Geophysical inverse theory applied to reconstruction of large-scale heterogeneities in electrical conductivity of earth's mantle.

This thesis addresses the non-linear ill-posed inverse problems of reconstructing the three-dimensional distribution of electrical conductivity in Earth's mantle. This problem has never previously been fully attacked. The major objective of this thesis is to develop a methodology allowing to resolve any large-scale three-dimensional inhomogeneities in Earth's mantle based on a regularised inversion of electromagnetic field data. We generalise the global three-dimensional forward problem of electromagnetic induction in the frequency domain for arbitrary sources, and solve it in a linear algebraic formulation. We develop the data sensitivities analysis based on the generalised forward problem, and derive the analytic and numerical expressions for the Jacobian and the derivative of the regularised least squares penalty functional. This allows us to set up a non-linear conjugate gradient inverse solution. In doing so, we parameterize the model space by layered spherical harmonics. This inverse solution is tested on a series of checkerboard experiments; on this basis, we discuss spatial resolution of our analysis at different depths in the mantel. This methodology is then applied to the most current low-frequency global observatory data set, and models are obtained satisfying the data statistically well. We discuss the features of these models and the implications of our experiments. We also plot and compare the corresponding magnetic fields and responses at the Earth's surface, and provide suggestions for future directions of research