Statistical Analysis of Directional Features

Abstract

Many geological features are directed in 2-D or 3-D space, either as undirected or directed lines. Unit vectors are used for their spatial representation. Vectors with magnitudes can be used in some applications. Axes of pebbles in glacial drift provide an example of undirected lines; strengths of magnetization in rock samples exemplify the situation of directed lines to be represented as unit vectors or as vectors with magnitudes. Methods of unit vector field construction can be used to extract regional variation patterns. If there is no significant change of direction within the domain of study, various statistical frequency distribution models can be used for estimating the mean direction or pole and measures of dispersion. Well-known examples are the Fisher distribution for directed lines and the Scheidegger-Watson distribution for undirected lines. In this chapter, unit vector fields are fitted to regional data with variable mean directions using extensions of polynomial trend surface analysis. A relatively simple example consists of determining the preferred paleocurrent directions in sandstones of the Triassic Bjorne Formation on Melville Island, Canadian Arctic Archipelago. Later examples are from structural geology of the Eastern Alps. Directions of the axes of Hercynian minor folds in the crystalline basement of the Dolomites in northern Italy show relatively strong spatial variability, both locally and regionally. Averaging measurements from different outcrops within relatively small sampling domains shows patterns of systematic regional variations that represent Alpine reactivation of Hercynian schistosity planes (s-planes) causing rotations of the original minor fold axis directions to the south of the Periadriatic Lineament. Interpretation of seismic data from along the north-south TRANSALP profile that intersects the Periadriatic Lineament near Bruneck (Brunico) in the Pustertal (Pusteria) indicates rotation of Hercynian basement rocks into subvertical positions with subvertical to steeply east-dipping Hercynian minor fold axes. Subsequently, Late Miocene northward and north northeastward movements of the Adria microplate underneath the Eurasian plate resulted in sinistral motion of the crystalline basement rocks in the Bruneck area and strong neo-Alpine compression of basement rocks in the Pustertal to the east. At the same time there was overthrust sheet formation in the Strigno area along the Sugana Fault located to the south of the Italian Dolomites.