Novel inversion approach to constrain plume sedimentation from tephra deposit data: Application to the 17 June 1996 eruption of Ruapehu volcano, New Zealand

Abstract

We introduce a new inversion approach to constrain eruption source parameters and the distribution of tephra sedimentation from a weak plume. Our model is parameterized as a set of point sources along the plume base, whose trajectory is constrained by satellite and photographic images. Each point source releases tephra that is dispersed according to an advection‐diffusion equation. This dispersion process is expressed as a system of linear equations with nonlinear dependence on diffusivity and wind speed. We employ inversion techniques to estimate the tephra mass released by each point source as well as diffusivity, stabilizing the inversion by regularization. We apply our method to the Ruapehu eruption on 17 June, 1996 in New Zealand, which was characterized by a strongly wind‐advected plume that can be studied via tephra isomass measurements and particle size distributions at 119 locations. We demonstrate that the approach is feasible by performing analyses with real and synthetic data at a single grain size, and gain insight into the effects of data gaps, presence of noise, and nonlinear parameters on the inversion results. The best fit value of diffusivity yields tephra fallout that decreases steadily with distance to vent, and the predicted deposit is a good fit to the field measurements. This study illustrates the potential of a direct inversion approach to constrain diffusivity, as well as to recover the tephra fallout, without assuming a physical model for mass transport inside the plume.