Η διερεύνηση της σεισμικής συμπεριφοράς αποτελεί σημαντική επιστημονική πρόκληση και αναπόσπαστη συνιστώσα ανάπτυξης της γνώση μας για την σεισμογένεση και την εκτίμηση της μελλοντικής σεισμικής δραστηριότητας. Οι κύριοι σεισμοί (π.χ. ) καθώς και οι μετασεισμοί αυτών μπορούν να προκαλέσουν καταστροφικές συνέπειες με απώλειες ανθρώπινων ζωών. Σκοπός της παρούσας διδακτορικής διατριβής είναι η εκτίμηση της μελλοντικής σεισμικής δραστηριότητας, για τον Ελληνικό χώρο, με βάση τη χρήση πολυμεταβλητών σεισμικών χρονοσειρών.
Στο δεύτερο και τρίτο κεφάλαιο της διατριβής, η εκτίμηση της μελλοντικής σεισμικής δραστηριότητας επιχειρείται μέσω της κατασκευής είτε ενός σεισμικού δικτύου συσχέτισης, που προϋποθέτει την δημιουργία πολυμεταβλητής σεισμικής χρονοσειράς, ή δικτύου επανάληψης. Κόμβο του σεισμικού δικτύου συσχέτισης αποτελεί η κάθε μεταβλητή της πολυμεταβλητής χρονοσειράς που αντιπροσωπεύει είτε καλά καθορισμένη σεισμική ζώνη είτε κυψελίδα η οποία προκύπτει από την διαίρεση του Ελληνικού χώρου. Κάθε παρατήρηση της πολυμεταβλητής σεισμικής χρονοσειράς αποτυπώνει είτε το σύνολο των σεισμών ή την σεισμική ροπή που απελευθερώνεται σε κάθε κόμβο, αντίστοιχα. Οι συνδέσεις του σεισμικού δικτύου συσχέτισης μεταξύ των κόμβων του δίνονται από τον γραμμικό συντελεστή συσχέτισης Pearson που υπολογίζεται για κάθε ζεύγος μεταβλητών της πολυμεταβλητής σεισμικής χρονοσειράς. Αντίθετα, κόμβο του δικτύου επανάληψης αποτελεί ο κάθε σεισμός και οι συνδέσεις του δίνονται όταν η διαφορά της σεισμικής ροπής μεταξύ των κόμβων του είναι μικρότερη από ένα αυθαίρετο κατώφλι. Έχοντας σχηματίσει το σεισμικό δίκτυο, η εκτίμηση της μελλοντικής σεισμικής δραστηριότητας επιτυγχάνεται είτε μέσω της χρήσης μέτρων δικτύου που το χαρακτηρίζουν ή μέσω της μελέτης των μη-τετριμμένων τοπολογικών ιδιοτήτων του, όπως της δομής του μικρόκοσμου και της ελεύθερης κλίμακας, που μπορεί να παρουσιάζει. Επομένως, η εκτίμηση της μελλοντικής σεισμικής δραστηριότητας, επιχειρείται από την μελέτη είτε της δυναμικής εξέλιξης των τιμών βασικών μέτρων δικτύου ή της δυναμικής εξέλιξης της δομής του σεισμικού δικτύου που εξετάζεται σε κυλιόμενα χρονικά παράθυρα είτε πριν ή μετά από κύριους σεισμούς ή μετασεισμούς, αντίστοιχα, που έγιναν στον Ελληνικό χώρο και τις γύρω περιοχές κατά την περίοδο 1999-2018. Βρέθηκε, ότι οι τιμές των μέτρων δικτύου, σε αρκετές περιπτώσεις, είναι στατιστικά σημαντικές όπως και ότι το σεισμικό δίκτυο παρουσιάζει την δομή του μικρόκοσμου λίγο πριν τους κύριους σεισμούς.
Στο τέταρτο κεφάλαιο της διατριβής, η εκτίμηση της μελλοντικής σεισμικής δραστηριότητας επιχειρείται μέσω του κανονικοποιημένου συντελεστή που υπολογίζει την συσχέτιση μεταξύ πολυμεταβλητών χρονοσειρών με την εύρεση γραμμικών συνδυασμών τους που συσχετίζονται ισχυρά. Οι μεταβλητές της πολυμεταβλητής χρονοσειράς παριστάνουν το μέγεθος του παρόντος σεισμού και τη χρονική διαδοχή του, σε ημέρες, μέχρι τον επόμενο σεισμό. Ο κανονικοποιημένος συντελεστής συσχέτισης χρησιμοποιείται ώστε να εξετάσει αν υπάρχει στατιστική σημαντικότητα, μέσω κατάλληλου στατιστικού ελέγχου, της συσχέτισης στο μέγεθος και στο χρόνο μεταξύ των πέντε τελευταίων σεισμών, ανά ζεύγη, πριν από κύριους σεισμούς που έγιναν στον Ελληνικό χώρο κατά την περίοδο 1964-2018 για κάθε σεισμική ζώνη. Τα αποτελέσματα, στις περισσότερες περιπτώσεις, υπογραμμίζουν την στατιστική σημαντικότητα της συσχέτισης μεταξύ των τελευταίων πέντε διαδοχικών, ανά ζεύγη, σεισμών πριν την γένεση κύριων σεισμών () για κάθε σεισμική ζώνη. Τέλος, παρουσιάζεται ο χάρτης που αφορά την πιθανότητα γένεσης του επερχομένου κύριου σεισμού () για κάθε σεισμική ζώνη που συμβάλει στην εκτίμηση της μελλοντικής σεισμικής δραστηριότητας.
Λέξεις κλειδιά: Δίκτυο συσχέτισης, Δίκτυο επανάληψης, Δίκτυο μικρόκοσμου, Δίκτυο ελεύθερης κλίμακας, Μέτρο δικτύου, Κανονικοποιημένος συντελεστής συσχέτισης, Πολυμεταβλητή χρονοσειρά, Σεισμική ζώνη, Σεισμική κυψελίδα, Σεισμική ροπή, Κύριος σεισμός, Μετασεισμική ακολουθία.

The investigation of the complex seismicity behavior constitutes a major scientific challenge and an indispensable component in improving our knowledge concerning seismogenesis and seismic hazard assessment. The strong earthquakes (e.g. ) as well as the aftershocks of them can cause catastrophic consequences with losses of human lives. The purpose of this doctoral thesis is the estimation of the future seismic activity for the Greek area, using the multivariate seismic time series.
In the second and third chapter of thesis, the estimation of the future seismic activity is attempted through the construction of either a correlation network or a recurrence plot. The node of the seismic correlation network is each variable of the multivariate seismic time series that represents a seismic zone as the Greek territory is divided. Each observation of multivariate seismic time series captures either the sum of the earthquakes that occurred or the cumulative seismic moment that released at each node, respectively. The connections of the seismic correlation network among of its nodes are given by the Pearson correlation coefficient. On the contrary, the node of the recurrence plot is each earthquake and the connections among of its nodes are given when the difference of magnitudes is less than an arbitrary threshold. Having formed the seismic network, the estimation of the future seismic activity is achieved either through the use of network measures or through the study of its non-trivial topological properties, such as the small-world and scale-free structure. Therefore, the estimation of seismic activity is attempted by studying either the dynamic evolution of network values or the dynamic evolution of network structure in sliding time windows either before or after from main shocks or strong aftershocks, respectively, that occurred in the Greek territory spanning the period 1999-2018. It is revealed that the values of network measures are, in many cases, statistically significant as well as that the seismic network presents the structure of the small-world shortly before the occurrence of main shocks.
In the fourth chapter of the thesis, the estimation of the future seismic activity is attempted through the canonical correlation analysis which calculates the correlation between multivariable time series by finding their strongly correlated linear combinations. The variables of the multivariate time series represent the magnitude of earthquake and its time succession, in days, until the occurrence of next earthquake. The canonical correlation analysis is used to examine whether there is statistical significance, using the appropriate statistical test, of the correlation between the last successive five earthquakes, per pair, that occurred before the occurrence of main shocks in the Greek territory spanning the period 1964-2018 for each seismic zone. The results reveal that the statistical significance of the correlation is present between the last five successive earthquakes, per pair, that occurred before the occurrence of main shocks in each seismic zone. In addition, the map for the probabilities of occurrence of the upcoming main shocks () for each seismic zone, is presented, to help the estimation of the future seismic activity for the Greek area.
Keywords: Correlation Network, Recurrence plot, Small-world network, Scale-free network, Network measure, Canonical Correlation Analysis (CCA), Multivariate time series, Seismic zone, Seismic cell, Seismic moment, Main shock, Aftershock sequence.

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