Characterization of the gas–magmatic outflow at a volcanic vent through integral-equation based inverse acoustics

A methodology to set up and solve a 3D inverse problem in volcano acoustics is developed. The method is used to estimate the acceleration of the gases at the volcanic vent from acoustic recordings at a microphone located on the erupting volcano. The assumption of linear acoustic propagation outside the volcanic vent is made. The Boundary Element Method (BEM) is used to extract the matrix transfer function relating the pressure at the location of the microphone to the acoustic acceleration at the volcano’s outlet. The BEM transfer function includes the complete scattering effect of the volcano topography under the assumption of acoustically rigid surface. The spectrum of the acoustic acceleration at the vent is obtained in two different fashions: (i) by inversion of the matrix transfer function; (ii) through the minimization of the deviation with respect to the measurements. The method was tested on the Stromboli volcano using the simplifying assumption of an axially symmetric orographic profile. The problem was also solved using a bi-objective optimization to maximize the matching of the simulations with the measurements. Both the techniques produced satisfactory results. The method could be used to optimize the distribution of pressure transducers around the vent.