Inversion of non-linear quantities derived from potential fields

In recent years, potential field quantities such as the Normalized Source Strength and the Total Gradient have been increasingly used in applied and environmental geophysics because of their properties. They are always non-negative and minimally affected by the direction of the source’s remanent magnetization. Despite the fact that these quantities are derived from nonlinear transformations of potential field data, a linear inversion approach of NSS and TG is often used in the literature without investigating its theoretical and practical limits. In this paper, we present an approach for the nonlinear constrained inversion of these quantities and apply it to synthetic data and measurements carried out at the Vredefort structure, South Africa. We show, through GSVD analysis tools, that the nonlinearity of the problem can hamper the inversion results when using a linear approach, whereas our nonlinear iterative approach leads to more reliable reconstructions of the subsurface density/magnetization distribution.