Space-Time Diffusion of Ground and Its Fractal Nature

TL;DR

This paper investigates the diffusive and fractal nature of ground motion, presenting experimental evidence and a mathematical model that describe how ground displacement scales with time and space in physics research environments.

Contribution

It provides new experimental evidence of fractal ground motion and introduces a mathematical model explaining the observed scaling laws.

Findings

Ground motion exhibits fractal scaling with displacement variance proportional to T^Alpha L^Gamma.

Experimental methods successfully detect microscopic and mesoscopic ground movements.

A mathematical model reproduces the observed fractal scaling law.

Abstract

We present evidences of the diffusive motion of the ground and tunnels and show that if systematic movements are excluded then 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 \propto T^(Alpha)L^(Gamma) with both exponents close to 1. We briefly describe experimental methods of the mesa- and microscopic ground motion detection used in the measurements at the physics research facilities sensitive to the 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.