**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes: application
to the ****September 29, 2009**** ****Samoa**** ****Islands**** Earthquake**

Tatsuhiko Hara

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

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

_{}

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 (e.g.,
Hara, 2007a). _{} 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 79.8 sec.__** The estimated magnitude using the
above formula is 8.31**.

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.

**References**

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.

Last Updated: 2009/10/07