An investigation of complex deformation patterns detected by using InSAR at Llaima and Tendürek volcanoes Surface displacement at volcanic edifices is related to subsurface processes associated with magma movements fluid transfers within the volcano edifice and gravity driven deformation processes. Understanding of associated ground displacements is of importance for assessment of volcanic hazards. For example volcanic unrest is often preceded by surface uplift caused by magma intrusion and followed by subsidence after the withdrawal of magma. Continuous monitoring of the surface displacement at volcanoes therefore might allow the forecasting of upcoming eruptions to some extent. In geophysics the measured surface displacements allow the parameters of possible deformation sources to be estimated through analytical or numerical modeling. This is one way to improve the understanding of subsurface processes acting at volcanoes. Although the monitoring of volcanoes has significantly improved in the last decades (in terms of technical advancements and number of monitored volcanoes) the forecasting of volcanic eruptions remains puzzling. In this work I contribute towards the understanding of the subsurface processes at volcanoes and thus to the improvement of volcano eruption forecasting. I have investigated the displacement field of Llaima volcano in Chile and of Tendürek volcano in East Turkey by using synthetic aperture radar interferometry (InSAR). Through modeling of the deformation sources with the extracted displacement data it was possible to gain insights into potential subsurface processes occurring at these two volcanoes that had been barely studied before. The two volcanoes although of very different origin composition and geometry both show a complexity of interacting deformation sources. At Llaima volcano the InSAR technique was difficult to apply due to the large decorrelation of the radar signal between the acquisition of images. I developed a model based unwrapping scheme which allows the production of reliable displacement maps at the volcano that I used for deformation source modeling. The modeling results show significant differences in pre and post eruptive magmatic deformation source parameters. Therefore I conjecture that two magma chambers exist below Llaima volcano: a post eruptive deep one and a shallow one possibly due to the pre eruptive ascent of magma. Similar reservoir depths at Llaima have been confirmed by independent petrologic studies. These reservoirs are interpreted to be temporally coupled. At Tendürek volcano I have found long term subsidence of the volcanic edifice which can be described by a large magmatic sill like source that is subject to cooling contraction. The displacement data in conjunction with high resolution optical images however reveal arcuate fractures at the eastern and western flank of the volcano. These are most likely the surface expressions of concentric ring faults around the volcanic edifice that show low magnitudes of slip over a long time. This might be an alternative mechanism for the development of large caldera structures which are so far assumed to be generated during large catastrophic collapse events. To investigate the potential subsurface geometry and relation of the two proposed interacting sources at Tendürek a sill like magmatic source and ring faults I have performed a more sophisticated numerical modeling approach. The optimum source geometries show that the size of the sill like source was overestimated in the simple models and that it is difficult to determine the dip angle of the ring faults with surface displacement data only. However considering physical and geological criteria a combination of outward dipping reverse faults in the west and inward dipping normal faults in the east seem to be the most likely. Consequently the underground structure at the Tendürek volcano consists of a small sill like contracting magmatic source below the western summit crater that causes a trapdoor like faulting along the ring faults around the volcanic edifice. Therefore the magmatic source and the ring faults are also interpreted to be temporally coupled. In addition a method for data reduction has been improved. The modeling of subsurface deformation sources requires only a relatively small number of well distributed InSAR observations at the earth’s surface. Satellite radar images however consist of several millions of these observations. Therefore the large amount of data needs to be reduced by several orders of magnitude for source modeling to save computation time and increase model flexibility. I have introduced a model based subsampling approach in particular for heterogeneously distributed observations. It allows a fast calculation of the data error variance covariance matrix also supports the modeling of time dependent displacement data and is therefore an alternative to existing method