Fractal Analysis of Earthquake Sequences in the Ibero-Maghrebian Region

The main topic of this study is to characterize the seismic activity in the studied region by performing qualitative and quantitative analyses of several selected seismic sequences (seismic swarms and aftershock sequences). Clustering analysis of the selected seismic sequences, located in recent years in the Ibero-Maghrebian region, has been performed using the concept of fractal dimension. Analyses of the temporal variation of the fractal dimensions D-2(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{ - 2} (T)$$\end{document}, D0(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{0} (T)$$\end{document} and D2(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{2} (T)$$\end{document}, as well as the spectral slope, have been also performed in order to characterize each analyzed sequence. The variation of the b-value parameter of the Gutenberg-Richter relationship with time has been derived using the windowing method, and a comparative analysis of the variation in time and space of the D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{2}$$\end{document}-value is assessed. Taking into account that b-value variations are often used in seismic hazard and earthquake forecasting studies, this type of work highlights the importance of fractal dimension research in seismic sequences. From our dataset, a positive correlation between b-value and the fractal dimension D2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{2}$$\end{document} has been obtained, as shown in the following relations D2=1.36±0.27b+0.59(±0.26)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{2} = 1.36\left( { \pm 0.27} \right)b + 0.59( \pm 0.26)$$\end{document} and b=0.74±0.13D2-0.44(±0.24).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b = 0.74\left( { \pm 0.13} \right)D_{2} - 0.44( \pm 0.24).$$\end{document}