11:00 AM - 1:00 PM
[SSS11-P03] Quantitative anomaly assessment method based on characteristics of “normal” seismic activity
Keywords:seismicity, frequency-magnitude distribution, tidal correlation
Nagata et al. (2021, JpGU) analyzed the frequency-magnitude distribution, tidal correlation, and other index values of seismic activity for the past 20 years across Japan, using a constant spatial grid size and a constant number of analytical sources. They reported the results of extracting the characteristics of "normal" seismic activity that cannot be distinguished from other activity in Japan by focusing on the statistical properties of the frequency distribution of each index value.
Here, we present models of the frequency-magnitude distribution of seismic activity and their occurrence timing that explains the characteristics of "normal" seismic activity extracted in the above analysis, and also show the results of quantifying the degree of anomaly of recent seismic activity using these models as a standard.
For the frequency-magnitude distribution, we used the b-value of the Gutenberg-Richter (GR) law and the η-value (Utsu, 1978), which indicates the degree of deviation from the GR law, as index values. The results of the analysis of η-values of past seismic activity show that the semi-log frequency distribution of the magnitude is not linear as usually expected from the GR law, but is slightly convex upward. Therefore, we adopted the equation proposed by Lomnitz-Adlar and Lomnitz (1979) as a functional form to explain the observed frequency-magnitude distribution. This equation, when rewritten using Mth , the lower bound of M used in the analysis, can be written as follows
logN(M) = A - [ b' (Mth)exp{B ( M - Mth )}] / B
b' (Mth)=dlogN/dM (M = Mth) = cB exp(BMth)
where N(M) is the number of earthquakes of a certain magnitude M or greater, A, B, and c are the parameters of the same equation shown by Utsu (1999), b'(Mth) corresponds to the slope of the frequency-magnitude distribution at M=Mth, and this value roughly corresponds to the observed b value, and B roughly corresponds to the observed η value. Based on the observed values of these index values, assuming a normal distribution for b'(Mth) and a lognormal distribution for B , we estimated their distributions so that the frequency distributions of each index value in the M-series data generated numerically from the model would explain the observed results well. The observed results have variations due to the finite nature of the data, and therefore depend on the way of gridding and the number of sources analyzed. The obtained model well explains also these variations.
For the tidal correlation, we used the D-value (D2=(Σi=1Ncosθi)2+(Σi=1Nsinθi)2, where θi is the phase angle of the i-th earthquake) as an index.From the analysis of past seismic activity, the values are often slightly larger than the Rayleigh distribution expected when seismic activity and tidal response are uncorrelated. This distribution is explained by a model that takes into account the proportion of earthquakes that occur in sufficiently short time intervals relative to the tidal period. Therefore, even if there is no tidal correlation, it can be explained by considering that earthquakes that occur according to the Poisson process are sometimes accompanied by aftershocks. In this case, the D-value can be regarded as a measure of the proportion of earthquakes that occur at sufficiently short time intervals relative to the tidal cycle.
The above index values (b -value, η-value, D -value) are uncorrelated each other in "normal" activity, and, hence, in addition to the frequency distribution of each index value, their joint probability distribution can be obtained from the obtained model. Using these models as standard models, it is possible to evaluate the degree of anomaly for observed seismic data sequentially. In this presentation, we show some examples of applying this method to recent seismic activity.
Here, we present models of the frequency-magnitude distribution of seismic activity and their occurrence timing that explains the characteristics of "normal" seismic activity extracted in the above analysis, and also show the results of quantifying the degree of anomaly of recent seismic activity using these models as a standard.
For the frequency-magnitude distribution, we used the b-value of the Gutenberg-Richter (GR) law and the η-value (Utsu, 1978), which indicates the degree of deviation from the GR law, as index values. The results of the analysis of η-values of past seismic activity show that the semi-log frequency distribution of the magnitude is not linear as usually expected from the GR law, but is slightly convex upward. Therefore, we adopted the equation proposed by Lomnitz-Adlar and Lomnitz (1979) as a functional form to explain the observed frequency-magnitude distribution. This equation, when rewritten using Mth , the lower bound of M used in the analysis, can be written as follows
logN(M) = A - [ b' (Mth)exp{B ( M - Mth )}] / B
b' (Mth)=dlogN/dM (M = Mth) = cB exp(BMth)
where N(M) is the number of earthquakes of a certain magnitude M or greater, A, B, and c are the parameters of the same equation shown by Utsu (1999), b'(Mth) corresponds to the slope of the frequency-magnitude distribution at M=Mth, and this value roughly corresponds to the observed b value, and B roughly corresponds to the observed η value. Based on the observed values of these index values, assuming a normal distribution for b'(Mth) and a lognormal distribution for B , we estimated their distributions so that the frequency distributions of each index value in the M-series data generated numerically from the model would explain the observed results well. The observed results have variations due to the finite nature of the data, and therefore depend on the way of gridding and the number of sources analyzed. The obtained model well explains also these variations.
For the tidal correlation, we used the D-value (D2=(Σi=1Ncosθi)2+(Σi=1Nsinθi)2, where θi is the phase angle of the i-th earthquake) as an index.From the analysis of past seismic activity, the values are often slightly larger than the Rayleigh distribution expected when seismic activity and tidal response are uncorrelated. This distribution is explained by a model that takes into account the proportion of earthquakes that occur in sufficiently short time intervals relative to the tidal period. Therefore, even if there is no tidal correlation, it can be explained by considering that earthquakes that occur according to the Poisson process are sometimes accompanied by aftershocks. In this case, the D-value can be regarded as a measure of the proportion of earthquakes that occur at sufficiently short time intervals relative to the tidal cycle.
The above index values (b -value, η-value, D -value) are uncorrelated each other in "normal" activity, and, hence, in addition to the frequency distribution of each index value, their joint probability distribution can be obtained from the obtained model. Using these models as standard models, it is possible to evaluate the degree of anomaly for observed seismic data sequentially. In this presentation, we show some examples of applying this method to recent seismic activity.