Observation of a potential future sensitivity limitation from ground motion at LIGO Hanford

A first detection of terrestrial gravity noise in gravitational-wave detectors is a formidable challenge. With the help of environmental sensors, it can in principle be achieved before the noise becomes dominant by estimating correlations between environmental sensors and the detector. The main complication is to disentangle different coupling mechanisms between the environment and the detector. In this paper, we analyze the relations between physical couplings and correlations that involve ground motion and LIGO strain data h(t) recorded during its second science run in 2016 and 2017. We find that all noise correlated with ground motion was more than an order of magnitude lower than dominant low-frequency instrument noise, and the dominant coupling over part of the spectrum between ground and h(t) was residual coupling through the seismic-isolation system. We also present the most accurate gravitational coupling model so far based on a detailed analysis of data from a seismic array. Despite our best efforts, we were not able to unambiguously identify gravitational coupling in the data, but our improved models confirm previous predictions that gravitational coupling might already dominate linear ground-to-h(t) coupling over parts of the low-frequency, gravitational-wave observation band.

Figure 1

Three-channel scheme of a directional, linear system, where $C_i$ denotes an observation, $s_i(n_i)$ mutually independent noise sources, which (do not) propagate through the system, and $a_{ij}$ the physical links between channels, e.g., representing elastic or gravitational forces. Directionality is a valid approximation here, since it is assumed that the physical links $a_{ij}$ are weak, and the signals obey the approximate hierarchy $a_{01}{s}_0\sim s_1$ and $a_{02}{s}_0\sim a_{12}{s}_1\sim s_2$.

Figure 2

Four-channel scheme of the directional, linear system used to study potential gravitational coupling between ground tilt $C_0$ and test-mass acceleration $C_3$.

Figure 3

Coupling at 15 Hz between ground tilt of an isotropic Rayleigh field measured at position $x$, $y$ along the $x$ direction and associated NN with the positions of the two inner test masses marked in black. The white marker shows the position of the main beam splitter and the green marker the location of the tiltmeter during the observation period used in this paper. Color scale is in arbitrary units.

Figure 4

Top: average coherences between ground tilt and suspension-point channels. Bottom: transfer functions from suspension point to h(t) including the statistical estimation error of the ITMX, L transfer function.

Figure 5

Top: the plot shows strain noise spectra comparing the Advanced LIGO reference design sensitivity, the sensitivity reached during O2 (averaged over the days used in our analysis), and spectra of LIGO Hanford noise correlated with the tiltmeter and with the seismic array including their estimation errors. Bottom: ground tilt-to-$h(t)$ transfer functions. Sus L, P show the multiplications of transfer functions from ground tilt to ITMX L, P and ITMX L, P to $h(t)$, while “measured” shows the direct ground tilt-to-$h(t)$ transfer function (together with its statistical estimation error).

Figure 6

Histograms of seismic speeds and propagation azimuths. Each sample in this plot is an average over 800 s (using 8 s Fourier transforms), and a total of about 4500 samples contribute to the histogram at each frequency.

Figure 7

Spectrum of the tiltmeter in comparison with the tilt spectrum inferred from the seismic-array data using Eq. (12).

Figure 8

The plot shows the transfer functions between tiltmeter and $h(t)$ using different levels of simplification of a gravitational-coupling model for Rayleigh waves propagating along a flat surface. The two dashed curves are based on ad hoc assumptions about isotropy (yellow), and isotropy and speed (violet). The two solid curves are entirely based on array data: the full wave-vector space is integrated for the blue curve, while only the discrete information of dominant modes is used for the red curve.

Figure 9

Amplitude (top) and phase (bottom) of the array Wiener filter. The seismometers are ordered according to their distance to the nearest test mass. Seismometer distances are marked by horizontal lines, and their corresponding Wiener filter is represented by the colors below that line.

Figure 10

Coupling terms used in Eqs. (2) (two-link) and (4) (three-link) considering ITMX SUS L,P. The two-link curves represent the simple model with either L or P as additional channel. The three-link curves $\{\mathrm{all},\mathrm{L},\mathrm{P}\}$ represent the first, second, and third terms on the right-hand-side of Eq. (4) using L and P as additional channels.