Physica A 391 (2012) 300–306
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Physica A
journal homepage: www.elsevier.com/locate/physa
Analysis of electromagnetic pre-seismic emissions using Fisher
information and Tsallis entropy
S.M. Potirakis
a
, G. Minadakis
b
, K. Eftaxias
c,*
a
Department of Electronics, Technological Education Institute (TEI) of Piraeus, 250 Thivon & P. Ralli, GR-12244, Aigaleo, Athens, Greece
b
Department of Electronic and Computer Engineering, Brunel University Uxbridge, Middlesex, UB8 3PH, UK
c
Department of Physics, Section of Solid State Physics, University of Athens, Panepistimiopolis, GR-15784, Zografos, Athens, Greece
article info
Article history:
Received 10 June 2011
Received in revised form 29 July 2011
Available online 23 August 2011
Keywords:
Fisher information measure
Tsallis entropy
Symbolic dynamics
Fracture-induced electromagnetic
emissions
abstract
In this work, we investigate the dynamics of electromagnetic precursors, recorded prior
to significant earthquakes in Greece. The analysis of these signals is performed using
Fisher information, which is a powerful tool for investigating complex and non-stationary
signals. Our results point to a decrease of the precursor complexity as the main tectonic
event is approaching. The results are compatible to those derived using Tsallis entropy.
The sensitivity of Fisher information and Tsallis entropy are compared on the basis of the
features of the underlying fracture process which they reveal.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Earthquakes (EQs) are large-scale fracture phenomena in the Earth’s heterogeneous crust. Fracture-induced electromag-
netic (EM) physical fields can be considered as the so-called precursors of general fracture [1, and references therein]. They
are detectable at both laboratory and geophysical scales. These precursors allow a real-time monitoring of damage evolution
during mechanical loading in a wide frequency spectrum ranging from kHz to MHz [1–4].
Our main observational tool is the monitoring of the fractures which occur in the focal area before the final break-up
by recording their kHz–MHz electromagnetic emissions. Clear kHz-to-MHz EM anomalies have been detected over periods
ranging from a few days to a few hours prior to recent destructive EQs in Greece [1,5–8]. MHz EM anomalies has been
found to be systematically emerging prior to kHz EM anomalies in both laboratory and geophysical scales [9]. Being non-
destructive, monitoring techniques based on these fracture-induced fields are a basis for a fundamental understanding of
the fracture mechanism.
The main objective of the present work is to reveal the amount of information contained in such a pre-seismic EM time
series related to an upcoming seismic event. We study kHz EM emissions recorded prior two significant EQs in Greece, by
analysing them using Fisher information [10]. In this frame, we introduce an estimation of the Fisher information measure
(FIM) in terms of symbolic dynamics [11], the symbolic Fisher information measure (SFIM). We study the evolution in time
of the SFIM and compare it with the corresponding evolution of the Tsallis entropy [1,12]. The reason why Tsallis entropy
was chosen for comparison is its well-documented physical meaning and the fact that is has a complementary nature to
Fisher information. Entropy and information are seen to be complementary quantities, in a sense: entropy ‘‘drops’’ have as
*
Correspondence to: National and Kapodistrian University of Athens, Faculty of Physics, Department of Solid State Physics, Panepistimiopolis Zografos
GR-15 784, Athens, Greece. Tel.: +30 210 7276733, +30 6947323259 (Mob), +30 6946978325 (Mob); fax: +30 210 7276733.
E-mail address: ceftax@phys.uoa.gr (K. Eftaxias).
0378-4371/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.physa.2011.08.003