 Solution

For the same geometry, field strength and induced magnetization model at the opposite magnetic inclination, replacing $I$ by $-I$ gives $\Delta T_{-I}(x)=\Delta T_I(-x)$. Thus the north–south asymmetry reverses: the principal low moves to the northern side and the high to the southern side. It is a horizontal reflection of the simple profile, rather than a necessary reversal of every anomaly's sign. At a magnetic pole the induced anomaly is symmetric; at the magnetic equator the symmetry is different again. If remanent magnetization dominates, a hemisphere change alone does not determine the new profile because that remanence direction also has to be specified.