A system experiences shocks that occur in accordance with a poisson process having a rate of 1/hour.10/19/2023 Here \(\hat V(t - t_0)\) is the filtered signal, in the range Hz, of the peak ground velocity V( t) shifted by t 0 and \(\). Also in our method, indeed, it is not necessary to locate earthquakes and to rely on assumptions on seismicity. This idea is, to a certain extent, similar to the proposal 23 of extrapolating the long-term probability of ground shaking directly from the frequency distribution of the maximum amplitude of seismograms 24. The method does not require the identification of aftershocks and provides the probability of strong ground shaking without attenuation relations. Here we present a novel method based on a fitting procedure applied to the ground velocity recorded at a site of interest. This requires accurate empirical attenuation functions 21, 22 which are usually only approximately known and often ignore site effects caused by local site conditions. Another problem of STAF methods is that, once λ( t) has been estimated, the predicted aftershock rate must be converted in terms of the probability of ground shaking at a given site. Some fitting procedures 11, 13, 16, 17, 18, 19, 20 have been recently developed to take into account this incompleteness of data sets, but they become efficient only when a sufficient number of aftershocks has been recorded. As a consequence small aftershocks are not recorded in the first part of seismic sequences and the evaluation of K and c is strongly biased 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. This, however, is a very difficult task because of the overlapping of coda-waves, among close in time aftershocks, which obscures the recordings of smaller events. This fitting procedure requires the identification of all aftershocks above a sufficiently small magnitude threshold. Conversely the parameters K and c exhibit huge fluctuations from one sequence to another 5 and, therefore, they must be fitted as soon as the ongoing earthquake sequence produces a sufficient number of aftershocks 3. The parameters b and p are similar for different sequences and setting b ≃ p ≃ 1 almost always provides reasonable results. Equation ( 1) may be used in STAF models once the four model parameters b, p, K, and c are known. Where Δ M = M m − M c and M m is the mainshock magnitude.
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