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 algorithms, 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 reduced 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 magnitude estimates (1) are observational rather than predictive and (2) have to be considered minimum estimates, depending on the amount of available data.