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Short Notes |
1 Hawaii Institute of Geophysics and
Planetology
University of Hawaii at Manoa
Honolulu, Hawaii
96822
cecily{at}soest.hawaii.edu
Recent results suggest that measurements of the average "predominant
period,"
p, of an earthquake using the first few
seconds of P waves provide a rapid approximate estimate of magnitude
that can be used for earthquake early warning systems. Although these prior
studies demonstrate the empirical value of such an approach, we here examine the
theoretical properties of the predominant period estimator. We show that this
estimator is a nonlinear function of spectral amplitude and period that gives
greater weight to higher amplitudes and higher frequencies in the spectrum. Our
results also demonstrate that there are inherent errors in individual
measurements using a time-dependent maximum value of the
p estimator derived from a recursion relation. Whereas
some of the observed variability in predominant period estimates of magnitude
likely is due to local site effects, our analyses suggest that the nonideal
properties of the estimator may also add noise to the results. Given the
potential importance for earthquake early warning systems, we suggest that more
detailed analyses into the magnitude dependence of the spectral characteristics
of initial P-wave data, such as using multitaper spectral or wavelet
approaches, could be helpful in designing improved methods to further optimize
performance.
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