The spatial profile of the magnetization of Mn12 crystals in a swept magnetic field applied along the easy axis is determined from measurements of the local magnetic induction along the sample surface using an array of Hall sensors. We find that the magnetization is not uniform inside the sample, but rather shows some spatial oscillations which become more prominent around the resonance field values. Moreover, it appears that different regions of the sample are at resonance at different values of the applied field and that the sweep rate of the internal magnetic induction is spatially non-uniform. We present a model which describes the evolution of the non-uniformities as a function of the applied field. Finally we show that the degree of non-uniformity can be manipulated by sweeping the magnetic field back and forth through part of the resonance.