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.