Density distribution functions of faults and scaling relations

Abstract

In the present note, we analyse various seismological datasets collected in different geological and tectonic settings as well as at different time and space scales, like seismic sequences, regional background seismicity, aftershock sequences, microseismic data, and swarms and induced seismicity. We investigate these datasets in terms of statistical distribution of single parameters focusing on stress drop (Δσ), scalar seismic moment (M₀) and fault's dimension (often referred to as faults' radius, r₀). In particular, we systematically obtain the density distribution functions (ddfs) of each parameter verifying the possible extension of the regression curves. We also analyse the correlations between the investigated parameters by comparing the slopes of the ddf for each dataset. Another goal of this investigation is to verify a possible similarity between comparable and different datasets (i.e. collected in similar or different geological and tectonic settings and range of magnitudes), to verify the stability of the ddf when using different methods as well as the variability of the stress drop even in the same seismological region. We suggest that even more accurate data covering wider ranges of values would be desirable in order to be of practical use like seismotectonic characterization, ground motion prediction and seismic hazard analyses, while the representation of the seismicity for any seismogenic region should be not limited to the b (or b₀) value of the Gutenberg-Richter curve.