Displacements obtained from double integration of digitally recorded ground accelerations often show drifts much larger than those expected for the true ground displacements. These drifts might be due to many things, including dynamic elastic ground tilt, inelastic ground deformation, hysteresis in the instruments, and cross feed due to misalignment of nominally orthogonal sensors. This article shows that even if those effects were not present, the analog-to-digital conversion (ADC) process can produce apparent “pulses” and offsets in the acceleration baseline if the ground motion is slowly varying compared with the quantization level of the digitization. Such slowly varying signals can be produced by constant offsets that do not coincide with a quantization level and by near- and intermediate-field terms in the wave field radiated from earthquakes. Double integration of these apparent pulses and offsets leads to drifts in the displacements similar to those found in processing real recordings. These effects decrease in importance as the resolution of the ADC process increases.