**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes: application
to the ****February 27, 2010**** ****Chile**** 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 138.6 sec. The estimated magnitude using
the above formula is 8.57**. Although this estimate is smaller than 8.8
from the Global CMT and USGS WPhase MT, it is consistent with them considering
its uncertainty (around 0.2 in magnitude unit).

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: 2010/03/01