Observations of Random Walk of the Ground In Space and Time

TL;DR

This paper reports high-resolution measurements of ground motions in large particle accelerators, revealing a stochastic 'random-walk' component in ground displacements across various spatial and temporal scales, with implications for accelerator stability.

Contribution

It provides the first detailed characterization of the stochastic ground motion component in accelerators, quantifying its scaling behavior over broad spatial and temporal ranges.

Findings

Ground motion exhibits a 'random-walk' character in space and time.

Mean square displacement scales linearly with time and distance.

Site-dependent constant A is approximately 10^-5 μm^2/(s·m).

Abstract

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).