Noise in the LIGO Livingston Gravitational Wave Observatory due to Trains

The detection of gravitational waves from extreme astrophysical events has opened the door to exciting discoveries. The Advanced LIGO [1] and Advanced VIRGO [2] detectors have detected many gravitational waves from coalescing binaries of black holes and neutron stars [3]. Since the first detection in 2015, there has been an influx of more events detected. By the end of the first observing run (O1) [4], both the LIGO Scientific Collaboration (LSC) and the LIGO Virgo and KAGRA (LVK) Collaboration had reported three binary black hole gravitational wave events. The second observing run (O2) [5] not only detected seven binary black hole mergers, but the first merger of two neutron stars. In the third observing run (O3) [3], a total of 79 events were detected with improved sensitivity due to increased laser input power and the introduction of squeezed light techniques  [6, 7]. These observations require measurements of differences in arm lengths of the order of $\rm 10^{-21}\,m/\sqrt{Hz}$ at $150~{}\mathrm{Hz}$.

Short duration non-astrophysical transients known as “glitches” adversely impact the detector’s data quality and complicate the process of identification of gravitational waves in the data  [8, 9, 10]. Environmental and instrumental noise are common sources of these brief transients. Earthquakes, ocean waves, trains, and human activity can “shake” the detector. Quadruple suspension systems and passive/active seismic isolation are used to dampen the effects. The in-vacuum optical tables incorporate an active vibration isolation system providing attenuation of environmental seismic noise below $1~{}\mathrm{Hz}$. Above $1~{}\mathrm{Hz}$, the quadruple pendulum optic suspensions provide passive isolation in the horizontal and vertical degrees of freedom. [11]. Although the ground motion is largest at low frequencies (below 10 Hz), it produces transients in gravitational wave strain data in the $10$–$150~{}\mathrm{Hz}$ range due to non-linear coupling. At the LIGO Livingston Observatory (LLO), 50$\%$ of the noise transients in the LLO detector in O3 were due to light reflected in mirrors and other surfaces (“scattered” or “stray” light) [12].

In this paper, we investigate scattering noise caused by trains passing near LLO. Noise from trains can enter the interferometer by causing displacements of particular scattering surfaces in the detector. In Section 2, we introduce how scattered light produces noise in the detector. In Section 3, we describe the methods used to investigate the effect of trains in producing transient noise in the detector. In Section 4, we present the results of our analysis showing the advantages of the methods used, and discuss possible surfaces producing the scattering glitches.

The motion of the ground where a gravitational wave detector is located can lead to bad data quality. Earthquakes and wind shake the instrument in $0.03$–$0.1~{}\mathrm{Hz}$ band, ocean currents in the Gulf of Mexico are the main source of increased microseismic motion in $0.1$–$0.3~{}\mathrm{Hz}$ band and human activities such as logging, construction work and vehicles can cause increased ground motion in $1$–$6~{}\mathrm{Hz}$ anthropogenic band. Although all of these frequency bands are not in the sensitive detector gravitational wave band (10Hz-4 kHz), ground motion can couple non-linearly into that band. For example, during O3 transients due to scattered light were the most frequent source of transient noise at both LLO and LHO (LIGO Hanford Observatory), and were a result of increased ground motion in one or more of these seismic bands.

Light from the main laser path is scattered by a mirror and can be reflected by another surface. A fraction of this scattered light can rejoin the main path, and introduce a time dependent phase modulation, shown in eq 2, to the phase of the laser field. The additional phase shows up as noise $h_{\rm{ph}}$ in the detector data, shown in eq 1.

$$h_{\rm{ph}}(f)=\frac{K}{2}\frac{\lambda}{2\pi L}\mathcal{F}[\sin{\delta\phi}]$$

(1)

where

$$\phi(t)=\phi_{0}+\delta\phi_{\rm{sc}}(t)=\frac{4\pi}{\lambda}[x_{0}+\delta x_{\rm{sc}}(t)],$$

(2)

here, $K$ is the ratio of stray light amplitude to the amplitude of light in the main beam (usually unknown but very small), $\lambda$ is laser wavelength (1064 nm) and $L$ is the length of interferometer arms (4km). $\mathcal{F}$ indicates a Fourier transform, $x_{0}$ is the static path which corresponds to $\phi_{0}$, and $\delta x_{\rm{sc}}$ is the time-dependent displacement of the scattering surface which gives rise to the additional phase $\delta\phi_{\rm{sc}}$. If the phase modulation is small, $\sin\phi\approx\phi$ and the noise couples linearly; if $\delta x_{\rm{sc}}$ is a large fraction of $\lambda$, the noise couples non-linearly. In this latter case, as a result of fringe wrapping, the phase noise $h_{\rm{ph}}(f)$ associated with scattered light can show up as arches in $h(t)$ spectrogram. If we differentiate the phase $\phi=2\pi ft$ in eq 2 with respect to time, we obtain the frequency of the noise:

$$f(t)=|\frac{2v_{\rm{sc}}(t)}{\lambda}|$$

(3)

where $v_{\rm{sc}}$ is the velocity of the scatterer and $f$ is the peak frequency of the transients. If the surface excited by ground motion is in approximately periodic motion, the noise will appear as arches in a time-frequency spectrogram shown in the left plot of Fig 1. From Eq 3 we can see that a scatterer moving with higher velocity will lead to transients at higher peak frequency. A scatterer receiving or reflecting too little light or moving with small velocity amplitude will cause transients below the gravitational wave band [13].

Transient scattered noise can be classified into two main categories, depending on the frequency of the ground motion producing it: “slow scattering” and “fast scattering”, shown in fig 1. Slow scattering is usually a result of increased ground motion in earthquake and microseismic band, whereas fast scattering transients are usually a result of high ground motion in the anthropogenic band. In this paper we focus on fast scattering transients caused by increased anthropogenic motion due to trains [14]. (For details on slow scattering and its reduction during O3, we refer to [13].)

A few conditions impact the rate of transients due to ground motion in the vicinity of the instrument. This involves the intensity of ground motion, resonant frequencies of the detector components and scattered light amplitude. As mentioned earlier, the amount of ground motion is captured by the seismometers at End X, End Y, and the corner station, and it shows a clear correlation with scattered light transients in DARM. As expected, higher ground motion leads to more noise for a given band of importance. The second key factor is the resonant vibrating motion of different detector components from which light can get scattered. Furthermore, these resonances are the reason why we have fast scatter at specific frequencies such as $2$ Hz, $4$ Hz, $3.3$ Hz. The spacing between the fast scattering arches helps us narrow down the list of possible suspects. So similar degree of ground motion in a band that contains vibration resonances will create more noise in DARM than in a band that does not. Finally, the third factor is how much light is scattered by the moving detector component, which depends on how much light is incident on it and what fraction of it is reflected towards the mirrors. This is often difficult to measure, and commissioners use different techniques, including taking photographs and videos of detector hardware to assess the amount of light on them. Since the coupling between ground motion and strain noise depends on all these aspects, it can get very difficult to find the exact source of noise. A component with large motion amplitude may not have enough light amplitude, another component receiving sufficient light may be damped properly and thus would require too much motion to create noise above the strain sensitivity. Trains near LIGO Livingston routinely create strain noise, mostly in 10-200 Hz frequency band. The ground motion amplitude due to these trains is highest at End Y but a priori it cannot be assumed to be location of noise coupling, as per the above discussion. In this paper, we answer two main questions with regards to noise due to trains. What ground motion frequency band correlates the most with strain noise? Which location (out of End Y, End X and Corner) has highest ground motion coupling with strain noise? To answer these questions we use two methods, the Lasso analysis and the Spearman correlation analysis. Using both these approaches, we find a high degree of correlation between ground motion in $1.8$–$2.2~{}\mathrm{Hz}$ at the Corner station and strain noise due to trains. Identification of frequency bands that correlate well with strain noise is an important step as it allows commissioners to narrow down the list of potential suspects with resonances within the band. These resonances may then be damped leading to reduction in the noise. We suspect the motion of ARM Cavity Baffle in the corner station could be responsible for increased noise in $h(t)$ during trains.

Here we provide more examples of seismic band pass plots of various trains.