In global seismology there has been a wide gap between the quality of observations and theory for a long time. It is important to note that only a fraction of the information contained in seismograms observed with the global seismic networks is today used in the imaging process.
In ray-theoretical approaches (high-frequency approximation) the seismogram is reduced to travel times picked for particular phases. In the intermediate frequency range one can model surface wave-forms using (non-)linear perturbation theory. These approaches have led to the picture of the Earth’s interior that we have today. While it is fascinating what has been learned even with these relatively crude approaches over the past two decades, it is important to note that a substantial amount of information on the Earth’s deep interior is still contained in the vast data volumes of the global seismic data archives. To be able to further interpret these data one important step forward (in addition to increasing the density of seismic networks for example in the oceans) is the development of wave propagation algorithms for 3D Earth models.