Seismic moment distribution

Abstract

We review possible errors in determining the size of earthquakes. We propose that the size distribution can be effectively defined only for earthquake sequences, not for ‘individual’ earthquakes. As a result of the error analysis, we question the validity of many reported correlations between the b-value and spatio-temporal characteristics of tectonics and seismicity. The study of the distribution of earthquake seismic moment largely avoids the influence of these errors and biases, and is therefore superior to the standard analysis of the magnitude-frequency law. The gamma distribution is applied to describe the distribution of seismic moments of earthquake sequences. This distribution which generalizes the well-known Gutenberg-Richter (G-R) relation, is characterized by two parameters. We use the maximum likelihood method to determine the parameters of the gamma distribution for worldwide earthquakes in different depth ranges. The empirical distribution is derived from the moment-tensor catalogue compiled by the Harvard group. The β-value for scalar seismic moment of earthquake sequences (an analogue of the b-value in the G-R magnitude-frequency law) is close to 1/2 for all earthquakes, the value predicted by a critical branching model of seismicity. This result which will be improved as more seismic moment data become available, provides input for modelling of seismicity based on percolation or on self-organized criticality models. If β equals 1/2, then using the critical branching model we find that most small earthquakes in available catalogues are dependent shocks, i.e., aftershocks. Even among earthquakes of intermediate magnitudes, the number of dependent events may exceed that of independent events.