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In this paper, a size-independent modification of the general detrended fluctuation analysis (DFA) method is introduced. With this modified DFA, seismic time series () pertaining to most seismically active regions of the world from the year  up to the year  are comparatively analyzed. An eminent homogeneity of spatial clustering behaviors in worldwide range is detected and DFA scaling exponents coincide with previous results for local regions. Furthermore, universal nontrivial spatial clustering behaviors are revealed from shallow to intermediate-depth earthquakes by varying the depth of the hypocenter: in shallow earthquakes, the depth range corresponding to the minimum spatial clustering is first verified to be spatiotemporal and identical; in intermediate-depth earthquakes, strong weakening long-range correlations compared to shallow earthquakes are unveiled to strengthen the recent findings in seismology. Our work aims to suggest a possible statistical approach to explore the dynamic mechanisms implied in the seismicity as well as in other analogous dynamic evolution processes.

Investigation of the Spatial Clustering Properties of Seismic Time Series: A Comparative Study from Shallow to Intermediate-Depth Earthquakes