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Statistical models are introduced for the simultaneous estimation of the changes of the b value and detection rate of earthquakes in a catalogue which develops in time or varies in space. The three characteristic parameters, including b, for the magnitude frequency distribution of detected earthquakes, are represented by respective three B-spline functions of time or location in a space. An objective Bayesian method is adopted for the optimal estimate of such functions with many unknown coefficients. The present procedure is applied to earthquake catalogues for Japanese seismic activity.
Ogata et al. (Tue,) studied this question.