Occam2: Regularized inversion to generate smooth, two-dimensional resistivity models from magnetotelluric data

The magnetotelluric inverse problem is a nonlinear problem which consists of finding a resistivity (or conductivity) model to fit a discrete set of noisy observations of the ratios of the electric and magnetic fields at the Earth's surface.;The major focus of this dissertation concerns the development of a regularized inversion method (Occam2) to solve for smooth two-dimensional resistivity models fitting magnetotelluric data. The inversion algorithm, which optimizes the step size and direction at each iteration, proves to be a robust, efficient means of model construction. It is shown that the regularization technique is flexible in allowing a priori information in the model.;Smooth regularized inversion is applied to the problem of determining the static shifts at each measurement site, by solving jointly for static shifts and resistivities. Static shift is defined as a uniform bias in the apparent resistivities over a broad frequency band. A regularization term penalizing roughness is applied to the resistivities, while the static shift parameters act upon the data. The solution yields the static shifts corresponding to the smoothest possible resistivity structure. Recovered static shifts agree well with the known values.;The algorithms are applied to magnetotelluric observations over the North American Central Plains (NACP) anomaly in Saskatchewan, Canada. The flexibility of smooth regularization is exploited to deal with special situations presented by the data, such as the approximate one-dimensionality of the near-surface resistivity structure. It is found that the NACP structure is not truly 2-D and that the data are affected by either off-axis structure or the effects of anisotropy.;Finally, it is noted that the determination of the electromagnetic fields necessary to form the model responses does not constitute an independent problem from that of determining the model conductivities. Therefore, an alternative method of inversion, in which one solves simultaneously for the EM fields and conductivities satisfying the observations and the EM induction equations, is presented and compared with the Occam2 inversion method. It is found the Occam inversion method, which interleaves forward calculations and changes to the conductivity model, yields a solution more quickly.