This thesis describes new inversion-oriented methodological developments and their seismological applications. In the first study presented the dynamic source parameters of some local Icelandic earthquakes are studied by employing a time domain moment tensor inversion method. A windowing method for direct P and S phases was used and the inversion was performed for frequencies lower than the associated corner frequency under the double-couple constraint. The inversion algorithm could determine the dynamic source parameters correctly, even under conditions of poor azimuthal coverage. The second study deals with a new method for calculating the empirical Green's function based on inversion of earthquake radiation patterns. The resulting Green's functions then may contain both body and surface waves. The validity of the method was then confirmed by applying the method to some Icelandic earthquakes. The lithosphere-asthenosphere transition along the TOR array is investigated in the last two studies. Separate and simultaneous teleseismic P and S relative arrival-time residuals were inverted via different methods (a singular value decomposition and a quadratic programming method) to investigate the reliability and the resolution of the model. The data were corrected a priori for the effect of travel-time perturbations due to crustal structure. The results indicate that the transition between thinner lithosphere in Germany to the thicker Baltic Shield in Sweden occurs in two sharp and steep steps. A sharp and steep subcrustal boundary is found below the Tornquist Zone, with a less significant transition below the Elbe Lineament. The lithospheric structure appears to be about 120 km thick under the Tornquist Zone, increasing to more than 200 km beneath the Baltic Shield