Estimation of tephra volumes from sparse and incompletely observed deposit thicknesses

We present a Bayesian statistical approach to estimate volumes for a series of eruptions from an assemblage of sparse proximal and distal tephra (volcanic ash) deposits. Most volume estimates are of widespread tephra deposits from large events using isopach maps constructed from observations at exposed locations. Instead, we incorporate raw thickness measurements, focussing on tephra thickness data from cores extracted from lake sediments and through swamp deposits. This facilitates investigation into the dispersal pattern and volume of tephra from much smaller eruption events. Given the general scarcity of data and the physical phenomena governing tephra thickness attenuation, a hybrid Bayesian-empirical tephra attenuation model is required. Point thickness observations are modeled as a function of the distance and angular direction of each location. The dispersal of tephra from larger well-estimated eruptions are used as leverage for understanding the smaller unknown events, and uncertainty in thickness measurements can be properly accounted for. The model estimates the wind and site-specific effects on the tephra deposits in addition to volumes. Our technique is exemplified on a series of tephra deposits from Mt Taranaki (New Zealand). The resulting estimates provide a comprehensive record suitable for supporting hazard models. Posterior mean volume estimates range from 0.02 to 0.26 km³. Preliminary examination of the results suggests a size-predictable relationship.