Estimating the Spatial Intensity of Volcanism

Analysis of the distribution of volcanoes on Earth has been driven largely by hazards assessments. Given the current distribution of known volcanoes, where are volcanoes likely to form in the future? In addition, analysis of the distribution of volcanoes has provided insight into the geological processes that give rise to these observed distributions. For example, NE-trending clusters of volcanoes on the Eastern Snake River Plain, Idaho, reflect partial melting processes, in contrast to NW-trending vent alignments that reflect near surface differential stress. Statistical models provide one means of relating the observed volcano distribution to these geological processes. The geological processes that result in a given event distribution are incompletely known. We can think of these geological processes as giving rise to a stochastic point process that describes the relationship between the set of events and the geological processes that led to their formation. As the stochastic point process is incompletely known, the true value of the local spatial intensity is also unknown. That is, the observed distribution of events is only one realization of the underlying process that gives rise to these events. Our goals are to find an estimate of the spatial intensity that approximates the true but unknown value of spatial intensity and to understand the uncertainty in this estimate. A nonparametric approach for estimating the spatial intensity involves kernel density estimation. One difficulty with elliptical kernels is that all elements of the bandwidth matrix must be estimated. Several methods have been developed for estimating an optimal bandwidth matrix based on the locations of the event data. Here we utilize two techniques to optimally estimate the smoothing bandwidth for our Gaussian kernel function. Application of these algorithms to volcano datasets in the western US, Japan, and Armenia illustrate the utility of spatial intensity maps in well-understood tectonic settings.