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Constructing eruptive histories at the Alaska Volcano Observatory: a harmonious integration of volcanology, petrology, and statistics

Jordan Lubbers , Matthew Loewen, Kristi Wallace

Abstract

Constructing eruptive histories for a given volcano or region is paramount in accurately assessing volcanic hazards. A significant portion of this work at the Alaska Volcano Observatory deals with using tephra-fall deposits to identify the sources, frequency, and size of eruptions throughout the geologic record in Alaska. Because of the large number of volcanoes and their similarity in chemical composition, linking tephra deposits to source volcanoes can be an extremely challenging and time-consuming endeavor. Recently, however, significant progress has been made using an applied data science approach for tephra correlations by combining the fields of volcanology, compositional data analysis, petrology, and statistics.  Using compositional data analysis techniques, we mitigate many of the pitfalls that commonly plague application of statistical tests to compositional data including unit sum constraints and mathematical artifacts. We then show how we can link geologic units, regardless of their source, using geometric means and the Fligner-Killeen test. A probabilistic assessment of the most likely source volcano is then created using two different approaches: machine learning classifier predictions and minimizing Mahalanobis distances. Variables considered for linking tephras to sources are incompatible trace element ratios commonly used in petrology to discriminate between unique magmatic sources. Finally, we use cooperative game theory to help explain which variables are most important in identifying each volcano and conformal prediction to assign accurate uncertainties to statistical predictions. Combined, these steps allow for the implementation of a robust methodology for assigning volcanic sources to tephra fall deposits, allowing more accurate eruptive histories to be constructed.