Overview

This book provides a wealth of geomathematical case history studies performed by the author during his career at the Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC). Several of the techniques newly developed by the author and colleagues that are described in this book have become widely adopted, not only for further research by geomathematical colleagues, but by government organizations and industry worldwide. These include Weights-of-Evidence modelling, mineral resource estimation technology, trend surface analysis, automatic stratigraphic correlation and nonlinear geochemical exploration methods. The author has developed maximum likelihood methodology and spline-fitting techniques for the construction of the international numerical geologic timescale. He has introduced the application of new theory of fractals and multi fractals in the geostatistical evaluation of regional mineral resources and ore reserves and to study the spatial distribution of metalsin rocks. The book also contains sections deemed important by the author but that have not been widely adopted because they require further research. These include the geometry of preferred orientations of contours and edge effects on maps, time series analysis of Quaternary retreating ice sheet related sedimentary data, estimation of first and last appearances of fossil taxa from frequency distributions of their observed first and last occurrences, tectonic reactivation along pre-existing schistosity planes in fold belts, use of the grouped jackknife method for bias reduction in geometrical extrapolations and new applications of the theory of permanent, volume-independent frequency distributions.

Full Product Details

Author:   Frits Agterberg
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2014
Volume:   18
Weight:   9.647kg
ISBN:  

9783319349473

ISBN 10:   3319349473
Pages:   553
Publication Date:   17 September 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Foreword Preface 1.  Complexity of the Geological Framework and Use of Mathematics 1.1  Use of Mathematics in Geology 1.2  Geological Data, Concepts and Maps 1.2.1  Map-Making 1.2.2  Geological Cross-Sections 1.2.3  Scientific Method in the Geosciences 1.2.4  Quality of Predictions 1.3  Use of Curves 1.3.1  Trend-Lines 1.3.2  Elementary Differential Calculus 1.3.3  Graphical Curve-Fitting 1.4  Use of Surfaces 1.4.1  Automated 3-Dimensional Map-Making: Central Baffin Example 1.4.2  Folds and Faults 1.5  Image Analysis 1.5.1  Geometrical Covariance, Intercept and Rose Diagram 1.5.2  Minkowski Operations: Bathurst Acidic Volcanics Example 1.5.3  Boundaries and Edge Effects   2.  Probability and Statistics 2.1  History of Statistics 2.1.1  Emergence of Mathematical Statistics 2.1.2  Spatial Statistics 2.2  Probability Calculus and Discrete Frequency Distributions 2.2.1 Conditional Probability and Bayes’ Theorem 2.2.2  Probability Generating Functions 2.2.3  Binomial and Poisson Distributions 2.2.4  Other Discrete Frequency Distributions 2.2.5  Oficina Formation Example 2.3  Continuous Frequency Distributions and Statistical Inference 2.3.1  Central-Limit Theorem 2.3.2  Frequency Distributions Derived from the Normal 2.3.3  Significance Tests and 95%-Confidence Intervals 2.3.4  Sum of Two Random Variables 2.4  Applications of Statistical Analysis 2.4.1  Statistical Inference: Grenville Potassium/Argon Ages Example 2.4.2  Q-Q Plots: Normal Distribution Example 2.5  Sampling 2.5.1  Pulacayo Mine Example 2.5.2  Virginia Mine Example   3.  Maximum Likelihood, Lognormality and Compound Distributions 3.1  Maximum Likelihood Method with Applications to the Geologic Timescale 3.1.1  Weighting Function Defined for the Inconsistent Dates Model 3.1.2  Log-Likelihood and Weighting Functions 3.1.3  Caerfai-St David’s Boundary Example 3.1.4  The Chronogram Interpreted as an Inverted Log-Likelihood Function 3.1.5  Computer Simulation Experiments 3.1.6  Mesozoic Timescale Example 3.2  Lognormality and Mixtures of Frequency Distributions 3.2.1  Estimation of Lognormal Parameters 3.2.2  Muskox Layered Intrusion Example 3.2.3  Three-Parameter Lognormal Distribution 3.2.4  Graphical Method of Reconstructing the Generating Process 3.3  Compound Random Variables 3.3.1  Compound Frequency Distributions and their Moments 3.3.2  Exploration Strategy Example   4.  Correlation, Method of Least Squares, Linear Regression and the General Linear Model 4.1  Correlation and Functional Relationship 4.2  Linear Regression 4.2.1  Degree of Fit and 95% - Confidence Belts 4.2.2  Mineral Resource Estimation Example 4.2.3  Elementary Statistics of the Mosaic Model 4.3  General Model of Least Squares 4.3.1  Abitibi Copper Deposits Example 4.3.2  Forward Selection and Stepwise Regression Applied to Abitibi Copper 4.4  Abitibi Copper Hindsight Study 4.4.1  Incorporation of Recent Discoveries 4.4.2  Comparison of Weight Frequency Distributions of Copper Metal and Ore 4.4.3 Final Remarks on Application of the General Linear Model to Abitibi Copper   5.  Prediction of Occurrence of Discrete Events 5.1  Weights-of-Evidence Modeling 5.1.1  Basic Concepts and Artificial Example 5.1.2  Meguma Terrane Gold Deposits Example 5.1.3  Flowing Wells in the Greater Toronto Area 5.1.4  Variance of the Contrast and Incorporation of Missing Data 5.2  Weighted Logistic Regression 5.2.1   Meguma Terrane Gold Deposits Example 5.2.2   Comparison of Logistic Model with General Linear Model 5.2.3  Gowganda Area Gold Occurrences Example 5.2.4  Results of the Gowganda Experiments 5.2.5  Training Cells and Control Areas 5.3  Modified Weights-of-Evidence 5.3.1  East Pacific Rise Seafloor Example   6.  Autocorrelation and Geostatistics 6.1  Time Series Analysis 6.1.1  Spectral Analysis: Glacial Lake Barlow-Ojibway Example 6.1.2  Trend Elimination and Cross-Spectral Analysis 6.1.3  Stochastic Modeling 6.2  Spatial Series Analysis 6.2.1  Finite or infinite variance? 6.2.2  Correlograms and Semivariograms: Pulacayo Mine Example 6.2.3  Applications to Other Ore Deposits 6.2.4  Geometric Probability Modeling 6.2.5  Extension Variance 6.2.6  Short-Distance Nugget Effect Modeling 6.2.7  Spectral Analysis: Pulacayo Mine Example 6.2.8  KTB Copper Example 6.3  Autocorrelation of Discrete Data 6.3.1  KTB Geophysical Data Example   7.  2D and 3D Trend Analysis 7.1  2D and 3D Polynomial Trend Analysis 7.1.1  Top of Arbuckle Formation Example 7.1.2  Mount Albert Peridotite Example 7.1.3  Whalesback Copper Mine Example 7.2  Kriging and Polynomial Trend Surfaces 7.2.1  Top of Arbuckle Formation Example 7.2.2  Matinenda Formation Example 7.2.4  Sulphur in Coal: Lingan Mine Example 7.3  Logistic Trend Surface Analysis of Discrete Data 7.4  Harmonic Trend Surface Analysis 7.4.3  Whalesback Copper Deposit Exploration Example 7.4.4  East-Central Ontario Copper and Gold Occurrence Example   8.  Statistical Analysis of Directional Features 8.1  Directed and Undirected Lines 8.1.1  Doubling the Angle 8.1.2  Bjorne Formation Paleodelta Example 8.1.3  Directed and Undirected Unit Vectors 8.2  Unit Vector Fields 8.2.1  San Stefano Quartzphyllites Example 8.2.2  Arnisdale Gneiss Example 8.2.3  TRANSALP Profile  Example 8.2.4  Pustertal Tectonites Example 8.2.5  Tectonic Interpretation of Unit Vector Fields Fitted to Quartzphyllites in the Basement of the Italian Dolomites 8.2.6  Summary of Late Alpine Tectonics South of Periadriatic Lineament 8.2.7  Defereggen Schlinge Example   9.  Automated Stratigraphic Correlation, Splining and Geological Timescales 9.1  Ranking and Scaling 9.1.1  Methods of Quantitative Stratigraphy 9.1.2  Artificial Example of Ranking 9.1.3  Scaling 9.1.4  Californian Eocene Nannofossils Example 9.2  Spline-Fitting 9.2.1  Smoothing Splines 9.2.2  Irregularly Spaced Data Points 9.2.3  Tojeira Sections Correlation Example 9.3  Large-Scale Applications of Ranking and Scaling 9.3.1  Sample Size Considerations 9.3.2  Cenozoic Microfossils Example 9.4  Automated Stratigraphic Correlation 9.4.1  NW Atlantic Margin and Grand Banks Foraminifera Examples 9.4.2  Central Texas Cambrian Riley Formation Example 9.4.3  Cretaceous Greenland-Norway Seaway Microfossils Example 9.5   Construction of Geologic Timescales 9.5.1  Timescale History 9.5.2  Differences between GTS2012 and GTS2004 9.5.3  Splining in GTS2012 9.5.4  Treatment of Outliers 9.5.5  Early Geomathematical Procedures 9.5.6  Re-Proportioning the Relative Geologic Time Scale   10.  Fractals 10.1  Fractal Dimension Estimation 10.1.1  Earth’s Topography and Rock Unit Thickness Data 10.1.2  Chemical Element Concentration Values: Mitchell-Sulphurets Example 10.1.3  Total Metal Content of Mineral Deposits: Abitibi Lode Gold Deposit Example 10.2  Fractal Modeling of Point Patterns 10.2.1 Cluster Density Determination of Gold Deposits in the Kirkland Lake Area on the Canadian Shield 10.2.2 Cluster Density Determination of Gold Deposits in the Larger Abitibi Area 10.2.3  Worldwide Permissive Tract Examples 10.3  Geochemical Anomalies versus Background 10.3.1  Concentration-Area (C-A) Method 10.3.2  Iskut River Area Stream Sediments Example 10.4  Cascade Models 10.4.1  The Model of de Wijs 10.4.2  The Model of Turcotte 10.4.3 Computer Simulation Experiments   11.  Multifractals and Singularity Analysis 11.1  Self-Similarity 11.1.1  Witwatersrand Goldfields Example 11.1.2  Worldwide Uranium Resources 11.2  The Multifractal Spectrum 11.2.1   Method of Moments 11.2.2   Histogram Method 11.3  Multifractal Spatial Correlation 11.3.1   Pulacayo Mine Example 11.4   Multifractal Patterns of Line Segments and Points 11.4.1   Lac du Bonnet Batholith Fractures Example 11.4.2   Iskut River Map Gold Occurrences 11.5  Local Singularity Analysis 11.5.1  Gejiu Mineral District Example 11.5.2  Zhejiang Province Pb-Zn Example 11.6  Chen Algorithm 11.6.1  Pulacayo Mine Example 11.6.2  KTB Copper Example   12.  Selected Topics for Further Research 12.1  Bias and Grouped Jackknife                         12.1.1  Abitibi Volcanogenic Massive Sulphides Example 12.2  Compositional Data Analysis 12.2.1  Star Kimberlite Example 12.3  Non-Linear Process Modeling 12.3.1  The Lorentz Attractor 12.4  Three-parameter Model of de Wijs 12.4.1  Effective Number of Iterations 12.4.2  Au and As in South Saskatchewan Till Example 12.5  Other Modifications of the Model of de Wijs 12. 5.1  Random Cut Model 12.5.2  Accelerated Dispersion Model 12.6   Trends, Multifractals and White Noise 12.6.1  Computer Simulation Experiment 12.7  Universal Multifractals 12.7.1  Pulacayo Mine Example 12.8  Cell Composition Modeling 12.8.1  Permanent Frequency Distributions 12.8.2  The Probnormal Distribution 12.8.3  Bathurst Area Acidic Volcanics Example 12.8.4  Abitibi Acidic Volcanics Example 12.8.5  Asymmetrical Bivariate Binomial Distribution Index  

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions