Review of observations of ground diffusion in space and in time and fractal model of ground motion

We present numerous observations of the diffusive motion of the ground and tunnels for scientific instruments and show that if systematic movements are excluded the remaining uncorrelated component of the motion obeys a characteristic fractal law with the displacement variance dY^{2} scaling with time and spatial intervals T and L as dY^{2}∝T^{α}L^{γ} with both exponents close to 1 (α≈γ≈1). We briefly describe experimental methods of the mesoscopic and microscopic ground motion detection used in measurements at physics research facilities sensitive to ground motion, particularly large high energy elementary particle accelerators. A simple mathematical model of the fractal motion demonstrating the observed scaling law is also presented and discussed. This paper is a subsequent full detail publication to [V. Shiltsev, Phys. Rev. Lett. 104, 238501 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.238501]