Silencing Newtonian noise using fusion sensor arrays

TL;DR

The paper addresses NN challenges for the Einstein Telescope by extending Wiener-filter NN cancellation to fusion sensor arrays that combine displacement seismometers with DAS-type strainmeters. It introduces analytic S-wave strain correlations and uses a hybrid DE+CMA-ES optimization to locate sensors, demonstrating that fusion arrays can achieve NN cancellation comparable to or better than seismometer-only arrays, especially with few sensors. It also assesses deployments constrained to the ET infrastructure, showing that interior strainmeter networks can substantially reduce drilling costs while retaining performance. The work highlights cost-effective pathways for ET-scale NN mitigation, while noting simplifying assumptions (isotropic, full-space, body-waves only) that warrant more realistic modeling in future studies.

Abstract

Newtonian noise (NN) from seismic density fluctuations is expected to limit the low-frequency sensitivity of third-generation gravitational-wave detectors, in particular the Einstein Telescope (ET). Current NN mitigation relies on seismometer arrays and Wiener filtering, while distributed acoustic sensing (DAS) offers a complementary, low-cost means of obtaining dense strain measurements. We investigate fusion sensor arrays composed of both displacement-measuring seismometers and strain-measuring DAS-type sensors. We extend the Wiener filter formalism to mixed sensor types and introduce analytic S-wave strain correlation coefficients. Using a hybrid differential evolution and covariance matrix adaptation scheme, we validate our approach against established seismometer-only results and analyze the geometry, robustness, and performance of optimized fusion arrays. Fusion arrays enhance P/S-wave disentanglement and achieve NN cancellation levels comparable to, and sometimes exceeding, those of seismometer-only arrays, particularly for small sensor numbers. When sensors are constrained to the ET infrastructure, we find that six seismometers complemented by fourteen strainmeters inside the ET arms can match the performance of twenty seismometers in boreholes, achieving a residual at the 10% level, and thereby offering a cost-efficient pathway toward ET-scale NN mitigation.

Figures (9)

• Figure 1: Comparison of the different correlation types between two sensors, including seismometer and strainmeter. The x-ordinate shows their separation distance $r$, normalized by the wavelength $\lambda$, for the seismic P- and S-wavelengths respectively. Both sensor types measure along the same direction, chosen to be parallel to their separation vector ($\mathbf{e}_1 = \mathbf{e}_2 = \mathbf{e}_{12}$). All of the correlations are normalized such that the auto-correlation between same sensor types are equal to one. Instrumental noise is neglected (infinite SNR).
• Figure 2: This figure shows the angular sensitivity of the seismometer and strainmeter sensors, for P- and S-waves, respectively. The angular sensitivity of strainmeter sensors is given by $(\mathbf{e}_1 \cdot \mathbf{e_\xi})^2$, for seismometer by $\mathbf{e}_1 \cdot \mathbf{e_\xi}$. The angles are defined as the angle between the wave-propagation direction and the sensor’s measurement direction.
• Figure 3: This figure shows the square root of the optimal WF residual, $\sqrt{\mathcal{R}}$, for different compositions of strainmeters ($N_{\mathrm{\text{strain}}}$) and seismometers ($N_{\mathrm{\text{seis}}}$) in a 6-sensor array. We assume a mixing value of $p = \frac{1}{3}$ and use an SNR of 15 for all sensors. All sensors are one axis sensors, which measure the same direction as the TMs' measurement direction. The benchmark value corresponds to $\sqrt{\mathcal{R}}$ reported in harms_optimization_2019.
• Figure 4: Sensor array geometries, which are optimized the to the WF filter residual. The TM measures along the $-x$ direction, and all sensors are aligned to measure in the same direction.
• Figure 5: Distribution of 1000 WF filter residuals $\mathcal{R}$ for sensor arrays using a Monte Carlo simulation. Each sensor coordinate was perturbed by an independent offset drawn from a normal distribution with standard deviation $\sigma = 0.005 \lambda$, and starting initially from an optimized configuration. The figure compares a fusion array with equal numbers of seismometers and strainmeters ($N_{\mathrm{seis}} = N_{\mathrm{strain}} = 3$, labeled “Fusion”) and a seismometer-only array ($N_{\mathrm{seis}} = 6$, $N_{\mathrm{strain}} = 0$, labeled “Seismometer”). The dashed lines show the optimized residual.