Numerical Petrology

Chapter 1. The Nature of Petrological Data 1.1 Introduction 1.2 Sources of Error in Chemical Analyses 1.2.1 Random Sampling Procedures 1.2.2 Homogeneity of Rock Powders 1.2.3 Precision versus Accuracy 1.3 Frequency distributions and probability 1.3.1 The Normal Distribution 1.3.2 The Lognormal Distribution 1.3.3 The Binomial Distribution 1.3.4 The Poisson Distribution 1.3.5 Transformation of Variables 1.3.6 Some Observed Petrological Frequency DistributionsChapter 2. Estimating and Testing Population Parameters 2.1 Introduction 2.2 Estimation of Population Mean µ, and Standard Deviation s 2.3 Standard Deviation of the Sample Mean 2.4 Principles of Hypothesis Testing 2.5 Confidence Limits for Population Mean when s Known 2.6 Sample Size 2.7 Confidence Limits for Population Mean when s Unknown 2.8 Testing for a Difference Between Two Means 2.9 Variance Ratio Test and F Distribution 2.10 Goodness-of-Fit or Chi-Square TestChapter 3. Analysis of Variance - Testing Differences Among Several Means 3.1 Introduction 3.2 One-Way Classification 3.3 Two-Way Classification with Single Observations 3.4 Two-way Classification with Multiple Observations 3.5 Homogeneity of VariancesChapter 4. Linear Relationships Between Two Variables 4.1 Introduction 4.2 The Correlation Coefficient 4.2.1 Testing the Correlation Coefficient for Significance 4.2.2 Confidence Limits for the Population Correlation Coefficient 4.2.3 The Problem of Closure 4.3 Linear Regression Analysis 4.3.1 Testing the Significance of a Regression 4.3.2 Confidence Limits for the Regression Coefficient and Intercept 4.3.3 Confidence Limits for the Location of the Regression Line 4.3.4 Confidence Limits for an Individual y Value 4.4 Functional and Structural Relationships 4.4.1 Significance TestsChapter 5. The Geometry of Petrological Data Space 5.1 Introduction 5.2 Distance Between Two Points 5.3 Definition of Directions in Space 5.4 Equation of a Line and the Addition-Subtraction Problem 5.5 Transformation of Coordinates 5.6 Equation of a Hyperplane 5.7 Some Limitations on the Use of RatiosChapter 6. Multiple Linear Regression and Petrological Mixing Models 6.1 Introduction 6.2 Multiple Linear Regression 6.2.1 Testing the Significance of the Regression 6.2.2 Confidence Limits for the Regression Coefficients 6.2.3 Confidence Limits for the Location of the Regression Surface 6.2.4 Confidence Limits for an Individual Value of y 6.3 Petrological Mixing Models 6.3.1 The Simple Mixing Model 6.3.2 The Constrained Simple Mixing Model 6.3.3 The Geometric Interpretation of Simple Models 6.3.4 The Generalized Mixing Model 6.3.5 Solutions Using Linear Programming 6.3.6 Weighted Mixing Models 6.3.7 Problem of Errors Associated with Petrological Mixing ModelsChapter 7. Principal Components Analysis 7.1 Introduction 7.2 Geometric Interpretation 7.3 Scaling the Variables 7.4 Basic Mathematics 7.5 Problems with Constructing Variation Diagrams 7.6 Use as a "Surface-Fitting" Procedure 7.7 Significance TestsChapter 8. Factor Analysis 8.1 Introduction 8.2 R-Mode Factor Analysis 8.2.1 Simplified Version Commonly Used in Geology 8.2.2 Rotation of Factors 8.3 Q-Mode Factor Analysis 8.4 Extended Q-Mode Factor Analysis 8.4.1 Graphical Representation and Rotation of Factors 8.4.2 Factor-Variance DiagramsChapter 9. Multiple Discriminant Analysis 9.1 Introduction 9.2 Geometric Interpretation 9.3 Basic Mathematics 9.3.1 The Problem of Singular Matrices 9.4 Testing the Significance of the Discrimination 9.4.1 An overall Test for Differences Between Group Means 9.4.2 Testing Successive Discriminant Functions 9.5 The Logic of Assignment Rules 9.5.1 For Two Group Discriminant Analysis 9.5.2 For Three or more group Discriminant Analysis 9.5.3 Use in Estimating Amount of Misclassification 9.6 Comparison with Principal Components Analysis 9.7 Application to Metamorphic Phase DiagramsChapter 10. Cluster Analysis and Classification 10.1 Introduction 10.2 Cluster Analysis 10.2.1 The Choice of Similarity Measure 10.2.2 The Choice of Linkage Method 10.3 Classification Procedure 10.3.1 Application to More than One Group 10.3.2 Using Prior Probabilities 10.3.3 Reducing the Dimensionality of the Problem 10.3.4 The Problem of Singular MatricesChapter 11. Propagation of Errors 11.1 Introduction 11.2 Counting X-Rays and Other Radiations 11.2.1 Single Counts 11.2.2 Testing Count Stability 11.2.3 Optimizing Peak and Background Counting Times 11.2.4 Measuring Concentration in an Unknown 11.2.5 Optimizing Unknown and Standard Counting Times 11.2.6 Lower Limit of Detection 11.3 Mineral Recalculations 11.3.1 Based on a Fixed Number of Oxygens 11.3.2 Partitioning Iron Between FeO and Fe203 11.3.3 Weighted Sums of Oxides 11.3.4 Weighted Cation Ratios 11.3.5 Weighted Oxide Ratios 11.4 Normative Calculations 11.4.1 Limitations on UseChapter 12. Petrological Data Management 12.1 Introduction 12.2 Petrological Databases 12.2.1 Some Source Databases 12.2.2 Some Reference Databases 12.2.3 Starting a Database 12.3 Data Processing Packages 12.3.1 The CLAIR Data Processing System 12.3.2 The KEYBAM Package 12.4 ConclusionsReferencesAppendixAuthor IndexSubject Index