Quantitative analysis of multi-component borehole electromagnetic induction responses using anisotropic forward modeling and inversion

In this thesis, I examine both new and established methods to interpret low-frequency borehole electromagnetic induction responses. Specifically, I use numerical modeling and inversion techniques to characterize multi-component electromagnetic fields in 1-D and 2-D isotropic and anisotropic media.; The first contribution is a numerical modeling study that illuminates the effects of tool configurations and geological variation on the multi-component induction response in fractured and anisotropic media. I provide numerical data on tool-specific responses to thin conductors as well as to more realistic near-borehole multi-layer models.; Next, I investigate the feasibility of inverting multi-component EM induction data assuming a 1-D transversely isotropic earth model. I have developed an efficient inversion scheme that solves for the anisotropic electrical properties of the earth with minimal required a priori information. The inversion algorithm is unique in that it stabilizes the ill-posed EM problem using linear inequality constraints and trust region methods based on physical parameter bounds.; I also present a simple but effective algorithm for the determination of electrical property boundaries in a 1-D medium. In order to efficiently solve the 1-D transversely isotropic EM inverse problem, the number of layers and an estimate of their positions must be known. To achieve the necessary accuracy in estimating 1-D layer boundaries, multi-component magnetic field derivatives are computed and correlated.; Finally, I investigate methods for appraisal of 1-D EM inverse solutions. I provide resolution tests to determine the limits of the 1-D inversion for imaging thinly-layered formations with large conductivity contrasts and high electrical anisotropy coefficients. I also demonstrate that there are practical limitations for characterizing 1-D cross-bedded and 2-D isotropic structures with transversely isotropic 1-D inversion. I then compare three methods for determining model uncertainty and solution fitness. The first two methods estimate uncertainty based on a single nonlinear inversion and are linear approximations to the full nonlinear model uncertainties. The third method implements a Monte Carlo simulation technique to determine model uncertainty for a statistical population of nonlinear inverse solutions with random error perturbations.