**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes: application
to the February 6, Santa Crus Islands earthquake**

Tatsuhiko Hara

*International *

* Building Research Institute*

We developed a 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 February 6, Santa Crus Islands earthquake (the
origin time: 01:12:27 UTC; the location 10.738‹S 165.138‹E depth=28.7km after
USGS). Figure 1 shows an example of measurements of high-frequency energy
radiation. ** The estimated duration is 90.7
sec. The estimated magnitude using the above formula is 7.74**, which is a
little smaller than M

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: 2013/02/06