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Quantitative interpretations of anomalous lead isotope abundances Kanasewich, Ernest Raymond 1962

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QUANTITATIVE INTERPRETATIONS OF ANOMALOUS LEAD ISOTOPE ABUNDANCES by ERNEST RAYMOND KANASEWICH B.Sc, University of Alberta, 1952 M.Sc, University of Alberta, 1960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1962 In presenting 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 of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree tha 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 reference and study. I f u r t h e r agree that permission f o r extensive 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 or by h i s representatives. It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Physics  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date August 28th, 1962. PUBLICATIONS 1. Garland, G.D.; Kanasewich, E.R.; and Thompson, T.L.; 1961, Gravity measure-, ments over the southern Rocky Mountain Trench area of British Columbia. Journal of Geophysical Research, 66, 2495-2505. 2. Kanasewich, E.R.; Gravity measurements on the Athabaska Glacier, Alberta, Canada. Journal of Glaciology, in press. 3. Kanasewich, E.R.; 1962, Approximate age of tectonic activity using anomalous lead isotopes. Geophysical Journal, accepted for publication. 4. Russell, R.D.; Kanasawich, E.R.; and Ozard, J.M.; Isotopic abundances of lead from a frequently-mixed source. Geochimica et Cosmochimica Acta, in press. The University of British Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ERNEST RAYMOND KANASEWICH B.Sc., University of Alberta, 1952 M.Sc, University of Alberta, 1960 MONDAY, AUGUST 27, 1962, at 9:30 A.M. IN ROOM 303, PHYSICS BUILDING COMMITTEE IN CHARGE Chairman: F. H. SOWARfr J. A. JACOBS W. F. SLAWSON R. D. RUSSELL R. M. THOMPSON J. C. SAVAGE J. TROTTER W. H. WHITE External Examiner: R. M. FARQUHAR University of Toronto QUANTITATIVE INTERPRETATIONS OF ANOMALOUS LEAD ISOTOPE ABUNDANCES ABSTRACT A new method has been proposed for determining the age of Lead sulfide mineralization from anomalous lead isotope abundances. The anomalous leads are most readily recognized by the linear relationship of the isotope ratios on any compositional diagram. The method assumes that the initial stage of lead isotope development occurred in a system having a uniform distribution of uranium, thorium and lead. This accords with experimental results obtained by the writer and other research workers at the University of British Columbia that single-stage isochrons as proposed by Houtermans are either very short or do not exist. Consider t± to be a time of tectonic activity during which ordinary leads were differentiated from a deep source and.either concentrated to form a lead deposit' at this time or disseminated throughout the upper crust. Contemporaneously uranium and thorium bearing solutions were incorporated into the same environment. At time t2 tectonic activity recurred in the area. Some of the ordinary leads were remobilized and became contaminated with radiogenic lead to form anomalous lead deposits. As an example, at Broken H i l l , Australia,' t^' is 1600 million years, while t2 is 510 + 80'm.y. This age correlates - with geological evidence'and independent potassium-argon dates of 504 and 525 million years. A large proportion of anomalous lead isotope measurements may be interpreted on the basis of the two-stage models outlined above. Extension of this model to an n-stage system is considered. GRADUATE STUDIES Field of Study: Interpretation of lead isotop abundances Advanced Geophysics J. A. Jacobs Radioactive and Isotopic Processes in Geophysics .... R. D. Russell-Waves '. ••• J. C. Savage Electromagnetic Theory G. M. Volkoff Introduction to Quantum Mechanics J.- Grindlay Related Studies: Crystal Structures J. Trotter and K. B. Harvey Analysis ........... E. Macskasy - i i -ABSTRACT A new method has been proposed for determining the age of lead sulfide mineralization from anomalous lead Isotope abundances. The anomalous leads are most readily recognized by the linear relationship of the isotope ratios on any compositional diagram. The method assumes that the i n i t i a l stage of lead isotope development occurred in a system having a uniform distribution of uranium, thorium and lead. This accords with experimental results obtained by the writer and other research workers at the University of British Columbia that single-stage isochrons as proposed by Houtermans are either very short or do not exist. Consider t-j_ to be a time of tectonic activity during which ordinary leads were differentiated from a deep source and either concentrated to form a lead deposit at this time or disseminated throughout the upper crust. Contemporane-ously uranium and thorium bearing solutions were incorporated into the same environment. At time t g tectonic activity recurred in the area. Some of the ordinary leads were remobilized and became contaminated with radiogenic lead to form anomalous lead deposits. Existing lead isotope analyses yield the following results. At Broken H i l l , Australia, t q i s 1600 million years, while t ? i s 510 ± 80 m.y. - I i i -For Goldfields, Saskatchewan, t-, i s 2015 m.y. while t i s 560 ± 2 5 0 m.y. At Sudbury, Ontario, t 1 i s 1730 m.y. and t g i s 870 i : 280 m.y. For lead deposits around the Ozark Dome area, including Joplin and Bonne Terre, Missouri, t^ is 1350 m.y. and t i s about 115 m.y. For leads in west-central New Mexico, i s 1490 m.y. and t g i s about 69 m.y. The errors in the estimates are generally quite large but the values quoted are consistent with available geological and chronological data. The simplest type of anomalous leads which can occur is a mixture of two ordinary leads. This has only been found to occur on the boundary between two geological provinces. Examples of this type have been identified in the Cobalt area, Ontario and in the Baltic Shield along the border between the Fenno-Karelides and Svecofennides. A large proportion of anomalous lead Isotope measure-ments may be interpreted on the basis of the two-stage " models outlined above. Extension of this model to an n-stage system l s considered. - i v -TABLE OF CONTENTS ABSTRACT i i LIST OF ILLUSTRATIONS v i LIST OF TABLES ix INTRODUCTION 1 CHAPTER 1 STUDIES OF LEAD ISOTOPIC ABUNDANCES 1.1 Introduction 6 1.2 Theory of Single-Stage Lead Models 9 1.3 Leads in Meteorites 14 1.4 The Earth and Meteorites 24 1.5 Single-Stage Models Employing a Unique Growth Curve 28 1.6 Use of P b 2 0 8 / P b 2 0 4 Ratios 33 1.7 Multi-stage Lead Models 36 CHAPTER 2 MULTI-STAGE LEAD MODELS 2.1 Introduction 44 2.2 Seismic and Geochemical Evidence 45 2.3 Division of the Continents into Geological Provinces 48 2.4 Relationship of Ordinary Lead Isotopes to Geological Provinces 51 2.5 A Two-Stage Lead Model 66 2.6 Short Period Anomalous Leads 75 2.7 Long Period Anomalous Leads 82 2.8 Multi-Stage Lead Models 90 - V -TABLE OF CONTENTS (Cont'd) CHAPTER 3 ANALYSIS OF LEADS WITH UNUSUAL I SO TOPIC COMPOSITION 3.1 Leads with Unusual Isotopic Composition 102 3.2 Sample Preparation and Analysis 103 3.3 Contamination of Lead Tetramethyl 104 3.4 Measured Lead Isotope Ratios 113 3.5 Interpretation of Results 113 3.6 Classification of Lead Isotope Ratios 127 3.7 Summary 131 CHAPTER 4 APPROXIMATE AGE OF TECTONIC ACTIVITY USING ANOMALOUS LEAD ISOTOPES 4.1 Introduction 132 4.2 Broken H i l l , Australia 132 4.3 Goldfields Region, Saskatchewan 141 4 e4 Sudbury, Ontario 144 4c5 Ozark Dome, Arkansas, Missouri and Oklahoma 146 4.6 New Mexico, U.S.A. 150 CONCLUSIONS 154 BIBLIOGRAPHY 158 APPENDICES 175 Linear Regression with both Variates having Errors 175 1. A Table for Constructing Growth Curves; t 0 = 4500 m.y. 180 2. A Table for Constructing Growth Curves; t = 4550 m.y. 181 3. A Table for Constructing Growth Curves; t Q = 4560 m.y. 182 - v i -APPENDICES (Cont'd) 4. A Table for Plotting Growth. Curves; t 0 s 4560 m.y. 183 5. A Table for Dating Ordinary Leads; t = 4500 m.y. 184 6. A Table for Dating Ordinary Leads; t 0 = 4550 m.y. 185 7. A Table for Dating Ordinary Leads; t 0 = 4560 m.y. 186 LIST OF ILLUSTRATIONS Fig. 1.1 Plot of Pb 2 0 7/:Pb 2 0 4 against Pfc206/pb204 for lead extracted from meteorites. 17 Fig. 1.2 Plot of Pb 2 0 8/Pb 2 0 4 : against P b 2 0 6 / P b 2 0 4 for lead extracted from meteorites. 18 Fig. 1.3 Isotopic composition of leads from manganese nodules and pelagic sediments 26 in the Pacific basin. Fig. 1.4 Location of samples shown in Figure 1.3. 26a Fig. 1.5 Relationship between isochrons and error lines. 30 Fig. 1.6 Relationship between x and y for some common leads. 34 Fig. 1.7 Relationship between z/x and y/x for some common leads. 37 Fig. 2.1 Geological provinces of North America 50 Fig. 2.2 Relationship of K-Ar ages to oldest model lead ages in the Cordilleran and Beltian geological provinces 53 Fig. 2.3 Relationship of K-Ar ages to oldest model lead ages In the Appalachian and Grenville geological provinces 55 Fig. 2.4 Relationship of K-Ar ages to oldest model lead ages in the Ozarkian geological province. 57 - v i i -LIST OF ILLUSTRATIONS (Cont'd) Fig. 2.5 Relationship of K~Ar ages to oldest model lead ages in the Penokian geological province. 58 Fig. 2.6 Relationship of K-Arages to oldest model lead ages in the Churchill and Bear geological provinces. 61 Fig. 2.7 Relationship of K-Ar ages to oldest model lead ages in the Superior and Slave geological provinces 64 Fig. 2.8 Lead isotope compositional diagrams for the Lake Di s t r i c t , England. 78 Fig. 2.9 Lead isotope compositional diagrams for Yellowknife, N.W.T., Canada. 81 Fig. 2.10 Lead isotope compositional diagrams for samples from the region between Cobalt and Chibougamau. 83 Fig. 2.11 Location of samples in Fig. 2.10. 84 Fig. 2.12 Lead Isotope compositional diagrams for the West Karelian zone of Finland 86 Fig. 2.13 Lead isotope ratios from the Central Finnish zone 88 Fig. 2.14 Relationship between Pb 2 0 8/Pb 2 0 6 and pD207/pb206 f o r SOme common leads from the Central Finnish Zone. 89 Fig. 2.15 Graph of P b 2 0 6 / R ) 2 0 4 and P b 2 0 7 / P b 2 0 4 for a theoretical two-stage lead model. 97 Fig. 2.16 Graph of P b 2 0 7 / P b 2 0 4 and Pb 2 0 6 / P b 2 0 4 for a theoretical three-stage model. 98 Fig. 2.17 Graph of P b 2 0 7 / P b 2 0 4 and Pb 2 0 6/R> 2 0 4- for a theoretical six-stage model. 100 Fig. 2.18 Graph of P b 2 0 7 / P b 2 0 4 and P b 2 0 6 / R ) 2 0 4 for a theoretical eleven-stage model. 101 Fig. 3.1 Lead isotope ratios for Bluebell, British Columbia. 1.05 - v i i i -LIST OF ILLUSTRATIONS (Cont'd) Fig. 3.2 Lead isotope ratios for Bluebell, B r i t i s h Columbia. 106 Fig. 3.3 Effect of contamination on a sample of Bluebell. 108 Fig. 3.4 Mass spectrogram of contaminant and lead tetramethyl. 109 Fig. 3.5 Lead isotope ratios for St. Magloire, Quebec. I l l Fig. 3.6 Lead Isotope ratios for St. Magloire, Quebec. 112 Fig. 3.7 Comparison of lead Isotope ratios from Ivigtut. 117 Fig. 3.8 Comparison cf lead isotope ratios from Ivigtut. 1.18 Fig. 3.9 Lead isotope ratios having an age of 1800 m.y. in the Baltio Shield. 121 Fig. 3.10 Lead isotope ratios having an age of 1800 m.y. in the Baltic Shield. 122 Fig. 3.11 Development of lead isotope ratios at Ivigtut on a three-stage model. 126 Fig. 4.1 Graph of P b 2 0 7 / P b 2 0 4 and P b 2 0 5 / P b 2 0 4 showing linear relationship between ordinary and anomalous leads at Broken H i l l , Australia. 135 Fig. 4.2 Chronological relationship between Russell-Farquhar model and the present one for Broken H i l l , Australia. 137 Fig. 4.3 Plot of P b 2 0 8 / P b 2 0 4 and P b 2 0 6 / F b 2 0 4 for leads from Broken H i l l , Australia. 139 Fig. 4.4 Graph of P b 2 0 7 / P b 2 0 4 and P b 2 0 6 / ^ 2 0 4 for leads from Goldf.ields, Saskatchewan. 143 Fig. 4.5 Plot of p b 2 0 8 / P b 2 0 6 against P b 2 0 7 / P b 2 0 6 for leads from Goldfields,Saskatchewan. 145 - ix -LIST OF ILLUSTRATIONS (Cont'd) Fig* 4.6 Fig. 4.7 Fig. a, Graphs of P b 2 0 7 / P b 2 0 4 and Pb 2 0 6 / P b 2 0 4 for leads from Ozark Dome and New Mexico, U.S.A. Plot of pb 208/ p b206 a n d p b leads from New Mexito, U.S.A. ,207 /Pb 2 0 6 for Appendix: Residuals, h^, in linear regression analysis. 147 152 176 . LIST OF TABLES Table 1,1 Symbols and Constants used .in age determination 12 Table 1.2 The Age of Meteorites using Pb 2 0 6/Pt> 2 0 4 andPb 2 0 7/Pb 2 0 4 data. 20 Table 1.3 The Age of Meteorites using P b 2 0 6 / P b 2 0 4 and P b 2 0 7 / P b 2 0 4 data. 20 Table 1.4 Th/U ratio using P b 2 0 6 / P b 2 0 4 and P b 2 0 8 / P b 2 0 4 data from meteorites. 21 Table 1.5 Isotopic composition of primordial lead 23 Table 1.6 Comparison of constants used in dating galenas. 32 Table 1,7 Comparison of constants used in dating galenas with Pb208/Pb204 ratios 35 Table 2.1 Properties of the Crust and Upper Mantle 46 Table 2.2 Physical Properties and Distribution of Elements in Typical Rocks. 47 Table 2.3 Binomial distribution of V. for frequently-mixed source. 95 Table 3,1 Apparent Age and YQ of some Unusual Leads. 103 Table 3.2 Measured Lead Isotope Ratios for Ivigtut, Greenland. 114 Table 3.3 Measured Lead Isotope Ratios for Bluebell, B.C. and St. Magloire, P.Q., Canada. 1.15 - X -LIST OF TABLES (Cont'd) Table 3.4 Measured Lead Isotope Ratios for Miscellaneous Samples 116 Table 4.1 Results of Calculations on Anomalous Leads 133 Table 4.2 Isotopic Analyses of Thackaringa Leads 140 APPENDICES Table 1 A Table for Constructing Growth Curves; t Q = 4500 m.y. 180 Table 2 A Table for Constructing Growth Curves; t Q = 4550 m.y. 181 Table 3 A Table for Constructing Growth Curves; t 0 = 4560 m.y. 182 Table 4 A Table for Plotting Growth Curves; t 0 = 4560 m.y. 183 Table 5 A Table for Dating Ordinary Leads; t Q = 4500 m.y. 184 Table 6 A Table for Dating Ordinary Leads; t 0 = 4550 m.y. 185 Table 7 A Table for Dating Ordinary Leads; t Q = 4560 m.y. 186 INTRODUCTION Significant advances have been made in the last few years in the f i e l d of geochronology and, indeed, in a l l branches of the earth sciences. The instrumentation has been greatly improved and chemical procedures have been developed which allow the preparation of much purer samples. In the study of lead isotope abundances, preci-sion greater by an order of magnitude i s being obtained on a routine basis as compared to results obtained several years ago. In the interpretation of old data, researchers necessarily relied on much averaging and an over-all s t a t i s t i c a l treatment before reaching conclusions of any validity. The new data i s f a l l i n g into striking patterns which are much more amenable to mathematical analysis. It is becoming apparent that the number of models which f i t this pattern of abundances is quite restricted. The net result of these developments is that the physical and chemical properties of the crust-mantle system may be out-lined more accurately with reference to the elements of uranium, thorium and lead. This thesis i s one in a series of researches on lead isotope abundances which are being carried out at the University of British Columbia under the direction of R. D. Russell and W. F. Slawson. The instrumental phase of the work was initiated by F. Kollar and i s being continued by J". S. Stacey. , The chemical preparation of both macroscopic - 1 -- 2 -and microscopic lead quantities is being studied by T. J". Ulrych. R. G. Ostic has been studying the isotopic compo-sition of certain conformable sulfide deposits containing galena and their relationship to tectonic events, while A. Bo L. Whittles is undertaking research into trace lead isotope abundances associated with sulfides such as pyrites and pyrrhotites. The present writer i s concerned with the development of suitable multi-stage models which w i l l account for the pattern of abundances observed in any region and provide information about the tectonic history of the area. A. J. Sinclair i s studying the geological aspects of lead isotope abundances as found in the Kootenay Arc of British Columbia. The writer's previous experience has been in the f i e l d of seismology and gravity interpretation. For several years he was in charge of a particular phase of geophysical interpretation in the petroleum industry both in Canada and the Middle East. During this time he became aware of the importance of studying regional and contin-ental scale geological features because of their effect on the interpretation of local problems. In 1960, while pursuing studies at the University of Alberta and carrying out gravity research in the Canadian Cordillera, he became aware of some of the new results which R. D. Russell and F. Kollar were obtaining with a newly designed mass - 3 -spectrometer. With his varied background in physics and geology, -it was thought that the writer might examine both old and new data with a fresh insight. Over 2000 analyses of galena from a l l over the world are available in the literature. A review of this data was made and i t was decided that despite i t s nominal precision, much of i t could be used in the interpretation of any area provided a small number of very precise measurements could be made to determine the cause of the scatter. In particular, i t was necessary to know how much variation was to be expected to occur naturally and how much was caused by chemical impurities and instrumental variation. Three test areas were selected, where the old data showed up to 5% variation along theoretical time lines called isochrons and the leads appeared to have been derived in anomalously low uranium/lead environments. The results indicated that most of the observed variation was due to d i f f i c u l t i e s in the laboratory and that true variations which are found in nature have a recognizable form which may often be distinguished from experimental errors. The importance of this may be appreciated i f i t i s realized that these very precise measurements require three or four times as much time to carry out. However, with a small number of precise measurements, i t should be possible to make use of much of the old data. - 4 -The f i r s t chapter of this thesis i s concerned with a review of the more s i g n i f i c a n t aspects of previous research into lead isotopes. The second chapter outlines the writer's approach to the t h e o r e t i c a l development of models for lead isotope abundances i n the broad framework of other f i e l d s of studies i n the earth sciences. A two stage model i n which the lead isotopes developed i n two d i s t i n c t uranium and thorium systems i s presented to account f o r anomalous isotope abundances which are observed. The extension of t h i s model to multi-stage systems i s noted. The r e s u l t s of the experimental phase of the program are presented i n chapter three together with some c r i t e r i a for defining d i f f e r e n t types of lead. The fourth chapter deals with the app l i c a t i o n of anomalous lead models to s p e c i f i c geologic d i s t r i c t s . Areas covered include Gold-f i e l d s , Saskatchewan; the Ozark Dome region, U.S.A.; New Mexico, U.S.A.; and Broken H i l l , A u s t r a l i a . Parts of chapter two and four have been combined into an a r t i c l e which has been accepted f o r publication (Kanasewich, 1 9 6 2 ) , Dr. R. M. Farquhar of the University of Toronto kindly allowed the use of his unpublished lead isotope measurements from the Cobalt, Larder Lake and Grenville areas. In addition, the writer would l i k e to acknowledge the assistance of Dr. Farquhar i n obtaining c r i t i c a l samples from the Bluebell, St. Magloire and Ivigtut d i s t r i c t s . - 5 -The successful completion of this investigation was made possible by the active interest and cooperation of many people. Dr. R. D. Russell suggested the problem and I am particularly Indebted to him and to Dr. W. F. Slawson for many useful discussions and aid in obtaining c r i t i c a l samples. Dr. W. H. White aided the writer on several features of the geology of the areas under discussion. Valuable assistance was obtained from R. G. Ostic, A.B.L. Whittles, J". S. Stacey, T. J. Ulryeh, A. J. Sinclair and P. Neukirchner in the preparation of samples and the operation of the mass spectrometer. The assist-ance of J". M. Ozard, Miss S. Hanmer and Miss J. Kelly in the computation of results i s gratefully acknowledged. The work was financed through grants from the Petroleum Research Fund of the American Chemical Society and the National Research Council of Canada. The author would like to express his appreciation for a fellowship from the International Nickel Company of Canada. CHAPTER 1 STUDIES OE LEAD ISOTOPIC ABUNDANCES Accuse not Nature, she hath done her part; Do thou hut thine. Milton, Paradise Lost, VIII, 561. 1.1 Introduction Geophysical application of radioactivity began with Boltwood's (190?) use of lead, uranium and thorium analyses to estimate the age of minerals. Since that time the study of radioactive atoms and their stable end products has b e e n used to further our knowledge about an expanding frontier of related earth sciences. Information has been obtained about the age of the earth and i t s relationship to extra-terrestrial objects, about the distribution of radioactive elements in the crust and mantle, about the source and the processes necessary for the concentration of sulfide ores, and about the frequency, duration and relationship of orogenic events in different continental units. The integration of this information with that obtained from other fields of studies is increasing our understanding of the forces which have shaped the earth In the form we see i t today and w i l l aid in the evaluation of current theories about continental growth, continental d r i f t and convection currents in the mantle. This study w i l l deal with the information obtainable - 6 -- 7 -from the stable end products of the U 2 3 8 , U 2 3 5 and T h 2 3 2 radioactive series. The stable isotopes produced are 206 207 208 Pb , Pb and Pb respectively. A fourth stable iso-tope of lead, Pb 2^ 4, occurs naturally and has not been generated by any radioactive decay. Mass spectrometers can only measure relative abundances so i t is useful to express a l l the other lead isotope abundances i n terms of the number of P b 2 0 4 atoms present. Only common leads w i l l be considered here. These are leads which now have an insignificant amount of uranium 206 and thorium associated with them. The isotopes of Pb , 207 208 Pb and Pb in any common lead may be thought of as consisting of two parts: Common lead = Primeval lead + Radiogenic lead. The isotopic composition of lead existing at the time when the earth formed is termed primeval lead and is taken to be the same for the earth and meteorites. The isotope pb204 ^ g gntireiy 0 f primeval origin. Radiogenic lead consists of the isotopes generated by uranium and thorium decay since the formation of the earth. These radiogenic atoms, which are indistinguishable from primeval atoms, become mixed with the original lead. The radiogenic portion i s governed by the amount of uranium and thorium present at any time and i f this i s known, the radiogenic addition may be predicted exactly by an integral equation - 8 -derived from the theory of radioactive decay. In practice, i t i s the isotopic composition of a group of common leads which is known and the inverse problem must be solved to determine the history of the lead, uranium and thorium isotopes in the area. Common leads are called "ordinary" or "anomalous" depending on the form of the integral equa-tion. Anomalous leads have been defined by Russell et a l (1961) as "leads of which the isotope ratios were produced in two or more distinct lead-uranium systems, as opposed to ordinary leads which were formed in a single lead-uranium system". The f i r s t mass spectrometer measurements on the isotopic composition of common leads were carried out by Nier (1938, 1941). Twenty-five samples of galena were analyzed and these formed the basis for estimates on the age of the earth by Gerling (1942) and Holmes (1946, 1947, 1949). These and subsequent estimates of the age of the earth were carried out by assuming a single stage model for the addition of radiogenic lead and using a geologic estimate for the time of mineralization. Later calcula-tions (Houtermans, 1946, 1947; Jeffreys, 1948, 1949; Bullard and Stanley, 1949) used a more sophisticated mathematical treatment but this has not increased the r e l i a b i l i t y to any appreciable extent. Gerling's estimate for the age of the earth was 3.23 b i l l i o n years, while - 9 -Holmes (1947) obtained a range of ages between 2 and 4 b i l l i o n years with a mean value of 3.35 b.y. On the basis of 80 samples of galena, Russell and Allan (1956) calculated ages between 2.8 and 5.0 b.y. with an arithmetic mean of 4.3 b.y. From the very beginning Holmes recognized d i f f i c u l t i e s in the application of terrestrial lead abundances because of the possibility that the "lead ore might be due to concentrations of rock-lead plus lead from older ore deposits" or "a lead ore might come from a source to which additions of the radioactive elements had been made at some time after the origin of the source but before the date of ore formation". Even earlier, Nier (1941) had commented upon the anomalous composition of leads from Joplin, Missouri and Ivigtut, Greenland. Another d i f f i c u l t y is that the isotopic abundance of P b 2 0 4 is always less than 2% of the total lead content and consti-tutes a very d i f f i c u l t measurement. Russell and Farquhar (1960, p.36) have shown that an error in P b 2 0 4 of 1 to 3$ can change the calculated age of the earth by over a b i l l i o n years. In a later chapter i t w i l l be shown that errors of this magnitude are easily made and erroneous conclusions are occasionally arrived at by assuming that these variations are real. 1.2 Theory of Single-stage Lead Models Each of the three parent radioactive nuclei considered - 10 -here produce another unstable nucleus so that a decay series results with the end product being a stable lead isotope. Each of the nuclei i s characterized by i t s own h a l f - l i f e which i s inversely proportional to the proba-b i l i t y of i t s decay. The half—lives of the intermediate members of the uranium and thorium decay series are short in comparison to geologic time so that after about one million years the rates of decay of the intermediate members are controlled by the rate of decay of the parent uranium and thorium nuclei. The decay systems may be indicated symbolically as •J238 > P b 2 0 6 + 8 He4 + Energy > P h 2 0 7 + 7 He 4 + Energy T h 2 3 2  > P b 2 0 8 + 6 He 4 + Energy From the law of radioactive decay dN = - X N dt 1.1 where X i s the decay constant for a particular nucleus and dN i s the number of nuclei out of a total N which are decaying in a short time dt. If N Q is the number of atoms present at the i n i t i a l time, t = 0, then the solution of 1.1 i s N = N Qe" X t 1,2 For the purposes of geochronology i t i s convenient to let the present time be t = 0 and count time postively into the past. In .this case, N Q is the number of atoms at the - 11 -present time and equation 1,2 becomes N = N e+Xt 1.3 o Gerling (1942), Holmes (1946) and Houtermans (1946) assumed that the ratios of U 2 3 8, U 2 3 5 and T h 2 3 2 to P b 2 0 4 remained constant in looally closed systems from the time t Q , when the earth formed to a time, t^, when mineralization isolated the lead from the uranium and thorium. Under these conditions the number of Pb atoms present at time in any such closed system is or\R 206 238 238 N(Pb 2 0 6) = N(Pb ) + N(U ) - N(U ) 1.4 *1 t Q t Q t x Both sides of the equation may be divided by the number 204 of Pb atoms and in terms of the symbols shown in Table 1.1 equation 1.4 becomes x = a + 137.8V (e X t° - e X t l ) 1 , 5 o o Similar expressions may be written for y and z which are the Pb 2 0 7/Pt> 2 0 4 and P b 2 0 8 / P b 2 0 4 ratios for a particular mineral. y = b Q + V 0 ( e X ' t 0 - e*'*!) 1.6 z - c D + W c ( e r t ° - e r t l ) 1.7 These three equations are one form of the "growth curves" for ordinary leads. The present day ratios of U to - 12 -TABLE 1.1 Symbols and Constants Used in Age Determination Isotope At present At time At time Ratio t = 0 t t„ P b 2 0 6 a x a c P b204 Pb 2°7 b y b D p b204 P b 2 0 8 PI 2 5* o U 2 3 8 137.8V0* 137.8V Ge X t 137.8V 0e X t° P b 2 0 4 U 2 3 5 V Q V0eXt V Q e x , t o P b 2 0 4 T h 2 3 2 WD W0e^Mt Woe*-"*© p b204 -9 -1 Decay Constants Value in 10 (years) Parent Atom X 0.1537** U X' 0.9722 U 2 3 5 X" 0.0499 T h 2 3 2 *a = U 2 3 8 : U 2 3 5 = 137.8 : 1 (Inghram, 1947) ••Kovarik, A.F. and Adams, N.E.,Jr. Phys. Rev. 98, 46, 1955. Fleming, E.H.,Jr., Ghiorso, A. and Cunningham, B.B. Phys. Rev. 88, 642, 1952. Picciotto, E. and Wilgain, S. Nuovo Cim. Ser. 10, 4, 1525, 1956. 204 Pb , Y , may be eliminated between equations 1,5 and 1.6. The right hand side of this equation i s a constant for a l l leads which were mineralized at time t , If the isotopic ratios, x and y, are plotted on a graph, a l l the leads with age t^ w i l l l i e on a straight line through the primeval lead abundances, a Q and b Q and having a slope 0 . This equation i s known as Houtermans* "isochron equation". Tables of 0 versus t-^  for t Q equal to 4.50, 4.55 and 4,56 b i l l i o n years are presented in the appendix. Collins, Russell and Farquhar (1953) assumed that there i s a single average growth curve to which a l l ordinary leads f i t within a few percent. Under this assumption, Y Q and W have remained essentially constant over the entire world. Small deviations of Isotopic ratios from the mean growth curve were explained as being due to variations in the uranium/lead and thorium/lead ratios with time and geographic locations (Russell et a l , 1954). The isotopic composition, a, b, and c, of a modern ordinary lead (t n = 0) are given by the equations 0 = 1.8 137.8(6**0- e**!) a = a Q + 137.8Vo(eA,'o - i ) 1.9 - 14 -b = b o + V 0 ( e X ' t o - 1 ) 1 - 1 G c = C Q + W 0 ( e r t ° - 1 ) 1.11 Substituting these transformations into 1.5, 1.6 and 1.7, i t is possible to obtain the equations used by Collins et a l (1953). x = a - 137.8V c(e X t l - 1 ) 1.12 y = b - V 0 ( e X , t l - 1 ) c -1.13 1.14 Thus, i t should be possible to evaluate the above equations i f we knew the present day values of the isotopic ratios, a, b, c, V 0 and WQ without knowing the age of the earth or the primeval lead abundances. Attempts at finding these t constants by Collins et a l (1953) and by Cumming (Wilson et a l , 1956) were only partially successful. Not only was i t necessary to know the time of mineralization, but independent evidence was necessary to support the hypothesis of a single-stage growth curve for each lead mineral. 1.3 Leads in Meteorites The interpretation of common leads was greatly - 15 -advanced by determinations of the isotopic composition of microgram quantities of lead in meteorites with the use of a solid source mass spectrometer. Patterson (1953) measured the isotopic ratios of lead from two t r o i l i t e s which had so small a quantity of uranium and thorium that their lead isotope composition had not changed since they were formed. Thus, the t r o i l i t e (FeS) phase of Canyon Diablo meteorite had 18 parts per million of lead but only 0.009 ppm of uranium. In a bold extrapolation Houtermans (1953) and Patterson (1953, 1955) assumed that these meteoritic lead isotope ratios could be used for the prime-val lead abundances of the earth. Combining terrestrial lead ores and primeval meteoritic abundances, they obtained a value of 4,5 b i l l i o n years for the age of the earth.. Considerations about the origin of the solar system are beyond the scope of this work. However, the evidence from lead isotopes definitely indicates that i t i s possible to find a unique time when meteorites cooled from a quasi-f l u i d state to a solid state before disruption. Patterson (1955, 1956) determined the lead isotopic composition of several stone meteorites. The isotopic composition of the stone and iron meteorites was found to be linearly related, showing that they represented isolated closed systems with widely varying uranium to lead ratios since a time t Q when they became differentiated. The time t is given by the slope of the meteoritic isochron and turned - 16 -out to be 4.55 i 0.07 b i l l i o n years (Patterson, 1956). Figures 1,1 and 1.2 present graphically a l l the published lead isotope results which consist of 51 analyses on 34 meteorites. The linear relationship 207 204 206 204 between Pb /Pb and Pb /Pb i s clearly evident; however, certain points f a l l off the line and must be considered individually. Holbrook N (No,7) i s a chondritic stone meteorite containing only 0,28 ppm of lead (Hess and Marshall, 1960). During analysis, a radio-genic spike (high P b 2 0 6 / P b 2 0 4 ratio) i s added to the meteoritic lead and i t is possible that a small error was made in the quantitative determinations to yield this anomalous result. Two other determinations on different parts of the same meteorite (8, 9) f a l l close to the zero isochron. A similar explanation probably holds for Norton County (28) and Elenovka (27). The meteorite with the greatest uranium and thorium to lead ratio is an achondrit* called Nuevo Laredo (1) (Patterson, 1956). An analysis on another portion of the same meteorite by Edwards and Hess (1956) indicated that this portion (15) developed In a lower uranium and thorium environment. Such a situation (Patterson, 1953, 1955, 1956; Edwards and Hess, 1956; Staryk et a l , 1958, 1960; Hess and Marshall, 1960, Chow and Patterson, 1961, Marshall and Hess, 1961; Marshall, 1962). 40 Figure 1-1. Plot of Pb 207/Pb 204 against Pb 206/Pb 204 for lead extracted from meteorites. I 204 - 19 -is quite possible and occurs in terr e s t r i a l galenas as shown by Slawson and Austin (1962) in their single crystal analyses of leads from New Mexico. A further series of measurements on this meteorite would be valuable as this would make i t possible to determine a lead age for a single meteorite. Regression analyses were made on the meteoritic data to determine the best f i t t i n g straight line. Since both ratios have errors, the square of the deviations was minimized perpendicular to the line Itself. The equation used together with a derivation of the standard deviation on the slope i s given i n the Appendix. The results are shown in Table 1.2 for different combinations of the data. The age of the meteorites was calculated by setting t^ equal to zero in equation 1.8. Table 1.3 gives the slope of the best straight line through Patterson's original primeval lead ratios. Table 1„4 presents the slope of the best straight line through the P b 2 0 8 / P b 2 0 4 and P b 2 0 6 / P b 2 0 4 ratios together with the calculated Th/U ratio. - 20 -TABLE 1.2 The Age of Meteorites Using P b 2 0 6/Pb 2 0 4 and P b 2 0 7 / P b 2 0 4 Data (Diagonal Linear Regression with no constraints on primeval abundances) Source Number of Slope and t Analyses Standard Deviation ( b i l l i o n years) Patterson 5 0.6027 ± .0090 4.58 .03 A l l American Data 24 0.6045 .0120 4.58 ± .03 A l l Russian Data 28 0.5578 +_ .0293 4.47 .08 A l l the Data 52 0.5950 + .0117 4.56 + .03 TABLE 1.3 The Age of Meteorites Using P b 2 0 6 / P b 2 0 4 and P b 2 0 7 / P b 2 0 4 Data (Diagonal Linear Regression through a Q = 9,50, b Q s 10.36.) Source Number of Slope and t Analyses Standard /,.,,. » Deviation ( b i l l i o n years) Patterson A l l American Data A l l Russian Data A l l the Data 5 0.5962 + .0084 4.56 .02 24 0.5933 .0094 4,56 .02 28 0.6026 .0160 4.58 +_ .04 52 0.5960 ± .0081 4.56 +_ .02 - 21 -TABLE 1.4 Th/U Ratio Using P b 2 0 6 / P b 2 0 4 and P b 2 0 8 / P b 2 0 4 Data from Meteorites (Diagonal Linear Regression through a Q = 9.50, c Q - 29.49.) Source Number of Slope and Analyses Standard - 321 Deviation V Patterson A l l American Data A l l Russian Data A l l the Data 5 0.942 + 24 0.915 + 28 0.951 + 52 0.925 + .010 3.72 + .10 .021 3.61 + .08 .036 3.76 £ .15 .018 3.65 + .07 The results of these calculations indicate that the age of meteorites can be computed quite accurately. The Russian data has a lower order of accuracy because the analyses were made on samples with a low uranium to lead ratio so that the line i s only one third as long as the line obtained using American data. Approximately one-half of the meteorites analyzed by the Americans had less than 1 ppm of lead whereas three-quarters of the meteorites used by the Russian researchers had less than 1 ppm lead content. Thus contamination with terrestrial lead and d i f f i c u l t i e s in measurement of the~Tatios were correspondingly increased. From a l l of the data in Table 1.3 i t i s concluded that a - 22 -value of 4,56 b i l l i o n years ± 0.02 is a valid figure for the age of meteorites. The isotope ratios of the t r o i l i t e phase of Canyon Diablo and Henbury Iron meteorites were determined within ifo (Patterson, 1956) whereas the isotope ratios in the stone meteorites could only be determined within 2%, These values have been used in Table 1,3 to determine the best f i t t i n g straight line which passes through them. The Russian data gives a high value for the slope of the zero isochron. The reason for this i s quite apparent from Figures 1,1 and 1.2. The Russian analyses are almost invariably higher than American data. These interlaboratory differences are due to small variations in method of measuring peak heights on mass spectrograms and also small errors in the calibration of the measuring system of the mass spectrometer. Since interlaboratory comparisons on standard samples have not been published with any of this data, i t is impossible to make a correction for these differences. Murthy and Patterson (1962) have proposed a new set of primeval ratios based on an average of American and Russian determinations. Their data is reproduced in Table 1.5 below. The values obtained by Staryk et a l . are significantly higher than the others. Moreover, Staryk ?s determination on Canyon Diablo was on the metallic phase which had only 0.14 ppm lead, whereas the other values listed are a l l from the t r o i l i t e phase which have one to - 23 -TABLE 1.5 ISOTOPIC COMPOSITION OF PRIMORDIAL LEAD (Murthy & Patterson, 1962) Meteorites and Source 206 Pb 204 Pb 207 Pb 204 Pb 208 Pb 204 Pb Patterson, 1955. Average of Canyon Diablo and Henbury. 9.50 10.36 29.49 Chow and Patterson, 1961b. Average of repeated analysis of Canyon Diablo t r o i l i t e . 9.61 10.39 29.87 Murthy, 1961. Sardis t r o i l i t e . 9.37 10.22 29.19 Staryk et al,^1959, 1960. Average of Canyon Diablo, Burgavli and Aroos t r o i l i t e . 9.74 10.70 30.28 AVERAGE 9.56 10.42 29.71 two orders more lead. For these reasons, i t is doubtful If the Russian data should be mixed s t a t i s t i c a l l y with American results. Using five stone meteorites and the new average ^ for primordial lead, Murthy and Patterson (1962) obtained a slope of 0.59 ± .01 Least squares was not used but the slope of the line joining each stone meteorite to primordial lead was calculated and weighted according to the amount of radiogenic lead. The value to the slope is equivalent to an age of 4.55 ± .03 b i l l i o n years for the age of meteorites. - 24 -A T b ^ / u * 0 0 ratio of 3.8 was similarly obtained. Patterson's original values for the primordial lead isotope ratios w i l l be used in this paper. From Table 1.3 i t is seen that the recommended value for the age of meteorites is 4.56 ± .02 b i l l i o n years. The Th/U ratio for meteorites is 3.72 ± .10 i f only Patterson's analyses are used. 1.4 The Earth and Meteorites The close relationship of the earth to the meteoritic system was established by noting that the isotopic composi-tion of recently mineralized oceanic leads falls i n a oluster close to a. point on the meteor i t i c or zero isochron (Patterson, 1955; Chow and Patterson, 1959, 1961.). This relationship is illustrated in-Figure 1.3a. The scale of this diagram has been greatly magnified and i t s relationship to the meteoritic or zero isochron i s indicated by the small rectangle drawn on Figure 1.1. Chow and Patterson (1959) state that most of the manganese nodules which were studied are probably less than 1 million years old since nodules cease to grow after being buried by sediments. The lead in manganese nodules and pelagic sediments represents an average sampling of a large amount of sea water. The lead in sea water is derived partly by extrusion from deep crustal or mantle sources in which case the isotopic composition should be such that the - 25 -ratios plot on the zero isochron i f there is a direct age relationship between terrestrial and meteoritic systems. Part of the lead in sea water is derived from continental areas by means of rivers and ocean currents. It is well established that granitic rocks have larger amounts of uranium than basic rocks which form the deeper parts of the continental crust and most of the oceanic crust. Therefore much of lead which is being carried down to oceans from continental sources has developed in a high radiogenic environment. Reference w i l l be made in later chapters to anomalous leads i n such regions as New Mexico and central British Columbia. In such areas leads have developed in radiogenic Precambrian rocks for over a b i l l i o n years. Because of the mixture of leads in ocean waters from many sources i t is d i f f i c u l t to predict how closely the isotope ratios should plot on the zero isochron. Leads close to an island arc environment should f a l l closer to the zero isochron than leads off the coast of North America. Indeed, this relationship is observed in Figure 1.3 i f attention i s directed to samples marked by solid circles. The location of these samples is indicated in Figure 1.4 by the region marked "A". Three leads from Japan are also shown on Figure 1.3. As can be seen by the time scale marked on the growth curve, their ages are less than 100 million years. From geologic evidence their time of mineralization i s given as either Cretaceous or Tertiary in agreement with - 26 -15.8 15.4 18.4 18.8 Vo = .0654 19.2 Diagram a Toronto analyses A Columbia analyses * Pasadena analyses area A • area B o r 15.8 15.4' Figure 1-3. Isotopic composition of leads from manganese nodules and pelagic sediments in the Pacific basin. Also included are three Cretaceous and Tertiary leads from Japan as analysed at Toronto and Lamont. Diagram a: Age of the earth assumed to be 4.56b.y. Diagram b: Age of the earth assumed to be 4.50b.y., and showing isochrons. Figure 1-4. Location of samples shown on Figure 1-3, diagrams a and b. (Chow and Patterson, 1959, 1962) - 27 -model lead ages. Figure 1.3b presents the same experimental results as Figure 1.3a. A zero isochron has been drawn in which the age of the earth is assumed to have been 4.50 b i l l i o n years. The primordial isotope ratios were taken to be Patterson's original values as given at the top of Table 1.5. These constants were proposed by Houtermans (1953) and have been used by most European researchers (Eberhardt, G-eiss and Houtermans, 1955; Moorbath, 1962; etc.). On this model i t is seen that Pacific Quaternary leads become over 100 million years old 1 The Japanese lead deposits in Cretaceous and Tertiary rocks have a model age of over 300 million years. There is l i t t l e justification for the use of 4.50 b.y. as the age of the earth from terrestrial samples or from meteoritic data as seen in Table 1.2. From Table 1.3 i t is clear that there is even less justification for the use of Patterson's original primordial isotope ratios without the corresponding value of 4.56 b.y. If the figure of 4.50 b.y. is the correct age of the earth, then larger primordial abundances should be used for the terrestrial system to account for radiogenic development between 4.56 and 4.50 b i l l i o n years. As w i l l be indicated in Chapter 2, European lead isotope ratios can be accounted for in a manner consistent with geological evidence by a two-stage lead model. In this paper, model lead ages of samples which are - 28 -believed to have developed in a single-stage system w i l l be determined using 4.56 b,y. as the age of the earth and primordial isotope ratios of a Q = 9.50, b 0 = 10,36 and c 0 . 29.49. 1.5 Single-Stage Models Employing a Unique Growth Curve Russell and Farquhar (1960) used Patterson*s meteor-i t l c data together with the isotopic composition of galenas from Bathurst, New Brunswick to derive a single-stage growth curve model, Stanton and Russell (1959) have argued that only leads which have not traversed crustal rocks are most l i k e l y to satisfy the requirements for this model. Mineral deposits which satisfy this criterion by virtue of having only limited contact with crustal rocks which might contaminate them with extra radiogenic lead are: 1. "Orthomagmatic deposits in mafic rocks derived from beneath the continental crust." 2, "Sedimentary deposits derived from the depth by basalt-andesite vulcanism along, or at some distance from continental margins, and quickly isolated in volcanic sediments." Equations 1.12 and 1.13 have been combined by Russell and Farquhar (1960) for dating purposes to obtain the ratio x/y in terms of t^. - 29 -* = 137.8 f ^ E E s — l l + 1 ^ rr-) ? o - e * + 1 The constants a, b and Y Q must be determined experimentally from a combination of meteoritic data and single-stage t e r r e s t r i a l leads. Equation 1.15 is independent of the 204 measured Pb abundance of the sample so that small errors in this quantity do not affect the calculated value of the age. Errors in the Pb 2 <^ 4 abundance are very commonly produced in measuring isotope abundances. When plotted on a graph of x versus y, samples of single-stage leads with 204 errors in the measured Pb abundanoes f a l l on a line between the origin and the point representing i t s true age on the growth curve. Such a line Is here termed an "error line" and i t s relationship to isochrons is illustrated in Figure 1.5. Error lines are referred to colloquially as "errorchrons" In this laboratory. An experimentally detgrmined pair of isotope ratios may be extrapolated back to the growth curve along an "error li n e " i f , and only i f , there is reason to believe that i t has developed in a single uranium-lead system since the time fcQ. In other words, there should be evidence that the ratios would plot 204 on the growth curve i f the relative amount of Pb was to be determined precisely. Vc= .0700 Growth Curves for VQ= .0654-VG= ,06( ero Isochron Figure 1-5. Relationship between Isochrons (solid straight lines) and "Error lines" (dashed straight lines). - 31 -The fundamental postulates underlying Houtermans isochron equation and the Russell-Farquhar growth curve equations are quite different and the data must be handled differently in each case. However, i t is clear that the mathematical basis for them is identical. Once YQ is specified, i t is possible to convert from one model to the other with the use of transform equations 1.9 and 1.10. Occasionally there has been confusion over the difference in ages given by the two models. As this analysis shows, the difference may be due to the use of different constants 204 or else an error in the Pb determination. If t^ i s o specified to be 4.56 b.y., differences in ages between the Houtermans isochron formula and Russell-Farquhar "error line" fouaula are greatest for the post Pre-Cambrian. The differences become progressively smaller as one proceeds backward into the Pre-Cambrian as is evident from Figure 1.5. It Is worthwhile to compare the constants which have been used by various authors in putting forward their models (Table 1.6). If a consistent set of constants i s used both the Houtermans and the Russell-Farquhar model w i l l give nearly identical ages as i s illustrated in the last two rows. It must be remembered that the Russell-Farquhar growth curve model can give no meaningful age unless the isotope ratios are also close to the conformable growth curve. Figure 1.6 shows the relationship between P b 2 0 6 / P b 2 0 4 and 207 204 Pb /Pb for some ordinary common leads which satisfy the TABLE 1 - 6 Comparison of Constants Used In Dating Galenas Author Date (b.y.) ao bo a b V X) Broken H i l l (m.y.) *1 Captain's Flat (m.y.) Collins et a l . 1953 3.5 11.35 13.46 18.45 15.61 .0714 1370 170 Houtermans 1953 4.5 9.41 10.27 - - - 1670 460 Cumming * 1956 (3.98) (9.50) - 18.80 15.85 .080 1420 360 Houtermans ** 1960 4.51 9.50 10.36 - - _ 1740 530 Rus sell-Farquhar 1960 4.56 9.50 10.36 18.72 15.82 .0659 1630 360 1 CO 340 M i Isochron Eq. + 1962 4.55 9.56 10.42 - - 1620 Isochron Eq. °* 1962 4.56 9.50 10.36 - - -" 1600 325 Conformable Eq. ° * 1962 4.56 9.50 10.36 18.65 15.80 .0654 1610 330 Notes on Table 1-6. The decay constants used in calculating ages are those used originally by the authors. For a comparison of ages obtained, the isotopic composition of Broken H i l l , Australia (Kollar, 1960) and Captain's Flat, Australia (Ostic, 1962) has been used. The mean isotopic ratios for Broken H i l l are x = 16.12; y - 15.54} z = 36.08. The mean isotopic ratios of Captain's Flat are x = 18.18} y = 15.77} z = 38.56. Values listed in brackets were calculated for the purposes of comparison and were not given originally by the authors. * Presented by Wilson et a l , 1956. ** Presented by Russell and Farquhar, 1960. + This row makes use of constants recommended for meteorites by Rama-Murthy and Patterson, °* The last two rows make use of constants recommended by the author. An average V Q was calculated on the basis of lead deposits from Broken H i l l , Mt. Isa, Captain's Flat and Cobar Australia (Kollar, 1960, Ostic, 1962). 1962. - 33 -requirements rather closely. More precise c r i t e r i a for detecting ordinary leads w i l l he given in the third chapter. Figure 1.6 also includes the isotopic composition of Ivigtut, Greenland as an example of a lead which does not satisfy the c r i t e r i a by a wide margin. As w i l l be evident in the chapter on anomalous leads, i t i s possible to distinguish most of these by making a large number of analyses from a l l geologic environments that contain galena over the representative area. This is not disadvantageous to the method as additional information i s gained about the orogenic activity In the area. Other methods such as the rubidium-strontium method (Compston and Jeffery, 1959; Falrbairn et a l , 1961), the potassium-argon method (Reesor, 1961), and the lead-uranium method (Tllton, 1960) also require widespread sampling and multiple analyses of hand specimens before valid conclusions can be made for an area. 1.6 Use of p b 2 0 8 / P b 2 0 4 Ratios Collins et a l . (1953) made the f i r s t attempt at using 208 204 Pb /Pb ratios as a dating technique. This attempt as well as a l l subsequent ones have not been particularly successful (see Table 1.7). Two problems have become apparent in using this data. The h a l f - l i f e of T h 2 3 2 i s nearly 14 b i l l i o n years while the primeval abundance makes up three-208 quarters of the total Pb content. Therefore very accurate measurements are necessary on the small amount of radiogenic - 34 -Figure 1-6. Relationship between X and Y for some common leads which appear to satisfy c r i t e r i a for a single stage model. Ivigtut is included as an example which does not f i t the model. TABLE 1-7 2f lR 2 0 4 Comparison of Constants Used in Dating Galenas with Pb /Pb Ratios. Author Date (b!y.) W, (Kanasewich) •oien Capli Broke Ca tain's H i l l Flat (m.y.) (m.y Collins et"al 1953 3.5 31.1 38.40 38.28 1180 -90 Cumming * 1956 (4.19) (29.49) 39.10 40.8 1430 260 Rus se11-Farquhar 1960 4.56 (30.06) 38.80 34.2 1530 140 Conformable Eq.** 1962 4.56 29.49 39.25 38.21 1600 360 Notes on Table 1-7. The decay constants used in calculating ages are those used originally by the authors. For a comparison of ages obtained, the isotopic composition of Broken H i l l (z m 36.08 - Kollar, 1960) and Captain's Flat (z - 38.56 - Ostic, 1962) has been used. Values liste d in brackets were calculated for purposes of comparison and were not given originally by the authors. * Presented by Wilson et a l , 1956. ** An average WQ was calculated on the basis of conformable lead deposits from ,. Broken H i l l , Mt. Isa, Captain's Flat and Cobar Australia (Kollar, 1960, Ostic, 1962) using the ages given by the isochron equation. - 36 -portion i f these are to be used for geochronological purposes. Secondly, even among ordinary lead deposits, the T h 2 3 2 / P b 2 0 4 r a t i o s s h o w m o r e variation than the u 2 3 8 / P b 2 0 4 ratios. The reason for this is not clear but i t must involve differences in the chemical properties of uranium and thorium relative to lead in the various possible source regions. In consequence, i t is a sensitive indicator of the degree to which the single-stage model breaks down in prac-207 206 tice. Figure 1.7 shows the relationship between Pb /Pb • and Pb 2 0 8/Pb 2 0^ for some ordinary leads. Ivigtut, Greenland is included as an example which does not satisfy the c r i t e r i a . Further discussion of this point i s deferred u n t i l later chapters wherein variations in the Pb 2^ 8/Pb 2 0^ ratios among anomalous leads w i l l be used in an attempt to define the properties of the source regions. 1.7 Multi-Stage Lead Models Damon (1954) formulated an interesting two-stage model for lead isotopes based on the continuous creation of the earth's crust. This model was an attempt to incorporate the hypothesis of continental growth as envisaged by Lawson (1932) and Wilson (1949, 1952). Earlier, Vinogradov et a l (1952) had carried out calculations on a similar model. 235 204 Let the abundance of U /Pb (extrapolated to the present time) in the sima be Tln and let the abundance in a a s i a l i c phase be V a« A third phase is considered in which - 37 -Figure 1-7. Relationship between Pb /Pb and P b 2 0 7 / P b 2 0 6 for some common leads which appear to s a t i s f y c r i t e r i a f o r a single-stage model. Ivigtut i s included as an example which does not f i t the model. - 38 -the mineral deposit is separated from contact with the parental elements and any further contamination by radio-genic lead w i l l be considered anomalous. The time of segregation of the slma from the basaltic protocrust i s t^ while the time of segregation of the s i a l i c material from the basaltic crust is t Q . The time of formation of the lead deposit is t m . Other symbols are defined as indicated in 206 204 Table 1.1. The equation of the growth curve for Pb /Pb w i l l be x a r t + 137.8 rV Q(e U i - eXt°) + 137.8V (e X t° - e X t * ) . 1.16 a Damon considers two limiting cases. In the f i r s t of these, t. = t so that the lead was formed from the oldest part of 1 0 the s i a l i c crust. x = 137.8V (e a Xt, - e Xt m • 1.17 In the second case, t Q = so that the lead deposit was formed directly from simatic material. This case is anala-gous to the one given by Russell-Farquhar 's conformable growth equation. - 39 -+ 137.8yV ( e Xt 1 Xt 1.18 A l l the P b / ^ a w k a b u n a a n c e s should f a l l within curves defined by the last two equations in the absence of compli-cating factors. More complicated models than the ones introduced so far have been presented from time to time. Their validity has been hard to justify beoause of the lack of very accurate data. Mention w i l l be made of a model due to Vinogradov et al (1959) because i t w i l l be discussed later in reference to data from the Baltic Shield. Vinogradov, larasov and Zykov make use of combinations of growth curve equations of the type: * •- * 0 + « V o ^ ° " e X t l ) + ffkoklVeXtl " e X t 2 ) + . . . + « k 0 k r . . k 8 V o < e X t 8 - e X t 9 ) . 1.19 The multistage model divides the history of the earth into nine stages each 500 million years long. Differentiation of the uranium relative to the lead is accomplished by - 40 -assigning specific values of k between 0,8 and 1.2758 for each of the stages. In general, sources known as acid differentiates use k > 1, while sources from the basic remainder use k < 1; however, this rule i s not strictly-adhered to. With a combination of two such growth curves for each of the lead isotopic ratios, employing suitable parameters, i t i s possible to obtain isochrons steeper than the conventional ones obtained with Houtermans' equation. The justification for the use of such a model must be in i t s a b i l i t y to explain observed data. In later chapters i t i s hoped to show that i t is the accuracy of the observed data which must be examined before such complicated models need be invoked. In particular, an error in the abundance 204 of Pb , which is easily made, may cause the data to l i e along "error lines" of greater than normal slope. This also accounts for the observation by Vinogradov et a l . that "the 207, 204 206. 204 isotope contours on the Pb /Pb versus Pb /Pb graph have very similar slopes, whatever the time of formation of the leads or the geographic position of the mineralized region from which they were taken". Multi-stage equations of the type Illustrated by 1.16 and 1.19 must be considered as describing anomalous leads by Russell's definition of ordinary and anomalous leads. Anomalous leads have been discussed by Holmes (1947), Vino-gradov et al (1952), Houtermans (1953), Damon (1954), and Zhirov and Zykov (1958). Quantitative determinations of age - 41 -relationships were f i r s t carried out by Russell et a l (1954) on anomalous leads from the Sudbury basin, Ontario. Russell et a l (1954) postulated that various anoma-lous leads from one deposit are a series of mixtures of a single ordinary and a single radiogenic lead in differing proportions. If significant amounts of radiogenic lead isotopes (x r, y r) produced between times t u (the time when uranium is introduced into the system) and t g are mixed in varying proportions, p, with ordinary leads of isotopic composition x Q, y Q, anomalous leads with composition x^, y^ w i l l be produced. x r « 137.8V(eXtu - e X t2) 1.20 y r = V ( e X , t u - e X * 2) 1.21 * i - y o + P y r 1.22 1.23 Equations 1.22 and 1.23 may be combined in the form given by Farquhar and Russell (1957). - 42 -R = y± - y - x. 1 3 7 . 8 ( 6 ^ - 6 ^ 2 ) 1.24 Equation 1.24 states that the lead isotopic ratios w i l l l i e on a straight line with slope R through the ordinary lead isotopic ratios. By taking the limiting case of t g = 0, i t i s possible to find the maximum value, t , of the time of incorporation of the uranium into the rocks. R - _ i f ' 1.25 137.8(e X t u m - 1 ) This is equivalent to the formula used in lead-lead dating of radiogenic leads. Application of L'Hopital's rule to equation 1.24 by taking the limit as t and t D approach each other leads to XX Ci R = * e 1.26 137.8XeXtr This equation gives the time, t p , at which the uranium isotopes were generating lead isotopes in the ratio R. It l s also possible to derive 1,26 from f i r s t principles (Russell et a l , 1954). If the radiogenic lead was generated - 43 -for a significant time compared to 713 m.y. (the half-235 l i f e of U ), then t^ is a weighted average of the times between which lead started being formed and when i t ended. In general, i t w i l l form the upper limit to the time of emplacement of the galenas, t g . The application of the anomalous lead theory given above has had considerable success in establishing limits on the times of mineralization of lead deposits and the Incorporation of uranium and thorium into the crust. This aspect of the subject w i l l be developed more f u l l y in chapter 2 where i t w i l l be shown that certain plausible restrictions on the conditions established above lead to a unique solution of the times of mineralization. CHAPTER 2 MULTI-STAGE LEAD MODELS Sooner or later - the mind finds i t s e l f so formidably beleagured by the mass of facts which i t has gathered around i t that, u n t i l i t has sorted them out and arranged them in some kind of order, i t can no longer sally out into the Universe to gather more. Toynbee, A Study of History, 1, 49. 2.1 Introduction The f i r s t part of this chapter consists of a review of pertinent information about the crust and the mantle. The North American continent can be divided into geological provinces on the basis of K-Ar, Rb-Sr, Pb-U and geologic chronological methods. The position of ordinary leads within this framework w i l l be discussed. A hypothesis w i l l be advanced that a large proportion of lead isotope results may be interpreted on the basis of development in two consecutive systems. Furthermore, each system w i l l be shown to have i t s own i n i t i a l characteristic composition of uranium, thorium and lead. Brief considera-tion w i l l be given to three-stage lead models but the discussion is limited to those models from which i t i s possible to obtain useful quantitative results. There are an Infinite variety of multi-stage models for which i t is impossible to obtain such information because they contain more constants than can be determined from the available experimental information. It is regrettable that - 4 4 -- 45 -restrictions must be placed on the format of the model but the considerable success of the single-stage model for ordinary leads in giving approximately correct results makes i t l i k e l y the slightly more complicated two-or three-stage models w i l l yield results which are in greater accordance with the true sequence of events. Two-stage or anomalous leads, as they are usually called, may be divided into two classifications depending on their relation i n time to orogenic sequences within geological provinces. Leads which have resided in a shallow, uranium ric h , crustal environment for less than about 400 million years before f i n a l mineralization are termed short period anomalous leads. Leads which have resided in a simi-lar environment for well over 400 million years have been recognized for nearly a decade and are here termed long period anomalous leads. Graphical examples of each type of anomalous lead w i l l be presented to illustrate the case. Discussion of quantitative results on anomalous leads from areas in which there are a sufficient number of accurate isotope determinations w i l l be presented in Chapter 4. 2,2 Seismic and Geoohemioal Evidence From seismic information, the earth has been divided into a series of concentric shells with well defined longi-tudinal and transverse wave velocities. For the purposes of this discussion we w i l l be concerned with the mantle, - 46 -which l i e s below the Mohorovic'ic' discontinuity, and the crust, which l i e s above i t . The crust i s subdivided into the sima and the s i a l which are separated by the seismic Conrad discontinuity. From the seismic evidence i t i s possible to obtain the ratio of bulk modulus to density ( h./p ) for these various layers and compare them to values determined experimentally for typical rock types. This data i s li s t e d in Tables 2.1 and 2.2, together with the distribution of lead and some radioactive elements in the earth's crust. TABLE 2.1 Properties of the Crust and Upper Mantle Continental Seismic Velocities k/> Layer Depth (km.) (km/s) v t (km/sj ( i o -•10 km2/s?) Sial 0 - 3 5 *6.14 ^3.55 *20.9 Sima 20 - 75 6.58-7.20 3.80? 24.0-32.6 Upper Mantle 30 - 120 8.20 4.65 38.4 Low Velocity Layer 120 - 220 7.85 4.35 36.4 Intermediate Mantle ~ 650 10.30 5.76 61.8 Reference: Altermans, et al (1961)} Diment et a l , (1961). TABLE 2.2 Physical Properties and Distribution of Elements in Typical Rocks Rock Type Granite Diorite (10" 1 0 km2/s2) Distribution in Parts per Million  K Rb Pb Th U 18.3 - 19.5 25,200-42,000 110-170 15-19 8.5-17 3.0 22.8 - 24.3 Basalt Gabbro Peridotite 27.8 - 28.2 30.7 8300 30 Ultrabasic Dunite Eclogite 36.2 - 38.3 34.2 - 37.0 40 0.2 0.1-0.01 0.004 0.001 Reference: Jeffreys, H. (1959); Turekian and Wedpohl (1961)\ Tilton and Reed (1960). - 48 -From this evidence we may infer that the s i a l is made up of predominantly granitic or granodioritic rocks and that there has been a large upward concentration of radioactive elements. There is insufficient evidence to decide i f the U/Pb and Th/Pb ratios are significantly different as one proceeds from acidic to more basic rocks. It seems certain that the variation of these ratios i s much greater in the s i a l as compared to the sima or the mantle, 2.3 Division of the Continents into Geological Provinces, A large amount of effort has been expended to subdivide the Canadian Shield into suitable units of study. Early classifications (M.E. Wilson, 1939; G i l l , 1948, 1949; J. T, Wilson, 1949) were based primarily upon stratigraphic, petrological and structural similarities. Features such as parallel fold belts, foliation trends and truncation of ancient orogenic centers by younger mountain belts were invaluable aids in this work. Lately, the classification has been carried out with the aid of geochronological data (Wilson, 1949, 1952; Cumming et a l , 1955; Farquhar and Russell, 1957; Hurley, 1958, Goldich et a l , 1961; Gastil, 1960; Stockwell, 1961; Burwash, Baadsgaard and Peterman, 1962.) The classification Is now based on the repeated recurrence of certain dates over widespread areas when K-Ar, Rb-Sr, and U-Pb dating methods are used. These dates are related to periods of severe metamorphlsm during which minerals crystallize or recrystallize. Often, they can be - 49 correlated with, similar events on widely separated regions of the earth. Hurley (1958) has referred to them as the "magic numbers" of tectonophysics. Most of the geochronological data for North America has been assembled on a large scale map and the continent has been subdivided according to the latest available information (references used are marked with an asterisk in the bibliography)• Minerals used for K-Ar ages are biotite, mica, lepidolite, muscovlte and hornblende. Rubidium-strontium and uranium-lead ages were only used in areas where potassium-argon ages were unavailable. A small scale copy, showing geological provinces but not the data, is reproduced in Figure 2.1. An effort was made to indicate the oldest principle orogenic event i n each area. The boundaries proved to be surprisingly sharp considering the presence of overthrusting, tectonic i n l i e r s and the effect of multiple metamorphism along adjaoent orogenic belts. Secondary features, such as miogeosynclinal mountains and belted plains known to be underlain by older crystalline rocks were not considered In this map; neither were such Igneous bodies as the Duluth Gabbro which has a well-established age of 1000 million years on the basis of K-Ar, Rb-Sr (Goldich et a l , 1961) and Rb-Sr whole rook analysis (Faure, 1961). This large s i l l occurs among rocks metamorphosed and folded during the Penokian orogeny and was emplaced in a series of intrusions into these older rocks - 50 -Main Main Provinces K-Ar Dates Model Pb Dates 2500 2950 Superior, Slave m 1750 2000 Churchill, Bear EZZl 1600 1750 Penokian 1300 1400 Ozarkian, Beltian n 1000 1100 Grenville IZD 350 300 Appalachian CZJ 70 - Cordilleran Figure 2-1. Geological provinces of North America based on K-Ar, Rb-Sr, Pb-U dating methods and stratigraphic information. Outcrop areas are in a darker shade. Other areas are classified on the basis of dated well core samples. - 51 -through fractures formed in response to the severe Grenville orogeny which took plaoe 500 miles to the east. The nomenclature closely follows that used by the Geological Survey of Canada (Stockwell, 1961). Gastil (1960) recognized that the data Indicates the necessity of at least two new geological provinces. The f i r s t of these is here oalled the Penoklan province (Goldich et a l , 1961) and includes the large strip from eastern California to Sudbury, Ontario. The second includes the area between the Penokian and Grenville provinces and i s here termed the Ozarkian after the Ozark U p l i f t in southeastern Missouri (age deter-mination by Allen, Hurley, Fairbalrn and Pinson, 1959). Outcrop areas with known ages have been marked by dark strips whose strike has been made to conform in a general manner with known structural trends. The l i g h t l y shaded areas are covered with a veneer of younger sediments and have been classified on the basis of dated d r i l l core samples. The pattern of ages for primary orogenic features is in agree-ment with what would be expected on the basis of the theory of Continental Growth (Lawson, 1932; Wilson, 1952). 2.4 Relationship of Ordinary Lead Isotopes to Geological  Provinces• In the preceding investigation we have established the existence of geological provinces which can be taken as independent entities in that a geological or geophysical study within each w i l l form a self-contained unit. It - 52 -remains to be ascertained how lead isotopes f i t into this basic unit. A series of histograms have been constructed to show the relationship of K-Ar dates to the oldest model lead ages in each of the geological provinces. Without making a large number of very accurate analyses i t is impossible to be certain that lead samples selected have undergone only one stage of development. However, a f a i r approximation is to choose the oldest common leads avail-able in each geological province, from available published data. Proven anomalous leads such as those recently analyzed by Farquhar (1962) In the Grenville area have been omitted. Model ages were obtained using Table 4.5 in Russell and Farquhar's book (1960). The K-Ar dates (Figure 2.2) for the Cordilleran area are Interesting beoause they show that the orogenic sequence involving this geologic province occupied over 350 million years. From a study of Individual age determina-tions (Baadsgaard et a l , 1961) and geologic information on the Cariboo orogeny (White, 1959) i t is evident that the entire eugeosyncline in the Western Cordillera was involved in diastrophlsm prior to the Devonian period and that the aotivity continued episodically into the Miocene. The strong episode of metamorphlsm in the Mid-Cretaoeous recrystallized most of the minerals over a wide area so that any 350 million year or older events have been obscured exoept in the extreme eastern border of this area. Unfortunately, - 53 -Figure 2=2„ Relationship of I>Ar ages to the oldest TOdel lead ages in the Cordilleran and Beltian geological provinces. Minerals used for K-Ar ages are biotite, mica, lepidolite, Muscovite, hornfel and aaiphibole. Histogram gives the siumber of determinations in each i n t e r v a l of 25 million years. Lead isotopes: Long et a l , I960; Bate, 1957J Farquhar and Gumming, 1954. Olest Lead Model Ages from Galenas Canadian Cordillera American Cordillera • Beltian £ 1 o. U <D n -A CQ CQ © © O U a u o CQ 0) fS o S3 w CO 43 M a © n , n 500 1000 1500 K~Ar Dates in Million Years - 54 -no lead Isotopic studies have been made i n the area west of the Beltian geologic province. Lead isotope evidence for a 1400 m.y. mineralizing event in the Beltian geological province has been avail-able for several years (Farquhar and Gumming, 1954; Long, Silverman and Kulp, i960). The K-Ar evidence for this has Just recently been obtained (Hunt, i960, 196l) from the Moyie s i l l s i n the Aldrich formation. The agreement between the two sets of dates i s highly satisfactory. Many of the low K-Ar dates In the Beltian are probably due to partial recrystallization during the Cordilleran orogenies. In Figure 2.1 the Beltian province i s corre-lated with the Ozarkian province. A very great amount of geoehronological research has been carried out on minerals from the Appalachian geological province. The scale on the ordinate of Figure 2.3 has been reduced by a half from the previous figure to take this into account. There i s a considerable amount of detail evident on the histogram with major peaks at 350 m.y. (late Devonian) and 220 m.y. (end of the Palaeozoic). Alkaline intrusives occurred loc a l l y in the Monteregian H i l l s , Quebec, during the Cretaceous period. Model lead ages from the Appalachian geological province conform within limits of error to the most intense stage of igneous activity. The histogram for the Grenville geological province (Figure 2.3) i s not nearly so well defined. The main - 5 5 -Figure 2-3, Relationship of K-Ar ages to the oldest model lead ages in the Appalachian and Grenville Geological Provinces, Minerals used for K-Ar ages are biotite, mica, lepidolite, hornblende and muscovite. Histogram gives the number of determinations in each interval of 25 million years. Lead isotopes: Russell and Farquhar, 1960j Bate et a l , 1957, Oldest Lead Model Ages from Galenas i r iH in u a o u • 55 M U +•> o at >> B H £ oi © CQ 55 Grenville Canadian Appalachian American Appalachian • 5 No. 500 1000 XL 1500 K-Ar Dates in Million Years - 56 -period of metamorphlsm probably took place about 1000 million years ago but episodic loss of argon from minerals during the Appalachian orogenies probably caused the distortion now evident. Tilton et a l (1961) have presented a large number of concordant uranium-lead ages which show that uraninlte and zircons were formed between 900 and 1150 m.y. ago. Two lead ages place the period of minerali-zation between 1100 and 1200 million years ago. The Ozarkian geological province (Figure 2.4) has only a small amount of data since Precambrian outcrops are small and widely scattered. This area underwent diastrophism between 1200 and 1500 million years ago. As in the G-renville province, the K-Ar and model lead ages agree within limits of error. The principle orogeny which affected the Penokian geological province occurred between 1600 and 1800 million years. The histogram (Figure 2.5) has been divided Into two parts to illust r a t e the special case of Sudbury within this framework. The lead analyses liste d from South Dakota and California (Bate et a l , 1957) are probably slightly anomalous. There are no published lead isotope analyses for the state of Minnesota. In Colorado a group of 1050 m.y, ages i s restricted to the area at Pike's Peak and probably represents a local episode of intrusion during the Grenville orogeny. Similar events can be found in such widely separated l o c a l i t i e s as - 57 -Figure 2-4. Relationship of K-Ar ages to the oldest model lead ages in the Ozarkian Geological Province. Minerals used for K-Ar ages are biotite, mica, lepidolite and muscovite. Histogram gives the number of determinations in each interval of 25 million years. Lead isotopes: Slawson and Austin, 1962j Bate et a l , 1957. Oldest Lead Model Ages from Galenas e o O O •rt M U ct N O No. 15 CD S3 10 500 1000 1500 K-Ar Dates in Million Years No. 10-5-- 58 -Figure 2-5. Relationship of K-Ar ages to the oldest model lead ages in the Penokian geological province. Minerals used for K-Ar ages are biotite, mica, lepidolite and muscovite. Histogram gives the number of determinations in each interval of 25 million years. Lead Isotopes: Phair and Mela, 1956; Bate et a l , 1957} Russell et a l , 1954. Oldest Lead Model Ages from Galenas 1000 l l III <H X •H rt H O cd • O CQ o o o o o o n 1 1500 L. Superior area: S. Dakota: Western U.S.A. Duluth Gabbro and contact rocks: 2000 1-5 No. 2500 K-Ar Dates in Million Years Oldest Lead Model Ages from Galenas No. 10- Sudbury and Blind River:• l~5 Copper C l i f f Rhyolite: • No. 5-1000 2000 2500 K-Ar Dates in Million Years - 59 -Duluth, Minnesota and near Cranbrook, British. Columbia. Gast (1960) has obtained a whole rock Rb-Sr age of 1500 m.y. near Gunnison, Colorado. Aldrich et a l (1956) have obtained discordant Ph* /Pb ages of 1700 m.y. for a zircon from the Quartz Creek granite and 1810 m.y. for an apatite from a granite at Uncompahgre, Colorado. The series of 1700 m.y. model lead ages in Colorado (Phair and Mela, 1956) Indicate that the area between Denver and Cotopaxi belongs to the Penokian geological province although the K-Ar evidence has largely been destroyed by orogenesis In the adjacent Ozarkian province. Mineral and rock ages for the Sudbury-Blind River area have been well summarized by Fairbairn et a l (1960). They state that "there Is considerable evidence by both K-Ar and Rb-Sr methods, of orogenic events at approximately 1.0 b.y., 1.2 b.y. and 1.6 b.y." They believe that "the nickel irruptive i s older than the 1.6 b.y. orogeny, but the upper limit i s undetermined". The five ordinary leads which have been analyzed at Toronto laboratories have an age of 1740 m.y. with a standard deviation of 100 m.y. A series of leads associated with pyrite have recently been analyzed at this laboratory by T. J. Ulrych and these confirm results obtained at Toronto. The agreement between K-Ar and model lead ages is highly satisfactory. From the map in Figure 2.1 i t i s abundantly clear why - 60 -the Sudbury area has such a complicated pattern of ages. It forms the focal point of five geological provinces and has consequently been affected to some extent by primary orogenesis in each of the provinces. This has undoubtedly been a factor which contributed to the abundant sulfide mineralization occurring in this area. The Churchill province forms an arcuate pattern around most of the Superior province and an early phase of orogenesis in the Churchill province correlates with ages for the Copper C l i f f Rhyolite which i s just south of the Sudbury basin. The main period of orogenesis at Sudbury probably occurred between 1700 and 1800 m.y. and coincides with the nickel irruptive, ordinary lead mineralization and uranium mineralization i n the Huronian sediments (Mair et al,1960). The group of 1300 m.y. ages for the Creighton and Cutler granites shows that events occurring in the Ozarkian province partially recrystallized the area south and west of the Sudbury basin. The Grenvllle "front" occurs less than 10 miles southeast of the Sudbury basin. This intense metamorphio event occurring 1000 m.y. ago has affected the Sudbury area and some of the discordant Rb-Sr whole rock, mica and K-feldspar dates (Fairbairn et a l , 1960) can probably be correlated to this period. In chapter 4 i t w i l l be shown that anomalous lead mineralization may also be correlated with the Grenville orogeny. The Churchill geological province (Figure 2.6) covers - 61 Figure 2-6. Relationship of K-Ar ages to the oldest model lead ages in the Churchill and Bear geological provinces. Data from the Cobalt and Chibougamau areas are also included. Minerals used for K-Ar ages are biotite, mica, lepidolite, muscovite and hornblende. Histogram gives the number of determinations in each interval of 25 million years. Lead isotopes: Russell and Farquhar, I960} Farquhar (personal communication); Bate et a l , 1957j Nier, 1938. Oldest Lead Model Ages from Galenas TIT U ctt CD CQ No. 20 H a •rl U Xi O o -"d •H . u d • ci a CD si o +> at M (0 el Churchill: Bear: Cobalt-Chibougamau: 15 -10 -a a bO 3 O Xi St 4-> ol Xi 0 20 No. .Lli 1000 1500 2000 K-Ar Dates in Million Years 2500 - 62 -a very large area and i t s history is undoubtedly quite complex. The main period of orogenesis appears to have occurred between 1800 and 2100 m.y. ago. The main peak on the K-Ar histogram occurs between 1600 and 1850 m.y. but this is l i k e l y due to episodic loss of argon during later metamorphic periods. Indeed, the present surface represents such a deep erosional level that what we now sample are the old mountain roots which were at a f a i r l y high temperature during much of geologic time. Consequently there has probably been a small but continuous diffusion of argon under the influence of thermal metamorphism. An analysis of uranium bearing minerals by Aldrich and Wetherill (1958) showed that there i s a linear relation-ship between the ratios of P b 2 0 7 / ! * 2 3 5 and p b 2 0 6 / r j 2 3 8 which intersect the concordia at 1900 m.y. Lead isotopes from such widely separated areas as Goldfields, Saskatchewan; Angikuni, N.W.T., F l i n Flon and Churchill, Manitoba; and the Knob Lake area In the Labrador Trough a l l yield ages close to 2000 m.y. and no older leads have been located In these areas. A few l o c a l i t i e s do not appear to have lost much argon and have K-Ar dates in agreement with the model lead ages. The Bear province underwent orogenesis at about the same time as the Churchill province and there seems l i t t l e reason to separate the two on a geochronological basis. A single specimen of lead from Great Bear Lake has been I ~ 63 -analyzed by three laboratories but may be somewhat anoma-lous „ The Cobalt and Chibougamau areas of Ontario and Quebec have been included in the Churchill province* They are usually included in the Superior province on the premise that they are underlain by crystalline rocks from this area. The K-Ar dates representing these areas form a group between 1680 m.y, and 2370 m.y. (Aldrich and Wetherill, 1960, Lowden, 1961). These scattered areas may have once repre-sented young isolated volcanic centers on the edge of the Superior nucleus. Support for this viewpoint i s seen in the series of lead isotopes from Cobalt and Chibougamau (Farquhar, personal communication) which appear to satisfy c r i t e r i a for ordinary leads. Their model ages are about 2300 m.y. The relationship of these ages to the 2000 m.y. old Churchill ages may be similar to that exhibited by the 350 m.y. ages in the eastern Cordillera to the main period of tectonic activity around 70 m.y. ago. The isotope ratios for Cobalt w i l l be discussed more f u l l y in section 2.7. The relationship between K-Ar dates and the model lead ages in the Superior and Slave geological provinces are shown in Figure 2.7. Indications of continuous argon loss previously noted in the Churchill province are much more conspicuous here. Nearly a b i l l i o n years separates the main orogenies in the Superior and Churchill provinces, - 64 -Figure 2-7. Relationship of K-Ar ages to the oldest model lead ages in the Superior and Slave Geological Provinces. The Beartooth Mountains Montana and the Bighorn Mountains Wyoming are also included. Minerals used for K-Ar ages are biotite, mica, lepidolite, muscovite, and hornblende. Histogram gives the number of determinations in each interval of 25 million years. Lead isotopes: Russell and Farquhar, I960) Farquhar (personal communication)) Gatanzaro and Gast, 1960. Oldest Model Ages from Galenas T xi +> o o +» u «t CD n No, 15-Superior: • Slave: EJ Beartooth-Bighorn: • a u CD O > xi at W> CQ CQ U si a o o CD Xi CD cr 10 No. ill 3000 K-Ar Dates in Million Tears - 65 -allowing a greater time for diffusion processes. The K-Ar peak is nearly 500 m.y. lower than the main body of model lead ages. From this brief survey i t may be concluded that ordinary lead mineralization appears to occur during the. most intense period of tectonic activity i n each geolo-gical province. The basio postulate, that the geological province i s a natural unit within which both lead isotopes and a l l geochronological information can be correlated, appears to be substantiated. It Is highly significant that within each geologic province the period of ordinary lead sulfide mineralization correlates with the K-Ar dates for the oldest crystallized basement rocks. The ordinary leads in North America are almost entirely found in a eugeosyn-c l i n a l environment and are most l i k e l y associated with volcanism in regions of great crustal mobility. In the next section a hypothesis for two-stage lead isotope development w i l l be based on the theory of episodic orogeny as held by King (1955). He believes that erogenic structures were built over long intervals by episodes of movement separated by longer periods of crustal quiescence. From the histograms the length of an orogenlc sequence appears to be between 200 and 400 m.y. A study of i n d i v i -dual areas indicates that each episode affects a relatively small area. It is therefore proper to speak of sulfide mineralization taking a relatively short period of time - 66 -(less than 50 m.y.) and then proceed to study how one or two subsequent episodes of remobilization in a variable uranium environment w i l l affect the isotope ratios. Isotopes of lead which have developed under these conditions are termed short period anomalous leads. In almost every geological province studied, there have been K-Ar dates which show that the rocks in the area have f e l t the effects of primary orogenesis taking place in adjacent geological provinces. The extra length of time available in a r i c h uranium crustal environment has contri-buted to the formation of extremely radiogenic leads. Classic examples of these long period anomalous leads occur in the Sudbury and Tri-State d i s t r i c t s . 2.5 A Two-Stage Lead Model. The necessity for a minimum of two stages in the production of anomalous leads such as Joplln has been recognized since Holmes' calculation of the age of the earth. Various authors, Houtermans (1953), Geiss (1954), Russell et a l (1954), Bate et al (1957) have suggested an equation similar to the one used below but none seem to have presented the model in such a manner that a quantitative determination could be made of the time of the second stage of mineralization. Russell and Allen (1956) have rewritten the equation of radioactive decay in terms of the number of lead atoms being generated relative to P b 2 0 4. Refer to Table 1.1 - 67 -for the symbols and constants used through this paper. x - a + o to jx [l37.8V(t)e X t J dt 2 .1 238 204-where the quantity i n brackets is the ratio of U / P b at any time t. V is a function of time and many investi-gators have tried various functions for this quantity. In general, this i s a different function for each deposit and a s t a t i s t i c a l treatment of measurements from many widely spaced l o c a l i t i e s w i l l obscure these differences. The function which w i l l be used here i s one i n which V is taken to be a constant for discrete intervals of time so that the integral reduces to = a Q + 137.8VQ( e X to - e X t l ) + 137.8V1( e X t l - e X t2) + 2.2 There is a similar expression for y which i s the 207 204 Pb /Pb ratio. For the purposes of geochronology, only the f i r s t term of the expression has been used with the explicit assumption that the lead has developed in a single lead-uranium system. This then forms a mathematical defini-tion for ordinary leads. Leads which have developed in more than one distinct lead-uranium system are termed - 68 -anomalous. The equation for the Pb r f U tyPb ratios i s z = c G + W Q( e x M t o - e A , M t l ) + W 1(e^' tl - e^ M t2) + 2 .3 At time t Q the material of the earth i s thought of as being in a molten state so that nearly complete homogenization of lead ratios occurred. Consider t^ to be a time of tectonic activity during which ordinary leads were differentiated from their source in the lower part of the crust and the upper part of the mantle and either concentra-ted to form a lead deposit at this time or disseminated throughout the host rock: close to the surface. Contempor-aneously, uranium and thorium bearing solutions were incorporated into the same environment. At time t 2 , tectonic activity recurred in the area. Some of the ordinary lead may have been remobilized and become contaminated with radiogenic lead which formed between time t-^  and tg to form anomalous leads. If the ordinary leads were disseminated at time tj_, they may be mixed with radiogenic lead and concentrated to form lead deposits at time tg. In either case , the equation for the growth curve can be written in the form x = x 0 + 137.8VX( e X t l - e X t2) 2 . 4 - 69 -y = y Q + V ] L C e ^ ' t l - e X , t2) 2.5 z o + ,X"t! _ e X " t 2 j The isotope ratios of the ordinary leads which formed at time t^ are denoted by x Q, y Q and Z q . Equations 2.4 and 2.5 are of the same form as the equations for the growth curve of ordinary leads. They form a straight line with slope R. y - y D ( eX't! - e * ' t 2 ) R = — = 2.7 x - x 0 137.8( e ^ l - 6**2) where x Q and y Q are the average isotope ratios of the ordinary leads. Equation 2.7 is similar to Russell and Farquhar's (1960) equation 5.3. Therefore, this theory i s a specialization of their more general model for anomalous leads. The P b 2 0 8 / P b 2 0 4 ratios do not yield an independent estimate of time, tg; however, i f this quantity is obtained from equation 2.7, i t i s possible to evaluate Wj_. In a - 70 -single-stage model such as formed by the meteoritic system 232 204 (Figure 1.2) the Th /Pb ratio is directly proportional to U /Pb . This simple relationship is due to thorium and uranium both being in a tetravalent state. In a crustal environment some of the uranium w i l l be oxidized to the hexavalent state while the thorium remains in the tetravalent state. There may be no functional relationship between thorium in the tetravalent state and uranium in the hexavalent state. The age of the ordinary leads can be determined in the usual manner with Houtermans* isochron equation i f l t is thought that the experimental data has an insignificant 204 amount of Pb error. I f such an error is suspected, the Russell-Farquhar growth curve equations should be used. Using a consistent set of constants, either dating method w i l l yield nearly identical results. Criteria for recognizing ordinary leads are given in Chapter 3* A l l of the isotope ratios of the ordinary leads from a given deposit are averaged to find x and y and this o o value i s used to find t-]_. If intercomparison techniques (e.g. Kollar, et a l , 1960) have been used to determine the isotopic composition then this point w i l l be much more accurately determined than any of the anomalous lead points. Following the theory, the straight line should be forced to pass through this point and also satisfy the requirements that the square of the deviations perpendicular to the line must be a minimum. Letting u j _ = x i - x Q and v^ = y^ - j Q , - 71 -where x^ and y^ are the isotopic compositions of n anomalous leads, the slope of the straight line i s found to he g J U i V i lil The time of mineralization i s best calculated graphically using equation 2.7. If there are less than four good determinations of the isotopic composition of ordinary lead i t i s not possible to obtain a reliable average value and i t is best to determine the best straight line by least square treatment (again minimizing diagonally since both ratios have errors) of a l l the ordinary and anomalous leads together. In this case the variates in equation 2,8 are measured from the centroid of the data, u^ = x^ - x ; v^ = y^ - y, where x and y are the average values of a l l the p b 2 0 6 / p b 2 0 4 and P b207/ P b204 determinations. It is useful to be able to solve for x Q , y Q and V 0 which are the ordinary Isotope ratios from which any particular anomalous lead (XJ_, y^) developed. This may be done graphically by finding the intersection of the t^ isochron and the line with slope R (equation 2,8) passing through Xj_, y^. Alternatively, this can be calculated from the following three linear equations in three unknowns, - 72 -x Q, y 0 and V Q. The value of tj_ i s obtained from the average of the measured ratios of the ordinary leads. + V 0 J 0 I 2 • 9 = b Q + V 0 K 0 1 2.10 y 0 = yi + RC xo - x i ) 2.11 where J 0 1 = 137.8(e X t° - e X t l ) and Kol = ( e x , t o - e r t l ) . The solution of these equations by the method of determin-ants i s Using this value, V-^  can be calculated from equation 2.4 for any particular anomalous lead. Because of extensive mixing of mineralizing solutions, this figure may not have much physical significance. If enough analyses are made from many lo c a l i t i e s in the area, the maximum V]_ for each loca-tion or mine may be related to the uranium to lead ratio in the underlying host rock. The maximum V-j_ ratios may then be contoured on a map of the area and checked for any correlation with basement structures. Such a correlation has actually been discovered by Slawson and Austin (1962) for the lead deposits In New Mexico. V Q = y. - R X l - b Q + aQR 2.12 K o l " R J o l - 73 -It is sometimes useful to plot the data in such a way 204 that the effect of Pb errors are minimized. Triangular plots (Cannon et a l , 1961) have been used to some advantage; however i t is f e l t that for quantitative work i t i s best to use a rectangular plot such as shown in Figure 1,7. Let T be the slope of the line through two anomalous leads / v 207 / 206 (x 1,y 1,z 1,x 2,y 2,z 2J on a plot of Pb /Pb versus Pb 2 0 8/Pb 2 0 6. Following previous terminology, the parental ordinary lead which was present at time t 1 i s x D , y 0 , z 0 and the extrapolated present day uranium/lead and thorium/lead ratios in the second stage are vi> wi>V 2,W 2 respectively for the two anomalous leads. Let J i 2 = 1 3 7 - 8 ( e K t l ~ e A , t 2 H K12 ( e ^ l - e X , t2,} L 1 2 = ( e ^ l - e V , t2,. The slope of the line between the two leads i s ?2 y i yQ + V2 K12 y o + V1 K12 *2 x l x o + V2 J12 x o + V1 J12 a — 2.13 z 2 z x z Q + W2Li2 z Q + W1 L12 ~2 " ?1 x o + V2 J12 " x o + V1 J12 - 74 -If W-j_ = ^ 1^1 a n d w g - ^1^2* t n e expression simplifies to x o 12 T 2.14 z J o 12 If x ^ 5 y 1 > z 1 were an ordinary lead and a series of anomalous leads were formed by a mixture of the ordinary lead and a radiogenic lead, an Identical expression i s obtained. Since the right hand side of 2.14 i s constant, T represents the slope of a line passing through the ordinary (y 0/x 0, z 0/x 0) and anomalous (yj_/xj_, z^/x^) isotope ratios. If the thorium and uranium to lead ratios are related by a more complicated expression In the crust, the straight line through the anomalous leads may not pass through the ordinary leads. This type of relationship can only arise by a growth process and i s not seen when there is extensive mixing of mineralizing solutions. An example of such a hypothetical case is i f where k Q and k^ are constants,. The slope of the line, T, through the point {yQ/^09 z 0 A 0 + x o k o L 1 2 ^ i s w l .= k o + k l V l 2 o 15 - 75 -x . T = Jo xo K12 o"12 z i - r ZQ + x 0 k 0 L 1 2 " | X o k l L 1 2 " z o J i 2 2.16 2.6 Short Period Anomalous Leads Many geologists (King, 1959, p. 64; McCartney and Potter, 1962) believe that ultramafic and mafic rocks are intruded early in the plutonic cycle of a eugeosyncline. In & situation some lead, uranium and thorium would be separated contemporaneously from their source which may be the mantle or the deeper parts of the crust. In some cases the lead may form a syngenetic lead deposit, in which case i t can be treated as a single-stage lead. In most cases, however, the lead would be disseminated among the thick accumulation of volcanic and pyroclastic rocks. Great thicknesses of sediments can accumulate in a relatively short time in a mobile belt. A section in eastern Vermont, believed to be of Cambrian to Devonian age, is at least 50,000 feet thick (King, 1959). In central British Columbia the upper Palaeozoic volcanic, clastic and chemical sediments known as the Cache Creek sequence is at least 24,000 feet thick (White, 1959). If such a sequence i s burled deeply, some of i t may later become molten and be - 76 -injected as magma into the upper part of the section. Leads- formed from the magma would have had two stages of development and the isotope ratios would l i e along a second stage isochron or an anomalous lead line as i t w i l l he called here to avoid confusion with primary isochrons. The length of the anomalous lead line would depend upon the uranium/lead ratio, the length of time available in the second stage, and the degree of homogenization in a magma chamber. Indeed, i f the system remained closed and complete homogenization occurred, the f i n a l isotope ratios of the mineralized lead sulfides could not be distinguished from an ordinary lead. The time of f i n a l mineralization could be calculated on a single-stage model. Such a situa-tion is probably approximated in a number of deposits. In most cases, the crust cannot be considered a closed system with respect to lead, uranium and thorium and an anomalous lead results. Russell and Farquhar (1960, p.89) have stated "that the majority of leads must be anomalous to some degree and that dating galenas is very imprecise unless some r i g i d criterion is invented to recognize non-anomalous leads". Recognition of non-anomalous leads has been only partially successful but many anomalous leads may be identi-fied by the linear relationship of their isotope ratios along an anomalous lead l i n e . In the case of short period anomalous leads, where the residence in a second stage has been less than 400 million years, experimental uncertainties - 77 -create great d i f f i c u l t i e s . In addition, only reconnaissance surveys, consisting of two or three samples, have been carried out in most districts., Moorbath (1962) has analyzed 14 specimens of galena from the Lake District in northern England. The isotope ratios are plotted in Figure 2.8. In the top diagram the p b206/ p b204 a n d p b 2 0 7 / p b 2 0 4 ratios have been multiplied by .1.012 to adjust for interlaboratory differences between Oxford and University of British Columbia, (see Ivigtut analyses, Chapter 3). The Pb 2 0 7/Pb 2 0 6 and Pb 2 0 8/Pb 2 0 6 ratios did not need to be adjusted since the difference was only i n the measurement of the Pb 2^ 4 peak. This procedure does not alter interpretation of ages but does allow comparison with the growth curve being used in our laboratory. Moorbath has interpreted the data as representing three periods of mineralization with mean ages of 470, 320 and 210 m.y. He quotes geologic evidence as follows: "Dixon (1928) and Trotter (1944) suggest that the presumed Tertiary haematite deposits of west Cumberland represent the'-outer zon6 ;6f the-Lake Dis t r i c t non-ferrous ore f i e l d and that the latter i s therefore Tertiary in age. From-a<geo chemical viewpoint Dunham. (1952) considers this to be unlikely. A general consideration of the geological evidence suggests that the greater part of the Lake District mineralization could be Hercynian, as was already postulated by Finlayson (1910)." It appears that the geological evidence i s inconclu-sive and can scarcely be used to support these model lead ages. An alternative method of interpretation i s to use a two-stage model. An order better precision is necessary - 78 -Figure 2-8. Lead isotope compositional diagrams for the Lake D i s t r i c t , England. (Oxford analyses-Moorbath.) - 79 -before quantitative calculations can be carried out on the P b 2 0 6 / P b 2 0 4 and P b 2 0 7 / P b 2 0 4 ratios. Under no circumstances can the data be used to support more than two periods of mineralization because of the size of the standard deviation. Support for a two-stage model is presented in Figure 2.8 on a plot of P b 2 0 7/Pb 2 0 6 versus P b 2 0 8/Pb 2 0 6 in which a linear relationship i s indicated. Projection of the line on a single-stage growth curve indicates that primary mineralization probably took place during the Cale-donian orogeny. A second stage of isotope development took place in a crustal uranium and thorium environment. The time of f i n a l mineralization cannot be determined but could have taken place as late as the Tertiary period. Trotter (1944) summarizes as follows: "In post-Triassic (presumably Tertiary) times the rocks of the North of England were subject to widespread horizontal tensile stress whioh gave rise to normal faults, dominantly of north-west'.trend. In the Lake District region the numerous post-Triassic faults, proved in the coalfield and ironfield, and in the adjoining New Red rocks, bear witness to this prevalent state of tension." "To sum up: The Tertiary earth movements gave rise to doming and tensional stresses in the Lake District and in the Alston Block, and the mineral fields occur within the domes, the veins occupying fissure gashes. Thus the tectonic evidence definitely points to the Tertiary era as the date of the copper-lead-zlnc mineralization." The isotope ratios from the Tellowknlfe area, Northwest Territories, Canada, form a better test case il l u s t r a t i n g short period anomalous leads. The isotope ratios as measured at Toronto have been multiplied by 0.99166 to remove inter-laboratory differences between Toronto and Vancouver - 80 -laboratories. As In a l l cases of short period anomalous leads, the slope of the line on a graph of P b 2 0 6 / P b 2 0 4 207 204 versus Pb /Pb (Figure 2,9) i s very nearly tangent to a growth curve. Equation 1.26 may be used to determine t r , which is a weighted average of the time between which the leads started in a second stage and when they were mineralized. Much of the scatter about the anomalous 204 lead line is along an "error line" indicating a Pb error. 204 In the lower diagram the Pb error does not appear and the linear relationship is much more evident. If the individual isotope ratios were interpreted point by point In a conventional manner using Houtermans" isochrons, a linear relationship between Y , W and t-, would result. It seems o o l highly improbable that there could be a correlation between the amount of uranium and thorium In the source region and the time of mineralization i n an area of only 10 square miles. The data may be interpreted as indicating ordinary lead, uranium and thorium being extracted from a deeper source and placed in a crustal environment between 2800 and 2900 m.y. ago. The lead isotopes developed in a crustal source for a short period of time. From the slope of the anomalous lead line, f i n a l mineralization appears to have occurred less than 300 m.y. after the formation of the ordinary leads. - 81 -Figure 2-9. Lead isotope compositional diagrams for Yellowknife, N.W.T., Canada. (Toronto analyses.) - 82 -2.7 Long Period Anomalous Leads The simplest type of anomalous lead which can be formed is a mixture of two ordinary leads. Characteris-tics of such a situation may be illustrated by the isotope ratios (personal communication, R. M. Farquhar) from the Cobalt-Larder Lake-Noranda areas of Ontario and Quebec (Figure 2.10). The isotope ratios should f a l l on a line between two points on the same growth curve. On a map (Figure 2.11) the samples should be close to the boundary between two geological provinces. A l l of the samples f a l l on a chord which intersects a growth curve between 3000 m.y. and 2200 m.y. (Figure 2.10). Samples such as those at Timmins, Noranda, and Val-d'Or, which are in Archadh lavas, greywaeke and pyroclastic rocks, f a l l on the section of the chord closest to 3000 m.y. Samples occurring in the Bruce and Cobalt series f a l l on a section of the chord closest to 2200 m.y. Leads at Chibougamau, Quebec, appear to have approximately the same time of genesis as the leads near Cobalt. Mines which are close to the contact between the two rock types as at Kirkland Lake and Larder Lake have lead isotope ratios showing the greatest amount of mixture. The correlation between K-Ar ages and model lead ages has already been noted in the histograms for the Churchill province (Figure 2,6) and the Superior province (Figure 2.7). If the Isotope ratios were to extend beyond the growth curve, a two-stage anomalous lead interpretation would be - 83 -1 3 y 1 5 - • 14 1 4 i_ 1 5 x 2000 mj Growth Curve V O = . 0 6 5 4 Anomalous lead line • Samples from Archaeh rocks • Sample from Kirkland Lake x Samples from Cobalt and Bruce S. A Samples from Chibougamau x 2 4 0 -2 3 0 Refer to diagram above for key to symbols. 7 /3000 / / m.y. Anomalous lead line?" /• / / Growth f Curve / V Q = . 0 6 5 4 W Q = S 3 8 . 2 1 >^5oo 1 0 0 1 0 5 Figure 2 - 1 0 . Lead isotope compositional diagrams for samples from the region between Cobalt, Ontario and Chibougamau, Quebec. (Farquhar-Toronto analysis.) Ontario • Archae^i lava, pyro-clastics and greywacke. (ZD Bruce and Cobalt series. UUPredominantly granites. • Galenas! with an apparent age 27O0 - 3000 m.y. * Galenas with an apparent age 2200 - 2500 m.y. • Kirklanjd Lake. 60 L 100 I 120 miles 200 km. 50u 4 8 " Figure 2-11. Location of samples shown in figure 2-10 for the region betwee Cobalt, Ontario and Chibougamau, Quebec. - 85 -necessary but the times of mineralization given above would s t i l l be approximately valid. It should also be noted that there i s a third group of leads, south of the area but s t i l l i n the Cobalt and Bruce series, which are d i s t i n c t l y anomalous and have had a different history. These occur in a northeast trending arc between Sudbury, Timagaml and Noranda. Only a few analyses are available but these indicate that the isotope ratios have had a history similar to Sudbury anomalous leads. A second example of a mixture of two ordinary leads forming an anomalous lead line occurs in the Karelian zone of the Baltic Shield (Figure 2.12). The analyses were carried out by Kouvo (1958)* The gneissic pre-Karelian base-ment in the area has an age of about 2700 m.y. cn the basis of Pb-U dating on zircons and Rb-Sr dating of microcline and muscovite (Wetherill et a l , 1962; Tilton, 1960). Results from K-Ar and Rb-Sr dating on biotites in the same area give ages close to 1800 m.y. This latter age corresponds to the period of primary orogenesis in the Svecofennides (Polkanov and G-erling, 1961). From Figure 2.12 i t appears that an early period of ordinary lead mineralization occurred about 2800 m.y. ago. A second period of ordinary lead minerali-zation occurred 1800 m.y. ago (see Figures 2.13 and 3.9) in the Svecofennides and along the border between the Fenno-Karelides and Svecofennides. Samples 28 and 29 represent a mixture of these two ordinary leads. Figure 2-12. Lead isotope composition diagrams for the West Karelian zone of Finland (Isotopic analyses - Kouvo, 1958). - 87 -A mixture of two ordinary leads can occur whenever two geological provinces are i n contact or overlap. In such a situation the isotope ratios cannot be interpreted point by point to yield a meaningful age. A large number of analyses must be made and the ages must be determined by the relationship of the lead isotope ratios to each other and to the growth curve. When this i s done, the correlation between periods of lead sulfide mineralization and ages given by the K-Ar, Rb-Sr and Pb-U methods is striking and direct. An example of a long period anomalous lead i n which the second stage of growth was i n a crustal environment i s illustrated In Figure 2,13. Lead Isotope analyses for the Central Finnish zone were carried out by Kouvo (1958). The ordinary leads with an age of 1800 m.y, are shown as crosses and correlate with K-Ar ages i n the same area (Kouvo, 1958; Polkanov and Gerling, 1960, 1961; Gerling and Polkanov, 1958). Vaasjoki and Kouvo (1959) also considered the galenas to be "close to the ages of their host rocks, which are considered to represent the synkinematic Svecofennian intrusive rocks." This is in agreement with investigations by Eskola (1914) at Orijarvi. The lead isotopes i n Figure 2,13 extend well to the right of the zero Isochron and cannot be interpreted as a mixture of two ordinary leads. When Pb 2^ 4 errors are eliminated as in Figure 2.14, the f i t of the anomalous lead Figure 2-13. Lead isotope ratios from the Central Finnish Zone. - 89 -- 90 -line i s excellent. Sample 24 i s from the island of , Sottunga and probably should not be included. The period of primary and secondary mineralization may be obtained from the slope of the line in Figure 2,13 and equation 2.7. Alternatively, the two periods of mineralization may be obtained graphically from the two intersections of the anomalous lead line with the growth curve. For our purposes, this procedure i s adequate since the data i s not accurate enough to obtain a very reliable figure for the seoond period of mineralization. Ordinary lead m i n e r a l i z a t i o n ^ ) occurred 1800 m.y. ago. If we assume that uranium and thorium were introduced into the crust at the same time, then the secondary mineralization, t g , could have occurred as late as the Caledonian orogeny. 2.8 Multi-Stage Lead Models The growth equation for P b 2 0 6 / P b 2 0 4 in an n stage system which satisfies expression 2-1 may be compactly expressed i n the form x = a„ + a £ v _ ( e X t i - l - eXt± ). 2.16 Similar expressions may be written for y and z which are the P b 2 0 7 / P b 2 0 4 and P b 2 0 8 / P b 2 0 4 ratios. The complications which would be produced by such a growth process are such that i t would be nearly impossible to determine how many stages of - 91 -growth occurred, let alone the properties of each system and the periods of time spent within each one. There are a number of theoretical predictions which can be made and which could serve as a guide in interpreting experimental results i f such a system i s expected. F i r s t , consider certain special cases of a three-stage model which can be interpreted with the accuracy of results currently being obtained In our laboratory. The equation for the P b 2 0 6 / P b 2 0 4 growth curve is x = a Q + « V 0 < e X t ° - e1*1) + flV]L(eXtl - e X t2, + a V 2 ( e ^ 2 - e X t 3 ) . 8.1? One special case occurs i f t^ and t g are separated by 100 to 200 m.y, or less. In this case a two-stage model would give results which would be approximately correct for t . A second special case occurs i f ^ and t g are widely separated in time but complete homogenization of isotope ratios occurs at time t g due to an intense period of meta-morphism. Interpretation would have to be carried out locally since complete homogenization of a widespread area seldom occurs i n practice. A possible example of this occurs i n the Monchegora area of the Kola peninsula in the Baltic Shield. The isotope ratios were analyzed by Vinogradov et a l (1959). 92 -A third special case occurs i f - 0. In this case there i s a gap between time t ^ and t g during which the single-stage system is not disturbed. At time t uranium Ci and thorium is introduced into the crustal system. At time t„ there occurs a mixture of the ordinary leads (t„) o _L and radiogenic leads produced between time t g and tg. If there Is independent information about either t g or tg, the time of ordinary lead mineralization may be solved. This method should be compared to the limiting case given by Russell and Farquhar (1960, p.56) In which an analysis f a l l i n g on a point below the growth curve is extrapolated backwards to the curve along a line having a slope of 0.046 to obtain a lower limit to the age of the orogeny at which the lead came from the mantle. Possible (but unproven) examples of this type occur i n the Grenville area, Canada and in Ivigtut, Greenland. Frequent geological mixing of continental materials has often been taken as a justification for the application of the assumption of a single-stage interpretation. Thus, Alpher and Herman (1951) assumed that multiple orogenies In the histories cf lead samples involved small changes in the lead-uranium ratios and that increases or decreases were equally probable. Acoording to this assumption they were able to consider average values of V and W for the entire surface regions of the earth. Since the calculation of Alpher and Herman did not involve the detailed - 93 -Interpretation of individual samples, this assumption was well justified. Several years later, Shaw (1957) argued that "The crust i s admittedly heterogeneous, but crustal processes, especially gradation, diastrophism and vulcanlsm, tend to restore homogeneity." Shaw's paper was a refu-tation of previous arguments by Wilson et a l (1956), Russell (1956) and others that the apparent f i t of observed lead isotope ratios to a single-stage model made a sub-crust a l origin for lead more l i k e l y than a crustal origin. Again Shaw's analysis was based on an interpretation of many leads, not of individual lead samples, and in this sense his argument seems a reasonable one. It i s i n the use of a hypothesis of repeated mixing of crustal materials to justify the application of a single-stage model to individual  lead minerals that the validity of the arguments are in question. Thus Moorbath (1962), for example, ju s t i f i e s his application of the single-stage formula to individual British galenas on the basis that "regional homogenization processes" tend to average out crustal heterogeneities over a period of time. The question seemed sufficiently important to warrant a detailed quantitative analysis of the effect of repeated mixing of hypothetical source rocks in which lead isotopes are being produoed. Since the purpose is solely to establish a principle, the particular numerical values chosen for the calculations are relatively unimportant. It w i l l be easy to generalize - 9 4 -the findings to different numerical examples. It is generally known that studies of the ages of ter r e s t r i a l rocks and minerals f a i l to show evidence for many events prior to about 3 0 0 0 m.y. ago. It may be supposed that surface conditions on the earth prior to about this time were such that rocks were not preserved in any abundance. Therefore, for the purpose of these calculations, i t has been assumed that mixing was so intense prior to that time that heterogeneities in lead isotope abundances were not produced, and that lead grew isotopically i n a regular way between the common starting time for the earth-meteorite systems and the time 3 0 0 0 m.y. ago. At the time 3 0 0 0 m.y. ago a l l lead w i l l be assumed to have the isotopic composition x n 1 3 . 4 1 , y « 1 4 . 7 2 , which values would have been produced in the given time interval by a single-stage closed system in which V had the value 0 . 0 6 6 . o For the f i r s t example, isotopio compositions were calculated for sixty hypothetical leads each of which grew in a closed system between time 3 0 0 0 m.y. ago and the present. For each of the hypothetical lead samples the value of was chosen at random (using tables of random numbers, Kenney and Keeping, 1 9 5 4 ) from the distribution of values shown in Table 2 . 3 . The population has a binomial distribution, with an arithmetic mean of 0 . 0 6 6 and a standard deviation of 0 . 0 0 5 6 . The distribution approxi-mates reasonably well to a Gaussian of the same parameters. - 95 TABLE 2.3 Binomial Distribution of V, for a Frequently Mixed Source 1 % Probability 1 0.051 0.463 2 0.053 1.389 3 0.055 2.778 4 0.057 4.630 5 0.059 6.944 6 0.061 9.722 7 0.063 11.574 8 0.065 12.500 9 0.067 12.500 10 0.069 11.574 11 0.071 9.722 12 0.073 6.944 13 0.075 4.630 14 0.077 2.778 15 0.079 1.389 16 0.081 0.463 - 96 -This example is a slightly special case of the two-stage model on which Kanasewich (196£) has based his interpreta-tions of anomalous leads. It is well known that such anomalous leads have isotopic compositions that f a l l on a chord, or i t s extension, to the single-stage growth curve between two points representing the times enclosing the duration of the second stage. Figure 2.15 shows the linear relationship of the calculated points. The points are not distributed continuously along the line because the d i s t r i -bution chosen permitted only discrete values of Y^. For these points, the average ratios l i e close to the zero point time on the 0.066 growth curve. This would be precisely true i f an i n f i n i t e number of examples had been calculated. This result is a consequence of the fact that the YQ values for the f i r s t growth stage coincided with the mean value for the distribution assumed for the second stage. This i s true for a l l the examples' to follow. For the second example, the second time interval has been divided into equal parts, forming a three-stage model. The V-values for the second and third stages were each drawn independently from the distribution shown in Table 2.3,. This corresponds to the physical assumption of complete mixing between the second and third stages. The sixty points calculated for the three-stage model are shown in Figure 2.16, where It i s seen that the points tend to follow the same trend as before, but that now there i s a small lateral spread. - 97 -y 16.2 H Single-stage 12 16 x Figure 2-15. Graph of Pb 2 0 6/Pb 2 0 4 and Pb Z° 7/Pb for a theoretical two-stage lead model, t^ = 3000m.y.j t 2 = Om.y.i At = 3000m.y. - 98 -y 16.2 15.8 15.4 Single-stage Growth Curve V G * .066 \ • • • * fi • \ • - • • / / • • • i — " ~ ~ — Anomalous lead l i n e — * * / ^ ^ ^ between 3000 m.y. and 0 m.y. 1 1 1 18.4 18.8 19.2 x Figure 2-16. Graph of Pb 2 0 7/Pb and P b 2 0 6 / P b Z 0 for a t h e o r e t i c a l three-stage model, = 3000 m.y.; tg = 0 s i .y.j At • 1500 m.y. - 99 As the total number of stages Increases to six (Figure 2.17) and to eleven (Figure 2.18), the distribution of points becomes shorter and broader, but the cluster i s always about the same straight l i n e . From the calculations made, i t must be concluded that the "frequently-mixed" model for lead isotope abund-ances approximates much more closely to the two-stage models commonly applied to anomalous leads, than to the single-stage model with variable V values. That i s , the concept of isoohrons through the primeval lead abundances has l i t t l e significance for such leads. Under certain circumstances the use of a two-stage model may provide a good f i r s t approximation to multi-stage leads. The calculations give additional reasons for the desirability of determining as precisely as possible the quality of the f i t of the isotope ratios of anomalous leads to the best straight line through them. The most important conclusion i s that the assumption of frequent mixing of the rocks from whioh leads are derived i s not sufficient for the polnt-by-point interpretation of such abundances on the basis of a single-stage (isochron) model. - 100 -16.2-Single-stage Growth Curve V Q • v.066 15.8- 49 0 m* 15.4 Anomalous lead line between 3000 m.y. and O m.y. 18.4 18.8 19.2 Figure 2-17. Graph of P b 2 0 7 / P b 2 0 4 and Pb 2 0 6/Pb 2 0 4 for a theoretical six-stage model which simulates a frequently-mixed source. t-, = 3000 m.y.} t f i = 0 m.y.j At = 600 m.y. - 101 -16.2 -15.8 15.4 Single-stage Growth Curve V n = .066 \ 400iay- X ... A • r"—. • A 200 mv. *»., ^ V . T — - — — ^ « V * ^ 1 — — • Anomalous lead line between 3000 m.y. and 0 m.y. — i 1 , 1 18.4 18.8 19.2 Figure 2-18. Graph of Pb 2 0 7/Pb 2 0 4 and Pb 2 0 6/Pb 2 0 4 for a theoretical eleven-stage model which simulates a frequently-mixed source, t j = 3000 m.y.; t 1 ] L = 0 m.y.; At = 300 m.y. CHAPTER 3 ANALYSIS OF LEADS WITH UNUSUAL ISOTOPIC COMPOSITION Data of one kind or another are not so d i f f i c u l t to obtain but generalization i s another matter. Duclaux, Pasteur: the History of a Mind, 111. 3.1 Leads with Unusual Isotopic Composition An examination of the published lead isotope ratios for nearly 2000 terrestrial samples revealed the presence of a small number with unusual composition. The areas having unusual lead isotope ratios include Bluebell, British Columbia; St. Magloire, Quebec; Ivigtut, Greenland; and several di s t r i c t s in the Baltic Shield. If interpreted conventionally on a single-stage model, this group indicates a very low uranium/lead (VQ) source region within the earth (Table 3.1). While interpreting lead isotope data, investigators have tended to avoid considering how these unusual samples fitte d into the' pattern of lead isotope abundances. To the author, these areas appeared to be c r i t i c a l ones in determining the properties of the mantle-crust system. A second characteristic of this group i s that analyses within an individual area appear to l i e approximately along an isochron. If the published ratios could be verified, there was the possibility of determining the existence of isochrons or modifying the theory along lines suggested by Damon (1954). - 102 -- 103 -TABLE 3.1 Apparent Age and V Q of some Unusual Leads (Calculations are based on a single-stage model.) Dist r i c t and Sample No. Apparent (m.y.) Apparent Vo Bluebell (Toronto 870) 340 .0574 St. Magloire (Toronto 300) 110 .0550 Ivigtut (Nier-Harvard 13) 1930 .0546 Ivigtut' (Harwell) 1920 .0532 Pechenga Kaula (Baltic) (Vernadsky Inst. 89) 1590 .0557 (Average V 0 for ordinary leads) .0654 Ref: Russell, R.D. and Farquhar, R.M. (1960). Moorbath, S, (1962). Nier, A.0. (1938). Vinogradov, A.P.j Tarasov, A.P. and Zykov, S.I. (1959). 3.2 Sample Preparation and Analysis Samples were obtained from a number of the key areas and galena was converted to lead iodide. The chemical procedure used to make lead tetramethyl was carried out in an evacuated system and involved the reaction of lead iodide with 3M methylmagnesium bromide in solution with diethyl ether. The sample containing lead tetramethyl and ether was vacuum d i s t i l l e d to a capsule and the d i s t i l l a t e - 104 -was purified in a vapour phase chromatographic column using a technique developed by T. Ulrych (1960). The stationary phase was paraffin o i l on a solid support consisting of 40-60 mesh firebrick. A fresh supply was used for each sample to avoid the possibility of contamina-tion between different samples of lead tetramethyl. Analysis of the Pb(CH3)g ions was on a University of British Columbia mass spectrometer designed and built by F. Kollar, R. D. Russell and J". S. Stacey. It i s a 90° sector, 12 inch radius, direction focussing instrument using a modified Nier-type gas source (Kollar, 1960). Pressure scattering corrections were made and an intercomparison technique was used with Broken H i l l as the primary standard (Kollar, 1960; Ostic, 1962). 3.3 Contamination of Lead Tetramethyl Analysis of Bluebell, British Columbia was f i r s t carried out at the University of Toronto in 1955. A varia-tion of nearly 4% was obtained on eight samples from the mine (Figures 3.1 and 3.2). The apparent low YQ sample i s identified as No. T-870 in Figure 3.1. I n i t i a l results on Bluebell at the University of British Columbia showed that- seven samples exhibited variations of about 1/2$ with no evidence for development in an extra-ordinary low V Q source region (Figures 3.1 and 3.2) . However specimen No. 237 (T-870) was analyzed on five separate occasions and a disturbing drop in the ratios relative to - 105 -Figure 3-1. Lead isotope ratios for Bluebell, British Columbia, Canada. Old ratios are shown to l i e closer to an error line than to an isochron. New analyses have nearly Identical isotopic composition. The crosses represent UBC results that have not been intercompared with a standard. - 106 -Figure 3-2. Lead Isotope ratios for Bluebell, British Columbia, Canada. Crosses represent UBC results that have not been Intercompared with a standard. - 107 -P b 2 0 4 was noted each time (solid points in Figure 3.3). This behaviour Indicated that the 249 mass range 304: (Pb (C H ) + } was being affooted by a contaminant which had a lower vapour pressure than lead tetramethyl. The presence of a contaminant in a few particular samples had previously been suspected at the University of Toronto (Russell, Farquhar and Hawley, 1957) and the Australian National University (personal communication, R. D. Russell; personal communication, J. R. Richards). Its effeot on the 249 mass range had been oorrelated with the appearance of additional peaks extending upwards from mass 281. A new preparation of Bluebell 237 was made using methylmagnesium bromide in iso-pentyl ether. This time the lead tetramethyl was found to be much more contaminated (open circles i n Figure 3.3). A good speotrogram was obtained (Figure 3.4) of the contaminant between mass ranges 281 and 286 and i t s effect on mass range 265 provided the key to i t s identification which was carried out by W. F. Slawson, A. C. James, R. D, Russell and 7. M. Ozard. The form of the molecule has not been identified positively but i t appears to be a cyclic siloxane tetramer, namely (-0-Si-(CH 3) 2) 4. Substitution of C 1 3 for C 1 2 and H 2 for H 1 yields the additional peaks between mass 282 and 286 with the correct relative heights. The contaminant at mass 265 may be due to a substitution of a carbon for a si l i c o n atom and similarly a substitution of two carbon atoms would - 108 -16.0 -15.6 -15.2 -17.0 17.4 17.8 Figure 3-3. Effect of contamination on a sample of Bluebell No. 237. The numbers and letters l i s t the order in which the analyses were carried out. Analysis e was very poor due to depletion of the sample. • Sample prepared with grignlard reagent in diethyl ether, o Sample prepared with grignfard reagent in i sQ-pentyl ether. X Toronto analysis (1954). J A A A J \ to 00 to 00 tn ts 00 to to to 00 00 00 CO CO M to to to to to Gi Gi <3> oo ^ tn to tn Pb(CH3)^ plus "Contaminant" "Contaminant" Mass spectrogram of a contaminated sample of lead tetramethyl. Mass spectrogram of an uncontaminated sample of lead tetramethyl, Figure 3=4. Mass spectrogram of contaminant and lead tetramethyl - 110 ~ affect the measurement of mass 249. The hypothesis that there are three different molecules responsible for the observed effect means that an empirical correction on the 249 peak height based on the peak height of 281 mass w i l l only be qualitatively successful. This is borne out by t r i a l computation. The contaminant i s suspected to result from the use of a s i l i c o n grease in sealing ground glass connections. However, i t is suggested that a trace amount of some unknown substance in the actual lead sample is required to promote formation of the contaminant. The contaminant affected only particular samples such as Bluebell 237 and St. Magloire 240 (Figures 3.5 and 3.6). Repeated attempts at making the contaminant with other samples such as Bluebell 226 ended in failure. Once the contaminant i s placed into the mass spectrometer i t requires about two days of baking and pumping to remove i t completely. There-fore care had to be taken not to contaminate subsequently analyzed samples. By using a grease that does not contain silicon (such as Apiezon N) no trace of the contaminant could be found in any of the specimens. The problem can therefore be considered solved. Through the kindness of Dr. R. M. Farquhar, the writer has had the opportunity of observing samples of Bluebell 237 (T-870) and 226 (T-871) being prepared and analyzed at the University of Toronto. The results are - I l l -is.a 15.4 15.0-o Toronto analyses (1954) a Toronto analyses (1962) c UBC analyses (1962) 500 my x — — moo m» ' " / , • / > r-330 / Growth Curve V0 = 0.0654 -r->,cl / / [sochron/*^ ^ E r r o r line . i 17.0 17.4 17.8 Figure 3-5. Lead isotope ratios for St. Magloire, Quebec, Canada. - 113 -38.0 37.6 37.2 36.8 36.4 o Toronto analyses (1954) 1 •*/ • Toronto analyses (1962) ® UBC analyses (1962) [/riot • ^^^^^^^ T 100 Growth Curve ~y J Vo=.0654 / / W0= 38.21 / / /Error line / r J¥ / / / / o / T 300 1 1 —H 1 1 , 17.0 17.4 17.8 x Figure 3-6. Lead isotope ratios for St. Magloire, Quebec, Canada. - 113 -presented in Figure 3.1 and 3.2. No trace of the contam-inant was present and the results agree satisfactorily with the analyses obtained at this laboratory. It seems clear that contamination has affected only a small number of samples. Procedures followed at both the University of Toronto and at the University of British Columbia are such that i t i s no longer produced during the preparation of lead tetramethyl. 3.4 Measured Lead Isotope Ratios The results of a l l the analyses carried out by the writer of this thesis are presented in Tables 3.2, 3.3 and 3.4. The results obtained for Ivigtut, Greenland are intercompared with results obtained from nine other labora-tories in Figures 3.7 and 3.8. Ratios obtained at the University of Br i t i s h Columbia for five specimens agree with each other within l/10th of one percent. They f a l l close to the center of the results obtained by a l l other laboratories. Intercomparison procedures have not been completed on most of the samples presented in Table 3.4; however, the P b 2 0 6/Pb 2 0 4 207 204 and Pb /Pb ratios are thought to be correct within + 0.03. 3.5 Interpretation of Results  Bluebell, British Columbia. The lead and zinc ore at Bluebell i s a sulfide replacement deposit in a lower Cambrian limestone (Irvine, TABLE 3-2 Measured Lead Isotope Ratios for Ivigtut, Greenland Sample No. and Description (Toronto No. in brackets) 100 times the ratio of 204/206 207/206 208/206 206/204 207/204 208/204 Broken H i l l Standard * Ivigtut, Greenland 259 (1052) (NBS No. 200) 6.205 96.44 209.43 16.116 15.542 36.068 (61.3° N 48.1° W) 260 (202) Lead with cryolite, chalcopyrite 261 (1019) Main cryolite pegmatite body in Ivigtut granite. 6.806 6.804 6.808 264 6.811 Galena, chalcopyrite and cryolite with weathered siderite 265 Cryolite with coarse galena slight chalcopyrite Mean ratios Standard deviation 6.799 6.806 +.0045 100.75 237.41 14.694 14.804 34.885 100.84 237.67 14.698 14.822 34.932 100.76 237.46 14.688 14.799 34.877 rf* 100.87 237,70 14.682 14.810 34.899 100.77 237.43 14.709 14.822 34.923 100.80 237.53 14.69 14.81 34.90 +.053 +.139 +.012 +.010 +.021 * Kollar, Russell and Ulrych, NATURE 187, 754-756 (1960) TABLE 3-3 Measured Lead Isotope Ratios for Bluebell, B.C. and St. Magloire, P.Q, Canada. Sample No. and Description 100 times the ratio of (Toronto No. in brackets) 204/206 207/206 208/206 206/204 207/204 208/204 • O s t i c , R.O., Journal Geophys. Research, 67, 1651-1652 (1962) Captain's Flat Standard (136) * 5.501 86.79 212.35 18.166 15.765 38.573 Bluebell, British Columbia (48° 45'N 116 50'W) 226 (871) 225H Stope 5.685 88.81 218.41 17.59 15.62 38.42 Kootenay Chief 228 (861) 225 ZQ Stope 5.692 88.86 218.50 17.5? 15.61 38.38 ^ C omf or t_zone H OI 229 (862) 225 ZR4 Stope 5.707 89.06 218.35 17.52 15.60 38.26 1 Comfort_zone 230 (863) 225 ZR5 Stope 5.699 88.86 218.32 17.55 15.59 38.31 Comfort zone 237 (870) 225 I Stope 5.675 88.73 218.38 17.62 15.63 38.48 Kootenay Chief 414 Raise. St. Magloire, Q u e b e c ( 4 6 ° 33'N 70° 14.5'W) 240 (300) 5.607 87.48 213.86 17.84 15.60 38.14 241 (301) 5.618 87.51 213.86 17.80 15.58 38.07 TABLE 3-4 Measured Lead Isotope Ratios for Miscellaneous Samples Sample No. and Description 100 times the ratio of (Toronto No. in brackets) 204/206 207/206 208/206 206/204 207/204 Broken H i l l Standard * 6.205 96.44 223.80 16.116 15.542 Korsnas, Finland 6.326 97.87 225.54 15.81 15.47 128 The following samples have not been intercompared with any standard. Bluebell, British Columbia 227 (860) 375 Q Stope 5.689 88,87 217.74 17.58 15.62 Kootenay Chief 236 (869) 375 Stope 5.686 88.83 217.71 17.59 15.62 Kootenay Chief Ivigtut, Greenland 262 6.794 100.77 237.55 14.72 14.83 cryolite with imbedded galena, sphalerite and chalcopyrite. * Kollar, Russell and Ulrych, NATURE 187, 754-756 (I960) - 117 -@ Minnesota (Nier) <=> Harwell © Oak Ridge (Harmon) 0 USGS (Stieff) A NBS (Dibeler) Figure 3-7. Comparison of lead isotope ratios from Ivigtut, Greenland as measured at U.B.C. and other laboratories. The scale i s twice as large as used on previous graphs. - 118 -35.40-35.20-35.00 34.8a 34.60 14.40 14.60 14.80 Figure 3-8. Comparison of lead isotope ratios from Ivigtut, Greenland as measured at U.B.C. and other laboratories. The scale is twice as large as used on previous graphs. - 119 -1957). It occurs on the extreme western edge of the Pre-Cambrian Windermere and Purcell series in an area known as the Kootenay Arc. Seven samples of galena from the Comfort and Kootenay Chief zones were analyzed and yielded isotope ratios which varied by less than 1/2% (Figures 3.1 and 3.2). There is no evidence for isochrons and the old Toronto results have been shown to l i e along an "error l i n e " indicating contamination of the P b 2 0 4 peak. The isotope ratios plot well off the growth curve along which "mantle" leads are thought to have developed (Stanton and Russell, 1959). These samples form part of an anomalous suite which occur in the Kootenay Arc. In view of their anomalous origin, yet Identical isotopic composition, the mineralizing solutions must have been homogenized in one of the associated batholiths in the area. Irvine (1957) states: "Ore deposition is.probably related to one or another of the granitic bodies but no direct evidence links the deposits to any one body." Because of the position of the isotope ratios on a plot of p b206/p b204 T e r s u s Pb 2 0 7/Pb 2 0 4, a large part of the lead at Bluebell must have been separated from a deep source in Pre-Cambrian rocks. The ore, as i t is now seen, i s a mixture of this ordinary lead and radiogenic lead which formed in a crustal environment between a Pre-Cambrian date and the Cordilleran series of orogenies. A. J. Sinclair is making a detailed study of the lead in the Kootenay Arc and w i l l be discussing the genetic relationship in detail. - 120 -St. Magliore, Quebec The St. Magloire area consists of sedimentary, extrusive, and intrusive igneous rocks of Palaeozoic age (Beland, 1957). Two samples of galena were analyzed from the area and they agree in isotopic composition within experimental error (Figures 3.5 and 3.6), As at Bluebell, there is no evidence for isochrons or for development in an unusually low uranium/lead environment. The lead tetra-methyl from sample 240 was slightly contaminated and not enough galena was available to make a new preparation. The absolute ratios are therefore slightly in error. The results are in agreement with a new analysis at Toronto (Farquhar, 1962), Farquhar (1962) has shown that these samples are part of an anomalous group of leads which occur in the Canadian part of the Grenville province. Korsnas, Finland A sample from Svecofennian deposits in the Baltic Shield was analyzed and the results are compared with ratios obtained at other laboratories (Figures 3.9 and 3.10). Four other specimens from the same geological province have been analyzed by A. B. L. Whittles with nearly identical results. This suite has sometimes been referred to as an example of an isochron (Schutze, 1962) or a modified isochron (Yinogradov et a l , 1959). The results a l l -lie closer to an "error line" than an isochron. Thus, the effect i s much more l i k e l y due to interlaboratory differences and errors - 121 -Figure 3-9. Lead isotope ratios having an age of 1800 m.y. in the Baltic Shield. Analyses used are 1,2,116,4,6,7,8,9, 10,12,15,16,34,35,41,42,46,87,88,89 as li s t e d by Vinogradov et a l (1959). - 122 -36.00-35.4a-34,80-34.20 15.20 15.60 16.00 - 123 -in measurement of the P b 2 0 4 peak. ,The samples analyzed at the University of British Columbia f a l l * close to the "mantle" growth curve and may be dated on a single-stage model. The age i s 1800 m.y. using Table 7 in the Appendix. This agrees closely with 'the group of 1750 to 1850 m.y. ages obtained by the Rb-Sr and Pb-U method (Wetherill et a l , 1962) and K-Ar ages (Gerling and Polkanov, 1958), in the same general area. Ivigtut. Greenland The lead samples from Ivigtut are unique in being the only proven example of P b 2 0 6 / P b 2 0 4 and P b 2 0 7 / P b 2 0 4 ratios which f a l l more than 10% below the "mantle" growth curve (Figure 1.6). Conventionally, the isotope ratios have been interpreted on a single-stage model (t-^ ^ 1.93 b.y., V Q— 0.054) with the growth taking place in a region with very unusual uranium/lead and thorium/lead ratios (Bate and Kulp, 1955). The postulated source region between 4.56 b.y. and 1.93 b.y. i s presumably a portion of the^crust or else a deeper part of the mantle (e.g. the low Velocity layer -Table 2,1). A low V Q source region in the crust i s certainly possible; however, i t i s d i f f i c u l t to see how i t could have remained a closed system for the.first 2^ b.y. of the earth's existence. The second possibility i s that there may be a low V Q region deep in the mantle. If this i s so, i t seems odd that the ,Th/U ratios should be 7% higher than - 124 -what is observed for ordinary leads and 20% higher than what i s observed in meteorites. One would also expect to find more examples of these types of leads in regions of unusual tectonic activity. A simple way out of the d i f f i c u l t i e s associated with a single-stage model was presented in Chapter 2 on multi-stage leads. It was suggested that the unusual ratios could be explained by a three-stage model with the second stage of growth missing. A lower limit on the age of the orogeny at which the ordinary leads were derived from the mantle may be obtained by following the method of Russell and Farquhar (1960, p. 56). If the isotope ratios (x,y) are extrapolated backwards to the growth curve at an angle of -2° 38*, the lower limit is found to be 2.9 b.y. The oldest leads which have been dated on the earth are 3.4 b.y. It i s reasonable to conclude that the ordinary lead miner-alization (t-jj occurred between 2.9 and 3.4 b.y. ago. It is assumed that nothing more happened u n t i l a time, tg, when uranium and thorium were introduced into the crustal system. At time tg the ordinary and radiogenic lead was mixed and thoroughly homogenized, at least locally at Ivigtut to produce the isotope ratios now observed. That such local homogenization i n a batholith can and does occur i s shown by the Bluebell anomalous leadswhich have nearly identical ratios in the mine but form part of an anomalous lead line when surrounding mining dis t r i c t s are considered. - 125 -The various sequences in the development of Ivigtut are illustrated in Figure 3.11. For the purposes of i l l u s t r a t i o n , some numbers w i l l be assumed for tg and t 3 . It w i l l then be possible to evaluate t^, Vg and Wg on the basis of a three-stage model. Moorbath et a l (1960) have obtained an age of 1590 m.y, by the Rb-Sr method for the Julianehaab granite. This body is intrusive into the Ketilidian Group, the oldest series of volcanics, gneiss and meta-sediments in the area (Wegmann, 1938). A Rb-Sr age of 1090 m.y. was obtained for the Ilimausak massif which i s intrusive into the younger Garder formation. These dates correlate very closely with events in Labrador (Lowden, 1961). For this i l l u s t r a t i o n , l e t tg - 1590 m.y. and t 3 - 1090 m.y. The age calculated for tj_ is 3020 m.y. This correlates closely with lead mineral-izing events in the Superior province (Figure 2.7). From a mathematical point of view, i t does not matter i f the ordinary leads at Ivigtut were derived directly from depth, 3 b.y. ago or i f they are det r i t a l minerals eroded from a 3 b i l l i o n year old province and transported to Igvitut at any time prior to t3« The latter suggestion appears to be more li k e l y to the author. The mean values computed for V g and Wg are 0,106 and 88.0 respectively. The mean ratio of thorium/uranium referred to the present i s 5,97. This agrees favourably with values of 4.1 to 6,9 for anomalous leads at Broken H i l l , Australia - 126 -y 14. 1 2 Growth Curve-'-•ordinary lead Primeval lead To 12" EST i i i * F i r s t Phase: Formation of ordinary leads at time t^. Growth curve for one anomalous lead. Anomalous leads formed at time t*. Second Phase: Formation of anomalous leads between times and tg. Homogenized r a t i o s at time t 3 Third Phase: Homogenization of lead isotope r a t i o s at time tg. Figure 3 - 1 1 . Development of lead isotope r a t i o s at Ivigtut on a three stage model. - 127 -(Russell, Ulrych and Kollar, 1961). Rogers and Ragland (1961) have measured the variation of thorium and uranium in selected granitic rocks from North America. The mean value of the thorium/uranium ratio for 75 samples was estimated to be between 4 and 5 from their figures 4 and 9. The solution given above i s not unique as different numbers might be selected for t 2 and tg. The good agreement obtained with broad tectonic events and particularly, the reasonable crustal value for the thorium/uranium ratio does suggest that the model chosen i s correct. A proof of i t s correctness could be obtained i f further Isotope analyses were made on lead from adjacent dis t r i c t s to establish the existence of an anomalous lead l i n e . 3*6 Classification of Lead Isotope Ratios Studies carried out so far have shown that the division of lead isotope ratios into single-stage (ordinary) and multi-stage (anomalous) i s sound from a geophysical and a geological point of view. Characteristics of each type w i l l be briefly summarized in the light of present day experi-mental knowledge. Use i s made of the author's analyses on Bluebell, British Columbia, St. Magloire, Quebec, Ivigtut, Greenland and Korsnas, Finland; F. Kollar.'s analyses on Broken H i l l and Mount Isa, Australia; R. G. Ostic's analyses on Captain's Flat and Cobar, Australia; and data published by other researchers. - 128 -Single-stage Leads Criteria for recognizing single-stage leads are d i f f i c u l t to specify and the limits given below are only tentative. The problem i s being studied in detail by R. G. Ostic and the conclusions reached here w i l l doubtless need some modification. In a l l cases, consideration must be given to interlaboratory differences and the amount of P b 2 0 4 error to be expected. Preliminary results indicate that four factors should be considered in the specification of an ordinary lead. The limits given in brackets are for samples which have not been analyzed with intercomparison techniques. (1) The isotopic composition of a group of ordinary leads from an area should be constant within 0.3$ (1$). (2) ,The P b 2 0 6 / P b 2 0 4 and P b 2 0 7 / P b 2 0 4 ratios of an ordinary lead should have a V 0 between 0.0650 and 0.0658 (0.063 and 0.067). (3) The P b 2 0 8 / P b 2 0 4 ratio of an ordinary lead should p r z p 204 yield a Th /Pb ratio between 37.6 and 38.9 (35 and 41), calculated on the basis of a single lead-thorium-uranium system. (4) The age of an ordinary lead should agree reason-ably well with other age dating techniques. The amount of disagreement allowed w i l l depend on the closeness of the geological setting and the method used for age determina-tions. - 129 -Anomalous Leads Leads which do not f i t the c r i t e r i a l i s t e d above are li k e l y anomalous. Anomalous leads are most frequently recognized by the linear relationship of the isotope ratios on an x~y and x-z plot. The linear relationship may not be evident from samples at individual mines (Bluebell, St. Magloire), but should always be recognized when samples are considered from related areas. Anomalous leads were classified into short or long period types depending on the length of time spent in a radiogenic environment in comparison to 400 m.y. A further subdivision of distinctive types of anomalous leads and their characteristics are list e d below: (a) Mixture of Two Ordinary Leads (1) A mixture of two ordinary leads w i l l have linearly related isotope ratios. The line should Intersect the "mantle" growth curve at two points and not extend beyond i t . (2) The isotope ratios of the two end points should satisfy the c r i t e r i a for ordinary leads. ( 5 ) Such mixtures w i l l occur most frequently close to the boundary of two geological provinces. (b) Two-Stage Growth Systems (1) The isotope ratios w i l l l i e along an anomalous lead line which intersects the "mantle" growth curve at tj_ and tg with some points usually f a l l i n g on the line beyond tg . - 130 (E) The uranium/lead and thorium/lead ratios in the second system w i l l be highly variable but the mean values w i l l be characteristic of a crustal system. (3) The Isotope ratios on an x«z graph may f a l l on several straight lines, not necessarily passing through the ordinary lead ratios. This i s a result of oxidation of the uranyl ion in a crustal environment. This characteristic arrangement of isotope ratios indicates that growth processes have predominated over mixing processes. ( 4 ) The degree of homogeneity of the isotope ratios and the amount of complexity displayed on an x-z graph is a qualitative indicator of the temperature at which two-stage leads were mineralized. (5) Given the appropriate experimental information, i t is possible to solve a two-stage growth process completely. (c) Three-Stage System with VT_ = 0. Ivigtut, Greenland was postulated to be an example of this type. It i s generally impossible to solve the system completely without independent information on the f i n a l period of mineralization. Useful limits may be determined for the various episodes in the development. (d) Multi-Stage Growth System Growth systems with three or more consecutive stages of development are probably quite rare. It was shown in Chapter £ that under appropriate circumstances they may be - 131 -treated as a two-stage system to find the i n i t i a l and f i n a l time, of mineralization. 3.7 Summary Experimental results obtained indicate that single stage isochrons as proposed by Houtermans (1953) are either very short or do not exist. Because of this, i t i s also impossible to establish the validity of Damon's (1954) model in which the sima separated from the proto-crust at some date after the formation of the earth. This indicates that either V and W of the original simatic surface of the earth was the same as in the mantle, or the layer i s too thin wher-ever ordinary leads are produced to be a significant source of lead. These findings tend to verify conclusions reached by Russell as early as 1956. In brief, these were, that a l l known isotope ratios may be considered as having: (1) A f i r s t stage of development in the mantle which would have a nearly constant V Q and WQ. (S) Formation of an ordinary lead with i t s introduc-tion into a crustal environment. (3) Subsequent optional stages of development in a crustal environment. CHAPTER 4 APPROXIMATE AGE OF TECTONIC ACTIVITY USING ANOMALOUS LEAD ISOTOPES And no synthesis or interpretation is ever f i n a l , because there are always fresh facts to be found after the f i r s t collection has been provisionally arranged. Toynbee, The Geneses of Civilizations, 1, 49. 4.1 Introduction Having set out a theory for two-stage leads, and having decided on a set of c r i t e r i a to distinguish ordinary leads, i t i s now possible to inquire how this description of the phenomenon accords with established geological and geochronological fact. Five test areas have been selected for which there is sufficient experimental information to carry out quantitative calculations. These test areas are Broken H i l l , Australia; Goldfields, Saskatchewan; Sudbury, Ontario; Ozark Dome area of Arkansas, Missouri and Oklahoma; and west-central New Mexico. The results of the calculations are summarized in Table 4.1. The individual areas are discussed in more detail below. 4.2 Broken H i l l , Australia A description of the area and the lead isotope ratios can be found in the literature (Russell and Farquhar, 1960, Kollar et a l , 1960, Russell et a l , 1961) and w i l l not be reviewed here. A l l of the age determinations were made using - 132 -TABLE 4-1 Results of Calculations on Anomalous Leads Area Number of Samples *o y 0 v 0 Standard R Dev. on R t l m.y. * t 2 m.y. * Broken H i l l 15 16.12 15.54 .0651 0.1139 +.0033 1600 +4 510 +80 Goldfields 7 15.28 15.32 .0643 0.1427 +.0063 2015 +75 560 +250 Sudbury 16 16.03 15.61 .0667 0.1369 +.0063 1730 +100 870 +280 Ozark Dome 30 16.52 15.59 .0649 0.0886 +.0104 ^1350 ^115 New Mexico 63 16.20 15.49 .0642 0.0938 +.0029 ~1490 ~ 69 H W * Standard deviation on? ages are calculated under assumption that constants a Q, b G, X , land a are perfectly known. i H Estimated error. - 134 -analyses obtained with the mass spectrometer at the University of British Columbia. A l l of the age determi-nations use the set of constants given in Table 1.1. Figure 4.1 shows the linear relationship between ordinary and anomalous lead isotope ratios. Collins et a l (1953) reported a Pb 2 0 7/Pb 2^ 6 age of 1510 m.y. on a davidite from Radium H i l l . Greenhalgh and Jeffery (1959) quote an age value for Crocker's Well, also carried out on davidite. Complete uranium, thorium and lead analyses were made for this sample so that three independent age values could be calculated. They are 1628 m.y. ( P b 2 0 6 / U 2 3 8 ) , 1702 m.y.. (Pb 2 0 7/Pb 2 0 6) and 1252 m.y. ( P b 2 0 8 / T h 2 3 2 ) . The very low value for the p b 2 0 8 / T h 2 3 2 age is very frequently observed, and does not detract from the rather good agreement between the uranium-lead ages. On the basis of six galena analyses, the age of the ordinary leads and the time of primary mineralization is between 1595 and 1604 m.y. The uncertainty in the isotopic composition of the leads introduces only about 5 m.y. uncertainty in the age but i t must be remembered that the uncertainty in a c, b Q and t may introduce an error which i s much larger. The age of secondary mineralization was found to be 510 ± 80 m.y. The uncertainty list e d i s only that due to the uncertainty of the measured isotopic abundances. Russell et a l (1961) obtained a slope of 0.122 for the straight line by taking i t through the lowest ordinary lead Figure 4-1. Graph of Pb 2 0 7/Pb 2 0 4 and Pb 2 0 6/Pb 2 0 4 showing the linear relationship between ordinary leads and anomalous leads at Broken H i l l , Australia. - 136 -point rather than the mean value as required by the present model. It i s useful to compare the limits on the ages using the Russell-Farquhar method for anomalous leads with the ages obtained by the present model. Lead i s found to be generated by natural uranium in the proportion R (= .1139) at time t r = 1110 m.y. ago. This i s the oldest time at which the Thackaringa (anomalous) leads could have been deposited. A uranium mineral 1890 m.y. old would yield lead with this isotopic composition at the present time. This data i s summarized on the upper time line in Figure 4.2 and compared with results from the present model. From this diagram i t is clear that the new model is a special case of the more general model for anomalous leads. It has the advantage of reducing the number of orogenic or mineralizing events to a minimum of two by requiring that the uranium and ordinary lead are mobilized contemporaneously. The time of secondary orogenesis, t , i s in the Upper Cambrian according to the Kulp (1961) time scale. Greenhalgh and Jeffery (1959) report that a specimen of biotite hand-picked from the thorian brannerite at Crocker's Well was found to have an age of 520 m.y. as determined by K-Ar measurements. Recently, Evernden and Richards (1961) have reported two potassium-argon ages at Broken H i l l . One specimen gave a value of 504 m.y. while a second one yielded 526 m.y. It is possible that t ? may correlate with the Tyennan - 1 3 7 -4560 '1 present 1890 1600 1110 Incorporation of U and Th in crust any time here. 0 m.y Anomalous lead miner-alization any time here. 4560 Ar t i 1600 *2 present 510 0 m.y Ordinary Pb, U and Th into crust here. Anomalous Pb mineral-ization here. Figure 4-2. Chronological relationship between the Russell-Farquhar model and the present one for Broken H i l l , Australia. Top diagram: Russell-Farquhar model for anomalous leads. Bottom diagram: Model proposed in present paper. Diamond shaped areas il l u s t r a t e the standard deviation assuming constants in formula are correctly chosen. - J.38 -orogeny which occurred in the Upper Cambrian and affected much of the area between Flinders Range and Tasmania. David (1950) mentions that "Certain of the numerous dykes"of pegmatite and acid granite invading the less altered rocks of the Willyama Series in the Barrier Ranges (N.S.W.) may be Cambrian, and the somewhat altered granites forming s i l l s in the Torrowangee Series farther to the north and north-east of Broken H i l l , as at Tibooburra, are most probably of this age." Thus, the calculated time of mineralization (t ) i s supported both by K-Ar data and by geological evidence. The P b 2 0 8 / P b 2 0 4 and p-b206/pb304 ratios are plotted on Figure 4.3. There i s a linear relationship between the lead isotope ratios from the Thackaringa vein deposits but the line does not pass through the Broken H i l l ordinary leads. This i s good evidence that this i s primarily a growth system and not a simple mixture of a single ordinary and a single radiogenic lead. The T h 2 3 2 / P b 2 0 4 ratio for the second stage of growth may be described by an equation of the form W_ = k + k-V 2 ° 1 5 1 o x i The presence of the term k Q indicates that during the process in which uranium and thorium were transferred from a mantle to a crustal environment, thorium was enriched relative to uranium. The constant k^ i s simply related to the slope of the line i n Figure 4.3 and the times of miner-alization. It represents the portion of the uranium and F i g u r e 4 - 3 . P l o t o f P b 2 0 8 / P b 2 0 4 and P b 2 0 6 / P b 2 0 4 f o r l e a d s from B r o k e n H i l l , A u s t r a l i a . - 140 -thorium which underwent a similar chemical process in the crust. Using equations 2.6, 2.15, and the slope of the line in Figure 4.3, the constant k Q was found to be 29.12 and k-j_ was found to be 295.7. Table 4.2 presents the uranium/lead, thorium/lead and thorium/uranium ratios for each of the anomalous leads; TABLE 4,2 Isotopic Analyses of Thackaringa-Type Leads UBC No. 7 i k l V l Th TJ 70 .0471 13.92 43.04 6.58 45 .0636 18.81 47.94 5.43 68 .0666 19.69 48.81 5.28 67 .0677 20.02 49.14 5.23 69 .0684 20.23 49.35 5.20 66 .0703 20.78 49.90 5.12 65 .1251 36.99 66.11 3.81 The portion of uranium and thorium which was chemically related had a thorium/uranium ratio of 2.1. This i s distinctly lower than the "mantle" ratio of 4.2 as obtained from ordinary leads. By comparing the value of W-^  in Table 4.2 with the T h 2 3 2 / P b 2 0 4 ratio of 38.2, obtained from ordinary leads, i t i s seen that the system - 141 -in which Thackaringa leads developed was considerably-enriched in thorium- Uranium was also differentiated, but the average ratio of U /Pb remained close to the value in the mantle as is evident from the cluster cf points around an apparent age of 500 m.y. in Figure 4.1. The age of the Broken H i l l ordinary leads and the time of primary mineralization i s 1600 m.y. The postulate that uranium and thorium mineralization occurred contempor-aneously is supported by dated uranium-bearing minerals in adjacent d i s t r i c t s . The second stage of development occurred in a thorium-rich crustal environment. The Th/U ratio varied between 3.8 and 6.6 on the basis of seven samples. This range i s typical of the variation obtained from crustal granitic rocks (Rogers and Ragland, 1961). The age of secondary mineralization i s found to be 510 ± 80 m.y. This calculated time of mineralization i s supported by both K-Ar and geological evidence. 4.3 Goldflelds Region, Saskatchewan The. Pb-U method of age determination for the Goldfields region has been widely discussed in the literature. There is 207 235 a linear relationship between the ratios of Pb /U and Pb206/TJ23'8 ^ n a n a i y S e s 0 f uranium-bearing crystals which intersect the ooncordla at an age of 1800 m.y. according to Russell and Ahrens (1957). Aldrich and Wetherill (1958) obtained an intersection at 1900 m.y, Eckelmann and Kulp (1956) concluded that i n i t i a l deposition of the pitchblende - 142 -occurred close to 1900 m.y. ago. They also reported there was evidence of either more than one generation of pitch-blende from depth or siiaply a local recrystallization due to elevated temperatures. Aldrich et a l (1958) obtained an age of 1780 m.y. by the K-Ar method and an age of 1970 by the Rb-Sr method. Lowden (1960, 1961) reports K-Ar ages of 1740, 1815 and 2015 m.y. from the immediate v i c i n i t y . There does not appear to be any discussion pf the lead Iso-tope analyses of common leads from this area so that this section w i l l present the f i r s t investigation of the age relationships by this method. The data used for calculation of ages i s from Russell and Farquhar (1960) and uses Toronto anlyses exclusively. There appears to be only one ordinary lead sample whose age is calculated to be 2015 m.y. Since this figure agrees reasonably well with the time of formation of pitchblende, Rb-Sr and K-Ar data, i t was used for t^ in the calculation of the time of mineralization of the anomalous leads. The Goldfields region i s remarkable in that the lead ratios l i e along the longest anomalous line (Figure 4.4) discovered to date. The time, t , when the ordinary leads and the Ct radiogenic leads were mixed is calculated to be 560 ± 250 m. It w i l l be worthwhile to re-analyze these leads with more accurate techniques now available. It i s conceivable that t 2 w i l l correlate with the value of 355 m.y. which Baadsgaard, Folinsbee and Lipson (1961) obtained for the - 144 -Fitton (Yukon) and. Ice River (British Columbia) intrusives on the basis of K-Ar dating. The thorium/uranium ratio i s related to t^, t g and 208 0^$"* the slope, T, of the line on a plot o f Pb /Pb"'""' versus Pb2Q7/ pi3206 (Figure 4,5). This type of graph i s used since there i s considerable uncertainty in the relative amount of P b 2 0 4 . Unlike Broken H i l l , the anomalous lead line inter-sects the ordinary lead ratios. The Th/U ratio i s obtained by solving for in equation 2.14 and finding ^/138.8«, It i s computed to be 0,2. The u 2 3 5 / P b 2 0 4 ratio (¥•,_) for the most radiogenic lead is 1,15, a value nearly 18 times larger than the value for V which characterizes the uranium/lead o ' environment in which ordinary leads developed. Thus, the lead isotope data confirm the well known fact that this i s a thorium-poor, uranium-rich province. 4,4 Sudbury, Ontario The Toronto analyses of the Sudbury ordinary leads have a f a i r l y wide scatter so that i t was d i f f i c u l t to make a reliable estimate of t ^ . From the mean of 5 samples, i t was calculated to be 1730 ± 100 m.y. The agreement with other age dating methods was discussed in section 2.4 and i l l u s -trated in Figure 2.5. Combining the data from ordinary and anomalous leads, the time of secondary orogenesis Is found to be 870 ± 280 m.y. This agrees within the limits of error with the time of the Granville orogeny. The slope of the line i s the same as found by Russell and Farquhar (1960) and - 145 - 146 -the conclusions reached here are in complete agreement with their analyses. A new set of more accurate lead isotope measurements i s . "being made by T. J. Ulrych and the present writer and further discussion of this area i s deferred u n t i l these have been completed. 4.5 Ozark Dome, Arkansas, Missouri and Oklahoma The Ozark Dome area Includes the Jbplin leads which are in the Tri-State region, the Bonne Terre leads which are in southeastern Missouri and lead mines in northern Arkansas. A regression analysis was made on 30 samples reported by Bate, Gast, Kulp and Miller (1957) of the Lamont Geological Observatory (Figure 4.6). The time of primary orogenesis was determined from two samples in granite, one at the Silver Mine (No. 117) and the other at Fredrlektown (No. 170). The average value i s x Q = 16.44, y Q - 15.52 which gives an age of t^ •- 1350 m.y. Sample No. 116 from the Silver Mine was taken to be slightly anomalous and the Pea Ridge sample (No.-285), also from the granite, Is the most anomalous lead in the entire area. Both of these samples are from the basement and in conformity with the model were treated s t a t i s t i c a l l y with the ordinary leads, No. 117 and 170, and the remaining 26 anomalous leads which are from massive sulphide bodies within the Palaeozoic sediments, to obtain the slope of the best straight line. From equation 2.12, V 0 was found to be 0.065 which 0(Y7 204 206 204 Figure 4=6. Graphs of Pb^VPb and Pb /Pb for leads from Ozark Dome and New Mexico, U.S.A. Note the magnified scale of the P b 2 ° 7 / P b 2 0 4 axis. - 148 -places the mean of the ordinary leads just below the "mantle" growth curve. The secondary period of orogenesis is calculated to have occurred 115 m.y. ago, which is i n the Lower Cretaceous. The standard deviation on the slope was calculated in a formal mathematical manner (see Appendix) and gives a very wide limit on t g . If we assume that we know t^ perfectly, the error i n t g i s ~t 300 m.y. In the Ozark Dome area the precision in the slope can be improved by searching for examples of ordinary lead and highly anomalous leads. From the data presented by Bate et a l , i t i s apparent that these are to be sought in the Pre-Cambrian granite outcrops where extensive mixing of mineralizing solutions has not occurred. The geologic record (Eardley, 1951) i s more or less complete up to the Pennsylvanian period in the vi c i n i t y of the lead deposits. There was l i t t l e activity aside from normal subsidence and sedimentation during the lower Palaeozoic. The Ozark Dome underwent epeirogenic u p l i f t during the Devonian and Mississippian periods. Some tectonic activity occurred in the Arbuckles in southern Arkansas during the late Pennsylvanian together with some high angle faulting extending into the Ozark Dome. Philpott (1952) reports that there was regional u p l i f t , folding, faulting and volcanism in Arkansas and Mississippi at the end of the Lower Cretaceous. As much as 7000 feet of section was truncated at the level of the Lower Cretaceous. In addition, - 149 -diamonds occur In ultra-basic igneous intrusives which penetrate Cretaceous sedimentary rocks near Murfreesboro in southwestern Arkansas. The Bonne Terre and TrI-State leads are on opposite sides of the Ozark Dome and they occur In d i s t i n c t l y different sedimentary environments. Therefore there is a possi b i l i t y that they were emplaeed In different geologic periods. These leads cannot be differentiated on the basis of published ratios, but certainly, more accurate, measure-ments are necessary to positively establish that they both l i e along the same straight line. From the available lead isotope data It i s concluded that primary orogenesis occurred in the Ozark Dome area about 1350 m.y. ago. This agrees with a K-Ar ages of 1350 m.y. from Precambrian igneous rocks at Silver Mine, Mo. (Allen et a l , 1959); 1280 m.y, at Granlteville, Mo.; 1405 m.y. at Fredriektowns Mo.; and 1290 m.y. at Decaturville, Mo. (Aldrich et a l , 1959). From a s t a t i s t i c a l analysis of anomalous leads, the most probable time of secondary orogenesis is 115 m.y. ago with a large probable error. This figure correlates with tectonic activity taking place in Arkansas at the end of the Lower Cretaceous. The Isotope data can therefore be interpreted in a consistent manner to yield a quantitative estimate of the time of deposition of the ores. This estimate agrees with the statement by Behre, Heyl and McKnight (1948) that "the deposition of ores - 150 -was contemporaneous with, the last stages of the regional tectonic deformation". 4.6 New Mexico, U.S.A. Slawson and Austin (1960, 1962) have made a study of 63 samples of galena from deposits in West-Central New Mexico. The isotope ratios were a l l analyzed at the University of Toronto and l i e close to a line with a slope of 0.0938± 0.0029 (Figure 4.6). Sample I from the Bosque del Apache site occurs in rocks classified as Pre-Cambrian and i s calculated to have an age of 1490 m.y. Tilton and Davis (1959) have obtained Rb-Sr and K-Ar ages which vary from 1300 to 1490 m.y. near Mora, Dixon and Albuquerque, an area which l i e s 100 to 200 miles northeast of the d i s t r i c t under consideration. The time of anomalous lead mineralization, according to the present model, i s found to be at the end of the Cretaceous, 69 m.y. ago. Assuming that there i s no error in t^, the standard deviation in t g i s ± 80 m.y. The true standard deviation i s probably somewhat greater than this, considering the unknown accuracy of t^. In view of the large error, the method does not appear to be very useful for cases of recent mineralization. As mentioned in the Ozark Dome area, the most feasible way of improving the precision is by extending the length of the anomalous lead line with highly radiogenic samples from the granitic basement. A Tertiary (?) age has generally been assigned (Loughlin et a l , 1942) to - 151 -igneous rocks in the area; however, there i s no direct stra-tigraphic correlation after the Permian. A direct correlation has been found between lead isotopes and geologic structure in this area (Slawson and Austin, 1962). The group of samples marked with a cross in Figure 4.6 coincides with a lineament which presumably formed a conduit for mineralizing solutions. A deep crustal origin is suspected for the solutions since the average uranium/lead (Yj_ » .073) ratio for the group of samples marked nB" i s only 10% higher than the value of V 0 for ordinary leads. The P b 2 0 7/Pb 2 0 6 and P b 2 0 8/Pb 2 0 6 ratios are plotted in Figure 4.7. The Th/U ratio for group "B", calculated from t 1 , t g and the slope of the line between I and N in Figure 4.7, i s 3.8. This i s only 10% lower than the ratio calculated for ordinary leads. The group of samples marked "C" In Figures 4.6 and 4.7 are located at various distances away from the lineament. The average uranium/lead ratio for this group i s 170% higher than the YQ value which characterizes ordinary leads. The Th/U ratio, calculated from t^, t g and the slope of the line between I and C in Figure 4.7 i s 2.6. This i s 40% lower than the value for ordinary leads. The variable but generally high uranium/lead ratio indicates that these leads have developed in basement rocks with a characteristically low thorium/uranium ratio. Some mixing of the leads from the two characteristic thorium/uranium environments has occurred as - 152 -70 80 90 Figure 4-7. Plot Of P b 2 0 8/Pb 2 0 6 and Pb 2 0 7/Pb^ 0 6 for leads from New Mexico, U.S.A. - 153 -i s indicated by the linear relationship of Isotope ratios between B and C on Figure 4.7. From lead isotope data i t i s possible to conclude that the most probable time of anomalous lead mineralization was in either the Cretaceous or Tertiary period. The second stage of development occurred in two distinct crustal environments, one probably very much deeper than the second. - 154 -CONCLUSIONS Experimental results obtained by the author and other research workers at the University of British Columbia indicate that single-stage isochrons as proposed by Houtermans (1953) are either very short or do not exist. The evidence for a unique ter r e s t r i a l growth curve or a narrow "growth band" supports an origin of ordinary leads from the mantle (Russell, 1956). Since the mantle i s commonly thought of as being molten during a very early phase of the earth's development (Jeffreys, 1952; DeSitter, 1959), i t would provide a large reservoir with a uniform world-wide distribution of uranium, thorium and lead. Within limits of error, the author has found that single-stage leads correlate with the oldest geological and chronological events inside units known as geological provinces. This evidence suggests that the crustal layer was thin prior to i n i t i a t i o n of primary tectonic activity within a geological province. The geographical and chrono-logical arrangement of the provinces i s in conformity with what i s expected i f continental growth (Lawson, 1932; Wilson, 1952) occurred. This theory postulates that continental blocks were absent from the face of the primeval earth. They evolved into their present form by outward growth from original "continental nuclei". The continents grew by successive marginal geosyncllnal belts, each one - 155 -containing a great thickness of volcanic and sedimentary-rock, thus giving rise to a s i a l i c rock type. From the material presented in Chapter 2, i t would appear that by the time of the Grenville orogeny, the North American continent closely resembled i t s present dimensions. The hypothesis of multi-stage lead development i s based on the episodic nature of orogenesis. It appears that a large proportion of lead isotope measurements may be interpreted on the basis of development in two or more uranium and thorium systems. The simplest type which can occur is a mixture of two ordinary leads. This has only been found to occur on the boundary between two geological pro-vinces. Examples of this type have been identified in the Cobalt area, Ontario and in the Baltic Shield along the border between the Fenno-Karelides and Svecofennides. Lead Isotope ratios which have developed in a uranium-rich crustal environment during primary orogenesis are here termed short period anomalous leads. They are most readily recognized by the linear relationship of lead isotopes on any compositional diagram. The approximate time of i n i t i a l and f i n a l mineralization may be obtained with a two-stage model. Examples of short period anomalous leads occur in the Lake Di s t r i c t , England and Yellowknife, Canada. If the isotope ratios are interpreted point by point In a conven-tional manner using Houtermans' isochron equation, a linear relationship between JQ, W0 and t x would result. It seems ~ 156 -highly improbable that there could be a correlation between the amount of uranium and thorium in the source region and the time of mineralization within a local d i s t r i c t . In the past, inadequate precision has been the major source of d i f f i c u l t y in interpreting lead isotope measure-ments. Re-analysis of samples from British Columbia, Quebec, Greenland and southern Finland has shown that this has been due to d i f f i c u l t i e s in obtaining a precise measurement of the relative abundance of lead-204. Results obtained by the author at the University of British Columbia on five galenas from Ivigtut are identical within 0.1$. The absolute ratios are close to the mean of the results obtained by nine other laboratories. In almost every geological province studied, there are potassium-argon dates which show that the rocks in the area have f e l t the effects of primary orogenesis taking place i n adjacent geological provinces. The extra length of time available in a rich uranium crustal environment has contri-buted to the formation of extremely radiogenic leads known as long period anomalous leads. The Russell-Farquhar model for anomalous leads has been modified by postulating that ordinary lead mineralization and incorporation of uranium and thorium into the crust occurred contemporaneously during an early period of tectonic ac t i v i t y . From a geological point of view this assumption appears to be a reasonable approximation. The five examples for which calculations - 157 -have been made indicate that the model yields a promising method for determining the time of anomalous lead mineral-ization. As an example, at Broken H i l l , Australia, primary mineralization of single-stage leads occurred 1600 m.y. ago. The Thackaringa vein deposits had two stages of development and secondary mineralization occurred 510 £ 80 m.y. ago on the basis of this model. This age correlates with geological evidence and independent potassium-argon dates (Evernden and Richards, 1962) of 504 and 525 million years. The major contribution of the present writer has been the proposal of a new method for determining the age of mineralization of a large class of anomalous lead sulfides. The method assumes that the i n i t i a l stage of lead isotope development occurred In a system having a uniform distribu-tion of uranium, thorium and lead. There are subsequent stages of development in systems with variable proportions of uranium and thorium. From the calculated thorium/uranium ratios i t has been shown that these later stages occurred in a crustal environment. - 158 -BIBLIOGRAPHY *Aldrich, L.T., 1.956, Measurement of radioactive ages of rocks; Science, 123, 871-875. •Aldrich, L .To, Davis, G .L., Tilton, G.R. and Wether111, G.W., 1956, Radioactive ages of minerals from the Brown Derby Mine and the Quartz Creek Granite near Gunnison, Colorado; Journal of Geophysical Research, 61, 215-232. *Aldrich, L.T. and Wetherill, G.W., 1960, Evaluation of mineral age measurements I; National Academy of Science, National Research Council, 147-150. #Aldrich, L.T. and Wetherill, G.W.,1958, Geochronology by radioactive decay; Annual Review of Nuclear Science, 8, 257. *Aldrlch, L.T., Wetherill, G.W., Bass, M.N., Compston, W., Davis, G.L., and Tilton, G.R., 1959, Mineral age measurement. Annual Report, Carnegie Institution of Washington, 1958-1959, 237-253. •Aldrich, L.T., Wetherill, G.W., Davis, G.L. and Tilton, G.R. 1958, Radioactive ages of micas from granite rocks by Rb-Sr and K-A methods; Transactions, American Geophysical Union, 39, 1124. *Aldrich, L.T. and Wetherill, G.W., 1960, Rb-Sr and K-A ages in Ontario and Northern Minnesota, Journal of Geophysical Research, 65, 337-340. •Allen, V.T., Hurley, P.M., Fairbalrn, H.W. and Pinson, W.H., 1959. Age of Precambrian igneous rocks of Missouri; Abstract in 1959 Annual Meetings, Geological Society of America, 2A. Alterman, Z., Jarosch, H. and Pekeris, C . L . , 1961, Propagation of Rayleigh waves in the Earth; Geophysical Journal, 4, 219-241. 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Vinogradov, A.P., Tarasov, L.S. and Zykov, S.I., 1959, Isotopic composition of leads from the ores of the Baltic Shield: Geochemistry, No. 7, 689-749. •Wasserburg, G.J. and Hayden, R.J., 1955, A^-K 4 0 dating: Geochimica et Cosmochimica Acta, 7_> 51-60. •Wasserburg, G.J., Hayden, R.J. and Jensen, K.J., 1956, A40-K40 dating of igneous rocks and sediments: Geochimica et Cosmochimica Acta, 10, 153-165. •Wasserburg, G.J., Wetherill, G.W., Silver, L.T., and Flawn, P.T., 1962, Ages in the Precambrian of Texas, (Abstract) Geophysical Journal of Research, 67, 1661. 173 -Wegmann, C.E., 1938, Geological investigation in southern Greenland: Meddelelser om Gronland 113, 1-148. *Wetherill, G.W., Tilton, G.R., Davis, G.L. and Aldrich, L.T., 1955, Comparison of radioactive age measure-ments on pegmatites: (Abstract) Transactions, American Geophysical Union, 3_6, 533. *Wetherill, G.W., Aldrich, L.T. and Tilton, G.R., 1956, Comparison of K-A ages with Concordant U-Pb ages of pegmatites: (Abstract) Transactions, American Geophysical Union, 37, 362. *Wetheril.l, G.W., Wasserburg, G.J., Aldrich, L.T., Tilton, G.R. and Hayden, R.J., 1956,Decay constants of K 4 0 as determined by radiogenic argon content of potassium minerals. 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Wilson, I.T., 1949, The origin of the continents and Precambrian history: Transactions, Royal Society of Canada, 43, 157-184. Wilson, I.T., 1952, Orogenies as the fundamental geologic process, Transactions of American Geophysical Union, 33, 444-449. - 174 -Wilson, T.T., Russell, R.D. and Farquhar, R.M., 1956, Radioactivity and age of minerals: Handbuch der Physik, 47, 288-363. #Zartman, R.E. and Wasserburg, G.J. 1962, A geochronolo-gical study of a granite pluton from the Llano U p l i f t , Texas. Journal of Geophysical Research, 67, 1664. Zhirov, K.K. and Zykov, S.I., 1958, Lead isotopic composi-tion of galenas from pegmatites In Northern Karelia: Ser. Gegr. Geol. No. 1, 258-265. - 175 -APPENDICES Linear Regression with both Varlates having Errors Consider a theoretical relation between two variables of the form y = a + Rx. (1) From physical measurement, a set of data i s obtained (xl» 3Tl) » (x2» ' ' • ^xn» yn^* B o t h x i a n d y i a r e subject to error. An expression for the slope of the line, in a least squares sense, has been obtained by Kummell (1879) and Deming (1938). By translating the coordinates to the center of gravity of the experimental data, a new set of coordinates may be defined: u i = x i " x ^ v i 83 y i " y ( 3 ) Since the least squares line passes through the center of gravity, • v = Ru . (4) The best f i t t i n g line i s found by obtaining the least square of the sum of the residuals measured perpendicularly from the line to the point. - 176 -V U 6V4 Figure a. Residuals, h^, In linear regression analysis. Letting }_ = 0 and solving the resultant dR quadratic equation for R, l t i s found that R = - 2 ^1 4 u i v i (5) a = y - R X (6) Birge (1947) has shown that "by the theory of errors, given a function Z where z-^ , z 2 . . • z n are Independent quantities, f ( z l * z 2 ' * * ' zn^ (7) - 177 -the probable error in Z i s r : where p^ =» assigned weight of z^ hi o residual n m number of observations s j + 1 where j. i s the degree of the polynomial. In the present case, of a f i r s t degree polynomial R i s a function of independent quantities u-j_, u 2, . . . u n, vl> v2> 0 * • T n ^ s e e e < l u a * i o n 5)« t n e weights on Uj_ and v^ be equal to unity. To find the standard devia-tion rather than the probable error, the constant, 0*6745 i s replaced by 1, The standard deviation on R i s : The differentiation i s straightforward but involved in detail. The result may be summarized as follows. Hrr = m~( u r p + v rD - u rS) - (10) - 178 --W r - m~( urD - v rP + v rS) - ^ g r (11) where S P 2 + D 2 N The c a l c u l a t i o n i s most r e a d i l y carried out with a d i g i t a l computer. An approximate expression f o r the standard deviation has been derived by R. D. Russell and has been used i n a l l the calculations i n t h i s thesis because of i t s simpler form. In t r i a l cases, the approximate expression agreed with r e s u l t s obtained with equation 9 to three s i g n i f i c a n t f i g u r e s . The derivation i s as follows: Rotate the l i n e through an angle 9 , where R * tan 0. The l i n e i s now horizontal and errors i n the new coordinate system (u* , v*) can be considered i n the v.1 d i r e c t i o n . The standard deviation i s d ( tan 9 ) 80 (12) - 179 -C T R ( 1 + R 2 )-60 (13) A good approximation for the angular uncertainty, 60 , is O" * / (14) (n - 2) £ u < 2 ^ ^ yZ(- uism 0 + Vjcos 8 ) 2 ( 1 5 ) (n - 2)£(u jcos 0 + v ^ i n 0 ) 2 Dividing the brackets by cos 9 and letting R - tan e , a-' * / L l i - R m ) 2 (16) fj (n - 2) £ ( u ± * R V i ) 2 The approximate relation for the standard deviation of the slope when both variates have errors i s (! + r 2 ) - Rui) 2 (17) (n - 2)EK + R v ± ) 2 - 180 -TABLE 1 A TABLE FOR CONSTRUCTING GROWTH CURVES Constants: t = U500 m.y. 1 • .1537 per b.y., X' = .9722 per b.y., X' *= .0U99 per b.y. J01 - 1 3 7 . 8 ( e A V e X t) Ko, - ( e ^ t o . e*'* ) 01 t m.y. j i 0 | 0 137.to 78.U3 0.2517 100 135.26 78.33 O.2U67 200 133.10 78.22 O.2U16 300 130.90 78.09 O.2366 koo 128.66 77.96 0.2315 500 126.UO 77.81 0.226> 600 12U.09 77.6^ 0.2212 700 121.75 77.^ 6 0.2162 800 119.36 77.26 0.2110 900 116.96 77.03 0.2058 1000 llU.51 76.79 0.2005 1500 101.66 75.13 0.1739 2000 87.81 72. hh 0.1U68 2500 72.83 68.07 0.1188 3000 56.68 60.95 0.0901 3500 39.20 1*8.98 0.0608 Uooo 20.37 30.58 O.0309 - 1 8 1 » TABLE 2 A TABLE FOR CONSTRUCTING GROWTH CURVES Constants: t - 5^50 m.y. X - .1537 per b.y., V - .9722 per b.y., X" « .OU99 per b.y. Jo, - 137.8(e X t° - e U ) K 0 1 s ( e r t o - e r t ) L 0| " ( e^"*o - e X"t ) t Joi KOI IIOI m.y. 0 139.51 82.39 0.2548 100 137.28 82.29 0.2498 200 135.21 82.17 0.2448 300 133.00 82.05 0.2397 Uoo 130.77 81.91 0.2346 500 128.50 8I.76 0.2295 600 126.20 81.60 0.2243 700 123.85 81. kl 0.2193 800 121.U7 81.21 0.2141 900 119.07 80.99 0.2089 1000 116.62 80.7U 0.2036 1500 103.76 79.09 0.1771 2000 89.91 76.U0 0.1499 2500 7 .^96 72.02 0.1219 3000 58.79 6k. 91 0.0932 3500 Ul.31 53.31* 0.0639 Uooo 22. U5 3U..5U. 0.0340 - 1 8 2 -TABLE 3 A TABLE FOR CONSTRUCTING GROWTH CURVES Constants: t Q - U560 m.y. X a .1537 per 'b.y., V~ .9722 per b.y., X" - .01*99 per b.y. Jo, ° 1 3 7 . 8(e A t o- e** ) K o l - (e*'*<>- e L o l - ( e ^ t o . e X"t , t J 0 , K0, L 0| m.y. 0 139.9^ 83.20 0.2555 100 137.80 83.10 O.2505 200 135.6k 82.99 0.2**55 300 133.^3 82.86 o.zkok 1*00 131.20 82.73 0.2353 500 128.93 82.58 0.2302 600 126.62 82.to 0.2251 700 I2U.28 82.23 0.2200 800 121.90 82.03 0 .2148 900 119.50 81.80 0.2096 1000 117.05 81.56 0.202*3 1500 10U.19 79.90 0 .1778 2000 90.3k 77.21 0.1506 2500 75-39 72.8U 0.1226 3000 59.21 65.72 0.09l»O 3500 to. 7* 5k. 16 0.061*7 Uooo 22.87 35.35 0.03l*6 - 183 -TABLE 4 A TABLE FOR FLATTING GROWTH CURVES Constants: t Q » 4560 m.y. Lambda (U -238) » 0.1537 per b.y. V 0 ».065U Lambda' (U -235) - 0.9722 per b.y. WQ «38.21 Lambda" (Th-232) » 0.0499 per b.y. a Q » 9.50 b Q = IO.36 c 0 - 29.49 t m.y. 100 z x z X 0 500 18.65 17.93 15.80 15.76 1000 1500 17.15 16.31 15.69 15.59 2000 2500 15.41 14.43 15.41 15.12 3000 3500 13.37 12.23 14.66 13.90 4ooo 11.00 12.67 39.25 38.29 84.72 87.90 210.46 213.55 37.30 36.28 91.49 95.58 217.49 222.44 35.24 34.18 100.00 104.78 228.68 236.87 33.08 31.96 109.65 113.65 247.42 261.32 30.81 115.18 280.09 - 184 -TABLE 5 A TABLE FOR DATING ORDINARY LEADS USING HOUTERMANS EQUATION Constants: t Q = U5OO m.y. , Lambda (U-238)«= O.I537 per "billion years, t in million years. lambda'(U=235)c 0.9722 per billion years, y - hn ( e X ' t o ~ eX') 0 t <f> 0.5707 0 0.6^72 800 0.5791 100 0.6586 900 0.5877 200 0.6706 1000 O.5966 300 0.7391 1500 0.6059 UOO 0.8250 2000 0.6155 500 0.93k6 2500 0.6257 600 I.O755 3000 O.6362 700 I.2U9U 3500 - 185 -TABLE 6 A TABLE FOR DATING ORDINARY LEADS USING HOUTERMANS EQUATION Constants: tQ» k550 m.y. , Lambda (U-238)« 0.1537 per billion years. t in million years. Lambda*(U-235)» 0.9722 per billion years. y - b Q (e*% » e*'*) ^ a x - ao " 137.8(eATo- e *) 0 t 0 t 0*5906 0 0.830k 1900 0.599k 100 0.8k97 2000 0.6077 200 0.8699 2100 0.6169 300 0.8909 2200 0.626k koo 0.9130 2300 0.6363 500 0.936k 2k00 0 . 6 4 6 6 600 0.9608 2500 0.6573 700 0*9866 2600 0.6686 800 l.OlkO 2700 0.6802 900 l*0k26 2800 0.692k 1000 l*072k 2900 O.705I 1100 1.10k2 3000 0.7184 1200 i.1377 3100 0.732k 1300 1*1725 3200 0.7k69 Ikoo 1.2098 3300 0.7622 1500 1.2k9k 3k00 0*7780 1600 1*2912 3500 0*79k7 1700 1.33k5 3600 0*8122 1800 1»5385 kooo — X86 — TABLE 7 A TABLE FOR DATING ORDINARY LEADS USING HOUTERMANS EQUATION Constants: t 0 - 4^60 m.y. , LaM>da (U-238)« O.I537 per "billion years, t in million year®. LaMbda'(U-235)» 0.9722 per billion years. y - \ ( ^ ' t o - e ^ 0 t 0 t 0 t 0 t 0.5946 0 O.5962 20 O.5979 40 O.5996 60 0.6013 80 O.6030 100 0.6047 120 O.6065 140 O.6083 I60 0.6101 180 0.6119 200 0.6137 220 O.6155 240 0.6173 260 0.6191 280 0.6210 300 0.6229 320 0.6248 340 0.6267 360 0.6286 380 0.6305 4oo 0.6324 420 0.6344 440 0.6364 460 0.6384 480 0.6404 500 0.6424 520 0.6445 540 0.6466 560 0.6487 580 0.6508 600 0.6529 620 0.6550 640 0.6572 660 0.6594 680 0.6616 700 0.6638 720 0.6660 74o 0.6683 760 0.6706 780 O.6729 800 0.6752 820 0.6775 840 O.6798 860 0.6822 880 0.6846 900 0.6870 920 O.6894 940 O.6918 960 O.6943 980 O.6968 1000 0.6993 1020 O.7018 1040 0.7044 1060 0.7070 1080 0.7096 1100 0.7122 1120 0.7148 Xt40 0.7175 l l 6 0 0.7202 1180 0.7229 1200 0.7257 1220 0.7285 1240 0.7313 1260 0 . 7 3 M 1280 0.7370 1300 0.7399 1320 0.7428 1340 0.7457 1360 0.7486 1380 O.7516 1400 0.7546 1420 O.7576 1440 0.7606 l46o 0.7637 1480 0.7668 1500 0.7699 1520 0.7731 1540 0.7763 1560 0.7795 1580 0.7828 1600 0.7861 1620 0.7894 1640 O.7927 1660 0.7961 1680 0.7995 1700 0.8029 1720 0.8064 1740 0.8099 1760 0.8135 1780 0.8171 1800 0.8207 1820 0.8243 1840 0.8280 i860 0.8317 1880 0.8354 1900 0.8392 1920 0.8430 1940 0.8468 i960 O.8507 1980 0.8546 2000 O.8586 2020 O.8626 2040 0.8666 2060 0.8707 2080 0.8748 2100 O.8789 2120 0.8831 2140 0.8873 2160 0.8916 2180 0.8959 2200 0.9003 2220 0.9047 2240 0.9092 2260 0.9137 2280 0.9183 2300 0.9229 2320 0.9276 2340 0.9323 2360 0.9370 2380 - 187 -TABLE 7 (Cont'd) A TABLE FOR DATING ORDINARY LEADS USING HOUTERMANS EQUATION Constants: t - U560 m.y. , Lambda (U-238)= 0.1537 per b i l l i o n years. t i n m i l l i o n years. Lambda'(U-235)= 0.9722 per b i l l i o n years. A 7 " ' *o ( e ^ ' t c * gA' 0 =» X -• a o 137.8(e**°-0 t 0 t 0 t 0 t 0.9417 2400 0.9921 2600 1.0485 2800 1.1100 3000 0.9465 2420 0.9975 2620 1.0543 2820 1.1166 3020 0.9513 2440 I.0030 2640 I.0602 2840 1.1232 3040 O.9562 24-60 I.0085 2660 1.0661 2860 1.1299 3060 O.96H 2480 1.0141 2680 I.0721 2880 1.1366 3080 0.9661 2500 1.0197 2700 I.0782 2900 1.1434 3100 0.9712 2520 1.0254 2720 1.0844 2920 1.1503 3120 0.9764 2540 I.03H 2740 I.0907 2940 1.1573 3140 0.9816 2560 I.0369 2760 1.0971 2960 1.1644 3l60 0.9868 258O 1.0427 2780 1.1035 2980 1.1716 3180 1.1788 3200 1.2357 3350 I.2969 3500 1.1971 3250 1.2556 3400 1.3182 3550 1.2159 3300 I.2760 3450 1.3409 3600 

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