Statistical Test of Spatio-Temporal Variation of b Value in Japan

The Gutenberg-Richter Law describes the relationship between the frequency of earthquakes and magnitude in previous studies. Studies showed that the slope (b value) of the frequency-magnitude regression line decreased before large earthquakes. Since b value depends very much on the magnitude of completeness (Mc), in this work, we investigated the Mc spatial variation of Japan, combining the maximum curvature (MAXC) technique and the bootstrap approach. Then for the area that has approximately equal Mc value, we applied the maximum likelihood estimation on the complete earthquake distribution, so that the temporal variation and spatial distribution of b value in this area and its uncertainty can be computed more properly. We used the bootstrap approach to generate reference b values and applied the Akaike Information Criterion (AIC) to assess the spatial variation of b value of the area statistically. Here, we define P(ΔAIC≧2) value, where P(ΔAIC≧2) means that the percentage of ΔAIC between the b value at the target space and time and that of the reference is larger or equals to 2. This gives the significance level of difference from the reference. In the area we narrowed a target area depending on P(ΔAIC≧2), After that we quantified the temporal variation of the target area and discuss the precursor of the large earthquake occurred in this area. In this paper, we will demonstrate capability of the proposed method. A case study of the 2011 Tohoku Earthquake (M9.0) shows a statistically clear decrease few months before the main shock. It indicates that the b value with statistical assessment may emerge positive impact for forecasting a future large earthquake.