Concepts in Geostatistics

A two-week summer short course entitled Current Statistical Methods in Geology supported by the National Science Foundation was held at the University of Illinois at Chicago Circle in Chicago, Illinois from June 19 to June 30, 1972. The aim of the short course was to bridge the gap between the traditional first courses in sta tistics offered at most educational institutions and geostatistics as it is being developed by geologists and statisticians engaged in the application of statistics in geology. The course was intended for geology college teachers who were either then teaching or preparing to teach a course within their department dealing with computer ap plications and the use of statistical methods in geology. This book arose out of the class notes which were prepared by the course director and the invited lecturers. We are grateful to the 28 teachers who attended for their enthu siastic interest and thoughtful responses to the many statistical concepts presented to them as geologists during the two weeks of the course. I am deeply grateful to my graduate assistants, Richard Kolb and Andrea Krivz, for the long hours spent in collating the course mater ials, testing the various computer programs, and instructing the par ticipants in the use of computer BASIC.

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1. Statistics and Probability.- 1.1 Sample Mean and Variance.- 1.2 Elements of Probability.- 1.3 Problems.- 1.4 Searching for Dikes.- 1.5 Rocks in Thin Section.- References.- 2. R- and Q-Mode Factor Analysis.- 2.1 Meaning of Factor.- 2.2 Data Matrices.- 2.3 Factor Analytic Modes.- 2.4 The R-Mode Model.- 2.5 A Practical Example.- 2.6 Factors.- 2.7 The Q-Mode Model.- 2.8 An Example.- 2.9 Oblique Rotation.- 2.10 Practical Examples.- References.- Appendix 1: A Primer on Matrix Algebra.- 3. Some Practical Aspects of Time Series Analysis.- 3.1 Generalities.- 3.2 Polynomial Curve Fitting.- 3.3 Iterated Moving Averages.- 3.4 Fourier Analysis.- 3.5 An Application.- References.- 4. Markov Models in the Earth Sciences.- 4.1 Fundamentals.- 4.2 A Spectrum of Models.- 4.3 The Markov Chain.- 4.4 Geometric Distribution.- 4.5 Probability Trees.- 4.6 Embedded Markov Chains.- 4.7 Extensions.- References.- 5. A Priori And Experimental Approximation Of Simple Ratio Correlations.- 5.1 Ratio Correlations.- 5.2 RTCRSM2.- 5.3 UNNO AND RANEX.- 5.4 Comments on Usage.- References.- Appendix 1: RTCRSM2 Program.- Appendix 2: RANEX and UNNO Programs.- 6. Computer Perspectives in Geology.- 6.1 Generalities.- 6.2 Early Beginnings.- 6.3 Usage in General.- 6.4 Usage in Geology.- 6.5 Patterns and Trends.- References.- 7. Problem Set in Geostatistics.- 7.1 A Paleontologist's Dilemma.- 7.2 Particle Size Distribution in Thin Section.- 7.3 Particle Diameter Sampling Experiment.- 7.4 Linear Regression of Porosity Data. I.- 7.5 Linear Regression of Porosity Data. II.- 7.6 Sunspots and Earthquakes.- 7.7 A Beginning and an End.- 7.8 Helmert Transformation.- 7.9 A Spine to Remember.- 7.10 Nearshore-Offshore Sediments.- References.