**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes: application
to the April 1, 2007 **

Tatsuhiko Hara

*International *

Recently, we developed a new method to determine earthquake
magnitudes using the following formula (Hara, 2007):

_{}

where M is an earthquake magnitude, _{} is the maximum displacement
during high-frequency energy radiation from the arrival time of a P-wave, _{} is the epicentral
distance, _{} is duration of
high-frequency energy radiation. The duration of high-frequency energy radiation
can be estimated by band-pass filtering of first arriving P-waves (Lomax, 2005;
Park *et al*., 2005; Ni *et al*., 2005; Hara, 2007). _{} are 0.79, 0.83, 0.69,
and 6.47, respectively (the units of _{} were m, km, and s,
respectively).

We applied this method to the April 1, 2007 Solomon Islands Earthquake
(the origin time: 20:39:56UTC; the location 8.453‹N, 156.957‹E after USGS).
Figure 1 shows an example of measurements of high-frequency energy radiation. __The estimated duration is 92.5 sec,
which is consistent with the centroid time shift 44.7 s of the Global CMT
solution.__** The estimated
magnitude using the above formula is 8.1, which agrees well with Mw 8.1 of the
Global CMT solution**.

Fig. 1. An example of measurements of high
frequency energy radiation. The upper and lower traces are an observed
seismogram and its smoothed time series of squares of band-pass (2-4 Hz)
filtered seismogram (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.

**References**

Hara, T., Measurement of duration of
high-frequency energy radiation and its application to determination of
magnitudes of large shallow earthquakes, accepted for publication in Earth
Planets Space, 2007.

Lomax, A., Rapid estimation of rupture
extent for large earthquakes: Application to the 2004, M9 Sumatra-Andaman
mega-thrust, *Geophys. Res. Lett.*, **32**, L10314, doi:10.1029/2005GL022437,
2005.

Ni, S., H. Kanamori, and D. Helmberger,
Energy radiation from the *Nature*, **434**, 582, 2005.

Park, J., K. Anderson, R. Aster, R. Butler,
T. Lay, and D. Simpson, Global seismographic network records the great
Sumatra-Andaman earthquake, *Eos Trans.
AGU*, **86**(6), 57, 2005.

Last Updated: 2007/04/03