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In recent years, gravitational lensing has been used as a means to detectsubstructure in galaxy-sized halos, via anomalous flux ratios inquadruply-imaged lenses. In addition to causing anomalous flux ratios,substructure may also perturb the positions of lensed images at observablelevels. In this paper, we numerically investigate the scale of such astrometricperturbations using realistic models of substructure distributions.Substructure distributions that project clumps near the Einstein radius of thelens result in perturbations that are the least degenerate with the best-fitsmooth macromodel, with residuals at the milliarcsecond scale. Degeneraciesbetween the center of the lens potential and astrometric perturbations suggestthat milliarcsecond constraints on the center of the lensing potential boostthe observed astrometric perturbations by an order of magnitude compared toleaving the center of the lens as a free parameter. In addition, we discussmethods of substructure detection via astrometric perturbations that avoid fulllens modeling in favor of local image observables and also discuss modeling ofsystems with luminous satellites to constrain the masses of those satellites.Comment: 15 pages, 13 figures, ApJ accepted version. 2 new figures, additional  section on halo-to-halo variatio

Astrometric Perturbations in Substructure Lensing