Modification and Automation of Fractal Geometry Methods: New Tools for Quantifying Rock Fabrics and Interpreting Fabric-Forming Processes
Axel Gerik · 2009
Practically all processes in Geology leave their signatures in the form of fabrics on different scales from single crystal to continental crust. In addition to the qualitative description of such fabrics, their quantification is an essential step towards understanding of geological processes. However, many geological fabrics have a complex structure that cannot be analyzed with common statistical approaches. In the scope of this work, methods that are specifically suitable for the analysis of pattern anisotropy and inhomogeneity were automated and their applicability on different geological fabrics was tested. This thesis is organized in two parts. The first part focuses on the methodological aspects of anisotropy and inhomogeneity in geological fabrics and the quantification of such. It defines the term “fabrics” in a geological context and gives an overview of the current state-of-the-art with respect to quantification of anisotropy and inhomogeneity in geological fabrics. Since geological fabrics often show complex geometries, fractal geometry provides important tools for their quantification. Principles of Fractal Geometry are introduced, classic techniques for quantification of fractals are presented and strategies for their automation are pointed out. Modified methods for quantification and visualization are examined and software implementations are presented along with exemplary applications. The second part presents practical applications of the developed tools on mathematically derived, experimentally produced and natural patterns. The automated analyses’ ability to extract information from the patterns is demonstrated and the implications of this information with respect to the pattern-forming processes are inferred. The developed software tools represent a new and promising step towards a time-efficient analysis of complex geological fabrics. They allow for analyses of large patterns and data sets, enable the quantitative comparison of patterns from nature, experiment and simulation and, therefore, give access to more profound investigations of geological processes.