The translational accelerations recorded by strong-motion seismometers are often contaminated by baseline offsets that prevent recovering the ground displacements by double integration. Detailed analysis of the K-NET95 strong-motion seismometer, and the improvement of the visual display of the recorded accelerations’ Fourier transform by addition of long zero pads to the acceleration records, made it possible to distinguish the origins of the long-period noise that contaminate the translational accelerations recorded in the near field of two studied earthquakes, the 2004 Niigata-ken Chuetsu earthquake and the 2007 Niigata-ken Chuetsu-Oki earthquake, Japan. They are the residual rotation of the instrument (residual tilt) or the 1/f digital semiconductor noise. The quantification of these two terms allows us to discuss the low-frequency content of the records and to describe when it is possible to obtain realistic displacement time histories. It happens when the residual tilt is removed in the time-domain or when the 1/f semiconductor noise overshadows the translational acceleration records up to sufficiently small frequencies. As a check of the method, displacement time histories obtained from acceleration records are compared with nearby 1-Hz GPS data. Good similitudes are obtained in the near field for collocated instruments.