Detailed analysis and modeling of regional gravity and magnetic data from the Stuart Shelf around the Olympic Dam iron oxide copper-gold (IOCG) deposit, constrained by geologic observations obtained from deep drill cores, show that the eastern Gawler craton basement at 1.61 to 1.59 Ga consisted of an Archean core with two sequences of successively younger supracrustal rocks stepping out eastward from it. These were overprinted by the tectonothermal Hiltaba event. Forward models of potential-field data show no convincing evidence for the presence of widespread mafic rocks or extensional basin systems developed immediately prior to, or during, IOCG mineralization. The high intrusive level and sill-like geometry of Hiltaba Suite plutons emplaced immediately prior to IOCG mineralization is difficult to explain in terms of a genetic association with a dominantly extensional tectonic setting. Instead, the tectonic setting inferred from the basement architecture during mineralization is one of low-strain shortening, consistent with regional field observations. A case can be made for intrusion of the Hiltaba Suite in localized accommodation zones in an overall orogenic setting. This style of low-strain shortening (<10%) is consistent with maximum rates and volumes of fluid flow in the upper crust, and access of these fluids to a variety of basement rock types to buffer metal-scavenging fluids. This fluid-driving mechanism does not necessitate a role for regional mafic magmatism and volcanism in the formation of IOCG deposits. Modeling of regional gravity and magnetic data is generally applicable to exploration for IOCG systems, and other mineral systems, in covered terranes that have distinctive geophysical signatures resulting from fluid–wall-rock redox geochemical reactions.