We present an evolutionary approach for magnitude estimation for earthquake early warning based on real-time inversion of displacement spectra. The Spectrum Inversion (SI) method estimates magnitude and its uncertainty by inferring the shape of the entire displacement spectral curve based on the part of the spectra constrained by available data. The method consists of two components: 1) estimating seismic moment by finding the low frequency plateau ω _0, the corner frequency f_c and attenuation factor (Q) that best fit the observed displacement spectra assuming a Brune w ~2 model, and 2) estimating magnitude and its uncertainty based on the estimate of seismic moment. A novel characteristic of this method is that is does not rely on empirically derived relationships, but rather involves direct estimation of quantities related to the moment magnitude. SI magnitude and uncertainty estimates are updated each second following the initial P detection. We tested the SI approach on broadband and strong motion waveforms data from 158 Southern California events, and 25 Japanese events for a combined magnitude range of 3 ≥ M ≥ 7. Based on the performance evaluated on this dataset, the SI approach can potentially provide stable estimates of magnitude within 10 seconds from the initial earthquake detection.
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