At the focus of an earthquake, elastic waves are produced that propagate through the planet. The speed of propagation depends on wave type (longitudinal or transverse) and the depth inside the planet. At the boundaries between the different layers of the planet (e.g. crust, mantle, core) the waves are refracted and reflected. After a quake, a seismograph at the surface can therefore register a large number of echoes of different amplitude. The timing of these echoes allows to deduce the interior structure of the planet. As an example, Robert Dixon Oldham was able to prove the existence of the earth's core, since it casts a "shadow" in a distance of about 11000km to about 15000km from the earthquake's epicenter. Seismology hence is a means to look directly into the interior of planets and thus can give important clues for the understanding of the dynamic processes inside planets. Besides on earth, seismological experiments have been carried out succesfully on the Moon. On the Moon, moonquakes are mainly generated by tidal deformation - the lunar lithosphere is not divided into distinct plates as the earth's lithosphere is.
Figure 1: When seismic p-waves reach the core at a certain angle, the velocity decreases and they refract to the inside. Direct waves therefore can't be measured in certain regions. This is called the core shadow. Source: Dr. Martin Knapmeyer.
Figure 2: Traveltime diagram of seismic waves. Source: Dr. Martin Knapmeyer.
Seismological Measurements of Mars could help to understand why the martian magentic dipole field deceased long ago (and if a comparable shutdown is also possible on earth), or why the Earth has volcanic arcs and belts of a global scale whereas Mars, besides some diffusely distributed smaller volcanoes, boasts few gigantic volcanic edifices. We are planning seismological networks for use under the constraints of a Mars mission. We are also evaluating existing lunar data to get constraints for modeling.