T he si s Improving potential - field processing and inversion through the use of gradient . D . T measurements and data - adaptive models

This thesis focuses on two distinct, yet complementary topics. First, I examine the use of observed gradient and total-field data acquired from aeromagnetic surveys as independent data sets for quantitative interpretation. Second, I develop a more efficient means of processing and inverting these large data sets. The first topic stems from the recent use of multiple magnetometers, which allows for measurements of magnetic gradients and minimizes diurnal variation and other common-mode noise. I develop equivalent source and 3D inversion algorithms for joint processing and inversion of total-field and gradient data, respectively. These approaches treat the observed gradients as an additional and independent data set rather than just as supplemental information. The direct result of joint processing is a set of enhanced data with increase information content and a higher signal-to-noise ratio. The method diminishes high-frequency noise and accentuates mid-frequency signals and produces a data set with more resolving power than total-field data alone. Likewise, the contribution of gradients in inversion leads to a better resolved 3D susceptibility distribution. The second topic addresses the fact that equivalent source processing and 3D inversion in potential-field methods involve large and dense coefficient matrices that often exceed the limit of physical memory in commonly available computers. Repeated matrix-vector multiplications during processing or inversion require an immense amount of CPU power. This poses a significant challenge when solving largescale problems and can render many problems intractable. To overcome these limitations, I have developed a new computational approach for this class of problems by combining an adaptive quadtree or octree model discretization and wavelet transforms on a re-ordered parameter set. To maintain resolution, the adaptive mesh discretizes the model region by starting with large cells and splitting the region into smaller cells