Evaluation of approximations in modeling the thermal history of a volcanic area

The thermal history of a relatively young volcanic area, characterized by a shallow magmatic reservoir and the occurrence of a major eruption accompanied by caldera collapse, is simulated numerically. Geometry, geology and volcanic history of the system are chosen having in mind the Campi Flegrei volcanic area, Southern Italy. The 3D axially symmetric model adopted is nonhomogeneous, with variable geometry and thermal properties depending on temperature. Heat transfer is treated using the conduction equations. Convection in the magma - undoubtedly vigorous in the early stages of the cooling process - is taken into account by a temperature-averaging procedure. Moderate convection in the permeable rocks overlying the reservoir is simulated by using effective thermal parameters. The mathematical problem is solved by a finite-difference method. This model is then adopted as “reality” and its results are compared with those obtained with other models, referred to as “approximations” in which some features of the conventional reality have been neglected. It is found that the temperature field of a static model (in which the eruption of about 110 km3 of magma, caldera collapse and the related physical changes are neglected) is in good agreement with “reality” 30,000 years after the eruption. The assumption of magma and surrounding rocks having the same constant thermal properties yields poor results (errors of 100–150°K at shallow depth on the axis of symmetry). If homogeneity is assumed only for the host rocks, while the magma is assigned “real” properties, the temperature field above the reservoir is affected by quite similar errors. The temperature field is quite well approximated by solving the “reality” in a vertical plane through the axis of symmetry (errors <20°K and 40°K in the central part of the caldera for t=120,000 years and t=250,000 years, respectively, after the emplacement of the magmatic body). The solution of “reality” in just one dimension yields slightly poorer results.