A statistical method for determining the volume of volcanic fall deposits

Abstract

Volumes of tephra-fall deposits are difficult to determine due to the commonly poor preservation of proximal and distal areas of the deposit. Typically, these volumes are found by extrapolating thinning trends found from isopach maps drawn for the areas of the deposits that are preserved. However, the construction of isopach contours is dependent on subjective interpretation of field measurements and can be highly variable. Here, we have investigated the spatial correlation relationships of thickness measurements from fall deposits to the vent location to produce a purely statistical method to objectively determine the volume of a fall deposit without the production of isopach maps. Integration of a log linear regression model for thickness measurements with distance from the vent is applied to the field measurements without any prior interpretation, and data and model uncertainty has been accounted for using Bayesian methods. Eruption volumes calculated from our method correspond well to those previously determined by alternative approaches for the deposits of Fogo A, Azores; Askja 1875, Iceland; Santa Maria 1902, Guatemala; and Pinatubo 1991, Philippines. The quantification of uncertainty in field measurements and model error, and the removal of subjectivity incurred in the production of isopach maps suggest that the method presented here can offer benefits in determining the volumes of deposits.