A Lognormal Distribution of Metal Resources

Singer Donald A.

U.S. Geological Survey, 345 Middlefield Road, Menlo Park, California 94025, USA

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Author Bio:
Donald A. Singer, E-mail: singer@usgs.gov

摘要

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Abstract: For national or global resource estimation of frequencies of metals, a lognormal distribution has commonly been recommended but not adequately tested. Tests of frequencies of Cu, Zn, Pb, Ag, and Au contents of 1 984 well-explored mineral deposits display a poor fit to the lognormal distribution. When the same metals plus Mo, Co, Nb₂O₃, and REE₂O₃ are grouped into 19 geologically defined deposit types, only eight of the 73 tests fail to be fit by lognormal distribution, and most of those failures are in two deposit types suggesting a problem with those types. Estimates of the mean and standard deviation of each of the metals in each of the deposit types are provided for modeling.
- mineral deposit model /
- spatial rule /
- grade and tonnage model

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Fig. 1. The copper content of porphyry Cu, reduced facies Cu, carbonate-hosted igneous related, volcanic-hosted massive sulfide felsic-related, and volcanic-hosted massive sulfide mafic-related deposits plotted against each type's straight line representing its standard normal distribution

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Table 1. Copper content distributions by deposit type and tests of lognormality. Mean metric tons of contained copper (log₁₀ data), standard deviation (log₁₀ data), median observed copper content of all deposits, Shapiro-Wilk goodness-of-fit probability of lognormal distribution, number of deposits with reported grade, and total number of deposits with reported tonnage (in thousands t)

Deposit type	Mean	St. dev.	Median Cu (kt)	Prob.	Number deposits	Total number deposits
CAam	4.355 1	0.941 2	0	0.797	9	132
CAig	4.315 4	0.876 4	0	0.892	86	187
FeOxideCuAu	5.644 4	0.779 4	376	0.819	32	36
Kipushi	5.438 5	0.894 1	480	0.668	8	8
MLig	4.854 3	0.735 3	0	0.587	12	38
MLme	4.207 3	0.761 1	0	0.296	5	12
PorCu	6.008 6	0.703 1	1 030	0.391	422	422
RedbedCu	4.494 0	0.804 0	21	0.030	33	33
Reduced Cu	5.819 9	0.898 3	500	0.647	62	62
Revett Cu	5.224 0	0.931 5	125	0.934	14	14
SedHstCu	5.076 4	0.920 1	120	0.952	31	31
SHam	5.107 2	1.133 5	0	0.983	7	25
SHig	4.503 4	0.822 4	0	0.487	13	32
SSPb	3.830 8	1.625 7	0	0.042	5	22
VMSBimodal	4.376 7	0.929 2	26	0.666	267	272
VMSFelsic	4.480 2	0.920 0	36	0.001	411	421
VMSMafic	4.061 3	0.983 6	11	0.066	174	175

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Table 2. Zinc content distributions by deposit type and tests of lognormality. Mean metric tons of contained zinc (log₁₀ data), standard deviation (log₁₀ data), median observed zinc content of all deposits, Shapiro-Wilk goodness-of-fit probability of lognormal distribution, number of deposits with reported grade, and total number of deposits with reported tonnage (in thousands t)

Deposit type	Mean	St. dev.	Median Zn (kt)	Prob.	Number deposits	Total number deposits
CAam	5.648 1	0.756 7	498	0.338	128	132
CAig	5.359 4	0.917 6	308	0.002	185	187
CAme	5.372 5	0.744 5	128	0.378	7	7
Kipushi	5.765 9	1.226 1	5	0.335	4	8
MLig	5.609 9	0.876 0	354	0.926	38	38
MLme	5.169 1	1.025 0	96	0.888	12	12
SHam	6.334 1	0.674 9	1 600	0.924	25	25
SHig	5.757 5	0.994 9	644	0.511	30	32
SSPb	4.628 2	1.543 8	8	0.264	16	22
VMSBimodal	4.716 6	0.923 1	30.5	0.407	217	272
VMSFelsic	5.043 7	0.892 7	75	0.000	349	421
VMSMafic	4.325 7	0.733 8	0	0.383	58	175

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Table 3. Lead content distributions by deposit type and tests of lognormality. Mean metric tons of contained lead (log₁₀ data), standard deviation (log₁₀ data), median observed lead content of all deposits, Shapiro-Wilk goodness-of-fit probability of lognormal distribution, number of deposits with reported grade, and total number of deposits with reported tonnage (in thousands t)

Deposit type	Mean	St. dev.	Median Pb (kt)	Prob.	Number deposits	Total number deposits
CAam	5.176 4	0.822 2	146	0.647	121	132
CAig	5.181 3	0.857 3	130	0.230	166	187
CAme	5.044 8	0.801 0	30	0.243	6	7
Kipushi	5.291 9	1.161 9	275	0.123	6	8
MLig	5.372 9	0.885 2	169	0.838	34	38
MLme	4.852 3	0.830 0	45	0.420	11	12
SHam	5.823 6	0.718 4	592	0.482	25	25
SHig	5.428 0	1.041 9	721	0.066	32	32
SSPb	5.167 4	0.852 6	204	0.691	22	22
VMSBimodal	4.058 6	0.844 2	0	0.006	77	272
VMSFelsic	4.497 6	0.982 0	7	0.005	273	421
VMSMafic	3.564 9	1.018 0	0	0.636 6	13	175

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Table 4. Silver content distributions by deposit type and tests of lognormality. Mean metric tons of contained silver (log₁₀ data), standard deviation (log₁₀ data), median observed silver content of all deposits, Shapiro-Wilk goodness-of-fit probability of lognormal distribution, number of deposits with reported grade, and total number of deposits with reported tonnage (in t)

Deposit type	Mean	St. dev.	Median Ag (t)	Prob.	Number deposits	Total number deposits
CAam	2.275 0	0.759 8	0	0.875	58	132
CAig	2.651 2	0.939 1	144	0.147	138	187
CAme	2.045 0	0.927 6	26	0.210	5	7
FeOxideCuAu	1.918 2	1.155 2	0	0.621	10	36
Kipushi	2.692 5	0.968 3	193	0.970	6	8
MLig	2.688 5	0.951 3	106	0.928	26	38
MLme	2.588 2	0.702 0	32	0.565	6	12
PorCu	2.897 5	0.692 6	0	0.584	172	422
RedbedCu	1.544 1	1.142 0	0	0.698	10	33
Reduced Cu	2.678 0	1.053 5	0	0.274	16	62
Revett Cu	2.807 3	0.756 3	140	0.097	8	14
SedHstCu	1.797 9	0.988 4	0	0.153	7	31
SHam	3.067 3	0.783 8	277	0.540	18	25
SHig	2.760 3	0.999 9	786	0.056	28	32
SSPb	2.041 5	0.904 8	2	0.344	11	22
VMSBimodal	1.754 9	0.936 8	10	0.816	172	272
VMSFelsic	2.051 3	0.958 1	32	0.003	300	421
VMSMafic	1.442 0	1.058 8	0	0.399	70	175

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Table 5. Gold content distributions by deposit type and tests of lognormality. Mean metric tons of contained gold (log₁₀ data), standard deviation (log₁₀ data), median observed gold content of all deposits, Shapiro-Wilk goodness-of-fit probability of lognormal distribution, number of deposits with reported grade, and total number of deposits with reported tonnage (in t)

Deposit type	Mean	St. dev.	Median Au (t)	Prob.	Number deposits	Total number deposits
CAam	0.985 7	0.402 7	0	0.424	3	132
CAig	0.676 6	1.026 3	0	0.002	70	187
FeOxideCuAu	1.313 5	0.797 8	12	0.563	27	36
MLig	0.408 9	0.766 9	0	0.039	7	38
PorCu	1.678 6	0.712 5	12	0.631	256	422
SHam	0.755 8	0.444 6	0	0.695	4	25
SHig	0.662 0	1.190 3	0	0.135	14	32
VMSBimodal	0.309 1	0.956 7	0	0.093	158	272
VMSFelsic	0.430 6	0.980 7	1	0.000	279	421
VMSMafic	0.058 6	1.042 8	0	0.121	72	175

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Table 6. Molybdenum, cobalt, Nb₂O₅, and REE₂O₃ content distributions by deposit type and tests of lognormality. Mean metric tons of contained molybdenum (median observed Mo content in all deposits), cobalt (median observed cobalt content in all deposits), Nb₂O₅, and REE₂O₃ (log₁₀ data), standard deviation (log₁₀ data), Shapiro-Wilk goodness-of-fit probability of lognormal distribution, number of deposits with reported grade, and total number of deposits with reported tonnage (in thousands t)

Deposit type	Mean Mo (median Mo (kt))	Mean Co (median Co (kt))	Mean Nb₂O₃ (median Nb₂O₃ (kt))	Mean REE₂O₃ (median REE₂O₃ (kt))	St. dev.	Prob.	Number deposits	Total number deposits
PorCu	4.618 (28)				0.765 4	0.592	228	422
Reduced Cu		5.088 1 (0)			0.800 4	0.633	15	62
Carbonatite			5.325 8 (0)		1.102 5	0.737	39	55
Carbonatite				5.558 9 (68)	1.079 3	0.925	35	55

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参考文献(18)

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