Large earthquakes follow highly unequal ones

TL;DR

This work investigates whether large earthquakes are preceded by highly unequal energy releases, signaling proximity to a critical point. It combines two SOC-inspired frameworks—the 1D train model and a 2D sandpile-like model—with sliding-window calculations of the Gini index $g$ and Kolkata index $k$, applied to real USGS catalogs from Southern Japan, SE Asia, North America, and Indonesia. Results show that high $g$ and $k$ values tend to precede larger events, with simulated energy $E$ rising with $g$ and peaking near $g \approx 0.87$, while empirical data exhibit similar patterns under Gutenberg–Richter scaling $E \propto 10^{1.5 M}$. The findings point to inequality-based indicators as potential hazard-analysis tools and offer a lens on universal features of systems near criticality in seismology.

Abstract

It was conjectured for a long time that the tectonic plates are in a self-organized state of criticality and that the Gutenberg-Richter (power) law is a manifestation of that. It was recently shown that for a system near criticality, the inequality of their responses toward external driving could indicate proximity to the critical point. In this work, we show with numerical simulations and seismic data analysis that large earthquake events have a tendency to follow events that are highly unequal. We have applied this framework to various tectonically active regions, such as North America, Southern Japan, parts of South-East Asia and Indonesia.

Figures (7)

• Figure 1: The top figure shows the time series plot of the avalanches for the train model. The bottom figure is the same series, but now sorted according to the corresponding Gini index associated with each event (calculated from the immediately preceeding 100 events. The larger avalanches tend to accumate near larger $g$ values.).
• Figure 2: The binned avalanches are shown as a function of $g$ values, with a binning range of 0.01 in the $g$ values for the different system sizes in the 1-d train model. A clear postive correlation is observed.
• Figure 3: The top figure shows the time series of the avalanches seen in the 2d SOC model. The bottom figure is the same time series, but now sorted according to the $g$ value associated with each event (calculated from the immediately preceeding 100 events). Similar to the train model, a clear correspondence is noted with high $g$ and large avalanches, except for the vary high $g$ values, where events are less.
• Figure 4: The binned avalanches with $g$ values for the 2d SOC model. The bin size is 0.01. A positive correlation with increasing $g$ is observed, as in the case of the train model.
• Figure 5: Earthquake energy distribution plots of real earthquake data. Earthquake magnitude was converted into energy using the relation $E \propto 10^{1.5M}$, where $M$ denotes the earthquake magnitude. The resulting energy is expressed in joules. This formula is taken from Peter Bormann et al. moment, in this paper they proposed $E =10^{1.5M} + 4.8$, but in our method we ignore the constant term as it do not effect the $g$ value, only the magnitude of earthquake energy increases. Exponent value for each region is mention on the right-most figure. The common fitted Power law exponent is $b_c=-1.733\pm 0.002$ with KS D (Kolmogorov-Smirnov Distance)$=0.166$.