Displacement and stress fields produced by a centre of dilation and by a pressure source in a viscoelastic half‐space: application to the study of ground deformation and seismic activity at Campi Flegrei, Italy

Analytical expressions for the static displacement field produced by a centre of dilation and by a pressure source in a viscoelastic half‐space are derived. The associated stress fields are also computed. The rheology of a standard linear solid (SLS) is adopted for the shear modulus, while the incompressibility is kept elastic. An instantaneous dilation or variation of pressure is considered as responsible for the deformation. In the centre of dilation model, if the two rigidities of the SLS are of the same order of magnitude, the viscoelastic contribution to the deformation is negligible; if the short‐term rigidity is at least two orders of magnitude higher than the other one, the results are indistinguishable from those obtained with a Maxwell solid rheology. In this case, it is found that the initial elastic displacement is amplified by 20 per cent. In the pressure source model, if the rigidities of the SLS are of the same order of magnitude, the initial elastic displacement is amplified by a factor of about 2, but unrealistically high pressure values are required. On the other hand, for a Maxwell solid rheology the displacement grows indefinitely in time, following a sudden application of a finite pressure. The uplift rate is evaluated and it is shown that, for obtaining values of the order of 1 m over one characteristic relaxation time, more reasonable values of pressure are allowed. Applications to ground deformation in volcanic areas are discussed, taking as an example the Campi Flegrei zone, near Naples, Italy.