Numerical Petrology (eBook)

Front Cover 1
Numerical Petrology: Statistical Interpretation of Geochemical Data 4
Copyright Page 5
Table of Contents 8
PREFACE 6
CHAPTER 1. THE NATURE OF PETROLOGICAL DATA 12
1.1 Introduction 12
1.2 Sources of error in chemical analyses 12
1.3 Frequency distributions and probability 18
CHAPTER 2. ESTIMATING AND TESTING POPULATION PARAMETERS 29
2.1 Introduction 29
2.2 Estimation of population mean µ, and standard deviation s 29
2.3 Standard deviation of the sample mean 30
2.4 Principles of hypothesis testing 31
2.5 Confidence limits for population mean when s known 33
2.6 Sample size 34
2.7 Confidence limits for population mean when s unknown 34
2.8 Testing for a difference between two means 35
2.9 Variance ratio test and F distribution 36
2.10 Goodness-of-fit or chi-square test 37
CHAPTER 3. ANALYSIS OF VARIANCE - TESTING DIFFERENCES AMONG SEVERAL MEANS 40
3.1 Introduction 40
3.2 One-way classification 40
3.3 Two-way classification with single observations 43
3.4 Two-way classification with multiple observations 45
3.5 Homogeneity of variances 46
CHAPTER 4. LINEAR RELATIONSHIPS BETWEEN TWO VARIABLES 50
4.1 Introduction 50
4.2 The correlation coefficient 50
4.3 Linear regression analysis 58
4.4 Functional and structural relationships 65
CHAPTER 5. THE GEOMETRY OF PETROLOGICAL DATA SPACE 69
5.1 Introduction 69
5.2 Distance between two points 71
5.3 Definition of directions in space 73
5.4 Equation of a line and the addition-subtraction problem 78
5.5 Transformation of coordinates 84
5.6 Equation of a hyperplane 87
5.7 Some limitations on the use of ratios 88
CHAPTER 6. MULTIPLE LINEAR REGRESSION AND PETROLOGICAL MIXING MODELS 91
6.1 Introduction 91
6.2 Multiple linear regression 91
6.3 Petrological mixing models 100
CHAPTER 7. PRINCIPAL COMPONENTS ANALYSIS 117
7.1 Introduction 117
7.2 Geometric interpretation 118
7.3 Scaling the variables 119
7.4 Basic mathematics 126
7.5 Problems with constructing variation diagrams 129
7.6 Use as a "surface-fitting" procedure 131
7.7 Significance tests 132
CHAPTER 8. FACTOR ANALYSIS 133
8.1 Introduction 133
8.2 R-mode factor analysis 134
8.3 Q-mode factor analysis 141
8.4 Extended Q-mode factor analysis 143
CHAPTER 9. MULTIPLE DISCRIMINANT ANALYSIS 152
9.1 Introduction 152
9.2 Geometric interpretation 153
9.3 Basic mathematics 156
9.4 Testing the significance of the discrimination 163
9.5 The logic of assignment rules 165
9.6 Comparison with principal components analysis 167
9.7 Application to metamorphic phase diagrams 169
CHAPTER 10. CLUSTER ANALYSIS AND CLASSIFICATION 174
10.1 Introduction 174
10.2 Cluster analysis 174
10.3 Classification procedure 181
CHAPTER 11. PROPAGATION OF ERRORS 189
11.1 Introduction 189
11.2 Counting x-rays and other radiations 190
11.3 Mineral recalculations 202
11.4 Normative calculations 211
CHAPTER 12. PETROLOGICAL DATA MANAGEMENT 222
12.2 Petrological databases 222
12.3 Data processing packages 227
12.4 Conclusions 230
REFERENCES 232
APPENDIX 244
AUTHOR INDEX 274
SUBJECT INDEX 279