Empirical relationships between aftershock area dimensions and magnitude for earthquakes in the Mediterranean Sea region

Fault dimension estimates derived from the aftershock area extent of 36 shallow depth (<= 31 km) earthquakes that occurred in the Mediterranean Sea region have been used in order to establish empirical relationships between length, width, area and surface-wave/moment magnitude. This dataset consists of events whose aftershock sequence was recorded by a dense local or regional network and the reported location errors did not exceed on average 3-5 km. Surface-wave magnitudes for these events were obtained from the NEIC database and/or published reports, while moment magnitudes as well as focal mechanisms were available from the Harvard/USGS catalogues. Contrary to the results of some previously published studies we found no evidence in our dataset that faulting type may have an effect on the fault dimension estimates and therefore we derived relationships for the whole of the dataset. Comparisons, by means of statistical F-tests, of our relationships with other previously published regional and global relationships were performed in order to check possible similarities or differences. Most such comparisons showed relatively low significance levels (< 95%), since the differences in source dimension estimates were large mainly for magnitudes lower than 6.5, becoming smaller with increasing magnitude. Some degree of similarity, however, could be observed between our fault length relationship and the one derived from aftershock area lengths of events in Greece, while a difference was found between our regional and global fault length relationships. A calculation of the ratio defined as the fault length, derived from our relationships, to the length estimated from regional empirical relationships involving surface ruptures showed that it can take a maximum value of about 7 for small magnitudes while it approaches unity at Ms similar to 7.2. When calculating the same ratio using instead global empirical relationships we see the maximum value not exceeding 1.8, while unity is reached at Mw similar to 7.8, indicating the existence of a strong regional variation in the fault lengths of earthquakes occurring in the Mediterranean Sea region. Also, a relationship between the logarithms of the rupture area and seismic moment is established and it is inferred that there is some variation of stress drop as a function of seismic moment. In particular, it is observed that for magnitudes