A numerical model of seismic Newtonian noise for the Einstein telescope

The Einstein Telescope (ET) is a third-generation underground gravitational wave observatory designed to achieve an unprecedented sensitivity down to 3 Hz. Waves propagating in the soil generate density fluctuations which result in gravitational attraction, known as Newtonian noise (NN), resulting in corresponding motion of the mirrors of the laser interferometer. As these forces cannot be shielded, NN must be estimated from the measured seismic field through wave field reconstruction and subtracted from the interferometer data. Seismic NN is computed by accounting for the density fluctuations due to seismic displacements and integrating over the soil domain surrounding the test mass [1, 2]. For the numerical evaluation of the NN integrals, a finite element (FE) model has been developed. The framework, hence, consists of two steps: (1) computation of the seismic wave field and (2) NN integration in a post-processing step on a FE mesh using Gaussian quadrature. The formulation is validated for plane P- and S-waves in a homogeneous fullspace, showing excellent agreement with analytical solutions, and subsequently extended to include Rayleigh waves in a homogeneous halfspace. As an application, NN generated by Rayleigh waves is computed for the Euregio Meuse-Rhine candidate site, based on the layered subsurface model of Terziet. The results demonstrate the influence of wave scattering, layer contrast, and the size of the cavern surrounding the test masses on the resulting NN levels. The proposed FE-based framework provides a physically consistent and computationally efficient approach for quantifying gravitational-seismic coupling in heterogeneous media. [1] J. Harms. Terrestrial gravity fluctuations. Living Reviews in Relativity, 22:6, 2019. [2] M. Bader et al. Newtonian-noise characterization at Terziet in Limburg - the Euregio Meuse-Rhine candidate site for Einstein Telescope. Classical and Quantum Gravity, 39(2):025009, 2022.