Cross-validated probabilistic seismic hazard

6 We propose a cross-validated seismic hazard (CVSH) method contrasting time-independent 7 and dependent models via the Poisson and Weibull probability cumulative distributions. 8 Based on the upper-limit spectral accelerations retrieved from the time-dependent models, 9 we infer that in the memoryless Poisson approach, the selected lifetime of buildings is 10 location-dependent rather than a fixed classical value of 50 years for all sites. All models 11 compute the seismic hazard for magnitudes M 5-7.83 by the influence of the interface 12 subduction zone in El Salvador at three locations, the Capital City San Salvador, the Port of 13 Acajutla on the coastline, and Arcatao Town in the North of the country returning average 14 spectral accelerations with less than 10% differences in all cases.


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The time-independent probabilistic seismic hazard assessment is the core of any building 22 design guidelines. After the seminal work of Esteva ( 1967Esteva ( ,1968 and Cornell ( 1968), and 23 later being Fortran coded by McGuire (1975), this method has been applied extensively 24 around the globe and replicated over and over through several computer codes. On the 25 other hand, Woo's exceptional work (1996) gave us light as an alternative approach to 26 compute free-zone design accelerations and compare with the rigid-zone former method. 27 However, there is a lack of a validation procedure in the results of a memoryless seismic 28 hazard assessment; although, in some cases, this method overestimates peak ground   corresponds to the centers inland of the isoseismal curves rather than being offshore. We 56 consider such location uncertainty in the seismic hazard calculation in Section 3.3. The 57 reverse-slip focal mechanism obeys Hauksson (1990), yielding rakes angles of 45⁰ to 135⁰ 58 and within ±20⁰ of the strike of the trench. The northern limit of the interface subduction 59 zone matches the southern limit of the volcanic chain seismogenic source in Central 60 America (Salazar, 2021).

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The completeness analysis of the catalog for several magnitude bins relies on Tinti & 62 Mulargia (1985) method; see Table 1 and Figure 2. The catalog and its completeness found 63 the study of the earthquake interoccurrence times in the following section. This section aims to corroborate the time between consecutive earthquakesthe 67 interoccurrence times -that belong to a particular magnitude bin follow a Poisson or 68 Weibull probability distribution. Once we assure that such distributions are adequate to the 69 interface subduction zone seismic activity, we evaluate the seismic hazard employing 70 magnitude likelihood distributions on time-independent and dependent models.

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The Poisson probability cumulative distribution F(t) is given by: where λ is the number of earthquakes per unit time, and t is the interoccurrence time  We first test the two probability functions depicted in Figure 3 and constants listed in Table   79 2 for several magnitude bins employing the whole earthquake catalog without removing  Figure 4 shows the conditional probability for several 107 magnitude bins; in general, the greater the magnitude, the lesser the conditional probability, 108 and the longer the interoccurrence time greater the probability of occurrence. We keep this 109 information to use in the time-dependent seismic hazard assessment of the next section 110 (e.g., Table 2 lists the conditional probabilities for the year 2070).

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We secondly test the Poisson probability function depicted in Figure 5 for several 113 magnitude bins removing from the catalog the foreshocks and aftershocks employing the  We present a basic theory of two time-independent models, the classical rigid-zone 136 Cornell-McGuire approach and the free-zone Woo (1993). An in-depth discussion of these 137 methods is elsewhere (e.g., Salazar, 2018).

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For the rigid zone approach, the mean annual rate E(z) for ground motion z is: where ν is the number of earthquakes per year between the minimum magnitude maximum An acceleration design level is retrieved usually at 2% and 10% of exceedance.  For the case of the rigid-zone method, the G-R relationship and magnitude probability f(M) 160 is presented in Figure 6a and b, yielding a B value of nearly onetypically of tectonic 161 earthquakes worldwide -after the completeness analysis and the declustering process 162 (Gardner & Knopoff, 1974). Figure 7 shows the bandwidth of epicentral distance-163 magnitude for the subduction interface zone used in the free-zone method.      3%, respectively, for 2 and 10% exceedance (Fig. 9c-d). Such a lifetime is a different one 251 of San Salvador city -100 years-and presumably the same 75 years between 2095 and 252 2020. We attribute that such differences of a selected lifetime with San Salvador due to the 253 nearest location of the Acajutla Port to the interface subduction seismogenic source. We   Table   267 3). However, average spectral ordinates from both methods yield similar when comparing  suitable for the Town of Arcatao 55 km away from the volcanic zone axis (Fig. 11a-c).

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The new seismic code regulations in El Salvador must include a seismic zonation and 323 correspondent lifetimes for each seismogenic source rather than one general zonation that 324 combines all influences of earthquake sources. For example, based on the first instance on 325 the PGA at the three sites evaluated, the coastal area yields 1.3 and 2.5 times more shaking 326 than the central and north parts of the country, respectively. Consequently, the building 327 code may charter three zones and their correspondent spectra due to the interface 328 subduction earthquake's influence with distinctive lifetimes. Our dependent hazard scheme 329 limits the analysis to the maximum magnitude reported in the catalog since conditional 330 probabilities are calculated only for the listed events within magnitude bins. In this case, 331 time-independent methods can incorporate a maximum magnitude (e.g., 0.2 to 0.5 units 332 more than the maximum one listed in the catalogue) after applying the cross-validated 333 procedure explained in this article.