Geomathematics: Theoretical Foundations, Applications and Future Developments

1. Front Matter

   Pages i-xx

   PDF

2. Complexity of the Geological Framework and Use of Mathematics

   • Frits Agterberg

   Pages 1-40

3. Probability and Statistics

   • Frits Agterberg

   Pages 41-72

4. Maximum Likelihood, Lognormality and Compound Distributions

   • Frits Agterberg

   Pages 73-104

5. Correlation, Method of Least Squares, Linear Regression and the General Linear Model

   • Frits Agterberg

   Pages 105-138

6. Prediction of Occurrence of Discrete Events

   • Frits Agterberg

   Pages 139-188

7. Autocorrelation and Geostatistics

   • Frits Agterberg

   Pages 189-233

8. 2-D and 3-D Trend Analysis

   • Frits Agterberg

   Pages 235-275

9. Statistical Analysis of Directional Features

   • Frits Agterberg

   Pages 277-304

10. Quantitative Stratigraphy, Splining and Geologic Time Scales

    • Frits Agterberg

    Pages 305-367

11. Fractals

    • Frits Agterberg

    Pages 369-411

12. Multifractals and Local Singularity Analysis

    • Frits Agterberg

    Pages 413-466

13. Selected Topics for Further Research

    • Frits Agterberg

    Pages 467-532

14. Back Matter

    Pages 533-553

    PDF

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.

• Exploration Geochemistry
• Geostatistics
• Mathematical Geoscience
• Mineral Resource Appraisal
• Three-dimensional Geological Maps
• quantitative geology
• mineral resources
• structural geology

• Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC), Ottawa, Canada

  Frits Agterberg

Policies and ethics