[en] Slow ground motion with frequencies much less than characteristic frequencies of an accelerator usually has been considered as not seriously affecting machine operation because of assumed complete space and time coherence of the magnet displacements. In this paper, we analyze geophysical and numerous accelerator data on uncorrelated ground motion. We demonstrate that these data in many cases can be approximated by the ''ATL law'' that assumes diffusive wandering of the ground elements. An equation is derived that governs closed orbit distortion caused by random (though correlated) quadrupole displacements in a large circular accelerator. Estimates for the Superconducting Super Collider (SSC) are carried out and compared with the ability of the corrections system to maintain the orbit in the collider