pp. 240-245. Goldsmith, L.B., and Sinclair, A.J., 1983, Spatial density of silver-lead-zinc-gold vein deposits in four mining camps in southeastern British Columbia; B.C. Ministry of Energy, Mines and Petroleum Resources, Paper 1983-1, pp. 251-265. Hansen, M.C., and Sinclair,.-A..J...,. 1984, A preliminary assessment of Zeballos mining camp; B.C. Ministry of Energy, Mines and Petroleum Resources, Report 1984-1, pp.219-232. Kelly, A.M., and Sheriff, W.J., 1969, A statistical examination of the metallic mineral resources of British Columbia; Proc. Symp. on Decision Making in Mineral Exploration II (eds. A.M. Kelly and A.J. Sinclair); Extension Dept., Univ. of British Columbia, pp. 221-243. Orr, J.F.W., 1971, Mineralogy and computer-oriented study of mineral deposits in Slocan City camp, Nelson Mining Division, British Columbia; M.Sc. Thesis, Dept. Geol. Sciences, Univ. of British Columbia. 77 Orr, F.J.W., and Sinclair, A.J., 1971, Mineral deposits in the Slocan and Slocan City areas of British Columbia; Western Miner, February, pp.22-34. Read, P.B., 1976, Lardeau West Half; Geol. Serv. Canada Open File Map 462 and Open File Report 464. Sinclair, A.J., 1982, Multivariate models for relative mineral potential, Slocan silver-lead-zinc-gold camp; B.C. Ministry of Energy, Mines and Petroleum Resources, Report 1982-1, pp. 167-175. Sinclair, A.J., 1979, Preliminary evaluation of summary production statistics and location data for vein deposits, Slocan, Ainsworth, and Slocan City camps, southern B.C.; in Current Research, Pt. B., Geol. Surv. Canada Paper 79-IB, pp. 173-178. Sinclair, A.J., and Hansen, M.C., 1983, Resource assessment of gold-quartz veins, Zeballos mining camp, Vancouver Island, A preliminary report; B.C. Ministry of Energy, Mines and Petroleum Resources, Report 1983-1, pp. 290-303. Sinclair, A.J., and Woodsworth, G.J., 1970, Multiple regression as a method of estimating exploration potential in an area near Terrace, B .C.; Econ. Geol., v. 65, no. 8, pp. 998-1003. 78 CHAPTER 5 CONCLUSIONS Production data from vein-type mining camps when treated in a rigorous format are of value in focussing attention upon metal content, spatial location, and size, and hence upon geological conditions which may have exerted influences upon the parameters of formerly mined orebodies. Average spatial densities may be used to compare vein camps, to assist in generating models of mineralization within a camp, or to examine the nature of clusters of deposits. Probability graphs allow a segregation of metal grades and tonnages (size) into populations which may then be examined for geological characteristics. Production tonnages can be an adequate single estimator of relative value of deposits. Triangular graphs emphasize the relationship between metals, and may accentuate a mode of occurrence, or demonstrate contrast in metal ratios among mining camps. Multiple regression models developed from each of five vein-type camps permit tonnage estimates in terms of average grades; these models have standard errors of one order of magnitude or less, an acceptable error when treating data which span five to seven orders of magnitude. Use of the predic-tive power of the technique requires that reliable assays for all elements which appear in the equation be obtained in the early exploration phase of an old deposit or a new showing. The methods described herein, once developed from readily available pro-duction data, are easy to apply. Companies or individuals with limited exploration budgets can obtain a first approximation of the potential of a target for relatively small cost. 80 A P P E N D I X 81 TRIANGULAR GRAPHS AS AN AID TO METALLOGENIC STUDIES OF POLYMETALLIC VEIN DEPOSITS By L. B. Goldsmith and A. J. Sinclair Department of Geological Sciences, University of British Columbia INTRODUCTION Triangular graphs are a common means of depicting relative variations of three components of multi-component systems. They are commonly used in petrology and rock classifications, for example, where the components in question generally constitute a large proportion of the system. In geochemistry they may be used to compare trace element ratios for samples from one environment to another. In this latter application it is possible to plot variables that span several orders of magnitude, certainly one of the advan-tages of this form of graphical representation. One application of triangular diagrams in the field of ore deposits classification concerns porphyry-type deposits (for.example, Kesler, 1973; Sinclair, et al., 1982). These authors use triangular diagrams to show variations in metal ratios involving copper, molybdenum, gold, and silver in several groupings. In order to spread plotted points over a reasonable proportion of the triangular field some of these variables had to be multiplied by a constant. For example, in constructing a copper-molybdenum-gold plot Kesler (1973) transformed all variables to the same units and then multi-plied copper by 1, molybdenum by 10, and gold by 10 000. These transformed figures were then recal-culated to a pseudo 100 per cent for plotting purposes. This multiplication procedure is essential or ail plotted points might be confined to a very small field (a point) or to one side of the triangular graph. Nevertheless, it is important to be aware that multiplying some of the components by different and large numbers has the effect of confusing our natural or automatic interpretation of the diagram. For example, in a triangular graph ABC, the line from A to the mid-point of side BC would normally be expected to represent a ratio for B:C of 1:1. If B has been multiplied by 1 000 and A and C have not, then the afore-mentioned line in reality represents a ratio of approximately 1 000:1. Obviously, such diagrams should contain labelled reference lines for important ratios. APPLICATION TO POLYMETALLIC VEIN CAMPS In our studies of vein camps in southern British Columbia (for example, Sinclair and Goldsmith, 1980) we have found triangular diagrams a useful means of comparing production data from various camps. Data available to us at the time of our study were entirely in per cent (for lead and zinc grades) or ounce per ton (for gold and silver grades). Because of this, and because ratios involving precious and base metals commonly used in the exploration industry are in ounces of precious metal per per cent of base metal (ounce per per cent), we adopted the procedure of plotting triangular diagrams as follows: average grade figures were accepted as quoted (per cent or ounce per ton) and for any three figures (for example, lead, zinc, and silver) the figures were recalculated to 100 per cent assuming they were all the same units, that is, 28 ounces silver per ton, 7 per cent lead, and 5 per cent zinc would be recalculated to apparent percentages of 70 per cent silver, 17.5 per cent lead, and 12.5 per cent zinc. The four vein-mining camps considered here are Ainsworth, Slocan (Sandon), Slocan City, and Trout Lake (Fig. 97). Each contains from 43 to 204 veins that have had at least one ton of production for which grade data are available in existing computer files (Orr and Sinclair, 1971; Read, 1976; Goldsmith and Sinclair, 1983; and MINFILE) that have been updated and edited by the writers. 82 Figure 97. Location of Ainsworth, Slocan (Sandon), Slocan City, and Trout Lake silver-lead-zinc-gold camps, southern British Columbia. TROUT LAKE CAMP: Triangular plots of average grade data for 43 past-producer vein deposits in Trout Lake mining camp are shown on Figure 98. The greatest spread of data appears in the silver-lead-zinc plot where all deposits for which these elements are available (n = 38) plot in about half the field represent-ed by silver(ounce)/lead(per cent) ratios greater than about 0.7. In fact, only five of the 38 deposits have silver(ounce/lead(per cent) ratios less than one. Large tonnage deposits (greater than 600 tons production) are distinguished from moderate to low tonnage deposits by symbols and it is apparent from the plot that no distinction of metal ratio field exists as a function of production tonnage. The other three plots of Figure 98 seem more effective in separating deposits into meaningful groups. In particular. Figure 98b and 98c clearly separate gold deposits from low to high tonnage silver deposits. AINSWORTH CAMP: Mean grades of production from 75 veins in Ainsworth camp are shown on tri-angular plots on Figure 99. The silver-lead-zinc plot is dramatically different from that for Trout Lake camp. Data plot as two clearly defined clusters, one with relatively high silver(ounce)/lead(per cent) ratios (greater than one) which is comparable to Trout Lake camp and a second with much lower silver/lead ratios containing most of the deposits in the camp. A second difference from the Trout Lake camp is that a much greater proportion of Ainsworth deposits are zinc rich. Other plots of Figure 99 point to the very low gold content of Ainsworth silver-lead-zinc ores, comparable to the silver-lead-zinc ores of Trout Lake camp. SLOCAN (SANDON): Average production grades for about 200 deposits from the Slocan (Sandon) camp are plotted as triangular diagrams on Figure 100. On Figure 100a virtually all deposits plot in little more than one-half of the triangular field with silver(ounce)/lead(per cent) ratio of greater than 0.7, com-parable to silver-lead-zinc deposits from Trout Lake camp, and to a small subset of deposits from Ainsworth Ot Ag/ion Figure 98. Triangular plots of average production grades for veins of Trout Lake mining camp. Ol Ag/ton Figure 99. Triangular plots of .average production grades for veins, Ainsworth mining camp. Ot Ag/lon Ol Ag/ion GO Figure 100. Triangular plots of average production grades for veins, Slocan (Sandon) mining camp. Figure 101. Triangular plots of average production grades for veins, Slocan City mining camp. 85 camp. Slocan ores differ slightly from the other two groups in that a significant group of zinc-rich deposits occurs and seems to form a separate grouping within the high silver(ounce)/lead(per cent) field. The remaining triangular plots of Figure 100 demonstrate that, like silver-lead-zinc ores from both Ains-worth and Trout Lake camps, Slocan (Sandon) ores are low in gold. Furthermore, the presence of a high zinc population is emphasized by the presence of some plotted points near the zinc vertex of Figure 100c. SLOCAN CITY: Average grade data for Slocan City polymetallic vein deposits are shown on Figure 101. The silver-lead-zinc plot is clearly comparable to the equivalent diagram for Slocan (Sandon) camp. The remaining diagrams are based on sparce data sets but one in particular, the lead-zinc-gold plot of Figure 101 d, shows that a large proportion (more than 40 per cent) of the plotted deposits are scattered throughout the triangular field rather than plotting along or very near the lead-zinc side. In this respect, Slocan City deposits differ clearly from Ainsworth and Trout Lake ores, and significantly, but to a lesser extent, from Slocan (Sandon) ores. This difference reflects the proportionately greater gold content of many Slocan City veins in comparison with veins from the other three camps considered. DISCUSSION Triangular graphs are a practical means of utilizing quantitative chemical information (average grades of recorded production) as a basis for comparing or contrasting polymetallic mineral deposits in vein camps. They probably have a comparable use for portraying other types of polymetallic deposits. The examples studied here involved four polymetallic vein camps with quantitative production data for silver, gold, lead, and zinc. We found advantages in preparing all four possible combinations of the three metals as triangular plots, that is, silver-lead-zinc, silver-gold-lead, silver-gold-zinc, and gold-lead-zinc. Such plots can be obtained rapidly and cheaply as computer-generated plots from computer-based mineral deposit files. Clustering of points is evident is some cases and differences from one camp to another become readily apparent. Of course, these differences represent relative proportions of various metals and give no indi-cation of differences in absolute amounts. One of the principal features that we observe is the common occurrence of a silver-rich group of deposits in all four camps, as shown by the occurrence of clusters towards the silver apex on the silver-lead-zinc plots. On this same plot Ainsworth stands out as being fundamentally different in terms of metal ratios because most deposits cluster in a low-silver field towards the lead vertex. The other major contrast that we note is that Slocan City camp differs from the others in having a much higher proportion of deposits that are relatively enriched in gold. From a metallogenic point of view the conclusions are of some interest. Slocan (Sandon) and Slocan City camps are clearly related in origin (LeCouteur, 1972) but are surrounded by totally different country rock. Slates, fine-grained quartzites, and tuffs occur in Slocan (Sandon) camp but plutonic rocks of the Nelson batholith predominate in Slocan City camp. It seems likely that country rock has exerted some control on metal content possibly due to: (1) changes in the fluid composition during transport through changing T-P conditions, or (2) local wallrock reaction at depositional sites. The preponderance of low silver (ounce)/lead (per cent) values for Ainsworth deposits and the clear indi-cation of relatively higher zinc values accentuates their differences from the other three camps examined. The difference is particularly striking in the case of Ainsworth versus Trout Lake because both camps occur in the same lower Paleozoic sequence (Lardeau Group); albeit rocks in the Ainsworth camp have undergone 86 much higher grade regional metamorphism compared with the Trout Lake camp. Goldsmith and Sinclair (1983) suggested that in Ainsworth camp sulphides first accumulated as seafloor exhalites and subsequently were remobilized locally to form the numerous veins now known, a suggestion supported by lead-isotope data (Andrew, 1982). No clear-cut genetic model has emerged for Trout Lake deposits nor for deposits in the other two camps, although deposits in all camps are clearly epigenetic veins. Differences-in metal ratios may reflect fundamentally different origins of the Ainsworth deposits. Some degree of quantitative information can be retained in triangular graphs by using different symbols for different categories of deposits. We illustrate this for Trout Lake camp (Fig. 98) where three categories of deposits are distinguished by symbols; large tonnage gold deposits, large tonnage silver-lead-zinc deposits; and medium-to-small tonnage silver-lead-zinc deposits. An alternative practical approach might be to re-present by one symbol all those deposits that exceed criteria for a minimum exploration target and to code all other deposits by a second symbol. ACKNOWLEDGMENTS This work utilized data files to which major contributions were made by J.F.W. Orr (deceased) and P. B. Read; A. Bentzen assisted in obtaining computer output. The study is a by-product of a more ex-tensive project on resource evaluation funded by the British Columbia Science Council in association with the MINDEP research project at the University of British Columbia and the British Columbia Ministry of Energy, Mines and Petroleum Resources. REFERENCES Andrew, A. (1982): A Lead Isotope Study of Selected Precious Metal Deposits in British Columbia, Unpub. M.Sc. Thesis, Department of Geological Sciences, University of British Columbia, Vancouver, 79 pp. plus appendices. B.C. Ministry of Energy, Mines & Pet. Res.: MINFILE, Computer-based file of mineral occurrences and deposits in British Columbia. Goldsmith, L. B. and Sinclair, A. J. (1983): Spatial Density of Silver-Lead-Zinc-Gold Vein Deposits in Four Mining Camps in Southeastern British Columbia, B.C. Ministry of Energy, Mines & Pet. Res. Geological Fieldwork, 1982, Paper 1983-1, pp. 251-265. Kesler, S. E. (1973): Copper, Molybdenum and Gold Abundances in Porphyry Copper Deposits, Econ. Geol., Vol. 68, pp. 106-112. Orr, J.F.W. and Sinclair, A. J. (1971): A Computer-Processible File for Mineral Deposits in the Slocan and Slocan City Areas of British Columbia, Western Miner, Vol. 44, pp. 22-34. Read, P. B. (1976): Lardeau West Half, Geo/. Surv., Canada, Open File Map 462 and Open File Rept. 464. Sinclair, A. J. and Goldsmith, L. B. (1980): Metallogeny of Silver-rich Lead-Zinc Veins, Central Kootenay Arc, Southeastern British Columbia, Abstract, CIMM, Bull., Vol. 73, No. 821, p. 74. Sinclair, A. J., Drummond, A. D., Carter, N. C, and Dawson, K. M. (1983): A Preliminary Analysis of Gold and Silver Grades of Porphyry-Type Deposits in Western Canada in Precious Metals in the Northern Cordillera, Assoc. Explor. Geochem., pp. 157-172. 51° LEGEND ORE TONNAGE PRODUCER LOCATION WITH READ IDENTIFICATION NUMBER. (SEE G.S.C. OPEN FILE 4 6 4 MAP, LARDEAU WEST-HALF). CONTOURED DENSITY OF MINERAL OCCURRENCES.CONTOUR INTERVAL 05,2,4,6 OCCURRENCES/km 2 

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