Complex Dynamical Systems and Natural Time. Application to seismicity

Doctoral Dissertation uoadl:1309289 293 Read counter

Τομέας Φυσικής Στερεάς Κατάστασης
Library of the School of Science
Deposit date:
Χριστόπουλος Σταύρος-Ρίτσαρντ
Dissertation committee:
Σαρλής Νικόλαος Αναπλ. Καθηγ. (Επιβλέπων), Βαρώτσος Παναγιώτης Καθηγητής, Σκορδάς Ευθύμιος Επίκ. Καθηγητής
Original Title:
Πολύπλοκα Δυναμικά Συστήματα και Φυσικός Χρόνος. Εφαρμογές στη σεισμικότητα
Translated title:
Complex Dynamical Systems and Natural Time. Application to seismicity
A new view of time, termed natural time "χ" -from the greek word "χρόνος"-
which means timewas
introduced by Prof. P. A. Varotsos, Asc. Prof. N. V. Sarlis, and Ass. Prof. E.
S. Skordas, in 2001.
This study aims to analyze complex systems by employing natural time and
focuses on its applications on seismicity.
The first step was to examine whether the global seismicity can be described by
the norm of a
stationary Poisson process. It was found that the occurrence time of main
seismic events are compatible with this norm. Thus, the corresponding
interoccurrence times exhibit randomness and hence they may not contain
essential information. After this observation, global seismicity was analyzed
in natural
time which takes into account the sequential order of the events and their
respective released energies.
Analysis of the Centennial Earthquake Catalog in natural time revealed
correlations between earthquake magnitudes in global seismicity for magnitudes
M greater or equal to 7.0. This result indicates that solid Earth crust behaves
as a single complex system.
The second step conducted was to examine the predictability of the coherent
noise model in natural time. For the quantification of the predictability, a
geometric description of the random predictor variance was proposed in the
Receiver Operating Characteristics diagram. Coherent noise model was studied
for an infinite number of agents and an analytic expression has been obtained
for the distribution function of the size of the next avalanche. This enables
the estimation of the expected size of the next avalanche which exhibits
q-exponential relaxation as a function of the number of the observed
avalanches. Two statistically significant prediction schemes for the coherent
noise model in natural time have been suggested.
During the third step, the generalization of one of the aforementioned
prediction schemes has been
attempted to real aftershock sequences. A prediction algorithm of the
aftershock magnitudes in natural time was constructed and assessed. After
examining various cases of significant earthquakes, i.e., Sumatra (26/12/2004),
Landers (28/6/1992), El Mayor-Cucapah (4/4/2010), Hector Mine (16/10/1999),
Northridge (17/1/1994), the second Superstition Hills (24/11/1987), Big Bear
aftershock (28/6/1992), first Superstition Hills (24/11/1987), Joshua Tree
(23/4/1992) and Methoni (14/2/2008), we conclude that the predictability of
aftershocks, on the basis of the natural time analysis of the coherent noise
model, can be applied in global scale with useful results.
Natural time, Complex Dynamical Systems, Seismicity, Coherent-noise model, Aftershocks
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