Information theory approach to the Landers aftershock sequence

Abstract

The study of seismicity is becoming increasingly important with recent disasters such as the Gorkha event in Nepal in 2015. Our models mostly depend on the information given by a seismic catalog, such as rates of events and magnitudes. It has also been shown that seismicity presents long-range correlations. Here, we think about how they should be introduced in our models. We divide the region into cells and represent their activity as a time series. We then calculate how much information one cell has about the others in a future time. We find that the higher information content is in each cell with itself. By representing the region as a complex network, we can see that the information between distant cells passes thorough hubs that correspond to the main events. So we conclude that long-range interactions should be introduced as the interaction with the mainshocks, not with other cells except, perhaps, in the nearest neighbourhood.

A visual method based on Lewis dot electron structures (VISLEDS) for teaching inorganic formulation

“…The mutual information represents the amount of information that one random variable has about another random variable, accounting for nonlinear correlations as well. This interpretation has been used in text analysis [32], computer vision [33], earthquakes [34], or psychology [35], for example. In the calculations, we divide the probability distributions into 10 intervals, because we found that this number of intervals satisfies the condition to find a robust estimator [36].…”