**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes: application
to the April 20, Sichuan, China earthquake**

We applied the magnitude determination method of Hara (2007a, b) to
the April 20, Sichuan, China earthquake (the origin time: 00:02:47 UTC; the location
30.284‹N 102.956‹E depth= 12.3 km after USGS). In this method, an earthquake magnitude, M, is
calculated by the following formula:

_{}

where _{} is the maximum
displacement (m) during high-frequency energy radiation from the arrival time
of a P-wave, _{} is the epicentral
distance (km), _{} is duration (s) of
high-frequency energy radiation. The duration of high-frequency energy
radiation is estimated by band-pass filtering of first arriving P-waves.

Figure 1 shows an example of measurements of high-frequency energy
radiation. The estimated duration is 20.5 sec. __The estimated magnitude using
the above formula is 6.87__, which is a little larger than M_{ww} 6.6
from USGS WPhase Moment Tensor Solution, and M_{w} 6.6 from the Global
CMT solution.

Fig. 1. An example of measurements of high
frequency energy radiation. The upper, middle and lower traces are an observed
seismogram, the squares of the band-pass (2-4 Hz) filtered seismogram, and its
smoothed time series (normalized by the maximum value), respectively. gAh and
gFh in the lower trace denote the arrival of P-wave and estimated end of high
frequency energy radiation, respectively.

**Acknowledgements**

We retrieved BHZ channel waveform data,
recorded at the Global Seismograph Network (GSN) stations, from IRIS DMC
(Incorporated Research Institutions for Seismology, Data Management Center). We
used SAC (Seismic Analysis Code) (Goldstein et al., 2007) for seismic waveform
data analyses.

**References**

Goldstein, P., D. Dodge, M. Firpo, L.
Minner, J. E. Tull, D. Harris, and W. C. Tapley, SAC - Seismic Analysis Code,
http://www.iris.edu/manuals/sac/manual.html, 2007.

Hara, T., Measurement of duration of
high-frequency energy radiation and its application to determination of
magnitudes of large shallow earthquakes, *Earth Planets Space*, **59**,
227–231, 2007a.

Hara, T., Magnitude
determination using duration of high frequency energy radiation and
displacement amplitude: application to tsunami earthquakes, *Earth Planets Space*, **59**, 561–565, 2007b.

This analysis was done by Tatsuhiko Hara.

Last Updated: 2013/04/23