NON-PARAMETRIC STATISTICAL ASSESSMENTS OF THE SPATIAL DISTRIBUTION OF POPULATIONS OF VOLCANIC VENTS

In this study we present a method to define the spatial distribution of point-like populations of geologic fields. Specifically, we have applied a non-parameterized Gaussian kernel function to characterize the spatial density of volcanic vents in a limited number of volcanic fields. This technique can also be easily applied to sink holes, epicenters, and any feature that is represented by a point on a map. A Gaussian kernel function and an optimized bandwidth selector algorithm are used to generate a non-parametric spatial density map of each vent population. Using an optimized bandwidth is important to this study because it is chosen by an unbiased routine based solely on vent location. The optimal bandwidth is a 2x2 matrix which specifies the amount of spatial variation in the E-W and N-S directions and also the overall directional trend of the data. Current methods used for the calculation of the total area of volcanic fields have been based on generalized boundaries that do not fully represent the field's shape and area. Maps generated in this study consist of contour lines that indicate the 25%, 50%, 75%, 95% and 99% of the total spatial density. This allows us to calculate the total area enclosed by the 99th percentile contour line which we describe as the boundary of the volcanic field. In addition, we can use the 50th and 1 percent contour lines to characterize areas with a high probability of volcanic activity. Furthermore, these contoured maps of vent density are a useful tool that may be applied to studies of volcanic hazards, as they already have been in places like the proposed nuclear waste repository at Yucca Mountain, or in assessing the distributions of volcanoes with respect to upper crustal structures or broader tectonic settings.