This thesis introduce a new parameterization of the model space in global inversion problems. The parameterization provides an explicit representation of the model space with a basis constrained on a priori information about the problem at hand. It is able to represent complex model structures with few parameters, and thereby enhancing the speed of the inversion, as the number of iterations needed to converge is heavily scaled with the number of parameters in stochastic, global inversion methods. A standard Simulated Annealing optimization routine is implemented, and further extended to be able to optimize for a dynamically varying number of variables. The method is applied on inversion of marine CSEM data, and inverts both synthetic and real data sets and is able to recover resistivity profiles that demonstrate good resemblance with provided well bore log data. The trans-dimensional, self-parameterizing Simulated Annealing algorithm which is introduced in this thesis proves to be superior to the regular algorithm with fixed parameter dimensions.