Piezomagnetic fields due to an inclined rectangular fault in a viscoelastic half-space: an application to the 2002–2003 Etna eruption

Time-dependent piezomagnetic fields due to inclined rectangular faults embedded in a viscoelastic, homogeneous half-space were investigated. A viscoelastic rheology of the surrounding medium was assumed to relate piezomagnetic changes at the surface to the stress field at depth. The viscosity of the medium strongly influences time-dependent stress changes. Especially in volcanic areas, rocks near magmatic sources are considerably heated. The presence of higher temperatures produces a lower effective viscosity in the crust, making it necessary to consider its inelastic properties. Rocks no longer behave in a purely elastic manner but permanently deform because the viscosity is significantly lowered. To determine the time-dependent piezomagnetic fields in a viscoelastic medium, we applied the Correspondence Principle to the analytical elastic solutions for dislocation sources. Among all the possible rheological models, we investigated three cases in which the bulk modulus is purely elastic and the shear modulus relaxes as for (i) a Maxwell solid, (ii) a standard linear solid (SLS) and (iii) a Kelvin solid. The piezomagnetic field completely vanishes after the relaxation process for a Maxwell rheology, whereas it is found to decrease over time and reach some finite offset values for SLS and Kelvin rheologies. A real case study concerning the magnetic anomalies observed during the 2002–2003 Mt Etna eruption is also investigated. Post-eruptive magnetic variations were in general agreement with a viscoelastic relaxation process of a SLS rheology undergoing in the volcano edifice.