Abstract: Methods and systems in accordance with this invention perform three-dimensional inversion of electromagnetic data, such as magnetotelluric (“MT”) data and controlled-source electromagnetic (“CSEM”) data, and three-dimensional joint inversion of MT and CSEM data. In exemplary embodiments, nonlinear conjugate gradient (“NLCG”) methods are used in lieu of iterative, linearized inversion, and line-search and preconditioning techniques are used that accommodate and exploit the structure of the MCSEM and MT problem.