The moon's permanent magnetic field - A cratered-shell model

The possibility is considered that the properties of the larger-scale lunar magnetic field may depend in a rather straightforward manner on the geometrical properties of the distribution of larger craters. The relevant effects of cratering are analyzed in the framework of a model of a spherically symmetric shell magnetized to some specific intensity by a concentric dipolar magnetic field. The remanent dipole moment of the model is determined by calculating the dipole moment of the material removed to form craters and them computing the remanent dipole moment for three mutually orthogonal orientations of the magnetizing dipole. The resulting absolute values for the remanent dipole moment are found to be comparable to the upper limit of 10 to the -19th power G-cu cm estimated from Apollo subsatellite measurements. It is concluded that for a crust with an empirically reasonable mean magnetization, the craters can account for a dipole moment as great as that indicated by the estimated upper limit.