An integrated approach for finding hidden alignments of point-like volcanic elements that occur in volcanic fields

In this paper a new approach is proposed for uncovering alignments in a point field of volcanic elements. Volcanoes, scoria (cinder) cones, maars, eruption points, submarine seamounts, fissures, vents, calderas, craters, dykes, fault ridges, fumaroles, pit craters, among others, can be considered as volcanic elements in so far as each individual element is treated as a point, for example by considering the centroid of the feature. This novel approach uses both a statistical method and an exact method to find alignments of points hidden in a point field. The statistical method uses both the global and the local approach, and an intermediate alternative is introduced between the global (all neighbours) and the local approach (nearest neighbour) by using the k-nearest neighbours. This new approach was found to be optimal for a value of k in the range of 5 to 20. In all cases, of both statistical and exact methods, the uncertainty of the estimates is evaluated by using confidence limits so as to minimize the acceptance of spurious alignments of volcanic features. The proposed procedures also avoid any bias introduced by the geometry of the study area. In addition, the spatial distribution of the volcanic points can be homogeneous or heterogeneous. The proposed methodology is illustrated with a point field of volcanic cones on La Palma island in the Canary archipelago. The alignments of volcanic features have applications in volcano-tectonics, volcanic geomorphology and the assessment of volcanic hazards. • Comparison of statistical and exact methods for finding point alignments. • New statistical method using the k-nearest neighbours. • In the new approach, a value of k in the range of 5 to 20 is optimal. • Statistical uncertainty and confidence limits for all the methods. • All the procedures adapted for heterogeneous distribution of the points. • A volcanology case study has been introduced.