## Exploring the validity of the point source approximation.

##### Summary

The point source approximation is widely used for earthquake representation because it is computationally efficient for certain kinds of synthetic calculations. It is based on the assumption that the seismic wave-field generated by a realistic source will match up with that generated by the corresponding centroid point source, as long as the waves investigated have sufficiently long wavelengths and periods. It is important to know whether this approximation is valid, otherwise unknown errors can be introduced into results based using the this approximation. In order to get an idea of the validity of the point source approximation, we compare the wave-field generated by various distributions of point sources to that generated by the corresponding centroid point source. While the point source distributions used do not represent the full complexity of seismic sources, these tests are still useful to explore some of the effects of combining multiple point sources into a single centroid point source, which is what the point source approximation is based on. In the case of an event consisting of two point sources, the time difference between the two point sources before the misfit with the centroid becomes significant, is approximately 7 seconds. In reality, this may represent events with durations over half the length of the shortest period investigated, since it is unlikely that all energy is released at the two ends of an event. For the spatial dimensions, the misfit may become significant for an offset close to 40 kilometres, while at 50 kilometres, around one third of the shortest wavelength, the misfit is already very large. Realistic rupture times indicate that for sources with spatial offset closer to 20 kilometres, the misfit should be very small. Events consisting of more than two point sources may interact in a way to create patches of high misfit that could affect stations located at the same location as these patches.