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Three-dimensional orientation data can be simplified by transforming them to refer to axes related to the symmetry of the distribution. Three uncorrelated scalar variates are generated by the transformation. Each of the scalar variates generally has direct geological significance. Each variate can be described individually by the usual statistical parameters. Thus, the orientation, tightness, asymmetry, shape and size of folds can be measured statistically; first, in the direction of greatest buckling; second, parallel to the fold axis. The degree to which a fold is cylindrical or conical in form can be estimated by a least-squares method. A Fortran IV program has been written to perform the computations. A consideration of the spatial variation of the parameters allows various types of folding to be discriminated quantitatively, and permits the testing of hypotheses of the origin of folding. (Author).
This book will help structural geologists keep abreast of rapid changes in work practices resulting from the personal computer revolution. It is organized into six parts: I Computer-Aided Learning; II Microstructural Analysis; III Analysis of Orientation Data; IV Strain and Kinematic Analysis; V Mathematical and Physical Modeling; VI Structural Mapping and GIS. The 45 contributing authors explain how to: set up computer-aided teaching and learning facilities on a low budget; illustrate tectonic strain concepts with a drawing program; integrate multimedia presentations into structural coursework; analyze microstructures with computer-aided microscopy; produce sophisticated stereonets with custom software for both the Mac and IBM PC; evaluate orientation data using a spreadsheet program; model the development of macrostructures and microstructures numerically; integrate structural and geophysical data; and apply PC technology to the production of structural maps, cross sections, and block diagrams. The editor's own contributions reveal the inner workings of his renowned structural research applications which are used in hundreds of universities worldwide. Commercial and non-commercial applications of particular interest to structural geologists are reviewed.This volume will prove an invaluable resource for professors, instructors, and research students, as well as research scientists in the public services and exploration industries. If you are such a person, have you lectured with the aid of a gyroscopic mouse? Or used Bézier curves to model heterogeneous deformation? Or analyzed a fold structure using a digital terrain model? If not, you'll need to rush out and buy this book before the next wave of new technology hits!
Extensive discussions cover the distribution, sampling, inference, analysis of variances; transformations of univariate statistical methods; analyses of geological trends and multivariate data; ratios and variables of constant sum; exploration for natural resources; and evaluation of computers and geology. No previous knowledge of statistics necessary.
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Statistics of Directional Data aims to provide a systematic account of statistical theory and methodology for observations which are directions. The publication first elaborates on angular data and frequency distributions, descriptive measures, and basic concepts and theoretical models. Discussions focus on moments and measures of location and dispersion, distribution function, corrections for grouping, calculation of the mean direction and the circular variance, interrelations between different units of angular measurement, and diagrammatical representation. The book then examines fundamental theorems and distribution theory, point estimation, and tests for samples from von Mises populations. The text takes a look at non-parametric tests, distributions on spheres, and inference problems on the sphere. Topics include tests for axial data, point estimation, distribution theory, moments and limiting distributions, and tests of goodness of fit and tests of uniformity. The publication is a dependable reference for researchers interested in probability and mathematical statistics.
Originally published in 1972. This book covers from ‘linear’ statistical methods, regression and variance analysis to multivariate methods to wider spatial analytic techniques, in which a clear association is maintained between quantitative data and the spatial coordinates which locate them. The purpose of this volume is to highlight this coherent area of scholarship under the general headings of spatial point systems, networks, continuous distributions, partitioning and simulation. Seventeen authors from Britain and the United States have been brought together to produce a book whose attention is on the body of spatial techniques necessary to enable the building of dynamic spatial models of landforms which formed the keystone of much geomorphic work in future years.