Algorithms to find and evaluate the Euler pole solution describing the orientation of geological structures
Method
The small circle of best fit and the corresponding Euler pole (axis) of rotation for an array of points are established by treating each point as the locus of a unit vector from the center of Earth and by minimizing the sums of the squares of the deviations of these unit vectors from a circular cone surface with its apex at the center of Earth (Ramsay, 1967, p. 20-21).
Prerequisites
You must have R installed on your system (see http://r-project.org). To install euler.reco from Github, you also need the remotes package. This can be installed by typing the following code at the R command line prompt:
install.packages("remotes")Installation
The most recent development version of euler.reco is available from Github and can be installed on your system as follows:
remotes::install_github('tobiste/euler.reco')
library('euler.reco')Documentation
The detailed documentation can be found at https://tobiste.github.io/euler.reco/
References
- Ramsay, J. G. (1967). Folding and fracturing of rocks. McGraw-Hill Book Company, New York
- Gray, N.H., Geiser, P.A., Geiser, J.R. (1980). On the least-square fit of small and great circles to spherically projected data. Mathematical Geology, 12(3)
- Kroner, U., Roscher, M., Romer, R. L. (2016). Ancient plate kinematics derived from the deformation pattern of continental crust: Paleo- and Neo-Tethys opening coeval with prolonged Gondwana–Laurussia convergence. Tectonophysics. 681, 330-233. https://doi.org/10.1016/j.tecto.2016.03.034
- Wdowinski, S. (1998). A theory of intraplate tectonics. Journal of Geophysical Research: Solid Earth, 103(3), 5037–5059. http://dx.doi.org/10.1029/97JB03390
- Price, R. & Carmicheal, D. (1986). Geometric test for Late Cretaceous-Paleogene intracontinental transform faulting in the Canadian Cordillera. Geology, 468, 14(6), 468-471. doi: 10.1130/0091-7613(1986)14<468:GTFLCI>2.0.CO;2