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Measurement naturally grades from linear at local magnitudes to logarithmic at distant magnitudes when compared to some local reference scale.
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There are various types of earthquake magnitudes, such as local magnitude, body-wave magnitude, surface-wave magnitude, and M w (e.g., Utsu 2001; Shearer 2009).
Finally, using random vibration theory, with the inputs of empirical parameters as described in previous sections, and adopting an empirical equation for the magnitude conversion, MW = 0.99ML + 0.052 (Wu, 2000), the predictions of the peak horizontal ground motions (PGA and PGV) at the reference sites for local magnitudes ML = 4.0, 5.0, 6.0, and 7.0, respectively, are shown in Fig. 7.
This supervenience on local magnitudes extends also to dynamics if the forces on the particles arise from fields defined at each spacetime point.
The corresponding local magnitudes of these events are also marked.
According to Son (2012), at least 331 earthquakes with a local magnitude of 3.0 6.8 occurred from 1903 to April 2012 in the vicinity of these fault zones (Fig. 2).
The origin time of the Oita earthquake was 32.5 s after that of the triggering Kumamoto earthquake, and its local magnitude was estimated at 5.9.
At 15:08 on March 11, the largest event with a local magnitude of 4.8 occurred in the southern part of the caldera (Fig. 2 a, b)).
It occurred on November 22 at local time 22 08 (UTC + 9) with an estimated local magnitude (M JMA) of 6.7.
Fig. 2. Pattern of local magnitude versus hypocentral distance for the analyzed accelerograms recorded at the reference stations.
The used data were the accelerograms recorded at two stations, DMG and KKA, and velocity seismograms co-recorded at the PKIN station during nine shallow local and regional earthquakes of local magnitude equal to or greater than 5.0.
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