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

Abstract

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.