Explorers are moving to increase the “discovery space” by exploring under cover and to greater depths, e.g., subsalt and sub-basalt exploration for oil and gas, and beneath transported cover for minerals. With this shift, there becomes an increased reliance on geophysical methods to delineate resources with no recognized geological or geochemical expressions. Different geophysical fields provide information about different physical properties of the Earth. Multiple geophysical surveys spanning gravity, magnetic, electromagnetic, and seismic methods are often interpreted to infer geology from models of different physical properties. In many cases, the various geophysical data are complementary, making it natural to consider a formal mathematical framework for their joint inversion to a shared Earth model. There are different approaches to joint inversion. The simplest case of joint inversion is where the physical properties are identical between different geophysical methods (e.g., Jupp and Vozoff, 1975). In other cases, joint inversion may infer theoretical, empirical, or statistical correlations between different physical properties (e.g., Hoversten et al., 2003, 2006). In cases where the physical properties are not correlated but, nevertheless, can be assumed to share a similar structure, joint inversions have been formulated as a minimization of the cross-gradients between different physical properties (e.g., Haber and Oldenburg, 1997; Gallardo and Meju, 2003, 2004). The latter has now been widely adopted by joint inversion practitioners as the de facto standard (e.g., Colombo and De Stefano, 2007; Hu et al., 2009; Jegen et al., 2009; De Stefano et al., 2011).