ABSTRACT
Homology is a tool within the mathematical field of topology, which can be used to associate a sequence of algebraic objects to other mathematical objects. For instance, this tool can differentiate between a circle and a disk by looking at holes, where one exists in the case of a circle, but not for a disk. Ultimately, homology can be described as a measure of similarity that solves beyond the shortcomings of statistics. As a tool, it can be applied to any data type as long as those data can be quantified algebraically. As such, homology can be a powerful tool to study patterns within geospatial data, such as deformation at tectonic boundaries. Tectonic boundaries are host to many deformation structures, such as faults, folds, and fractures. These structures that can occupy areas of different sizes are studied by geologists to infer a geologic history for a particular region through time. We present a case study on synthetic geospatial deformation structures, giving us a control to validate the data set, to show the power of homology in detecting patterns. From our results, we conclude that homology not only detects the patterns we expected from our synthetic data set, but also shows how “strong” the patterns are (persistence). The application of homology to large and real geospatial data sets may identify patternsets beyond what traditional statistical and visual assessments have provided geologists to date.
