Fractal dimension analysis for seismicity spatial and temporal distribution in the circum-Pacific seismic belt

In this study, we present the fractal characteristics of the spatio-temporal sequence for seismic activity in the circum-Pacific seismic belt and vicinity regions, which is one of the most active seismic zones worldwide. We select the seismic dataset with magnitude M≥4.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\ge 4.4$$\end{document} in the circum-Pacific seismic belt region and its vicinity from 1900–2015 as the objects. Based on the methods of capacity dimension and information dimension, using ln(1/δ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {ln}(1/\delta )$$\end{document}–lnN(δ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {ln }N(\delta )$$\end{document} of the relationship to evaluate and explain, the results show that (1) in the circum-Pacific seismic belt and the surrounding areas, for the seismic activity with magnitude M≥4.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\ge 4.4$$\end{document}, the time series dimension is 0.63, the spatial distribution dimension is 0.52 and they have fractal structure. (2) For the earthquakes with M≥7.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\ge 7.0$$\end{document}, the time series dimension increases greatly, which indicates that the cluster characteristics in time is greatly reduced. And the earthquakes with magnitude 7.0≥M≥4.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.0 \ge M \ge 4.4$$\end{document} have significant impact on the characterized by clustering in time in the study region. (3) There is significant fractal structure at spatio-temporal distribution of earthquakes in the circum-Pacific seismic belt. It reveals the tectonic movements keep continuous, obvious anisotropism characteristic of geological structure and the distribution of surface stress field is spatio-temporal heterogeneity in the study area.