Earthquake dynamics on circular faults: a review 1970-2015

We review the development of earthquake dynamics taken from the point of view of the origin of seismic radiation instead of the detailed study of rupture propagation on complex surfaces. Many features of seismic radiation can be explained by simple models that serve as elementary canonical problems. Some of these properties are very well known like the fact that at low frequencies, the seismic spectrum is proportional to the seismic moment. At high frequencies, on the other hand, radiation is generated by the motion of the rupture front, in particular stopping phases and geometrical obstacles (barriers). A rupture front moving at constant speed does not produce far-field radiation. For many practical applications, for determining source size and stress drop, for example, it is not necessary to determine geometrical details of the rupture. For such cases, a simple circular crack model is quite sufficient. An improvement on this method is to do dynamic inversion on simple, elliptical-shaped sources and letting the rupture start arbitrarily from a point on the fault. This problem can be solved nowadays with finite differences and a variety of inversion techniques.