In some embodiments, an apparatus and a system, as well as a method and article, may operate to model electromagnetic data to provide modeled electromagnetic data by solving a first set of surface integral equations that include earth model parameters corresponding to an earth model of a geological formation. Additional activity may include publishing at least some of the modeled electromagnetic data in human-readable form, and/or controlling drilling operations in the geological formation based on the earth model when error between the modeled electromagnetic data and measured electromagnetic data is less than a selected threshold. Additional apparatus, systems, and methods are disclosed.