Pattern recognition problems in geology and paleontology (Q1057661)

This book is an example based study of pattern recognition problems specific to geology and paleontology, aiming to elucidate the possibility to classify forms and to control the behavior of complex algorithms by a qualitative geometrical approach. The book is organized in 4 chapters. The first chapter presents the main ideas of the book. Chapter 2 entitled ''Noisy Systems and Folded Maps'' deals with the problems involved in the reconstruction of some ancient state from the present remains, a situation often encountered in geology and paleontology. In this chapter, three examples related to the superposition of density functions and to the multiple valued local solutions of the reconstruction process are presented: reconstruction of sediment accumulation, intraspecific variability of paleontological species and reconstruction of surfaces from sparse point patterns by computer methods. In Chapter 3 ''Nearly Chaotic Behavior on Finite Point Sets'' is analyzed in 5 sections. The first section deals with the topological aspects of iterated maps and it underlines their relation to the concept of bifurcation and chaos. The \(Chi^ 2\)-testing of directional data is presented in the second section. After discussing the problems of sampling strategies in sedimentology, the centroid cluster strategies are presented with references to pattern recognition techniques in paleontology. Further, the morphology of tree-like structures is presented, especially the connection between branching pattern and overall shape. ''Structural Stable Patterns and Elementary Catastrophes'' constitute the topic of Chapter 4, which is organized in three sections. In the first section singularities are discussed, which occur as discontinuities in the two-dimensional images of three-dimensional objects. In the second section the theory of elementary catastrophes is applied to the linear ray model in reflection seismology. The traveltime record is analyzed as a map which transforms the three-dimensional spatio-temporal system into the traveltime record. In the third section some aspects of folds and faults are discussed in terms of 'parallel surfaces'. This discussion takes up the 'pre-computer' analysis of large scale deformations in tectonics and reviews the 'early' kinetic approach in terms of recent developments in singularity theory.