Effects of topography and rheological layering on ground deformation in volcanic regions

The ground deformation produced by a spherical overpressure source in a heterogeneous elastic and/or viscoelastic medium is investigated by numerical models based on the finite element method. Sources are assumed to be located at different depths beneath Mount Etna, Sicily, Italy, the structure of which is approximated as axially symmetric. Finite element modelling allows to incorporate in the analysis realistic features such as topographic relief and the laterally heterogeneous multi-layered structure inferred from seismic tomography. In order to avoid introducing artifacts in the solution, great care was taken to calibrate the computational domain necessary to reproduce analytical results accurately. An elastic analysis, performed initially, shows significant changes of the deformation field with respect to homogeneous half-space solutions: topography induces slight but detectable changes in the deformation field; in particular the maximum value of the vertical component is shifted away from the symmetry axis. When introducing the elastic heterogeneities, the ground deformation is found to be more confined to the proximity of the axis and its amplitude is mostly sensitive to the presence of low rigidity layers above the source. The ratio of maximum radial to vertical deformation is significantly larger for deeper sources. A further development of the model includes the study of inelastic properties assuming a Maxwell viscoelastic rheology for different layers. If the viscoelastic rheology is applied only to layers deeper than the source, the solutions are affected in different ways according to the distance of the source from the viscoelastic layer. If a viscoelastic layer is present above the source, a very large amplification (by more than 100%) of the surface deformation is predicted by the model; moreover, uplift transients are found to be followed by subsidence, without invoking any decrease in source overpressure. The most striking effects are observed when the source is embedded within a viscoelastic layer: in this case a static equilibrium configuration is not attained and, in the long term, both components of deformation reverse their signs in proximity to the axis. Furthermore, the surface deformation becomes nearly independent of source depth, in the long term. Simple physical explanations are proposed for the different cases.