Με σκοπό την επίλυση προβλημάτων υπολογισμού των χαρακτηριστικών μεγεθών του μαγματικού θύλακα του ηφαιστείου Σαντορίνης με δεδομένα που βασίζονταν σε γεωδαιτικές μετρήσεις, αναπτύχθηκε αριθμητική-τοπολογική μέθοδος επίλυσης (υπερστατικών) συστημάτων πολύπλοκων και μη γραμμικών εξισώσεων με πλεονάζουσες παρατηρήσεις. Η συνόρθωση (adjustment) των συστημάτων αυτών δεν είναι δυνατόν να πραγματοποιηθεί με βάση συμβατικές αλγεβρικές μεθόδους, όπως αυτή των Ελαχίστων Τετραγώνων. Επιπλέον, οι αριθμητικές τεχνικές που έχουν αναπτυχθεί οδηγούν σε ατελείς λύσεις, πολλές φορές εγκλωβισμένες σε τοπικά ελάχιστα, με υψηλό βαθμό συσχέτισης μεταξύ συγκεκριμένων παραμέτρων και σε λύσεις μη ελεγχόμενες, όσον αφορά την αβεβαιότητα της εκτίμησης των παραμέτρων. Με στόχο να ξεπεραστούν τα προβλήματα αυτά, αναπτύσσεται μια εναλλακτική μέθοδος επίλυσης μη γραμμικών συστημάτων εξισώσεων (συνόρθωση). Η μέθοδος αυτή, βασίζεται σε αριθμητική – τοπολογική προσέγγιση και αναζήτηση στοιχείων πλέγματος Ν διαστάσεων, και είναι εμπνευσμένη από την μέθοδο εντοπισμού της θέσης ενός πλοίου με την βοήθεια των φάρων και άλλες χαμηλής ακρίβειας μεθόδους που χρησιμοποιούνται σε 2-D προσδιορισμό θέσης με βάση WiFi κλπ. Η διαδικασία περιλαμβάνει δύο στάδια. Αρχικά υπολογίζονται οι γεωμετρικοί τόποι των σημείων που επαληθεύουν την κάθε εξίσωση του συστήματος και στη συνέχεια προκύπτει η τελική λύση ως η κοινή τομή αυτών. Η αποτελεσματικότητα αυτής της μεθόδου έγκειται στο γεγονός ότι έχει την δυνατότητα να συνυπολογίζει τα σφάλματα των μετρήσεων και να βελτιστοποιεί την λύση με βάση αυτά, να επιτρέπει τον έλεγχο της ευαισθησίας της λύσης και να εξασφαλίζει πλήρως τον υπολογισμό του σχετικού μητρώου μεταβλητότητας – συμμεταβλητότητας των παραμέτρων. / At the present study a numerical-topological methology of solving systems of highly non-linear, redundant equations, deriving from observations of certain geophysical processes and geodetic data was examined. The motivation of developing this technique was to estimate the characteristic values of the magma source of the Santorini volcano during a slow-inflation episode. The adjustment of such systems cannot be based on conventional least-squares techniques, and is based on various numerical inversion techniques. Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solutions with poor error control. To overcome these problems, a numerical-topological, grid-search based technique in the RN space is proposed, a generalization and refinement of techniques used in some cases of low-accuracy 2-D positioning using Wi-fi etc. The basic concept is to define a grid in RN space which contains the true solution. In this grid the set of the estimated solution is mapped as the intersection of grid spaces of each observation. The efficiency of the proposed method is that it can incorporate weights of observations and optimize the solution based on them, and also it can compute variance-covariance matrices.

Tephra deposits are one of the possible outcomes of explosive volcanic eruptions and are the result of vertical settling of volcanic particles that have been expelled from the volcanic vent into the atmosphere, following magma fragmentation within the volcanic conduit. Tephra fallout represents the main volcanic hazard to populated areas and critical facilities. Therefore, it is crucial to better understand processes that lead to tephra transport, sedimentation and hazards. In this study, and based on detailed mapping and sampling of the tephra deposit of the 2450 BP Plinian eruption of Pululagua volcano (Ecuador), I investigate tephra deposits through a variety of approaches, including empirical and analytical modeling of tephra thickness and grain size data to infer important eruption source parameters (e.g. column height, total mass ejected, total grain size distribution of the deposit). I also use a statistical approach (smoothed bootstrap with replacement method) to assess the uncertainty in the eruptive parameters. The 2450 BP Pululagua volcanic plume dynamics were also explored through detailed grain size analysis and 1D modeling of tephra accumulation. Finally, I investigate the influence of particle shape on tephra accumulation on the ground through a quantitative and comprehensive study of the shape of volcanic ash. As the global need for energy is expected to grow in the future, many future natural hazard studies will likely involve the assessment of volcanic hazards at critical facilities, including nuclear power plants. I address the potential hazards from tephra fallout, pyroclastic flows and lahars for the Bataan Nuclear Power Plant (Philippines) posed by three nearby volcanoes capable of impacting the site during an explosive eruption. I stress the need for good constraints (stratigraphic analysis and events dating) on past eruptive events to better quantify the probability of future events at potentially active volcanoes, the need for probabilistic approaches in such volcanic hazard assessments to address a broad range of potential eruption scenarios, and the importance of considering coupled volcanic processes (e.g. tephra fallout leading to lahars) in volcanic hazard assessments.

The conventional approach for estimation of in-situ porosity is the combined use of neutron and density logs. These nuclear borehole measurements are influenced by fundamental petrophysical, fluid, and geometrical properties of the probed formation including saturating fluids, matrix composition, mud-filtrate invasion and shoulder beds. Advanced interpretation methods that include numerical modeling and inversion are necessary to reduce environmental effects and non-uniqueness in the estimation of porosity. The objective of this dissertation is two-fold: (1) to develop a numerical procedure to rapidly and accurately simulate nuclear borehole measurements, and (2) to simulate nuclear borehole measurements in conjunction with inversion techniques. Of special interest is the case of composite rock formations of sand-shale laminations penetrated by high-angle and horizontal (HA/HZ) wells. In order to quantify shoulder-bed effects on neutron and density borehole measurements, we perform Monte Carlo simulations across formations of various thicknesses and borehole deviation angles with the multiple-particle transport code MCNP. In so doing, we assume dual-detector tool configurations that are analogous to those of commercial neutron and density wireline measuring devices. Simulations indicate significant variations of vertical (axial) resolution of neutron and density measurements acquired in HA/HZ wells. In addition, combined azimuthal- and dip-angle effects can originate biases on porosity estimation and bed boundary detection, which are critical for the assessment of hydrocarbon reserves. To enable inversion and more quantitative integration with other borehole measurements, we develop and successfully test a linear iterative refinement approximation to rapidly simulate neutron, density, and passive gamma-ray borehole measurements. Linear iterative refinement accounts for spatial variations of Monte Carlo-derived flux sensitivity functions (FSFs) used to simulate nuclear measurements acquired in non-homogeneous formations. We use first-order Born approximations to simulate variations of a detector response due to spatial variations of formation energy-dependent cross-section. The method incorporates two- (2D) and three-dimensional (3D) capabilities of FSFs to simulate neutron and density measurements acquired in vertical and HA/HZ wells, respectively. We calculate FSFs for a wide range of formation cross-section variations and for borehole environmental effects to quantify the spatial sensitivity and resolution of neutron and density measurements. Results confirm that the spatial resolution limits of neutron measurements can be significantly influenced by the proximity of layers with large contrasts in porosity. Finally, we implement 2D sector-based inversion of azimuthal logging-while-drilling (LWD) density field measurements with the fast simulation technique. Results indicate that inversion improves the petrophysical interpretation of density measurements acquired in HA/HZ wells. Density images constructed with inversion yield improved porosity-feet estimations compared to standard and enhanced compensation techniques used commercially to post-process mono-sensor densities. / text