pith. sign in

arxiv: 2606.21110 · v1 · pith:7VPQDBEJnew · submitted 2026-06-19 · 🌌 astro-ph.IM · gr-qc

Optimization and robustness of cost-efficient seismic arrays for Newtonian noise cancellation at the Einstein Telescope

Patrick Schillings , Johannes Erdmann This is my paper

Pith reviewed 2026-06-26 13:38 UTC · model grok-4.3

classification 🌌 astro-ph.IM gr-qc
keywords Newtonian noiseseismic arraysEinstein Telescopenoise cancellationborehole seismometersmitigation factorsgravitational wave detectorsarray optimization
0
0 comments X

The pith

Arrays using multiple seismometers per borehole plus tunnel sensors achieve stable Newtonian noise mitigation above 3-4 Hz for the Einstein Telescope.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper optimizes the placement of seismometer arrays to reduce Newtonian noise caused by seismic waves that produce density fluctuations around the interferometer. It demonstrates that configurations with several sensors in each borehole can match the performance of somewhat larger single-sensor arrays, and that adding sensors inside the tunnels further improves results. Broadband mitigation from 1 to 10 Hz is quantified for arrays tuned at 10 Hz, along with robustness to small shifts in sensor positions. A reader would care because Newtonian noise is expected to limit low-frequency sensitivity at the Einstein Telescope, and these layouts point to lower-cost ways of reaching usable cancellation levels.

Core claim

Arrays with multiple seismometers per borehole combined with additional seismometers in the interferometer tunnels provide promising broadband mitigation above 3 to 4 Hz; such arrays remain particularly stable against variations in seismometer positions, delivering mitigation factors greater than 6 for an array of 20 boreholes with 3 sensors each and greater than 15 for a large array of 50 boreholes with 10 sensors each.

What carries the argument

Position optimization of borehole and tunnel seismometers to cancel Newtonian noise via measurements of the seismic wave field.

Load-bearing premise

The seismic wave field model used for optimization accurately represents real conditions at the site so that computed mitigation factors translate to actual performance.

What would settle it

A side-by-side comparison of measured Newtonian noise reduction at the Einstein Telescope site against the model's predicted mitigation factors for the same array layout.

Figures

Figures reproduced from arXiv: 2606.21110 by Johannes Erdmann, Patrick Schillings.

Figure 1
Figure 1. Figure 1: Left: Mitigation factor M for Newtonian noise mitigation as a function of test frequency f for different values of numbers of seismometers N for fopt = 10 Hz, p = 0.2 and SNR = 15. The optimization was performed with Adam after initialization with PSO. Right: Same, but in addition the optimized positions were displaced by a random distance drawn from a Gaussian distribution with σ = 50 m. p = 0.2, a P-wave… view at source ↗
Figure 2
Figure 2. Figure 2: Left: Mitigation factor M for Newtonian noise mitigation as a function of test frequency f for different numbers of seismometers per borehole for N = 20 boreholes, fopt = 10 Hz, p = 0.2 and SNR = 15. The optimization was performed with Adam after initialization with PSO. Right: Same, but in addition the optimized positions were displaced by a random distance drawn from a Gaussian distribution with σ = 50 m… view at source ↗
Figure 2
Figure 2. Figure 2: If there are at least n = 5 seismometers in each borehole, the mitigation factor is > 5 for f ≳ 3 Hz, similar to 60 boreholes with a single seismometer each. The mitigation factors for n = 3 are only slightly worse. As an example, the optimized array for n = 5 is shown in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: Mitigation factor M for Newtonian noise mitigation as a function of test frequency f for different numbers of seismometers per borehole for N = 20 boreholes, fopt = 10 Hz, p = 0.2 and SNR = 15. The optimization was performed with Adam after initialization with PSO. Additionally, 100 seismometers were added in the ET tunnels. Right: Same, but in addition the optimized positions were displaced by a ran… view at source ↗
Figure 5
Figure 5. Figure 5: Left: Mitigation factor M for Newtonian noise mitigation as a function of test frequency f for different numbers of seismometers per borehole for N = 50 boreholes, fopt = 10 Hz, p = 0.2 and SNR = 15. The optimization was performed with Adam after initialization with PSO. Additionally, 100 seismometers were added in the ET tunnels. Right: Same, but in addition the optimized positions were displaced by a ran… view at source ↗
read the original abstract

Newtonian noise is expected to be the dominating noise source for low frequencies at the Einstein Telescope. It originates from seismic waves that cause density fluctuations in the rock around the interferometer. The mitigation strategy for Newtonian noise relies on an array of seismometers, placed at depth in boreholes, which provides measurements of the seismic wave field. We optimize the positions of the individual seismometers for the mitigation capabilities of the array for a full corner of the Einstein Telescope. We find that the mitigation capabilities of arrays with multiple seismometers in each borehole match the capabilities of only somewhat smaller arrays but with only one seismometer per borehole. Mitigation is further improved by extending the array with seismometers in the interferometer tunnels. Such configurations may hence provide a cost-effective way towards realizing an efficient seismic array. In each case, we quantify the broadband mitigation performance in the range from 1 to 10 Hz for arrays that are optimized for a frequency of 10 Hz, as well as the robustness of the arrays with respect to variations from their optimized positions. We find that larger arrays with several seismometers per borehole and additional seismometers in the tunnels provide promising broadband performance above 3 to 4 Hz and that such arrays are particularly stable against variations in the seismometer positions with mitigation factors $>6$ for an array of 20 boreholes with 3 seismometers each and $>15$ for a large array of 50 boreholes with 10 seismometers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper optimizes the geometry of seismic arrays (boreholes with multiple seismometers plus tunnel sensors) to cancel Newtonian noise at a corner of the Einstein Telescope. Using forward modeling of the seismic wave field, it reports that arrays optimized at 10 Hz achieve broadband mitigation factors >6 (20 boreholes, 3 sensors each) and >15 (50 boreholes, 10 sensors each) above 3–4 Hz, with good robustness to position perturbations; multi-sensor boreholes are claimed to be nearly as effective as larger single-sensor arrays.

Significance. If the underlying seismic model is faithful to site conditions, the results identify cost-effective array designs that could substantially reduce a dominant low-frequency noise source for ET, directly supporting interferometer sensitivity goals.

major comments (1)
  1. [Seismic model and optimization procedure (methods/results sections)] The mitigation factors and robustness claims rest entirely on the fidelity of the forward seismic wave-field model (spatial correlations, dispersion, density fluctuations between 1–10 Hz). No validation against site-specific data, no error propagation, and no sensitivity analysis to model assumptions (isotropy, layering, scattering) are described; without these the quoted factors >6 and >15 cannot be shown to translate to on-site performance.
minor comments (2)
  1. [Results on broadband performance] Clarify whether the broadband factors are computed from the same optimization run or require separate frequency-dependent optimizations.
  2. [Discussion of array configurations] Specify the exact cost metric used when claiming multi-sensor boreholes are 'cost-efficient' relative to single-sensor arrays of comparable performance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive comments on our manuscript. We address the major comment regarding the seismic model below.

read point-by-point responses

  1. Referee: [Seismic model and optimization procedure (methods/results sections)] The mitigation factors and robustness claims rest entirely on the fidelity of the forward seismic wave-field model (spatial correlations, dispersion, density fluctuations between 1–10 Hz). No validation against site-specific data, no error propagation, and no sensitivity analysis to model assumptions (isotropy, layering, scattering) are described; without these the quoted factors >6 and >15 cannot be shown to translate to on-site performance.

    Authors: We agree that the reported mitigation factors are dependent on the assumptions of the forward seismic model used. The manuscript presents an optimization procedure and results for a generic model of the seismic wave field at the ET site, without site-specific validation or sensitivity analysis to model parameters such as isotropy or scattering. This is a limitation of the current work, as detailed site data for the 1-10 Hz range may not be fully available or the study focused on the array optimization methodology itself. We have revised the manuscript to include a new subsection in the discussion explicitly stating the model assumptions and noting that the quantitative mitigation factors (>6 and >15) should be interpreted as indicative for the assumed model, with on-site performance requiring calibration using local seismic measurements. No error propagation was included, which we acknowledge as a point for future work. The robustness analysis to position variations is performed within the model framework. revision: partial

Circularity Check

0 steps flagged

No circularity: mitigation factors obtained via forward modeling of array response

full rationale

The derivation consists of optimizing seismometer positions inside an explicit forward model of the seismic wave field, then computing mitigation factors as the resulting cancellation performance of those optimized arrays. These steps are independent computations; the quoted broadband factors (>6, >15) and robustness metrics are outputs of the optimization, not parameters fitted to the target quantities or renamed inputs. No self-citations, uniqueness theorems, or ansatzes are invoked in a load-bearing way. The chain is self-contained against external benchmarks and does not reduce by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full model assumptions, free parameters in the optimization, and any invented entities cannot be audited without the manuscript body.

axioms (1)
  • domain assumption A sufficiently accurate model of the seismic wave field exists that permits reliable prediction of Newtonian noise mitigation from array geometry.
    Optimization and quoted performance numbers rest on this premise.

pith-pipeline@v0.9.1-grok · 5790 in / 1189 out tokens · 21992 ms · 2026-06-26T13:38:32.548823+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

27 extracted references · 14 canonical work pages · 3 internal anchors

  1. [1]

    Design Report Update 2020 for the Einstein Telescope, 2020.url:https://apps.et-gw.eu/tds/?r=18715

    ET Steering Committee Editorial Team. Design Report Update 2020 for the Einstein Telescope, 2020.url:https://apps.et-gw.eu/tds/?r=18715

    2020

  2. [2]

    Advanced LIGO

    J. Aasi et al. Advanced LIGO.Classical and Quantum Gravity, 32:074001, 2015.doi: 10.1088/0264-9381/32/7/074001. arXiv:1411.4547 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264-9381/32/7/074001 2015

  3. [3]

    Advanced Virgo: a 2nd generation interferometric gravitational wave detector

    F. Acernese et al. Advanced Virgo: a second-generation interferometric gravitational wave detector.Classical and Quantum Gravity, 32:024001, 2015.doi:10.1088/0264- 9381/ 32/2/024001. arXiv:1408.3978 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264- 2015

  4. [4]

    doi:10.1088/0264-9381/29/12/124007

    K.Somiya(fortheKAGRACollaboration).DetectorconfigurationofKAGRA–theJapanese cryogenic gravitational-wave detector.Classical and Quantum Gravity, 29:124007, 2012. doi:10.1088/0264-9381/29/12/124007. arXiv:1111.7185 [gr-qc]

    work page doi:10.1088/0264-9381/29/12/124007 2012

  5. [5]

    Aso et al

    Y. Aso et al. Interferometer design of the KAGRA gravitational wave detector.Physical Review D, 88:043007, 2013.doi:10 . 1103 / PhysRevD . 88 . 043007. arXiv:1306 . 6747 [gr-qc]

    2013

  6. [6]

    P. R. Saulson. Terrestrial gravitational noise on a gravitational wave antenna.Physical Review D, 30:732, 1984.doi:10.1103/PhysRevD.30.732

    work page doi:10.1103/physrevd.30.732 1984

  7. [7]

    Amann et al

    F. Amann et al. Site-selection criteria for the Einstein Telescope.Review of Scientific In- struments,91:094504,2020.doi:10.1063/5.0018414.arXiv:2003.03434 [physics.ins-det]

    work page doi:10.1063/5.0018414.arxiv:2003.03434 2020

  8. [8]

    J. Harms. Terrestrial Gravity Fluctuations.Living Reviews in Relativity, 18:3, 2015.doi: 10.1007/lrr-2015-3

    work page doi:10.1007/lrr-2015-3 2015

  9. [9]

    G. Cella. Off-Line Subtraction of Seismic Newtonian Noise. In B. Casciaro, D. Fortunato, M. Francaviglia, and A. Masiello, editors,Recent Developments in General Relativity, page 495, Milan. Springer, 2000.doi:10.1007/978-88-470-2113-6_44

    work page doi:10.1007/978-88-470-2113-6_44 2000

  10. [10]

    Badaracco and J

    F. Badaracco and J. Harms. Optimization of seismometer arrays for the cancellation of Newtonian noise from seismic body waves.Classical and Quantum Gravity, 36:145006, 2019.doi:10.1088/1361-6382/ab28c1. arXiv:1903.07936 [astro-ph.IM]

    work page doi:10.1088/1361-6382/ab28c1 2019

  11. [11]

    Badaracco, J

    F. Badaracco, J. Harms, and L. Rei. Joint optimization of seismometer arrays for the cancellation of Newtonian noise from seismic body waves in the Einstein Telescope.Clas- sical and Quantum Gravity, 41:025013, 2024.doi:10.1088/1361-6382/ad1715. arXiv: 2310.05709 [astro-ph.IM]

    work page doi:10.1088/1361-6382/ad1715 2024

  12. [12]

    Schillings and J

    P. Schillings and J. Erdmann. Fighting Newtonian noise with gradient-based optimization at the Einstein Telescope.Classical and Quantum Gravity, 42:065025, 2025.doi:10 . 1088/1361-6382/adb898. arXiv:2411.03251 [astro-ph.IM]. 9

    arXiv 2025

  13. [13]

    Badaracco et al

    F. Badaracco et al. Machine learning for gravitational-wave detection: surrogate Wiener filtering for the prediction and optimized cancellation of Newtonian noise at Virgo.Clas- sical and Quantum Gravity, 37:195016, 2020.doi:10.1088/1361-6382/abab64. arXiv: 2005.09289 [astro-ph.IM]

    work page doi:10.1088/1361-6382/abab64 2020

  14. [14]

    Koley et al

    S. Koley et al. Design and implementation of a seismic Newtonian noise cancellation system for the Virgo gravitational-wave detector.The European Physical Journal Plus, 139:48, 2024.doi:10.1140/epjp/s13360-023-04834-0. arXiv:2310.17781 [gr-qc]

    work page doi:10.1140/epjp/s13360-023-04834-0 2024

  15. [15]

    Subtraction of Newtonian Noise Using Optimized Sensor Arrays

    J. Driggers, J. Harms, and R. Adhikari. Subtraction of newtonian noise using optimized sensor arrays.Physical Review D, 86, 2012.doi:10.1103/PhysRevD.86.102001. arXiv: 1207.0275 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.86.102001 2012

  16. [16]

    Ophardt, F

    P. Ophardt, F. Badaracco, and K.-S. Isleif. Silencing Newtonian noise using fusion sensor arrays, 2025. arXiv:2512.13554 [gr-qc]

    arXiv 2025

  17. [17]

    Rading et al

    R. Rading et al. Distributed Acoustic Sensing for Environmental Monitoring, and Newto- nian Noise Mitigation: Comparable Sensitivity to Seismometers, 2025. arXiv:2507.13523 [astro-ph.IM]

    arXiv 2025

  18. [18]

    van Beveren et al

    V. van Beveren et al. A study of deep neural networks for Newtonian noise subtraction at Terziet in Limburg—the Euregio Meuse-Rhine candidate site for Einstein Telescope. Class. Quant. Grav., 40:205008, 2023.doi:10.1088/1361-6382/acf3c8

    work page doi:10.1088/1361-6382/acf3c8 2023

  19. [19]

    Koley et al

    S. Koley et al. Adaptive algorithms for low-latency cancellation of seismic Newtonian- noise at the Virgo gravitational-wave detector.Physical Review D, 110:022002, 2024. doi:10.1103/PhysRevD.110.022002. arXiv:2404.13170 [gr-qc]

    work page doi:10.1103/physrevd.110.022002 2024

  20. [20]

    Kelleter et al

    J. Kelleter et al. NNNN: Neural Networks for Newtonian Noise Mitigation at the Einstein Telescope, 2026. arXiv:2606.19907 [astro-ph.IM]

    Pith/arXiv arXiv 2026

  21. [21]

    Wiener.Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications

    N. Wiener.Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications. Wiley, New York, 1949

    1949

  22. [22]

    Kennedy and R

    J. Kennedy and R. Eberhart. Particle swarm optimization. InProceedings of ICNN’95 - International Conference on Neural Networks, volume 4, page 1942, 1995.doi:10.1109/ ICNN.1995.488968

    arXiv 1942

  23. [23]

    D. P. Kingma and J. Ba. Adam: A Method for Stochastic Optimization, 2014. arXiv: 1412.6980 [cs.LG]

    Pith/arXiv arXiv 2014

  24. [24]

    Amann et al

    F. Amann et al. Tunnel Configurations and Seismic Isolation Optimization in Under- ground Gravitational Wave Detectors.Appl. Sciences, 12:8827, 2022.doi:10 . 3390 / app12178827. arXiv:2204.04131 [astro-ph.IM]

    arXiv 2022

  25. [25]

    Pieter, X

    R. Pieter, X. Kuci, S. François, and G. Degrande. An efficient finite element formulation for Newtonian noise analysis, 2026. arXiv:2603.15157 [physics.app-ph]

    Pith/arXiv arXiv 2026

  26. [26]

    arXiv:2603.15424 [astro-ph.IM]

    P.Schillings,S.Yao,J.Erdmann,andA.Rietbrock.AnumericalframeworkforNewtonian- noise estimation at the Einstein Telescope: 2-D simulations beyond the plane-wave ap- proximation, 2026. arXiv:2603.15424 [astro-ph.IM]

    arXiv 2026

  27. [27]

    DeSalvo et al

    R. DeSalvo et al. A dual tunnel structure for the Einstein Telescope, 2026. arXiv:2601. 13438 [astro-ph.IM]. 10

    2026