Abstract: Disclosed embodiments include well ranging apparatus, systems, and methods which operate to determine an approximate range between a drilling well and a target well using field equations and the set of measurements by repeatedly receiving the signals and determining the approximate range at increasing depths along the drilling well to build a model of current distribution along the target well, and when a comparison of a measurement predicted by the model to at least one component in the set of measurements indicates nonlinearity in the current distribution, inverting the approximate range to determine a model response that matches the set of measurements, using the model response in place of at least one component in the set of measurements, to determine an actual range to substitute for the approximate range. Additional apparatus, systems, and methods are disclosed.