Rather than only working with hypocenters of single earthquakes we chose to relate the statistical analysis with stress tensors derived from number of microearthquakes limited in time and space. Before applying the stress tensor inversion we pre-process the dataset to minimize the time/space span but ensuring stable stress tensor solution. For this we have developed a algorithm based on correlation of spectral amplitudes. The SIL network frequently records swarms of microearthquakes where the individual events in the swarm occur very close to each other and often the events can be interpreted as occurring on the same fault. Assuming that this interpretation is correct and that the events in the swarm have similar slip directions, the radiation patterns from these events will be very similar. We should thus be able to observe strongly correlated amplitude and polarity recordings from the events in such a swarm.
We investigated amplitude recordings from a swarm of microearthquakes in Ölfus in SW Iceland. Since the events were not always registered by the same number of stations, or had the same number of phases registered at the stations, we picked out stations and phases common to the two events we wanted to compare. Shown in Figure 7 is a comparison of four events. Each of the pillars in this figure are spectral amplitutes (DC-level) of P-radial - P-vertical, SV and SH at 9 stations. Event number nine, in the lower right corner, is compared to itself and to events six to eight. For each event pair we sorted the logarithm of common phases according to ascending order of event nine's amplitudes and then plotted the two events common amplitudes next to each other. Since event nine is compared to itself in the lower right the amplitude pairs are exactly the same height. For the other three plots we see that the amplitude pairs are not identical but that there is great similarity in the shapes of the amplitudes. A cross-correlation algorithm was constructed which calculates the linear correlation coefficient for all pairs of events in a dataset. Only common amplitudes above the threshold are included in each correlation, and the logarithms of the amplitudes are used in order to down weight the importance of the amplitudes at the closest station, which would otherwise dominate the correlation.
