Three nonhomogeneous Poisson models for the probability of basaltic volcanism: Application to the Yucca Mountain region, Nevada

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Abstract
The distribution and timing of areal basaltic volcanism are modeled using three nonhomogeneous methods: spatio‐temporal nearest neighbor, kernel, and nearest‐neighbor kernel. These models give nonparametric estimates of spatial or spatio‐temporal recurrence rate based on the positions and ages of cinder cones and related vent structures and can account for migration and shifts in locus, volcano clustering, and development of regional vent alignments. The three methods are advantageous because (1) recurrence rate and probability maps can be made, facilitating comparison with other geological information; (2) the need to define areas or zones of volcanic activity, required in homogeneous approaches, is eliminated; and (3) the impact of uncertainty in the timing and distribution of individual events is particularly easy to assess. The models are applied to the Yucca Mountain region (YMR), Nevada, the site of a proposed high‐level radioactive waste repository. Application of the HopkinsFtest, Clark‐Evans test, and K function indicates volcanoes cluster in the YMR at the >95% confidence level. Weighted‐centroid cluster analysis indicates that Plio‐Quaternary volcanoes are distributed in four clusters: three of these clusters include cinder cones formed 2area of the proposed repository by formation of a new basaltic vent is calculated to be between 1 × 10−4and 5 × 10−4in 104years (the kernel and nearest‐neighbor kernel methods give a maximum probability of 5 × 10−4in 104years), assuming regional recurrence rates of 5–10 volcanoes/m.y. An additional finding, illustrating the strength of nonhomogeneous methods, is that maps of the probability of volcanic eruption for the YMR indicate the proposed repository lies on a steep probability gradient: volcanism recurrence rate varies by more than 2 orders of magnitude within 20 km. Insight into this spatial scale of probability variation is a distinct benefit of application of these methods to hazard analysis in areal volcanic fields.