Boundary value problems required for modelling plane wave propagation in electrically anisotropic and inhomogeneous media relevant to the surface impedance methods in electromagnetic geophysics are formally posed and treated. For a homogeneous TM-type wave propagating in a half space with both vertical and horizontal inhomogeneities where the TM-type wave is aligned with one of the elements of the conductivity tensor, it is shown using exact solutions that the shearing term in the homogeneous Helmholtz equation for inclined anisotropic media: [Equation 1], unequivocally vanishes and solutions need only be sought to the homogeneous Helmholtz equation for biaxial media: [Equation 2]. This implies that those problems posed with an inclined uniaxial conductivity tensor can be identically stated with a fundamental biaxial conductivity tensor, provided that the conductivity values are the reciprocal of the diagonal terms from the Euler rotated resistivity tensor: [Equation 3], [Equation 4], [Equation 5]. The applications of this consequence for numerical methods of solving arbitrary two-dimensional problems for a homogeneous TM-type wave is that they need only to approximate the homogeneous Helmholtz equation and neglect the corresponding shearing term. The self-consistent impedance method, a two-dimensional finite-difference approximation based on a network analogy, is demonstrated to accurately solve for problems with inclined uniaxial anisotropy using the fundamental biaxial anisotropy equivalence. The problem of a homogeneous plane wave at skew incidence upon an inclined anisotropic half space is then formally treated. In the half space, both TM- and TE-type waves are coupled and the linearly polarised incident TM- and TE-type waves reflect TE- and TM-type components. Equations for all elements of the impedance tensor are derived for both TM- and TE-type incidence. This offers potential as a method of predicting the direction of anisotropic strike from tensor impedance measurements in sedimentary environments.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20921号 / 理博第4373号 / 新制||理||1628(附属図書館) / 京都大学大学院理学研究科地球惑星科学専攻 / (主査)教授 大志万 直人, 准教授 吉村 令慧, 教授 中西 一郎 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Radio magnetotellurics (RMT), crosshole ground penetrating radar (GPR), and crosshole electrical resistance tomography (ERT) were applied in a range of hydrogeological applications where geophysical data could improve hydrogeological characterization. A profile of RMT data collected over highly resistive granite was used to map subhorizontal fracture zones below 300m depth, as well as a steeply dipping fracture zone, which was also observed on a coinciding seismic reflection profile. One-dimensional inverse modelling and 3D forward modelling with displacement currents included were necessary to test the reliability of features found in the 2D models, where the forward models did not include displacement currents and only lower frequencies were considered. An inversion code for RMT data was developed and applied to RMT data with azimuthal electrical anisotropy signature collected over a limestone formation. The results indicated that RMT is a faster and more reliable technique for studying electrical anisotropy than are azimuthal resistivity surveys. A new sequential inversion method to estimate hydraulic conductivity fields using crosshole GPR and tracer test data was applied to 2D synthetic examples. Given careful surveying, the results indicated that regularization of hydrogeological inverse problems using geophysical tomograms might improve models of hydraulic conductivity. A method to regularize geophysical inverse problems using geostatistical models was developed and applied to crosshole ERT and GPR data collected in unsaturated sandstone. The resulting models were geologically more reasonable than models where the regularization was based on traditional smoothness constraints. Electromagnetic geophysical techniques provide an inexpensive data source in estimating qualitative hydrogeological models, but hydrogeological data must be incorporated to make quantitative estimation of hydrogeological systems feasible.

Ceramic-matrix composites of alumina and silicon carbide whiskers have recently found novel commercial application as electromagnetic absorbers. However, a detailed understanding of how materials issues influence the composite electrical response, which underpins this application, has been absent until now. In this project, such composites were electrically measured over a wide range of conditions and modeled in terms of various aspects of the microstructure in order to understand how they work. For this purpose, three types of composites were made by different methods from the same set of ceramic powder blends loaded with different volume fractions of whiskers. In doing so, the interfaces between whiskers, the preferred orientations of whiskers, and the structure of electrically-connected whisker clusters were varied; the whisker aspect-ratio distributions were the same for all methods. At the electrode interfaces, Schottky barriers at the junctions of the electrically-percolating wide-bandgap semiconductor whiskers on the surface were responsible for a significant portion of the total measured impedance. The associated electrical response was studied on the microscopic and macroscopic level, and the gap between these different scales was bridged. Also, a modeling approach was developed for the non-linear behavior of the composite which results from these barriers. In regards to the whiskers within the composite bulk, the effects of various factors on the wide-band frequency dependence of the dielectric response and dc conductivity were explained and contextualized for the electromagnetic absorber application. Such factors include whisker preferred orientation, electrical percolation and cluster structure, the interfaces between electrically-connected SiC whiskers, and porosity. A quantitative correlation between the anisotropy of the microstructure and that of the conductivity was found, and was understood in terms of the interfacial SiC-Al2O3-SiC conduction mechanism. This behavior was shown to differ from the behavior commonly observed for other disordered mixtures of relatively conductive particles dispersed inside insulating polymer hosts. A description of this new mechanism was developed based on an observed correlation between the temperature dependencies of the static and radio-frequency electrical responses. Also, the aforementioned non-linear response model was expanded upon to describe conduction through and across electrically-percolated clusters. The model demonstrates how loading and interface behavior influence the topology and the strength of the non-linear response of the clusters.

During this thesis, it has been proved that the electrical conductivity of multilayered and electrically anisotropic carbon fiber materials can be expressed by an equivalent second order tensor, which is equal to sum of each layer’s electrical conductivity tensor. The aforementioned equivalent electrical conductivity tensor is valid assuming that the material’s thickness is negligible compared to the other dimensions of the body. The mathematical expression for the prediction of the electrical conductivity of a multilayered material for any stacking sequence, is based on the electric current conservation, and was validated using different methods. Each layer’s electrical conductivity was experimentally studied at the two principal directions. Transverse to the fibers’ direction, an empirical model was developed for the prediction of the electrical conductivity as a function of the layer’s thickness, of the fibre volume fraction and of temperature. All cases involved the study of multidirectional and unidirectional carbon fiber materials without the presence of matrix (porous form – CF preform) as well as in the presence of polymeric matrix (CFRP). The validation of the equivalent tensor was achieved through three different ways: a) through the measurement of the electric resistance, for various stacking sequences, b) through the Joule heating effect, by recording and comparing the developing temperature field to the respective numerically calculated, c) through 3D numerical models which approximate the analytical solution of the 2D domain problem. Moreover using the finite difference method, certain electrothermal models were developed in order to study the temperature field for different stacking sequences. The electrical problem can be expressed by an elliptic PDE, for the case where the material is electrically anisotropic and homogeneous, or non-homogeneous. On the other hand, the transient heat transfer problem involves the case where the material is thermally anisotropic and homogeneous. Using the equivalent tensor, the 3D domain problem is simplified to a 2D domain problem resulting in less computational requirements for the solution of the problem. The present research study could be used in a plethora of application, such as the development of carbon fibre reinforced heating elements (direct heating CFRP molds) as well as damage detection in multidirectional composite materials with electrical conductive reinforcement. / Κατά τη διάρκεια της παρούσας διδακτορική διατριβής, αποδείχθηκε ότι η ηλεκτρική αγωγιμότητα των πολύστρωτων και ηλεκτρικά ανισότροπων υλικών με ίνες άνθρακα, μπορεί να εκφραστεί από έναν ισοδύναμο τανυστή δεύτερης τάξης, ο οποίος είναι το άθροισμα των τανυστών κάθε στρώσης. Ο ισοδύναμος τανυστής ισχύει υποθέτοντας ότι το πάχος συγκριτικά με τις υπόλοιπες διαστάσεις του υλικού είναι πολύ μικρό. Η μαθηματική έκφραση με την οποία μπορεί να προβλεφθεί η ηλεκτρική αγωγιμότητα ενός πολύστρωτου υλικού για οποιαδήποτε αλληλουχία στρώσεων αποδείχτηκε με συστηματικό τρόπο και βασίζεται στην αρχή διατήρησης του ηλεκτρικού φορτίου. Η ηλεκτρική αγωγιμότητα κάθε στρώσης μελετήθηκε πειραματικά στις δύο κύριες διευθύνσεις. Κάθετα στη διεύθυνση των ινών αναπτύχθηκε ένα εμπειρικό μοντέλο πρόβλεψης της ηλεκτρικής αγωγιμότητας συναρτήσει του πάχους της στρώσης, της περιεκτικότητας σε ίνες άνθρακα και της θερμοκρασίας. Σε όλες τις περιπτώσεις μελετήθηκαν πολύστρωτα υλικά ινών άνθρακα χωρίς μήτρα (πορώδης μορφή-CF preforms) και με πολυμερική μήτρα (CFRPs). Η επιβεβαίωση της εγκυρότητας του ισοδύναμου τανυστή έγινε με τρεις διαφορετικούς τρόπους: α) μέσω μετρήσεων της ηλεκτρικής αντίστασης, για διαφορετικές αλληλουχίες στρώσεων, β) μέσω του φαινομένου Joule, καταγράφοντας και συγκρίνοντας το αναπτυσσόμενο θερμοκρασιακό πεδίο με το θερμοκρασιακό πεδίο που υπολογίζεται αριθμητικά, γ) μέσω τρισδιάστατων αριθμητικών μοντέλων όπου τείνουν στην αναλυτική λύση του δισδιάστατου προβλήματος. Στη συνέχεια αναπτύχτηκαν ηλεκτροθερμικά μοντέλα με τη μέθοδο των πεπερασμένων διαφορών με σκοπό τη μελέτη του θερμοκρασιακού πεδίου για διαφορετικές αλληλουχίες στρώσεων. Το ηλεκτρικό πρόβλημα εκφράζεται από μία ελλειπτική διαφορική εξίσωση όπου το υλικό είναι ηλεκτρικά ανισότροπο και ομογενές ή μη ομογενές ενώ το θερμικό πρόβλημα είναι θερμικά ανισότροπο και ομογενές. Χρησιμοποιώντας τον ισοδύναμο τανυστή το τρισδιάστατο πρόβλημα μετατρέπεται σε ένα δισδιάστατο πρόβλημα με αποτέλεσμα να απαιτούνται λιγότεροι πόροι για την επίλυση του προβλήματος. Η συγκεκριμένη εργασία μπορεί να χρησιμοποιηθεί σε μία πληθώρα εφαρμογών όπως στην ανάπτυξη και στη λειτουργία θερμαινόμενων στοιχείων ενισχυμένων με ίνες άνθρακα (καλούπια όπου το θερμαντικό στοιχείο το αποτελούν οι ίνες άνθρακα) αλλά και στην ανίχνευση βλάβης συνθέτων υλικών με αγώγιμη ενίσχυση.

The anisotropy of the Biscayne Aquifer which serves as the source of potable water for Miami-Dade County was investigated by applying geophysical methods. Electrical resistivity imaging, self potential and ground penetration radar techniques were employed in both regional and site specific studies. In the regional study, electrical anisotropy and resistivity variation with depth were investigated with azimuthal square array measurements at 13 sites. The observed coefficient of electrical anisotropy ranged from 1.01 to 1.36. The general direction of measured anisotropy is uniform for most sites and trends W-E or SE-NW irrespective of depth. Measured electrical properties were used to estimate anisotropic component of the secondary porosity and hydraulic anisotropy which ranged from 1 to 11% and 1.18 to 2.83 respectively. 1-D sounding analysis was used to models the variation of formation resistivity with depth. Resistivities decreased from NW (close to the margins of the everglades) to SE on the shores of Biscayne Bay. Porosity calculated from Archie's law, ranged from 18 to 61% with higher values found along the ridge. Higher anisotropy, porosities and hydraulic conductivities were on the Atlantic Coastal Ridge and lower values at low lying areas west of the ridge. The cause of higher anisotropy and porosity is attributed to higher dissolution rates of the oolitic facies of the Miami Formation composing the ridge. The direction of minimum resistivity from this study is similar to the predevelopment groundwater flow direction indicated in published modeling studies. Detailed investigations were carried out to evaluate higher anisotropy at West Perrine Park located on the ridge and Snapper Creek Municipal well field where the anisotropy trend changes with depth. The higher anisotropy is attributed to the presence of solution cavities oriented in the E-SE direction on the ridge. Similarly, the change in hydraulic anisotropy at the well field might be related to solution cavities, the surface canal and groundwater extraction wells.

Northeastern British Columbia was occupied by the Cordilleran (CIS) and the Laurentide (LIS) ice sheets, however, the timing and extent remains contentious. The late Quaternary and Holocene history of this area is examined by exploring geomorphic, stratigraphic, geochemical and geochronologic components of glacial, deglacial, paraglacial and non-glacial landsystems. New tools, such as GIS, LiDAR, and new geochronologic methods, such as optical dating are used to understand the Quaternary geology and geomorphology of the region. Bedrock topography represents the base of the Quaternary section and modelling shows that paleovalleys, common in this region, host extensive Neogene sedimentary records. Stratigraphies from the Murray and Pine valleys indicate glaciation prior to the Mid-Wisconsinan (MIS 3) and during the Late Wiconsinan (MIS 2). Glacial landforms record Late Wisconsinan ice-sheet coalescence and reflect the complex interaction of the LIS and CIS margins. During deglaciation, the LIS and CIS separated and glacial Lake Peace (GLP) formed. Shoreline features enable reconstruction of lake and ice configurations. Four phases of GLP are preserved. Optical ages from Phase II indicate GLP occupied the area some time between ca. 16 – 14 ka yrs ago. The apparent tilt on the shorelines provides a measure of isostatic adjustments and suggests asynchronous retreat of first the LIS, then the CIS. The transition from paraglacial to boreal conditions was driven by climate change and is recorded by vegetation sucession and cessation of paraglacial processes. Optical ages from stabilized dunes and radiocarbon ages from organics date the transition between 12 – 11.5 ka yrs ago with full boreal conditions established by 10 ka yrs ago. The Holocene is dominated by erosional processes, however some systems are aggrading. A case study on a floodplain demonstrates that resistivity (Ohmmapper) surveys provide a grain-size proxy to suppliant GPR studies, which is essential for geophysical fluvial architectural analysis. In the study, the discrepancy between planform style (classic meander model) and subsurface geophysical surveys (indicative of vertical accretion associated with braided and wandering fluvial styles) reiterates cautions that planform may not always be a functions of depositional process and one may not be used to predict the other. / Graduate / 0372 / 0373 / 0368