A Bayesian approach to the real-time estimation of magnitude from the early P and S wave displacement peaks

[1] It has been shown that the initial portion of P and S wave signals can provide information about the final earthquake magnitude in a wide magnitude range. This observation opens the perspective for the real-time determination of source parameters. In this paper we describe a probabilistic evolutionary approach for the real-time magnitude estimation which can have a potential use in earthquake early warning. The technique is based on empirical prediction laws correlating the low-frequency peak ground displacement measured in a few seconds after the P and/or S phase arrival and the final event magnitude. The evidence for such a correlation has been found through the analysis of 256 shallow crustal events in the magnitude range Mjma 4–7.1 located over the entire Japanese archipelago. The peak displacement measured in a 2-s window from the first P phase arrival correlates with magnitude in the range M = [4–6.5]. While a possible saturation effect above M ≃ 6.5 is observed, it is less evident in an enlarged window of 4 s. The scaling of S peaks with magnitude is instead also observed at smaller time lapses (i.e., 1 s) after the first S arrival. The different scaling of P and S peaks with magnitude when measured in a 2-s window is explained in terms of different imaged rupture surface by the early portion of the body wave signals. We developed a technique to estimate the probability density function (PDF) of magnitude, at each time step after the event origin. The predicted magnitude value corresponds to the maximum of PDF, while its uncertainty is given by the 95% confidence bound. The method has been applied to the 2007 (Mjma = 6.9) Noto Hanto and 1995 (Mjma = 7.3) Kobe earthquakes. The results of this study can be summarized as follows: (1) The probabilistic algorithm founded on the predictive model of peak displacement versus final magnitude is able to provide a fast and robust estimation of the final magnitude. (2) The information available after a few seconds from the first detection of the P phase at the network can be used to predict the peak ground motion at a given regional target with uncertainties which are comparable to those derived from the attenuation law. (3) The near-source S phase data can be used jointly with P data for regional early warning purposes, thus increasing the accuracy and reliability of magnitude estimation.