We compare the three-dimensional force field obtained from frequency-distance measurements above the NaCl͑001͒ surface to atomistic calculations using various tip models. In the experiments, long-range forces cause a total attractive force even on the similarly charged site. Taking force differences between two sites minimizes the influence of such long-range forces. The magnitude of the measured force differences are by a factor of 6.5-10 smaller than the calculated forces. This is an indication that for the particular tip used in this experiment several atoms of the tip interact with the surface atoms at close tip-sample distances. The interaction of these additional atoms with the surface is small at the imaging distance, because symmetric images are obtained. The force distance characteristics resemble those of a negative tip apex ion which could be explained, e.g., by a neutral Si tip.