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 dY²≈ATL over a broad range of the intervals, and the site dependent constant A is of the order of 10^-5±1  (μm²/s)/m.