The Gutenberg Algorithm: Evolutionary Bayesian Magnitude Estimates for Earthquake Early Warning with a Filter Bank

Earthquake early warning (EEW) is a race against time. In particular, at proximal sites to the epicenter (typically the most heavily affected sites), strong ground motion starts shortly after the P-wave onset. For these sites, regional-type EEW systems that wait until data from several stations are available before issuing a warning and that require fixed data windows following a trigger are not fast enough. Single-station algo-rithms, on the other hand, have high uncertainties that compromise their usefulness. In this article, we propose that uncertainties of the earliest warning messages can be re-duced substantially if the broadband frequency information of seismic signals is fully exploited. We present a novel probabilistic algorithm for estimating EEW magnitudes. The Gutenberg algorithm uses a filter bank for a time–frequency analysis of the real-time signals and estimates the posterior probabilities of both magnitude and source– station distance directly from the observed frequency content. It starts off as a single-station algorithm and then naturally evolves into a regional-type algorithm, as more data become available. Using an extensive near-source waveform data set, we demonstrate that the Gutenberg parameter estimates reach the estimation accuracy and precision of existing regional-type EEW systems with only 3 s of data from a single station. The magnitude estimates, however, saturate at a threshold magnitude that depends on the available signal length that is used for the estimation, suggesting that current EEW mag-nitude estimates (1) are observational rather than predictive and (2) have to be consid-ered minimum estimates, depending on the amount of available data.