5:15 PM - 6:45 PM
[SSS08-P03] Comparison of b-positive estimation with traditional method: A case study of aftershocks from magnitude-7 class earthquakes around the Japanese archipelago
Keywords:B-positive, Gutenberg-Richter law, Aftershocks
The traditional approach to estimating the b-value (power-law exponent) in the Gutenberg-Richter law for earthquake magnitude-frequency distribution has long relied on the maximum likelihood method using earthquakes greater than a cut-off magnitude Mc (Utsu, 1965; Aki, 1965). This traditional method is significantly influenced by the value of Mc, leading to extensive research on methods to determine Mc more accurately (e.g., Wiemer and Wyss, 2000; Mignan and Woessner, 2012). However, a recent study (van der Elst, 2021) proposed a new method based on the frequency distribution of magnitude differences, named the b-positive method. This new approach does not require Mc, potentially allowing for more robust b-value estimation.
This study focused on analyzing aftershocks of magnitude 2 and above, associated with 25 magnitude-7 class earthquakes identified from the Japan Meteorological Agency's hypocenter catalog around the Japanese archipelago. We estimated the b-values using both the b-positive method and a traditional approach for comparison. In the traditional method, we employed the technique of Wiemer and Wyss (2000), which calculates the cut-off magnitude Mc based on the fit of a straight-line regression to the log-linear cumulative frequency distribution of magnitudes. The aftershock data were examined over two distinct timeframes: the initial 10 days following each mainshock and an extended period of 1000 days.
The test results revealed that the estimated values by the b-positive method were consistently 0.0 to 0.2 higher than those by the traditional method. Furthermore, we investigated the correlation between the 10-day and 1000-day aftershock estimation results for both the b-positive and traditional methods. In the case of b-positive method, the correlation coefficient is 0.95, whereas with the traditional method, it is 0.69, indicating that the estimates from b-positive are less affected by the selection of the time range for aftershocks compared to the traditional method. This suggests the robustness of the b-positive solution, which does not estimate Mc each time like the traditional method. However, the fact that the b-positive solutions are systematically higher than those obtained by the traditional method raises a separate issue as to whether they are closer to reality, necessitating further scrutiny.
This study focused on analyzing aftershocks of magnitude 2 and above, associated with 25 magnitude-7 class earthquakes identified from the Japan Meteorological Agency's hypocenter catalog around the Japanese archipelago. We estimated the b-values using both the b-positive method and a traditional approach for comparison. In the traditional method, we employed the technique of Wiemer and Wyss (2000), which calculates the cut-off magnitude Mc based on the fit of a straight-line regression to the log-linear cumulative frequency distribution of magnitudes. The aftershock data were examined over two distinct timeframes: the initial 10 days following each mainshock and an extended period of 1000 days.
The test results revealed that the estimated values by the b-positive method were consistently 0.0 to 0.2 higher than those by the traditional method. Furthermore, we investigated the correlation between the 10-day and 1000-day aftershock estimation results for both the b-positive and traditional methods. In the case of b-positive method, the correlation coefficient is 0.95, whereas with the traditional method, it is 0.69, indicating that the estimates from b-positive are less affected by the selection of the time range for aftershocks compared to the traditional method. This suggests the robustness of the b-positive solution, which does not estimate Mc each time like the traditional method. However, the fact that the b-positive solutions are systematically higher than those obtained by the traditional method raises a separate issue as to whether they are closer to reality, necessitating further scrutiny.