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Effects of near-surface sedimentary structure on Newtonian noise for the Einstein Telescope: a 2-D numerical study

This 2-D numerical study demonstrates that near-surface sedimentary structures significantly alter Newtonian noise estimates for the Einstein Telescope through frequency-dependent wave trapping and interference, necessitating explicit modeling of sediment properties and geometry, particularly for test masses located between 200 m and 300 m depth.

Original authors: Shi Yao, Patrick Schillings, Johannes Erdmann, Andreas Rietbrock

Published 2026-08-25

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CC BY 4.0

Original authors: Shi Yao, Patrick Schillings, Johannes Erdmann, Andreas Rietbrock

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep underground, far beneath the bustling surface of our world, scientists are building a new kind of telescope. Unlike traditional telescopes that look up at the stars with lenses or mirrors, this machine, known as the Einstein Telescope, listens for ripples in the fabric of space and time called gravitational waves. These ripples are created by the most violent events in the universe, such as colliding black holes. To hear these faint whispers, the telescope must be incredibly sensitive, capable of detecting movements smaller than the width of a single atom. However, this extreme sensitivity brings a major problem: the Earth itself is never perfectly still. Even deep underground, the ground vibrates with the constant hum of ocean waves, wind, and distant earthquakes. These vibrations do more than just shake the equipment; they change the density of the rock and soil around the detector. Because mass attracts mass, these shifting densities create tiny, fluctuating gravitational pulls on the telescope's test masses—the delicate mirrors suspended inside the machine. This invisible tug, known as Newtonian noise, cannot be blocked by walls or rubber pads. It is a fundamental limit to how quiet the machine can get, and if not understood and managed, it will drown out the cosmic signals the telescope is designed to find.

To solve this puzzle, a team of researchers turned their attention to the ground right above the planned detector sites. They focused on the layers of soft, loose sediment that often sit on top of hard, solid bedrock. In many places, including the potential locations for the Einstein Telescope, the ground is not uniform; it is a sandwich of soft, slow-moving soil over hard, fast-moving stone. The researchers wanted to know exactly how this specific geological setup changes the way seismic waves travel and, more importantly, how it alters the gravitational noise that reaches the detector. Using powerful computer simulations, they modeled a slice of the Earth's crust, filling it with the properties of real sediment and rock, and then watched how a field of random, natural vibrations moved through it. They did not just look at the surface; they placed virtual detectors at various depths, from the top of the sediment down to two kilometers underground, to see how the noise changed as it traveled deeper.

The study revealed that the shape and thickness of that soft sediment layer act like a filter for the Earth's vibrations. When the sediment layer is a flat, uniform blanket of constant thickness, it traps the seismic energy and creates a very strong, clear resonance at specific frequencies, much like a drum skin that vibrates loudly at a single pitch. This creates a sharp peak in the noise that the telescope would have to contend with. However, when the sediment layer is shaped like a basin, getting thicker in the middle and thinner at the edges, the story changes. The uneven shape breaks up the uniform vibration, scattering the energy and smoothing out the noise. Instead of one sharp, loud peak, the noise becomes a broader, more complex mix of frequencies. The researchers found that the speed at which waves travel through the sediment is the primary factor that decides which frequencies get amplified, while the ability of the sediment to absorb energy determines how loud that amplification is. Softer, more absorbent sediment acts like a sponge, soaking up the vibrations and reducing the noise, whereas stiffer sediment lets the vibrations ring out more clearly.

Perhaps the most critical discovery concerns where the detector is placed. The simulations showed that the influence of this surface sediment is not felt equally at all depths. For test masses located within the sediment layer or just a few hundred meters below it, the structure of the ground above has a massive impact. The noise levels and the specific frequencies that dominate the signal change dramatically depending on exactly how thick the sediment is at that spot and how deep the detector sits. However, as the researchers pushed their virtual detectors deeper, the effect began to fade. At a depth of two kilometers, the noise levels became nearly identical regardless of whether the ground above was a flat layer or a deep basin. The deep underground environment is shielded from the chaotic details of the surface geology. This suggests that for the Einstein Telescope, the most critical factor in predicting and managing noise is not just how deep the machine goes, but the precise, local details of the sediment directly above it. If the detector is placed between 200 and 300 meters deep, the engineers must know the exact thickness and composition of the soil above, because a small change in the ground's shape could significantly alter the noise floor.

These findings provide a clear roadmap for the future of the Einstein Telescope. The researchers demonstrated that simply assuming the ground is uniform is not enough; the complex, real-world structure of the sediment must be mapped and included in the noise predictions. The study confirms that the ground is not just a passive foundation but an active participant in the detection process, shaping the very noise the telescope must overcome. By understanding how the sediment layer traps, scatters, and absorbs seismic energy, scientists can better choose the best locations for the telescope and design strategies to cancel out the noise. The work does not claim to have solved the problem of Newtonian noise entirely, but it has illuminated the specific role of the near-surface geology, turning a vague concern into a set of concrete, measurable factors that can be addressed before the first shovel hits the ground.

Technical Summary: Effects of Near-Surface Sedimentary Structure on Newtonian Noise for the Einstein Telescope

Problem Statement
The Einstein Telescope (ET), a proposed third-generation underground gravitational-wave observatory, aims to extend sensitivity to frequencies of a few hertz. At these low frequencies, detector sensitivity is limited by Newtonian noise (NN)—fluctuating gravitational forces on suspended test masses caused by time-dependent density perturbations in the surrounding medium due to seismic displacement. While ambient seismic noise is routinely measured, the specific influence of near-surface geological structures on NN remains poorly quantified. Candidate ET sites (Euregio Meuse-Rhine, Sos Enattos, and Lusatia) exhibit complex near-surface conditions, including low-velocity sedimentary layers overlying hard-rock basements, weathered zones, and sharp material contrasts. Previous studies have established that such layers amplify ground motion through wave trapping and resonance, but their systematic impact on the NN experienced by subsurface test masses—particularly regarding interface geometry, material properties, and test-mass depth—has not been rigorously evaluated.

Methodology
The authors employ 2-D viscoelastic numerical simulations to investigate the first-order effects of sedimentary structure on seismic wavefields and the resulting NN.

Numerical Framework: The seismic wavefield is computed using Salvus by solving the viscoelastic wave equation. Intrinsic attenuation is incorporated via linear isotropic viscoelasticity, parameterized by P- and S-wave velocities ( $c_P, c_S$ ), density ( $\rho$ ), and quality factors ( $Q_P, Q_S$ ). Density perturbations are derived from the displacement field using the linearized continuity equation. The resulting time-dependent gravitational perturbation is calculated via a 3-D volume integral (assuming translational invariance in the out-of-plane direction) to obtain the NN force.
Model Configuration: The physical domain is 50 km $\times$ 4 km, surrounded by 4 km absorbing layers. The model consists of a two-layer system: an upper unconsolidated sediment layer (low $c_S$ , high attenuation) and a lower hard-rock basement (high $c_S$ , low attenuation).
Source and Receiver: The excitation is modeled as a spatially distributed stochastic noise field generated by 100 random vertical point forces distributed along the surface. This approximates continuous ambient seismic excitation. Receivers and test masses are placed at various depths and lateral positions to probe the response.
Controlled Experiments: The study isolates the effects of four parameters by comparing models against a reference:
1. Interface Geometry: Flat (constant thickness) vs. Basin-shaped (laterally varying thickness).
2. Sediment Shear-Wave Velocity ( $c_S$ ): Varied between 400 m/s and 600 m/s.
3. Sediment Attenuation ( $Q_S$ ): Varied between 5 (strong attenuation) and 100 (weak attenuation).
4. Test-Mass Position: Varied in depth (20 m to 2 km) and lateral location.

Key Results
The simulations reveal that near-surface sedimentary structures induce frequency-dependent modifications to NN through wave trapping, interference, and attenuation.

Interface Geometry:
- A flat interface with constant sediment thickness generates a laterally coherent wavefield and a sharp spectral enhancement in NN (e.g., a pronounced peak around 5 Hz).
- A basin-shaped interface (laterally varying thickness) disrupts uniform resonance, resulting in a less coherent wavefield, a broader spectral response, and generally lower amplitudes in the 3–7 Hz range compared to the flat case.
Material Properties:
- Shear-Wave Velocity ( $c_S$ ): Primarily controls the frequency of spectral features. Lower $c_S$ shifts characteristic resonance peaks to lower frequencies and increases the contrast between sediment and basement responses.
- Attenuation ( $Q_S$ ): Primarily controls the amplitude and persistence of the response. Strong attenuation (low $Q_S$ ) dissipates seismic energy, suppressing coherent amplification and reducing the contrast between surface and subsurface amplitudes. Weak attenuation (high $Q_S$ ) allows trapped energy to persist, enhancing near-surface amplification.
Position Dependence:
- Depth: NN is most sensitive to sediment structure for test masses located within the sediment layer or several hundred meters below it (e.g., 200–300 m). At these depths, spectral enhancements are significant. At 2 km depth, the influence of near-surface lateral variations becomes weak, and the NN response converges toward that of a homogeneous basement model, particularly at lower frequencies.
- Lateral Variation: Changes in sediment thickness shift spectral features (thinner sediment shifts resonance to higher frequencies) and modify amplitudes. These lateral differences are strongest for shallow test masses and diminish rapidly with depth.
Comparison with Homogeneous Models:
- Relative to a homogeneous basement model, the sediment layer produces comparable NN at very low frequencies (<2.5 Hz), enhanced amplitudes in the sediment-related spectral band (3–4 Hz), and reduced amplitudes at higher frequencies for near-surface test masses.

Significance and Claims
The paper concludes that near-surface sedimentary structure must be explicitly represented when assessing site-dependent Newtonian noise for the Einstein Telescope. The study demonstrates that:

Simplified 1-D resonance models may be insufficient for sites with complex basin geometries, as lateral variations significantly broaden and shift the NN spectrum.
The sensitivity of NN to sedimentary structure is highly depth-dependent; it is critical for test masses located between 200 m and 300 m but becomes negligible at depths of 2 km in the modeled scenarios.
Accurate NN prediction requires a holistic consideration of local sediment thickness, shear-wave velocity, attenuation, and the specific depth of the test mass, rather than relying on burial depth alone.

The authors note that these findings are based on 2-D viscoelastic simulations and idealized source configurations. Future work is identified as necessary to incorporate 3-D geological structures, topography, caverns, measured seismic spectra, and uncertainties in sediment properties.

Technical Summary: Effects of Near-Surface Sedimentary Structure on Newtonian Noise for the Einstein Telescope

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