Law for the distance between successive earthquakes
Sumiyoshi Abe (1), Norikazu Suzuki (2)((1)Institute of Physics,, University of Tsukuba, Ibaraki, Japan,(2)College of Science, Technology,, Nihon University, Funabashi, Chiba, Japan)

TL;DR
This paper reports a new law governing the three-dimensional spatial distances between successive earthquake foci, revealing complex geometric patterns in seismic activity through analysis of data from southern California.
Contribution
It introduces a novel law describing the spatial distribution of earthquake foci, supported by empirical data analysis and fitting a modified Zipf-Mandelbrot distribution.
Findings
Distances follow a modified Zipf-Mandelbrot law
Reveals complex geometric structure of seismic events
Supports new understanding of earthquake spatial patterns
Abstract
Discovery of a new law for three dimensional spatial distance between the foci of successive earthquakes is reported. Analyzing the seismic data taken between 1984 and 2001 in southern California, it is found that the cumulative distribution of the distances follows the modified Zipf-Mandelbrot law, showing complexity of geometry of the events.
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