AGU Fall Meeting, San Francisco CA, USA, 10-14 December, 2007
M. Caprio, M. Lancieri, G. Cua, A. Zollo
An effective regional earthquake early warning system (EEWS) requires the capability to estimate earthquake location and magnitude while the event is still occurring. Attenuation relations are then used to predict the spatial distribution of expected peak ground motion amplitudes. To maximize available warning time, early warning algorithms should be capable of producing source and ground motion estimates as soon as possible after the initial event detection (using a few seconds
of data on a few stations), and updating these estimates as additional data become available at stations further from the source region.
The Spectrum Matching (SM) method is a Bayesian approach to estimate magnitude (and its uncertainties) by matching the observed displacement spectra of available waveforms with theoretical source spectral models. Magnitude and uncertainty estimates are updated at each second after the first P-arrival.
The method consists of three main steps:
a) comparison between observed data and theoretical model,
b) estimate of magnitude and its error,
c) introduction of a prior distribution:
This inversion technique is based on the comparison between the recorded displacement spectra and a set of theoretical omega-square curves, evaluated for several magnitude values from the range 3.0-9.0 M. The misfit between the observed spectra and theoretical curves is measured, defining a cost function based on the L2 norm. The comparison between spectra is performed in the frequency
range 1/n - 15 Hz, where n indicates the length of the recorded signal in seconds. As the duration of the recorded signal increases, the spectrum becomes richer in low frequencies content and thus allowing more accurate magnitude estimates. For every station recording, the estimated earthquake magnitude at each time step is provided as a probability density function (PDF), which incorporates in its definition the uncertainties related both to the model employed and to the available data. The total PDF is expressed as the likelihood product of all the PDF of magnitude relative to the recording stations at the given time t.
To better constrain our magnitude estimation, we used a Bayesian approach. We introduced as a prior the Gutenberg-Richter earthquake size distribution to constrain our initial estimate, and then use the estimated PDF for subsequent updates. Once we start to record the S-wave, we use as a prior the entire P-phase PDF. This guarantees that an outlier observation does not strongly influence the final estimation. The SM method has been tested on a database of records from the 1999 M 7.6 Chi Chi, Taiwan earthquake and its aftershocks, the 2003 M 6.8 Tottori, Japan earthquake, and a suite of events from Switzerland and California, with magnitudes ranging between 4-7.3 Ml