Observations of Random Walk of the Ground In Space and Time

We present results of micron - resolution measurements of the ground motions in large particle accelerators over the range of spatial scales L from several meters to tens of km and time intervals T from minutes to several years and show that in addition to systematic changes due to tides or slow drifts, there is a stochastic component which has a "random - walk" character both in time and in space. The measured mean square of the relative displacement of ground elements scales as dY**2 \approx ATL over broad range of the intervals, and the site dependent constant A is of the order of 10**-5\pm1 mu m**2/(s-m).