Comparing teleseismic array back-projection source images of the 2011 Tohoku-Oki earthquake with results from static and kinematic finite source inversions has revealed little overlap between the regions of high- and low-frequency slip. Motivated by this interesting observation, back-projection studies extended to intermediate frequencies, down to about 0.1 Hz, have suggested that a progressive transition of rupture properties as a function of frequency is observable. Here, by adapting the concept of array response function to non-stationary signals, we demonstrate that the 'swimming artifact', a systematic drift resulting from signal non-stationarity, induces significant bias on beamforming back-projection at low frequencies. We introduce a 'reference window strategy' into the multitaper-MUSIC back-projection technique and significantly mitigate the 'swimming artifact' at high frequencies (1 s to 4 s). At lower frequencies, this modification yields notable, but significantly smaller, artifacts than time-domain stacking. We perform extensive synthetic tests that include a 3D regional velocity model for Japan. We analyze the recordings of the Tohoku-Oki earthquake at the USArray and at the European array at periods from 1 s to 16 s. The migration of the source location as a function of period, regardless of the back-projection methods, has characteristics that are consistent with the expected effect of the 'swimming artifact'. In particular, the apparent up-dip migration as a function of frequency obtained with the USArray can be explained by the 'swimming artifact'. This indicates that the most substantial frequency-dependence of the Tohoku-Oki earthquake source occurs at periods longer than 16 s. Thus, low-frequency back-projection needs to be further tested and validated in order to contribute to the characterization of frequency-dependent rupture properties.