The South Atlantic magnetic Anomaly (SAA) is an important feature of the present geomagnetic field. In this paper we model the space-time evolution of this anomaly over the past 400 years in terms of the resultant between a decrease of a global axial dipole and an increase of a virtual local monopole source. Certain characteristics of this evolution are investigated and some considerations are made in the light of a possible special state of the global geomagnetic field dynamical regime. Among the possible speculations, one is made regarding the topography of the coremantle boundary (CMB) and its possible aspect beneath the SAA region in terms of simple sinusoidal undulations met by the monopole source during its centennial motion.