Tsallis Entropy and Mutability to Characterize Seismic Sequences: The Case of 2007-2014 Northern Chile Earthquakes

Abstract

Seismic data have improved in quality and quantity over the past few decades, enabling better statistical analysis. Statistical physics has proposed new ways to deal with these data to focus the attention on specific matters. The present paper combines these two progressions to find indicators that can help in the definition of areas where seismic risk is developing. Our data comes from the IPOC catalog for 2007 to 2014. It covers the intense seismic activity near Iquique in Northern Chile during March/April 2014. Centered in these hypocenters we concentrate on the rectangle Lat-22-18 and Lon-68-72 and deepness between 5 and 70 km, where the major earthquakes originate. The analysis was performed using two complementary techniques: Tsallis entropy and mutability (dynamical entropy). Two possible forecasting indicators emerge: (1) Tsallis entropy (mutability) increases (decreases) broadly about two years before the main MW8.1 earthquake. (2) Tsallis entropy (mutability) sharply decreases (increases) a few weeks before the MW8.1 earthquake. The first one is about energy accumulation, and the second one is because of energy relaxation in the parallelepiped of interest. We discuss the implications of these behaviors and project them for possible future studies.

Keywords: Tsallis entropy; information theory; subduction seismicity.

Figure 1

Number of daily earthquakes in the selected IPOC catalogue from years 2007 to 2014, fully displayed in the inset. On the abscissa axis in the main body, day 0 corresponds to 1 April 2014, coinciding with the $M_w$8.1 earthquake. It can be noticed that the pre−shock activity appears about 17 days before. The aftershock response extended months afterwards.

Figure 2

We analyzed the data from the IPOC catalog using the Gutenberg-Richter law, including earthquakes from 2007 to 2014 with epicenters within 18 °S–22 °S and 68 °W–72 °W. Circles denote the cumulative number of earthquakes; triangles denote the abundance of earthquakes for a magnitude. Based on the maximum curvature (MAXC) technique (Wiemer and Wyss, 2000), $M_0=$ 2.2.

Figure 3

Depth distribution of earthquakes at different longitudes. Seisms at different latitudes are accumulated on this two−dimensional view. A histogram with respect to depth is presented on the right panel.

Figure 4

Epicentral map of the area under study: the black circle marks the city of Iquique, 95 km from the epicenter. Magnitude of the seisms are illustrated by both a proportional diameter and the color of the circles: yellow $3.0\le M_w\le 3.9$, cyan $4.0\le M_w\le 4.9$, pink $5.0\le M_w\le 5.9$, orange $6.0\le M_w\le 6.9$. The red star positions the great earthquake of Iquique with $M_w$8.1, while the red triangle shows the epicenter of its main aftershock with $M_w$7.6.

Figure 5

Tsallis entropy on magnitude sequence in terms of real time, using four different dynamic windows W as indicated in the code on top. (A) With 256 seismic events, (B) with 512 seismic events, (C) with 1024 seismic events and (D) with 2048 seismic events. Stars give the time of the most important earthquakes of the series whose magnitude is given in the inset.

Figure 6

Mutability on magnitude sequence in real time using four different dynamic windows W as indicated in the insets. Construction is similar to previous figure but this time we choose to report the time in days, grouped in years. Stars report the three major earthquakes as given in the inset.

Figure 7

Approximation to the main shock by a dynamical window of W = 512 events. The data is the same in the four plots but time is stopped at 80, 40, 20 or 2 days before the strongest $M_{w}8.1$ quake. Eventually, a video could be a more appropriate way to represent this evolution, but the most relevant information is obtained from these four pictures. The black curve represents mutability and the blue curve Tsallis entropy.

Figure 8

Mutability on magnitude sequence in natural time using four different dynamic windows W as indicated in the insets. Despite that the data is the same as in Figure 6, the texture of the curve looks different. In particular, the stars denoting the main seisms now open up.