Optimal likelihood-based matching of volcanic sources and deposits in the Auckland Volcanic Field

Abstract

In monogenetic volcanic fields, where each eruption forms a new volcano, focusing and migration of activity over time is a very real possibility. In order for hazard estimates to reflect future, rather than past, behavior, it is vital to assemble as much reliable age data as possible on past eruptions. Multiple swamp/lake records have been extracted from the Auckland Volcanic Field, underlying the 1.4 million-population city of Auckland. We examine here the problem of matching these dated deposits to the volcanoes that produced them. The simplest issue is separation in time, which is handled by simulating prior volcano age sequences from direct dates where known, thinned via ordering constraints between the volcanoes. The subproblem of varying deposition thicknesses (which may be zero) at five locations of known distance and azimuth is quantified using a statistical attenuation model for the volcanic ash thickness. These elements are combined with other constraints, from widespread fingerprinted ash layers that separate eruptions and time-censoring of the records, into a likelihood that was optimized via linear programming. A second linear program was used to optimize over the Monte-Carlo simulated set of prior age profiles to determine the best overall match and consequent volcano age assignments. Considering all 20 matches, and the multiple factors of age, direction, and size/distance simultaneously, results in some non-intuitive assignments which would not be produced by single factor analyses. Compared with earlier work, the results provide better age control on a number of smaller centers such as Little Rangitoto, Otuataua, Taylors Hill, Wiri Mountain, Green Hill, Otara Hill, Hampton Park and Mt Cambria. Spatio-temporal hazard estimates are updated on the basis of the new ordering, which suggest that the scale of the ‘flare-up’ around 30 ka, while still highly significant, was less than previously thought.