Induction logging is a well-developed geophysical method with multiple applications. It has been used extensively in academic research as well as in industry. Induction logging is a controlled-source electromagnetic (CSEM) exploration method. It characterizes geologic formations through the measurements of induced magnetics fields. The purpose of this research project is to better understand induction logs and the effects fractured geologic formations have on them. Computer modeling is used to generate synthetic logs for analysis in this research project. The original program required certain modifications to fit this research project’s goals. The computer program, Seatem is based on the finite element method. It is able to use a layered Earth model that is the basis for the synthetic log analysis. The geologic layers in this model are assigned various conductivities and also have the option of being assigned a geologic roughness value. The geologic roughness parameter is used to simulate fractured rocks in the subsurface. The synthetic logs generated by the modified Seatem program produce some encouraging results. In a thinning bed analysis, it is shown that as a conductive bed is thinned in a step-size procedure, the resulting induction log underestimates the actual conductivity of the layer. It also shows that the boundary layers around the thinned layer are better characterized in the log. The next synthetic log was calculated for a fractured resistive layer. This log shows that as the layer becomes more fractured, there is an increase in the underestimation of the actual conductivity. This layer is then thinned down and another synthetic log is calculated. The resulting log shows similar traits to the thinning bed analysis and shows an underestimation of the apparent conductivity. The same procedure is performed for a fractured conductive layer. The analysis produce similar results; however, that are much more drastic changes in the induction logs. As the unit becomes more fractured, the apparent conductivity is lower then the actual conductivity, as in the resistive case. However, smaller increases in the roughness parameter produced more severe underestimations than larger increases in the roughness parameter did for the resistive layer.

Controlled-Source Electromagnetics (CSEM) is a method that has been used since the 1980’s in the marine environment for determining electrical properties of the subsurface. Receivers on the seafloor collect total electric and magnetic fields which are produced as a result of interaction of the transmitter generated primary fields with the seawater and subsurface. Badea et al. (2001) coded an existing algorithm for solving Maxwell’s equations. This finite element 3D forward modeling algorithm is used to simulate CSEM experiments. The objective of the present study is to model the changes in electromagnetic response for a resistive disk and a more geometrically complex structure, which are rough approximations of hydrocarbon reservoirs. The parameters that are varied in studying these subsurface structures are the disk radius, disk depth, the transmitter frequency, the transmitter location, and the structure orientation.The results showed that a disk of finite radius behaves similar to an infinite disk at short range and grades into double half-space behavior at longer ranges. The frequency of the transmitter must be tuned to the disk depth as certain frequencies will penetrate too shallow or too deep to probe the disk. Moving the transmitter away from the receivers causes a decrease in signal strength, but exhibits a greater capacity to distinguish between the double half-space and infinite disk scenarios. The disk was then replaced by a more complex structure. To determine if the 3D nature of the structure may be located a study was undertaken to probe the structure from different perspectives using different transmitter locations and azimuths. It is determined that the 3D nature of the structure could not be observed until the structure’s thickness is sufficiently large.The goal of the study is to better understand the effect of subsurface parameters on the total fields and show the usefulness of the 3D forward modeling code. Understanding the relationships between these parameters and the resulting signals is important in terms of setting up a real experiment. Marine CSEM studies are costly and using a valuable tool such as an accurate finite element 3D forward modeling algorithm may save time and money.

Controlled-Source Electromagnetics (CSEM) is a method that has been used since the 1980’s in the marine environment for determining electrical properties of the subsurface. Receivers on the seafloor collect total electric and magnetic fields which are produced as a result of interaction of the transmitter generated primary fields with the seawater and subsurface. Badea et al. (2001) coded an existing algorithm for solving Maxwell’s equations. This finite element 3D forward modeling algorithm is used to simulate CSEM experiments. The objective of the present study is to model the changes in electromagnetic response for a resistive disk and a more geometrically complex structure, which are rough approximations of hydrocarbon reservoirs. The parameters that are varied in studying these subsurface structures are the disk radius, disk depth, the transmitter frequency, the transmitter location, and the structure orientation.The results showed that a disk of finite radius behaves similar to an infinite disk at short range and grades into double half-space behavior at longer ranges. The frequency of the transmitter must be tuned to the disk depth as certain frequencies will penetrate too shallow or too deep to probe the disk. Moving the transmitter away from the receivers causes a decrease in signal strength, but exhibits a greater capacity to distinguish between the double half-space and infinite disk scenarios. The disk was then replaced by a more complex structure. To determine if the 3D nature of the structure may be located a study was undertaken to probe the structure from different perspectives using different transmitter locations and azimuths. It is determined that the 3D nature of the structure could not be observed until the structure’s thickness is sufficiently large.The goal of the study is to better understand the effect of subsurface parameters on the total fields and show the usefulness of the 3D forward modeling code. Understanding the relationships between these parameters and the resulting signals is important in terms of setting up a real experiment. Marine CSEM studies are costly and using a valuable tool such as an accurate finite element 3D forward modeling algorithm may save time and money.

Falkenberg area is located in southwest Sweden formed in the Sveconorwegian orogen and contains an extremely complex geological structure. Multiple geophysical datasets have been acquired and together with available petrophysical information, models corresponding to the subsurface geological structures were generated. The collected data comprise ground magnetic, AMT (Audio Magnetotelluric) and RMT (Radio Magnetotelluric) data. The available airborne magnetic and ground gravity data acquired by the Geological Survey of Sweden (SGU) as well as the reflection seismic section from a study made by Uppsala University further aids in obtaining substantially improved interpretation of the geometry of the structures along the AMT profile. The principal objective of this profile was to delineate and map the possible deformation zone crossed by the profile. The AMT study was expected to complement existing geophysical data and improve existing interpretations. The Ullared deformation zone contains decompressed eclogite facies rocks. The presented results were obtained by comparison of different geophysical methods along the profile. The susceptibility model and resistivity model show that eclogites have higher resistivity and susceptibility than the surrounding structures. However use of the Occam type of inversion on the AMT data, makes the resistivity model smoother than the susceptibility model and as a results it is difficult to estimate the dip of the structures. The AMT profile and the seismic section show the same dip direction (NE) for the eclogite bearing structures although due to the smoothing in the AMT model the dips seen in the seismic section cannot be recovered in the resistivity model.

<p dir="ltr">The Cascadia margin in the Pacific Northwest of US is characterized by the subduction of the young and warm Juan De Fuca beneath the North American plate. This region shows strong correlations in spatial heterogeneities in geophysical observations such as thickness of low shear wave velocity zones in the lower crust, tremors distribution, intraslab seismicity, topography, uplift rates, and Bouguer gravity anomalies. In this thesis, both 3D and 2.5D forward gravity modeling have been conducted to understand the composition of the materials at ~20-40 km along the Cascadia subduction margin, that can explain the spatial heterogeneities by linking them together.</p>

Forward and inverse modeling studies of the relationship between tree ring width and bivariate climate are performed using a model called VS-Lite. The monthly time-step model incorporates two simple but realistic nonlinearities in its description of the transformation of climate variability into ring width index. These features ground VS-Lite in scientific principles and make it more complex than empirically-derived statistical models commonly used to simulate tree ring width. At the same time, VS-Lite is vastly simpler and more efficient than pre-existing numerical models that simulate detailed biological aspects of tree growth. A forward modeling validation study shows that VS-Lite simulates a set of observed chronologies across the continental United States with comparable or better skill than simulations derived from a standard, linear regression based approach. This extra skill derives from VS-Lite's basis in mechanistic principles, which makes it more robust than the statistical methodology to climatic nonstationarity. A Bayesian parameterization approach is also developed that incorporates scientific information into the choice of locally optimal VS-Lite parameters. The parameters derived using the scheme are found to be interpretable in terms of the climate controls on growth, and so provide a means to guide applications of the model across varying climatologies. The first reconstructions of paleoclimate that assimilate scientific understanding of the ring width formation process are performed using VS-Lite to link the proxy data to potential climate histories. Bayesian statistical methods invert VS-Lite conditional on a given dendrochronolgy to produce probabilistic estimates of local bivariate climate. Using VS-Lite in this manner produces skillful estimates, but does not present advantages compared another set of probabilistic reconstructions that invert a simpler, linear, empirical forward model. This result suggests that future data-assimilation based reconstructions will need to integrate as many data sources as possible, both across space and proxy types, in order to benefit from information provided by mechanistic models of proxy formation.

Processes that take place in the Earth’s mantle are not accessible to direct observation. Natural samples of mantle material that have been transported to the surface as xenoliths provide useful information on phase relations and compositions of phases at the pressure and temperature conditions of each rock fragment. In the past, considerable effort has been devoted by petrologists to investigate upper mantle processes experimentally. Results of high temperatures, high pressure experiments have provided insight into lower crust-upper mantle phase relations as a function of temperature, pressure and composition. However, the attainment of equilibrium in these experiments, especially in complex systems, may be very difficult to test rigorously. Furthermore, experimental results may also require extrapolation to different pressures, temperatures or bulk compositions. More recently, thermodynamic modeling has proved to be a very powerful approach to this problem, allowing the deciphering the physicochemical conditions at which mantle processes occur. On the other hand, a comprehensive thermodynamic model to investigate lower crust-upper mantle phase assemblages in complex systems does not exist. ¶ In this study, a new thermodynamic model to describe phase equilibria between silicate and/or oxide crystalline phases has been derived. For every solution phase the molar Gibbs free energy is given by the sum of contributions from the energy of the end-members, ideal mixing on sites, and excess site mixing terms. It is here argued that the end-member term of the Gibbs free energy for complex solid solution phases (e.g. pyroxene, spinel) has not previously been treated in the most appropriate manner. As an example, the correct expression of this term for a pyroxene solution in a general (Na-Ca-Mg-Fe2+-Al-Cr-Fe3+-Si-Ti) system is presented and the principle underlying its formulation for any complex solution phase is elucidated.¶ Based on the thermodynamic model an algorithm to compute lower crust-upper mantle phase equilibria for subsolidus mineral assemblages as a function of composition, temperature and pressure has been developed. Included in the algorithm is a new way to represent the total Gibbs free energy for any multi-phase complex system. At any given temperature and pressure a closed multi-phase system is at its equilibrium condition when the chemical composition of the phases present in the system and the number of moles of each are such that the Gibbs free energy of the system reaches its minimum value. From a mathematical point of view, the determination of equilibrium phase assemblages can, in short, be defined as a constrained minimization problem. To solve the Gibbs free energy minimization problem a ‘Feasible Iterate Sequential Quadratic Programming’ method (FSQP) is employed. The system’s Gibbs free energy is minimized under several different linear and non-linear constraints. The algorithm, coded as a highly flexible FORTRAN computer program (named ‘Gib’), has been set up, at the moment, to perform equilibrium calculations in NaO-CaO-MgO-FeO-Al2O3-Cr2O3-Fe2O3- SiO2-TiO2 systems. However, the program is designed in a way that any other oxide component could be easily added.¶ To accurately forward model phase equilibria compositions using ‘Gib’, a precise estimation of the thermodynamic data for mineral end-members and of the solution parameters that will be adopted in the computation is needed. As a result, the value of these parameters had to be derived/refined for every solution phase in the investigated systems. A computer program (called ‘GibInv’) has been set up, and its implementation is here described in detail, that allows the simultaneous refinement of any of the end-member and mixing parameters. Derivation of internally consistent thermodynamic data is obtained by making use of the Bayesian technique. The program, after being successfully tested in a synthetic case, is initially applied to pyroxene assemblages in the system CaO-MgO-FeO-Al2O3-SiO2 (i.e. CMFAS) and in its constituent subsystems. Preliminary results are presented.¶ The new thermodynamic model is then applied to assemblages of Ca-Mg-Fe olivines and to assemblages of coexisting pyroxenes (orthopyroxene, low Ca- and high Ca clinopyroxene; two or three depending on T-P-bulk composition conditions), in CMFAS system and subsystems. Olivine and pyroxene solid solution and end-member parameters are refined, in part using ‘GibInv’ and in part on a ‘trial and error’ basis, and, when necessary, new parameters are derived. Olivine/pyroxene phase relations within such systems and their subsystems are calculated over a wide range of temperatures and pressures and compare very favorably with experimental constraints.

Presence of cultural refuse has long posed a serious challenge to meaningful geological interpretation of near surface controlled–source electromagnetic data (CSEM). Cultural refuse, such as buried pipes, underground storage tanks, unexploded ordnance, is often highly conductive and magnetically permeable. Interpretation of the CSEM response in the presence of cultural noise requires an understanding of electromagnetic field diffusion and the effects of anomalous highly conductive and permeable structures embedded in geologic media. While many numerical techniques have been used to evaluate the response of three dimensional subsurface conductivity distributions, there is a lack of approaches for modeling the EM response incorporating variations in both subsurface conductivity σ and relative permeability μr. In this dissertation, I present a new three dimensional edge–based finite element (FE) algorithm capable of modeling the CSEM response of buried conductive and permeable targets. A coupled potential formulation for variable μ using the vector magnetic potential A and scalar electric potential V gives rise to an ungauged curl–curl equation. Using reluctivity (v=1/mu ), a new term in geophysical applications instead of traditional magnetic susceptibility, facilitates a separation of primary and secondary potentials. The resulting differential equation is solved using the finite element method (FEM) on a tetrahedral mesh with local refinement capabilities. The secondary A and V potentials are expressed in terms of the vector edge basis vectors and the scalar nodal basis functions respectively. The finite element matrix is solved using a Jacobi preconditioned QMR solver. Post processing steps to interpolate the vector potentials on the nodes of the mesh are described. The algorithm is validated against a number of analytic and multi dimensional numeric solutions. The code has been deployed to estimate the influence of magnetic permeability on the mutual coupling between multiple geological and cultural targets. Some limitations of the code with regards to speed and performance at high frequency, conductivity and permeability values have been noted. Directions for further improvement and expanding the range of applicability have been proposed.

Understanding and modeling seismic wave propagation is important in regional and exploration seismology. Ray tracing is a powerful and popular method for this purpose. Wavefront construction (WFC) method handles wavefronts instead of individual rays, thereby controlling proper ray density on the wavefront. By adaptively controlling rays over a wavefront, it efficiently models wave propagation. Algorithms for a quasi-P wave wavefront construction method and a new coordinate system used to generate wavefront construction mesh are proposed and tested for numerical properties and modeling capabilities. Traveltimes, amplitudes, and other parameters, which can be used for seismic imaging such as migrations and synthetic seismograms, are computed from the wavefront construction method. Modeling with wavefront construction code is applied to anisotropic media as well as isotropic media. Synthetic seismograms are computed using the wavefront construction method as a new way of generating synthetics. To incorporate layered velocity models, the model based interpolation (MBI) ray tracing method, which is designed to take advantage of the wavefront construction method as well as conventional ray tracing methods, is proposed and experimental codes are developed for it. Many wavefront construction codes are limited to smoothed velocity models for handling complicated problems in layered velocity models and the conventional ray tracing methods suffer from the inability to control ray density during wave propagation. By interpolating the wavefront near model boundaries, it is possible to handle the layered velocity model as well as overcome ray density control problems in conventional methods. The test results revealed this new method can be an effective modeling tool for accurate and effective computing.

The four pillars of material science and engineering namely structure, processing, properties and performance form the so-called material paradigm. At the heart of the material paradigm is materials characterization, which is used to measure and identify the relationships. Materials Characterization typically reconstructing the conditions giving rise to a measurement, a classic inverse problem. The solutions of these inverse problems are under or over determined and not unique. The solutions of these inverse problems can be greatly improved if accurate forward models exist for these characterization experiments. In this thesis, we will be focusing of developing forward models for electron diffraction modalities. Specifically, four different forward models for electron diffraction, namely the Electron Backscatter Diffraction, Electron Channeling Patterns, Precession Electron Diffraction and Transmission kikuchi Diffraction modalities are presented. Further, these forward models are applied to important materials characterization problems, including diffraction pattern indexing using the dictionary approach and forward model based orientation refinement. Finally, a novel pole figure inversion algorithm using the cubochoric representation and model based iterative reconstruction is also presented.