Airborne electromagnetic (AEM) surveys provide vast amounts of data over remote areas that may not be ground accessible. Typical surveys may contain hundreds of thousands of data points sampled every few meters. Quantitative interpretation of this large amount of data is computationally very time consuming and challenging.; This dissertation presents two methods, based on the integral equation (IE), to invert AEM data in three dimensions. One inversion method is based on the localized quasi-linear (LQL) approximate inversion, which I have modified so the inverse and forward operators only include a small area of the inversion domain. This is possible for airborne data interpretation because the footprint, or region that affects the response of each measurement, is relatively small relative to the typical survey area. This modification to the approximate LQL inversion enables interpretation of full airborne surveys using tens of thousands of data points and hundreds of thousands of cells. The method is tested on both synthetic and field data, each showing accurate results.; The second interpretation method is a rigorous inversion, which uses the full accuracy of the IE method. It is based on the iterative solution of the domain and field equations, while keeping the inverse operator linear to speed the inversion process. The domain equation is solved using a preconditioned form of the complex generalized minimum residual solver to guarantee convergence. This inversion includes the footprint method developed for the LQL inversion. It has also been tested on both synthetic and field data, demonstrating excellent results with respect to both the speed and accuracy of the method.; With present computing power, the rigorous method is intended to interpret subsets of AEM surveys. The LQL inversion can be applied to entire survey areas, but the accuracy is limited by the approximate nature of the inversion. These two methods pair nicely, with the LQL method used to identify geologically significant AEM anomalies among the hundreds of anomalies that may be observed with a survey. The rigorous inversion is then used to further delineate these anomalies to provide more accurate geological interpretation.; These two methods are then extended to include areas with hilly or mountainous terrain. Including the effects of terrain are important, since the response of the topography may be much greater than the response of the geology. I present an algorithm that incorporates these effects into both inversion schemes, allowing one to "see" through terrain and discover the underlying geology. The algorithm is shown to work well on a synthetic text example.; Other phenomenon such as induced polarization (IP) also affect airborne data. Both the LQL and rigorous inversion algorithms were modified to include inversion for complex conductivity. I use a field survey with both a known IP response from ground based methods and an airborne survey to test this interpretation method. The interpretation of the ground based method and the airborne data inversion are shown to correlate. These encouraging results open the door to more research in this direction.
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