A numerical framework for Newtonian-noise estimation at the Einstein Telescope: 2-D simulations beyond the plane-wave approximation

Abstract

The Einstein Telescope (ET) is a third-generation underground gravitational-wave observatory designed to extend the detection sensitivity down to a few Hertz. Newtonian noise is expected to limit the low-frequency sensitivity of ET, particularly in the 1.7-6 Hz band. Most existing estimates rely on analytical or semi-analytical models assuming homogeneous or layered media, neglecting geological heterogeneity and complex wave interactions. In this work, we present a numerical framework for Newtonian-noise estimation based on spectral-element simulations of a seismic wave field. As a proof of concept, we first benchmark the numerical results against analytical plane-wave predictions in a two-dimensional homogeneous medium with a single surface source, demonstrating excellent agreement for both bulk and cavern contributions. We then extend the model to an array of 30 stochastic surface sources to approximate stationary ambient seismic excitation. The P-wave fraction inferred from the simulated wave field is, in this simple homogeneous case, significantly lower than commonly assumed, indicating enhanced prospects for Newtonian-noise mitigation. The framework is readily applicable to three-dimensional simulations and to integration of detailed local seismic models and topography, offering strong potential for site-specific Newtonian-noise estimation.

Figures (6)

• Figure 1: Workflow for the numerical estimation of Newtonian noise from simulated seismic wave fields.
• Figure 2: Model geometry and source configuration. The meshed computational domain is shown in the left panel, where the red star denotes the seismic source. The right panel displays the $2Hz$ Ricker wavelet used as the source time function.
• Figure 3: The displacement field and its derivatives from the numerical simulation of a single source pulse at the surface of the homogeneous medium. It shows the $x$-component of the displacement $\xi_x$ (upper left), the $y$-component $\xi_y$ (upper right), the divergence $\vec{\nabla}\cdot\vec{\xi}$ (lower left) and the curl $\vec{\nabla}\times\vec{\xi}$ (lower right) in the simulated two-dimensional domain. The green cross marks the test-mass position and the circle around it the integration domain. In the upper left plot, we have marked the different wave-field components: The P-wave (P), the S-waves (S) and the Rayleigh wave (R).
• Figure 4: Different Newtonian-noise (NN) estimates calculated at the test-mass position for a single source at the surface: Shown are the result of the volume integral over density fluctuations (blue, solid), and the full Newtonian-noise estimate assuming a virtual (not simulated) small spherical cavern according to the dipole formula (orange, solid). Also shown are the analytically predicted Newtonian noise from the (virtual) displacement at the test-mass position for monochromatic plane waves: for density fluctuations only (green, dashed), for density fluctuations and cavern wall movements (= P wave, red, dashdotted), as well as cavern wall movements only (= S-wave, purple, dotted)). The left part of the plot (up to $t=6.5s$) contains an almost pure plane P-wave and the right part an almost pure plane S-wave.
• Figure 5: Source configuration for the ambient-noise simulations. The top panel shows the spatial distribution of 30 force sources along the free surface. The bottom panel presents two representative realizations of the stochastic time-domain inputs used to approximate stationary ambient seismic excitation.