Seismic Hazard Parameters in Major Cities of Northern Algeria Using Statistical Tools

In this study, the earthquake frequency–magnitude relationship is modeled using two different designs: the truncated Gutenberg–Richter distribution and the generalized linear model. A goodness-of-fit statistical model is applied to the generalized linear model, and the generalized Poisson regression model appears to be superior to the generalized negative binomial regression model when considering the model selection criteria, namely the Akaike information criterion, Bayesian information criterion, likelihood ratio, and chi-square statistics. The primary goals of this study are to determine the annual rate above Mw 4.0 and the b-value of the truncated Gutenberg–Richter relationship, the probability of exceedance within a time period of 25, 50, and 100 years, and the return period of magnitude above Mw 4.0, and to compare these results to those obtained using the selected generalized Poisson regression model. According to the analyses, the generalized Poisson regression model can be effectively used to derive seismic hazard parameters instead of the Gutenberg-Richter model. Among the obtained results, the b-value at Algiers city is equal to 0.73±0.03\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.73 \pm 0.03$$\end{document} and the annual rate above Mw 4.0 is 4.48±0.19\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4.48 \pm 0.19$$\end{document}: the values of maximum possible magnitude obtained using the Kijko–Sellevoll and Tate–Pisarenko estimators are very close, 7.74±0.46\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.74 \pm 0.46$$\end{document} and 7.50±0.10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.50 \pm 0.10$$\end{document}, respectively, whereas they are equal to 7.40±0.15\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.40 \pm 0.15$$\end{document} and 7.43±0.16\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.43 \pm 0.16$$\end{document} for their Bayesian versions, respectively. The mean return periods derived using the truncated Gutenberg–Richter model with Kijko–Sellevoll estimator are similar to those derived using the generalized Poisson model for magnitudes less than Mw 5.0 and differ for magnitudes greater than Mw 5.0.