Finite element deformation of an elastic, non‐uniform medium produced by a dilating or pressurized magma chamber

SUMMARY Vertical and horizontal ground deformations accompanied by seismic activity are typical features of volcanic areas within quiescent calderas such as Long Valley Caldera (California), Yellowstone (Wyoming), Rabaul (Papua New Guinea) and Campi Flegrei (Italy). Ground deformation can be related to the existence of a shallow pressurized magma chamber. Migration processes of hot pressurized fluids are also responsible for the observed uplift. A finite element model is derived and the solutions are checked against the analytical deformation field due to a pressurized, spherical cavity embedded in an infinite, homogeneous, elastic space. The effects related to the finite size of the magma chamber buried in a half‐space are investigated and compared with the analytical results obtained for a point‐like deformation source. In the latter case, a dilation or an overpressure at the source are equivalent in terms of ground displacement, while in the former the choice of the boundary condition at the magma chamber walls (fixed displacement, i.e. dilation, or pressure) is found to be crucial. A pressurized shallow magma chamber produces a larger (even of a factor of two) ground deformation than a point‐like source located at the same depth. This effect can be explained by the existence of a free surface towards which the medium is allowed to deform more easily. Finally, lateral and vertical variations of the rigidity are taken into account and it is shown how they can affect the solution: modelling the caldera as a low‐rigidity zone, much larger ground displacement can be obtained. The results obtained help to overcome one of the major problems so far encountered in the interpretation of the ground deformation in quiescent calderas with point‐like source models: the need for unreasonably high overpressures in order to produce the observed uplift.