Figure - available from: Journal of Seismology
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![Epicentral distribution of 1000 earthquakes occurred just before the Tohoku earthquake (left) and the corresponding 2D entropies normalized as S/SxI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S/{S}_x^I $$\end{document} vs log10(K/N); the vertical lines are for reference and correspond to K = N and K = 2N; the shaded (yellow) area indicates the difference between SU and SP; ΔSH and ΔSN are the areas defined in (15) and (16)](profile/Ewa-Glowacka/publication/354655299/figure/fig18/AS:1069071894323237@1631898010995/Epicentral-distribution-of-1000-earthquakes-occurred-just-before-the-Tohoku-earthquake.png)
Epicentral distribution of 1000 earthquakes occurred just before the Tohoku earthquake (left) and the corresponding 2D entropies normalized as S/SxI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S/{S}_x^I $$\end{document} vs log10(K/N); the vertical lines are for reference and correspond to K = N and K = 2N; the shaded (yellow) area indicates the difference between SU and SP; ΔSH and ΔSN are the areas defined in (15) and (16)
Source publication
The concept of Poisson renormalized entropy is presented as an observable of background seismicity with precursory possibilities. The usual way of estimating entropies evaluating probabilities directly from the normalized number of incidences is shown to be lacking in sensitivity and seriously subject to saturation. As an example, the concept of Po...
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Citations
... g) Renormalized Poisson entropy. The detailed explanation of this concept can be found in Nava et al. (2021); a brief explanation is that as background seismicity tends to cluster or concentrate in space it will be more "ordered" than when it occurs completely randomly, so its Shannon entropy (Shannon, 1948) should decrease. The Shannon entropy is ...
... where i is the index of each of the K cells in which the region is divided for a given cell length, and p i is the probability assigned to the number of events in the cell. For a population of N events with n i events in cell i, the probability is commonly estimated as p i = n i /N, but, as shown in Nava et al. (2021) the entropy computed using these probabilities saturates quickly for small cells. Hence, we use the Poisson probability of n i given λ = N/K ...
... ΔS is expected to be low before a major event (Nava et al., 2021), but no clear low is seen before EMC or other SEQs. ...
