This proposal requests support to continue the principal investigator's study of Earth's interior structure using body and surface waves. In order to analyze seismic waveforms between the period range of 10 and 50 sec., we propose to develop a perturbative propagator approach. This method is potentially more efficient, at least within this period range, than the normal mode approach that has been successful and widely used for longer period (> 50 sec.) waves. We will apply the method to study the Earth structure on the global, regional and local scale problems in order to sharpen the image and increase our understanding of seismic velocity structure.