The results of electronic structure calculations of the induced dipoles and quadrupoles on an anion in a locally distorted rocksalt crystal are described. Such information is of interest in the construction of ionic interaction potentials and for modeling the dielectric behavior of ionic materials. The systems included in the study are LiF, NaF, KF, LiCl, NaCl, KCl, LiBr, MgO and CaO. The results are used to characterize short-range contributions to the induced multipoles- those not included in a point-charge, point-polarizable ionic model (the "asymptotic" model). It is shown that these short-range effects are large, opposing and sometimes reversing the asymptotic contribution. The representation of the short-range effects in a computationally tractable form, suitable for use in computer simulations, is examined. A pairwise additive form, containing a steplike function of the interionic separation, is found to provide a good representation of the ab initio data for both dipoles and quadrupoles. Furthermore, the parameters involved in the fitted functions transfer from one material to another in a physically transparent and predictable way.