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Analysis of the geomagnetic field transfer functions
during the 2009 L’Aquila seismic sequence
A. De Santis1,3, G. Cianchini1,2, Di Lorenzo C. 1, Di Mauro D.1, Di Persio M.1, Iezzi B.3, P. Palangio1, E. Qamili.1,2, Wu L. X.4
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Istituto Nazionale di Geofisica e Vulcanologia – 2 Scuola Dottorato Università Siena – 3 Università “Gabriele D’Annunzio” Chieti -
With the aim of understanding the physical phenomena associated with L’Aquila (Central Italy) seismic sequence, culminated with the 6 April 2009 M6.3 earthquake, and of possibly
identifying any possible sign of precursors, we analyze the Cartesian components of the geomagnetic field measured at the Geomagnetic Observatory of L'Aquila in the period 20072009. On one hand, we see weak but peculiar anomalies in the transfer functions between the horizontal and vertical magnetic components in the frequency domain. In post data analysis
these anomalies could be easily put in relation with some hypothetical variations of the lateral and in-depth geoelectric characteristics of the site of observation. However, their statistical
significance can be discarded because their appearance could be just occurred by chance. On the other hand, when we analyse the same data in terms of the spectral entropy of the
magnetic transfer functions over a time preceding the main shock of the sequence, the most significant result is the presence of distinct temporal regimes that cannot be expected by external
field contaminations. We find clear entropy anomalies that may be related to migration of fluids and / or changes in micro and mesofracturations that likely affected most of the lithosphere
beneath the region of L'Aquila before the occurrence of the main significant event. However, although the found indications are important to understand some of the physical processes
preceding the main shock, they do not seem at present to have any practical forecasting potential.
1. The “Conventional” Way: Transfer Function Analysis
From the 1 Hz magnetic data recorded at the Magnetic Observatory of L'Aquila (Central Italy), a magnetovariational analysis is
carried out to study the electromagnetic state of the crust under the measuring site, which is only a few kilometers far from the epicentre.
In the frequency domain, the equation that links the changes in the vertical Z to horizontal X and Y magnetic field components is as
follows:
Z(ω) = A(ω)·X(ω) + B(ω) ·Y(ω)
where A(ω) and B(ω) are the complex transfer functions
computed at the single station. A(ω) and B(ω), where ω
is the angular frequency, are related to the electrical
resistivity which, might vary over time due to tectonic
activity (eg. Honkura and Niblett, 1980). The main
shock, occurred on the 6th April, 2009 is indicated by
the red vertical line and the asterisk.
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EGU Vienna 3-8 April, 2011
Board Number XY411
Display Time
Thursday, 07 April 2011 08:00 – 19:30
Attendance
17:30 – 19:00
2. “Non-conventional” Way: Transfer Function Entropy Analysis
With the above term we mean an analysis of the spectral Entropy characterizing the order / disorder state of the
layered crustal volume beneath the measurement site, considered as “a whole” system. We do this with the
objective to search for any peculiar feature of the system under investigation before the main shock and to look at
individual spectral contributions corresponding to specific frequencies, which, in turn, correspond to some depths.
This is a typical approach to study a complex system (eg De Santis, 2009). The starting hypothesis under
scrutiny is that the 6th April, 2009 earthquake is only the "culmination" of a long and complex process that has
“significantly” affected the volume of the crust, where the main mechanical failure (i.e. the sequence main event)
took place. Under this hypothesis, we analyzed the transfer functions A(ω), B(ω) and their spectral entropy
through the concepts and tools of the Information Theory (Shannon,1948).
A(ω) and B(ω) contain information about the state of conductivity of the layer of crust at depth d (called skin
depth):
d = (2/mws)0.5
Then we define the (normalized) Transfer Function Entropy as
E (t) = −Si=1,n pi(w,t)·log pi(w, t)/log n
where pi (w,t) = K (w,t)/ Si Ki (w,t), n = total number of harmonics and K(w,t)=Ar(w,t), Br(w,t) at time t.
We impose that pi(w,t)·log pi(w, t) = 0 for pi(w,t) = 0.
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Beijing Normal University
Seismo EM Phenomena
and Earthquake Precursors
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3. Conclusions
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The figures on the right show the example of the
absolute value of the real part of B (i.e. |BR|) at
different periods. For periods higher than 30-40
seconds (i.e. frequencies lower than 25 mHz) we do not
notice anything anomalous, while at 30 seconds (yellow
figure) we observe that there are two large peaks around
a year before L’Aquila earthquake. Do they occur by
chance? Are they real? And if so, how can they be
interpreted?
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Session NH4.1/SM5.8
Date
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2008
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2009
A “conventional” transfer function analysis of L’Aquila magnetic data do not detect clear anomalies during the interval 2007-2009:
indeed, some apparent differences in behavior of the transfer functions appear to be episodic and random. It is only by the
subsequent analysis of the same magnetic data in terms of the Shannon entropy, the so-called Transfer Function Entropy, that we
can identify some distinct temporal regimes in which there is a significant decrease of this amount to about one year before the main
shock, and subsequent oscillations at 10 and 6 months earlier. Although the absolute minimum of E(t) practically coincides with the
maximum Kp index, successive minima have no equivalent correspondence in Kp behaviour. The most remarkable outcome, however, is
that in contrast to this overall decrease, some single harmonics show a counter-trend contribution. In particular, the periods between
30 and 40 seconds (frequency of 25-33 mHz, corresponding to skin depths of 15-20 km) show values of entropic contributions
significantly higher than the background value. We interpret this result as due to the complex phenomenology associated with the
evolution of the L’Aquila seismic sequence occurring in the deep crustal layers at around d = 15-20 km. These entropic anomalies
can be related probably to migration of fluids and / or changes in the micro- and meso-rupture process that affected much of the
lithosphere beneath the region of L'Aquila, with particular concentration at 15-20 km depth, so just below the mean hypocentral
depth (approximately 10 km) of the L’Aquila earthquake sequence. However, although the found indications are important to
understand some of the physical processes preceding the main shock, they do not seem at present to have any practical forecasting
potential.
The above figure shows the behaviour from 1/1/2007 to 31/12/2009 of the modified Kp index (Kp*, top of
figure), the total entropy E(t) for the real part of the transfer function A(w) (middle). By the bold red line we
indicate the 20-day moving averages. Finally (bottom), for each angular frequency w, the individual contribution p(w)·log[p(w)] to the total entropy is shown. Although the absolute minimum of E(t) practically coincides with the
maximum Kp index (see the 20-day moving average) the subsequent relative minima have no equivalent in Kp
behaviour. However, the most remarkable outcome is that the contribution of some individual harmonics are
opposite with respect to the overall decrease of entropy. In particular, the periods between 30 and 40 seconds
(i.e. w/2p = 25-33 mHz, corresponding to d = 15-20 km) show significantly higher values than the background
entropic contribution. This result is particularly important because it is detected when the system responds
mostly with an overall decrease of entropy to the increase in external magnetic activity.
4. Bibliography
De Santis A. (2009). Geosystemics, Proceedings of the 3rd IASME/WSEAS International Conference on
Geology and Seismology (GES’09), Feb. 2009 Cambridge, 36-40.
Niblett E.R. and Y. Honkura (1980). Time-dependence of EM transfer functions and their association with tectonic
activity, Geophysical Surveys, 4, 97-114
Shannon, C. E. (1948). A mathematical theory of communication, Bell Syst.Tech. J. 27, 379, 623.