Reliability of determining the parameters of Gutenberg-Richter distribution for weak Earthquakes in Garm, Tajikistan

Abstract

The behavior of the Gutenberg-Richter distribution (the frequency-magnitude relation for the earthquakes) in response to advancing the system of seismic observations and applying various methods for estimation of the Gutenberg-Richter b value is studied. The long highly accurate time series of seismological measurements at the Garm geophysical testing site in Tajikistan is an input for the study. We analyzed the data from the detailed catalogue of earthquakes with magnitude M = 0–5 that occurred within the test site from 1955 through 1992. It is shown that the changes in the design of measurements both as to the number of observation sites and as to the measurement capacities during the development of the seismic network in 1955–1966 have strongly affected the content of the catalogue. Our study revealed spatiotemporal changes in the minimum magnitude of completeness, which were associated with advancing the design of observations. We have analyzed the accuracy of the calculation of the b value as a function of the reliability of determining the actual minimal magnitude of completeness (the cutoff magnitude) for the catalogue (Mc), the method of calculation of the b value, and the volume of the spatial sample of the earthquakes used. It is established that the pattern of horizontal distribution of the b value is closely correlated to the tectonic structure of the test area, while its vertical distribution distinctly reflects the crustal waveguide at a depth of 9–17 km, which has been previously revealed approximately in this depth interval according to other seismological data. This suggests that, in the first approximation, the lateral and vertical variations in the b value observed in our study are caused by the changes in the strength properties of the crustal material, namely, by the increased plasticity of the rocks within a thick sedimentary layer and in the waveguide.