Displacement and stress produced by a pressurized, spherical magma chamber, surrounded by a viscoelastic shell

Theoretical arguments and petrological observation indicate that magma chambers are surrounded by a thermal metamorphic shell. Owing to their higher temperature, the rocks of this shell have mechanical behaviour different from that of the cooler, more distant crustal rocks. This situation is represented by a model in which a spherical magma chamber is surrounded by a viscoelastic shell. The shell is elastic dilatational and Maxwell deviatoric; outside, the medium is elastic. Displacement and stress fields outside the magma chamber are calculated analytically, assuming that the chamber is internally pressurized, with different source functions. The model illustrates some time-dependent effects which are a result of the presence of the viscoelastic shell: amplification of displacement in the surrounding medium, relaxation of shear stress within the shell and stress concentration outside it. These phenomena may be relevant to the interpretation of some aspects of the ground deformation and induced seismicity, which were observed in the Campi Flegrei volcanic area, Italy, during the period 1982-1984.