Magnitude Estimation in Real-Time for Earthquake Early Warning applications using Inversion of Displacement Spectra

The Spectrum Inversion Method (SIM) is an evolutionary approach developed to estimate magnitude with potential application in earthquake early warning (EEW). Given an EEW location estimate, continuously updated estimates of magnitude and its associated uncertainty are calculated by inverting the observed displacement spectra of available waveforms in order to define the corner frequency, the frequency independent quality factor and the low frequency plateau. The method consists of two main steps: a) inversion of observed displacement spectra to define the request parameters, b) estimation of magnitude and its uncertainties. We use a Brune omega-squared spectral model to relate displacement spectra to seismic moment, and the Hanks Kanamori relationship to relate seismic moment to moment magnitude. The SIM doesn’t require any kind of calibration, we just need to know a 1D velocity model. The SIM assumes that EEW location estimates from other algorithms. Given a location estimate, the SIM can provide an initial magnitude and magnitude uncertainty estimate with 1 second of waveform data after the P-wave arrival at a single station. These estimates are updated at each second, as the ground motions propagate to further stations, and longer waveform time series are available at closer stations. We use the corner frequency to define the biggest window of signal corresponding to the maximum energy released, the Q value to correct the spectrum for eventual site effects and the low frequency plateau to evaluate the seismic moment and from the Aki-Richards relation linking this quantity to the seismic moment for every single component spectrum. We average the obtained measures for on the component for every station and than on all the station. This will be our final evaluation, which we associate an error depending on the spreading of all the different measures from the average. This method has been tested on waveform datasets from 3≤M≤7 events in Southern California, and Japan. On average, the SIM can give stable and reliable magnitude estimates within 20 seconds of the earthquake origin time, although the final size of the earthquake and the source-station geometry can result in event-specific variations.