**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes:
application to the ****October 25,
2010**** Southern ****Sumatra**** 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 109.7 sec. The estimated magnitude using
the above formula is 7.61**, which agrees with M

The contribution to the magnitude from the maximum displacement
amplitude and epicentral distance (the first and
second terms of the above formula) and that from the duration of high frequency
energy radiation (the third term of the above formula) are shown in Fig. 2 with
those obtained for the large (Mw>=7.2) earthquakes that occurred since 1995
including the past tsunami earthquakes. __Considering
the low amplitude and long duration, which are the characteristics of tsunami
earthquakes, the event that occurred this time is likely to be a tsunami
earthquake.__

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.

Fig. 2. Contributions to magnitudes from maximum displacement amplitudes
and epicentral distances (the horizontal axis) and
those from durations of high frequency energy radiation (the vertical axis) are
plotted for the October 25, 2010 Southern Sumatra earthquake (denoted by the
red diamond) and the large (Mw>=7.2) earthquakes that occurred since 1995
(the blue squares: past tsunami earthquakes; the dots: others). The results for
the latter are from Hara (2007b).

**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: 2010/11/01