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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.