**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes: application
to the ****January 13, 2007**** East of the ****Kuril**** Islands**** earthquake**

Tatsuhiko Hara

*International **Institute** of **Seismology** and
Earthquake Engineering, Building Research Institute*

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 __The
estimated duration is 83.1 sec.__** The
estimated magnitude using the above formula is 8.2**, which agrees with Mw
of the Global CMT solution (8.1).

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: 2007/01/14