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Fig. 6 Frequency magnitude distribution and relationship between the largest foreshock and its mainshock for the long-term data.
The larger the magnitude of the foreshock, the longer is the time difference between the largest foreshock and mainshock.
The distribution of the distance between the largest foreshock and mainshock ((Delta r)) is shown in Fig. 7b.
Fig. 7 Cumulative probability and frequency density distribution of the time difference ((Delta t)) and the epicentral distance ((Delta r)) between the largest foreshock and mainshock for long-term data.
Thus, from the difference of the moment magnitudes between the largest foreshock (M w 6.2) and the main shock (M w 7.0), about one-third of the estimated slip on the Hinagu fault (Fig. 4) would be caused by the largest foreshock.
Approximately 50% of the mainshocks occurred within a day after the largest foreshock (M ≥ 1.0, Fig. 7a), and the time difference between the largest foreshock and mainshock ((Delta t)) attenuates as (1/Delta t) between 0.1 and 10 days (Fig. 7c).
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b Relationship between the magnitude of the largest foreshock and the corresponding mainshock magnitude for each earthquake cluster.
We also analyzed the characteristics of the magnitude and occurrence time differences, as well as epicentral distance between the mainshock and the largest foreshock and confirmed that they follow a power law.
Our findings have important implications for understanding spatial relationship between the source faults of the largest foreshock and mainshock, or between fault geometries and rupture initiation points.
The localized low-(Q_{text{P}}) patch, including the hypocenters of the largest foreshock and mainshock, is put between two high-(Q_{text{P}}) and high-(Q_{text{S}}) patches (along strike, 0 20 km in the Futagawa segment and 5 25 km in the Hinagu segment).
We also observed that the frequency distribution of the magnitude difference between the mainshock and largest foreshock (Fig. 6b) follows a power law; that is, the mainshock magnitude tends to be close to the magnitude of the largest foreshock.
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