Some Ideas to Improve Pyroclast Density and Vesicularity Data Analysis

Abstract:

Pyroclast density and vesicularity are critical parameters in physical volcanology used to reconstruct eruptive dynamics and feed numerical models. Pyroclastic deposits typically present a wide range of density and vesicularity values, so measurements must be repeated tens of times. These data are generally treated using classical statistical analysis including averages and frequency histograms. One issue in this approach is that density and vesicularity are intensive properties and therefore they cannot be added or averaged directly. We encourage the use of weighted density and vesicularity averages and histograms, which is, until now, done only in few studies. In order to insure an adequate and efficient use of the weighting equations, we introduce an open-source R code to calculate the most common statistical parameters such as range and weighted averages, and produce abundance histograms. An important question when working with statistics is whether or not the sample size is large enough. To address this matter we also included a stability analysis based on a Monte Carlo approach which enables to quantify the reliability of the results. To illustrate this methodology we chose two large datasets from Chachimbiro (Ecuador) and Unzen (Japan) volcanoes. Our first results indicate that the use of weighted analysis instead of frequency analysis can change the density and vesicularity averages up to 4% and the shape of the abundance histogram leading to different interpretations. The stability analysis reveals that the number of measurements required for reliable results depends greatly on the distribution of density and vesicularity values. Therefore the number of measurements must be fixed on an ipso facto basis using a large sample size at the beginning and reducing it to achieve time efficiency.