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 kilometers 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) approximate to ATL over a broad range of the intervals, and the site dependent constant A is of the order of 10(-5+/-1) (mu m(2)/s)/m.