# Probabilistic Seismic Hazard Assessment for United Arab Emirates, Qatar and Bahrain
## 6 Logic Tree Framework and Seismic Hazard Computations
They are: (a) the minimum magnitude (M\({}_{\text{min}}\)) that should be defined in the integration process, which we considered to be equal to Mw 4.0 in our assessment for all included seismic sources (considered as the appropriate magnitude to be used in a good design and construction of buildings e.g., [105]), (b) the annual rate of occurrence for earthquakes of magnitudes equal to or greater than the M\({}_{\text{min}}\), (c) the Gutenberg-Richter \(\beta\)-value (\(\beta=b\times\ln 10\)), and finally, (d) the maximum expected magnitude for each source. Additionally, coefficients of variation for the \(\beta\) values and the standard deviations for the M\({}_{\text{max}}\) values were also included to account for the epistemic uncertainties (see Tables 3 and 4). In order to implement the chosen ground-motion attenuation models into the software, R-CRISIS [94] allows only three categories of attenuation relationships. They are the attenuation tables that could be provided by the analyst, the built-in attenuation models, and the generalized attenuation models. For this current assessment,two attenuation tables for the models by [PERSON] et al. (2018) and [PERSON] et al. (2019) were prepared and built following the guided structure defined in, and compatible with, the R-CRISIS ([PERSON] et al., 2018) software. Additionally, the other two models by [PERSON] et al. (2017) and [PERSON] et al. (2019) were defined using a built-in attenuation relationship. The obtained ground-motion values in the current assessment are presented for two different probabilities of exceedance: 10% in 50 years (475-year return period), and 5% in 50 years (975-year return period), both for the considered site conditions (B/C NEHRP boundary). Seismic hazard results are presented in a series of contour maps (Figure 6) of peak ground horizontal acceleration, and spectral accelerations (for a 5% damping ratio) at periods of 0.2 s and 1.0 s, for each probability of exceedance. The selection of those depicted oscillation periods is considered because of the fact that the hazard values for 0.2 s and 1.0 s spectral periods are greatly representative for the overall shape of the UHS. Additionally, these two values for the spectral periods permit the application of the [PERSON] (2016) criterion (based on the procedure by [PERSON] and [PERSON] (2017)) to propose a design spectrum for each studied site. Figure 6: Seismic-hazard maps, for B/C NEHRP boundary site conditions, depicting the mean PGA and spectral accelerations [SA (0.2 s), and SA (1.0 s)] for return periods of 475 and 975 years [AAN, Al-Ain, ABD, Abu Dhabi; AJM, Ajman; DOH, Doha; DUB, Dubai; FUJ, Fujaira; MAN, Manama; RAK, Ras Al-Khaimah; SHJ, Sharjah; UAQ, Umm Al-Quwain]. In addition, the seismic hazard results are presented for ten selected emirates and cities (eight major emirates in the UAE, and the two capital cities of Qatar and Bahrain) in terms of hazard curves (Figure 7) for PGA, as well as their UHS in Figure 8. Two horizontal lines on the hazard curves plots (Figure 7) are highlighting the two considered return periods (475 and 975 years). The choice of those significant cities is mainly based on their geographic distribution, population density, and their socio-economic importance in the UAE, Qatar, and Bahrain. As a result of the computed hazard curves and UHS, different characteristic seismic hazard values (mean PGA, SA\({}_{\text{max}}\), SA (0.2 s), and SA (1.0 s)) for the studied cities were derived and listed in Table 5.  
Finally, seismic hazard values were deaggregated in terms of distance and magnitude (Figure 9), following [PERSON] and [PERSON] (2018) methodology. For each city, the deaggregation was computed and depicted for four spectral periods (PGA, SA (0.2 s), SA (1.0 s), and SA (2.0 s)) for a return period of 475 years, which is usually considered as input for the seismic design of buildings all over the world.