Statistical Analysis of Directional Features - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 275

Chapter 8
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 exten-
sions 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 exam-
ples 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.