## 1. Introduction
### Why Underground  
The Einstein Telescope (ET) will be a European third-generation GW detector that will be built underground. It will be constituted by three nested GW interferometers in a triangular shape with sides of 10 km [1]. The ubiquitous seismic waves propagating with sub-micron amplitude through Earth's crust cause the so-called seismic noise, which is a mechanical movement that can be filtered away from a gravitational wave detector noise budget using sufficiently long and well-designed seismic attenuation chains [2]. Seismic waves also induce a much subtler effect that cannot be shielded. They cause tiny fluctuations of rock's density and position, which in turn generate tiny, local fluctuations of Earth's gravitational field that are seen by the detector as fluctuating space-time warps. This is called Newtonian noise [3]. Its effect on the test masses cannot be distinguished from the effect of a passing gravitational wave. The Newtonian noise acceleration depends linearly on the amplitude spectral density of the seismic displacement, which, at the frequencies of interest for ET, decays as \(1/f^{2}\). Therefore, the Newtonian noise displacement amplitude spectral density will fall as \(1/f^{4}\)[4] affecting the sensitivity below 30 Hz and intervening in the noise budget only at low frequency. Gravitational wave detectors that are built underground are substantially less influenced by Newtonian noise. Yet, Newtonian noise will eventually limit the sensitivity at low frequency of any Earth based detector. At the surface, air density fluctuations due to infrasound pressure waves and wind turbulence contribute to Newtonian noise [5]. The air density fluctuations in the atmosphere are not too relevant for underground detectors that are sufficiently deep [6]. The large density difference between soil and air, the low elastic constant of soil and the larger displacement amplitude of both surface and body waves that increase their amplitude when surfacing cause large Newtonian noise on test masses hanging near the surface. Surface waves dominate the surface Newtonian noise spectrum, but their amplitude diminishes exponentially with depth and frequency [3]. This means that their contribution to Newtonian noise decreases exponentially with depth. Body waves are present at all depths. Even if their amplitude diminishes with the higher stiffness of deep rock, their Newtonian noise remain present at all depths. The depth chosen for the Einstein Telescope, about 300 m, was chosen as a tradeoff between diminishing returns and cost. In theory, Newtonian noise could be estimated from a densely spaced network of seismometers surrounding the test masses and subtracted from the detector signal. This would require many high-precision seismometers optimally located in the rock surrounding the detector at distances comparable to the seismic wavelength generating the Newtonian noise, i.e., hundreds of meters. The method is further limited by the precision and the number of seismic sensors installed and by the mixing of shear and compressional waves that spoil the correlations between the inertial sensors used for the Newtonian noise estimation [7]. The quieter conditions inducing less Newtonian noise are the main rationale why future gravitational wave detectors aiming to detect gravitational waves down to 3 Hz [8] will be built underground. It will be shown that the proposed topology also allows almost optimal deployment of the inertial sensors required for an effective Newtonian noise subtraction. All these improvements make ET a powerful and exciting instrument for gravitational wave astronomy. An alternative approach, chosen for the Cosmic Explorer design [9], is to make a longer detector on the surface, diluting the fractional error of the larger surface noise with the larger amplitude of signals detected over longer distances. Subtraction of the much larger Newtonian noise present at the surface is possible but not sufficient to reach the desired low-frequency sensitivity of the Einstein Telescope.