A statistical method to determine total H2O and CO2 budgets in magmas

A recently developed method based on the TVLine concept (Papale, 2005) allows to determine total H2O and CO2 budgets in magmas from melt inclusion data. This method, however, can not be easily applied when multiple groups of inclusions are present in the dataset. This is unfortunately a frequent occurrence in many relevant cases, including recent eruptions of Etna, Stromboli, Campi Flegrei, Vesuvius, and Kilauea volcanoes. We have developed a statistical method which allows to treat analytical uncertainties and group the data according to a probabilistic criterion. The method includes the following steps: i) hypothesize a number of pairs of total H2O and CO2 necessary to explain the observed data; ii) minimize a χ2-like quantity for each datum by varying the possible H2O-CO2 pairs, and using a model for compositional dependent multicomponent H2O+CO2 saturation in silicate melts (Papale et al., 2006). This step allows the assignment of each datum to a given total H2O-CO2 pair; iii) perform a Monte Carlo simulation to determine the probability of exceeding the obtained χ2, therefore the likelihood of the assumed number of total H2O-CO2 pairs to explain the database. This sequence is repeated for many possible numbers of H2O-CO2 pairs and many assumed values of analytical uncertainty characterizing the dataset. Application of the method to about 30 melt inclusion data from a recent Kilauea eruption spanning CO2 contents in the range 10-300 ppm shows that a minimum of two total H2O-CO2 pairs is required. These pairs show that the melt inclusions formed under two different conditions, the first one characterized by a few wt%, and the second one by less than 1 wt% CO2 abundance.