Numerical simulation of stress induced piezomagnetic fields at Etna volcano

3-D magneto-elastic models based on finite element method (FEM) have been developed to compute piezomagnetic fields caused by magmatic overpressure sources. We solved separately (i) the elastostatic equation for the stress field and (ii) the coupled Poisson's equation for magnetic potential field. The numerical computations were focused on a more realistic modelling of Etna volcano, where remarkable magnetic changes have been observed during eruptive events. We evaluated the effects of topography and medium heterogeneities considering different multilayered crustal structures constrained by seismic tomography and geological evidences. When topography and magneto-elastic heterogeneities are included in the numerical models, the piezomagnetic field changes show significant deviations from the homogeneous half-space solution. Generally, it was found that the analytical model overestimates the expected magnetic changes. The numerical models of the piezomagnetic field showed significant differences in presence of strong magnetization contrasts and in proximity of steep cliffs, that is, at the volcano summit. The FEM approach presented here allows considering a picture of a fully 3-D model of Etna volcano, which could advance the reliability of model-based assessments of magnetic observations.