3D analytical and numerical modelling of the regional topography influence on the surface deformation due to underground heat source

Thermo-elastic strains and stresses play a considerable role in the stress state of the lithosphere and its dynamics, especially at pronounced positive geothermal anomalies. Topography has a significant effect on ground deformation. In this paper we describe two methods for including the topographic effects in the thermo-viscoelastic model. First we use an approximate methodology which assumes that the main effect of the topography is due to distance from the source to the free surface and permits to have an analytical solution very attractive for solving the inverse problem. A numerical solution using Finite Element Method (FEM) is also computed. The numerical method allows to include the local shape of the topography in the modelling. In the numerical model the buried magmatic body is represented by a finite volume thermal source. The temperature distribution is computed by the higher-degree FEM. For analytical as well as numerical model solution only the forces of thermal origin are considered. The comparison of the results obtained using both analytical and numerical techniques shows the qualitative agreement of the vertical displacements. In the numerical values small differences were obtained. The results show that for the volcanic areas with an important relief the perturbation of the thermo-viscoelastic solution (deformation and total gravity anomaly) due to the topography can be quite significant. In consequence, neglecting topography could give erroneous results in the estimated source parameters.