Statistical properties of travel time measurements and the structure of the Earth's mantle

The Earth's deep interior is sampled daily by waves originating from earthquakes. Different types of waves gather information along various paths of propagation. Each seismogram recorded by one of the several hundred seismological stations is full of clues about the structure of the Earth. Seismologists have the task to unravel this information coded in the many wiggles. Different techniques have been developed to access at least part of this information from seismograms (measurement). In a next step these data have to be translated into the elastic properties of the Earth (inference). As a final target of seismology, these properties are related to thermodynamic quantities of our interest, such as temperature, composition and dynamic processes of the Earth (interpretation). The objective of this thesis is to make some contributions to all three parts: measurements (Chapters 2-4), inference (Chapter 4) and interpretation (Chapter 5).