**Determination of earthquake magnitudes using duration of
high-frequency energy radiation and maximum displacement amplitudes: application
to the August 15, 2007 Near the coast of Central Peru Earthquake**

Tatsuhiko Hara

*International *

Recently, 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 August 15, 2007 Near
the coast of ** The estimated duration is 155.0 sec,
which is consistent with the centroid time shift 61.0
s of the Global CMT solution.** Due to concentration of seismic stations
in the northern hemisphere, and due to the effect of directivity reported by
studies of rupture processes (e.g., Ji and Zeng, http://earthquake.usgs.gov/eqcenter/eqinthenews/2007/us2007gbcv/finite_fault.php),
the estimate probably has uncertainty on the order of 10 sec.

** The estimated
magnitude using the above formula is 8.2, which is consistent with Mw 8.0 of the
Global CMT solution**. Figure 2
shows the contribution from the maximum displacement amplitude (with correction
for epicentral distance), and the one from duration
of high frequency energy radiation in the above formula for this 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. The contribution
to the magnitude from the maximum displacement amplitude and epicentral distance (the horizontal axis) and the one from the
duration of high frequency energy radiation (the vertical axis) are shown for
this earthquake with the events analyzed by Hara (2007a, b) (modified from Fig.
2 of 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: 2007/08/20