Applying the mathematical deformation models to various geodetic data and using nonlinear inversion schemes, I infer the parameters of deformation sources in volcanic areas. Using mixed traction and displacement boundary conditions in the models, I simulate processes like pressure change in cavities and slip on tectonic faults. These cavities and faults, and also the surface topography in the model may have any complex geometry. Using this approach, I have investigated stress interactions between regional and local sources of inflation (Lazufre-Lastarria volcanic complex in Chile; manuscript in preparation). Interpreting the estimated stresses throughout the whole model space, it is possible to study the formation and geometrical shape of new deformation sources. In another case study, my colleagues and I focused on the 2013 Volcán de Colima eruption (Salzer et al., 2014). The pressurized cavities in this case were located at different parts of the upper conduit system.

As another example, we showed that the subsidence and westward surface displacements observed at Tendürek volcano can be simulated by the deflation of a small sill and slip on a ring-fault structure that encircles the volcano (Bathke et al., 2015). The inferred ring-fault geometry reveals that the vertical orientation of the ring fault varies gradually from inward dipping on the eastern side to outward dipping on the western side. This geometry along with the down-dip slip on the eastern and western sides, and also the strike-slip on the northern and southern sides of the ring fault form a sliding-trapdoor mechanism that contributes the most to the observed westward surface displacements.