Inverse modeling of geophysical observations is becoming an important topic in volcanology. The advantage of exploiting innovative inverse methods in volcanology is twofold by providing: a robust tool for the interpretation of the observations and a quantitative model-based assessment of volcanic hazard. This paper re-interprets the data collected during the 1981 eruption of Mt Etna, which offers a good case study to explore and validate new inversion algorithms. Single-objective optimization and multi-objective optimization are here applied in order to improve the fitting of the geophysical observations and better constrain the model parameters. We explore the genetic algorithm NSGA2 and the differential evolution (DE) method. The inverse results provide a better fitting of the model to the geophysical observations with respect to previously published results. In particular, NSGA2 shows low fitting error in electro-optical distance measurements (EDM), leveling and micro-gravity measurements; while the DE algorithm provides a set of solutions that combine low leveling error with low EDM error but that are characterized by a poor capability of minimizing all measures at the same time. The sensitivity of the model to variations of its parameters are investigated by means of the Morris technique and the Sobol' indices with the aim of identifying the parameters that have higher impact on the model. In particular, the model parameters, which define the sources position, their dip and the porosity of the infiltration zones, are found to be the more sensitive. In addition, being the robustness a good indicator of the quality of a solution, a subset of solutions with good characteristics is selected and their robustness is evaluated in order to identify the more suitable model.
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