Estimation of completeness magnitude with a Bayesian modeling of daily and weekly variations in earthquake detectability

Abstract:

In the analysis of seismic activity, assessment of earthquake detectability of a seismic network is a fundamental issue. For this assessment, the completeness magnitude Mc, the minimum magnitude above which all earthquakes are recorded, is frequently estimated. In most cases, Mc is estimated for an earthquake catalog of duration longer than several weeks. However, owing to human activity, noise level in seismic data is higher on weekdays than on weekends, so that earthquake detectability has a weekly variation [e.g., Atef et al., 2009, BSSA]; the consideration of such a variation makes a significant contribution to the precise assessment of earthquake detectability and Mc.

For a quantitative evaluation of the weekly variation, we introduced the statistical model of a magnitude-frequency distribution of earthquakes covering an entire magnitude range [Ogata & Katsura, 1993, GJI]. The frequency distribution is represented as the product of the Gutenberg-Richter law and a detection rate function. Then, the weekly variation in one of the model parameters, which corresponds to the magnitude where the detection rate of earthquakes is 50%, was estimated. Because earthquake detectability also have a daily variation [e.g., Iwata, 2013, GJI], and the weekly and daily variations were estimated simultaneously by adopting a modification of a Bayesian smoothing spline method for temporal change in earthquake detectability developed in Iwata [2014, Aust. N. Z. J. Stat.]. Based on the estimated variations in the parameter, the value of Mc was estimated.

In this study, the Japan Meteorological Agency catalog from 2006 to 2010 was analyzed; this dataset is the same as analyzed in Iwata [2013] where only the daily variation in earthquake detectability was considered in the estimation of Mc. A rectangular grid with 0.1° intervals covering in and around Japan was deployed, and the value of Mc was estimated for each gridpoint. Consequently, a clear weekly variation was revealed; the detectability is better on Sundays than on the other days. The estimated spatial variation in Mc was compared with that estimated in Iwata [2013]; the maximum difference between Mc values with and without considering the weekly variation approximately equals to 0.2, suggesting the importance of accounting for the weekly variation in the estimation of Mc.