New statistical methods for detecting point alignments

Detection of straight-linear point alignments has a number of geological applications. Assessing the statistical significance of such alignments is relatively straightforward in the case of overall lineament orientation, but becomes complicated for non-stationary point patterns where the orientations as well as positions of individual lineaments are to be determined. False positive (Type I error) rates are here estimated using Monte Carlo simulation, both for the existing “blade” method and for some new, simple procedures. For the blade method, the false positive rate can be an order of magnitude higher than specified by the α level, while for the new methods the false positive rate is in good accordance with the α level. The methods are also compared using two synthetic data sets, and a real example of pockmarks from the Norwegian Sea.