Measurement and subtraction of Schumann resonances at gravitational-wave interferometers

Correlated magnetic noise from Schumann resonances threatens to contaminate the observation of a stochastic gravitational-wave background in interferometric detectors. In previous work, we reported on the first effort to eliminate global correlated noise from the Schumann resonances using Wiener filtering, demonstrating as much as a factor of two reduction in the coherence between magnetometers on different continents. In this work, we present results from dedicated magnetometer measurements at the Virgo and KAGRA sites, which are the first results for subtraction using data from gravitational-wave detector sites. We compare these measurements to a growing network of permanent magnetometer stations, including at the LIGO sites. We show the effect of mutual magnetometer attraction, arguing that magnetometers should be placed at least one meter from one another. In addition, for the first time, we show how dedicated measurements by magnetometers near to the interferometers can reduce coherence to a level consistent with uncorrelated noise, making a potential detection of a stochastic gravitational-wave background possible.

Figure 1

Median power spectral density of the North-South Poland, North-South Colorado, North-South Villa Cristina, North-South Patagonia, KAGRA X-arm direction, LIGO Hanford X-arm direction, and LIGO Livingston X-arm direction magnetometers. These are computed using 128 s segments. In addition to the sharp instrumental line features in the Villa Cristina magnetometer at 8 Hz and 24 Hz, the Schumann resonances are visible in all of the magnetometers. The 20 Hz line at LIGO Livingston is likely due to power lines which cross the site on the Y-arm.

Figure 2

The plot shows the location of the 7 magnetometer stations with available data during this study (Here V1 and Villa Cristina are treated as being co-located). We show the networks used in the Wiener filtering analysis, represented as green, blue and red lines with the distance in kilometers shown. The purple line is a pair (Villa Cristina and LIGO Livingston) which is used in both the red and blue networks.

Figure 3

Locations of the magnetometers at Virgo, Livingston, Hanford and KAGRA. Their coordinates in the interferometer system (x,y) are: $V1=(80,-72)\mathrm{m}$; $L1=(120,3000)\mathrm{m}$; $H1=(1030,195)\mathrm{m}$; $K1=(400,-600)\mathrm{m}$.

Figure 4

On the left is the coherence between KAGRA and the North-South Poland, North-South Colorado, and Villa Cristina magnetometers over 2 days of coincident data. In this analysis, KAGRA 1 is the magnetometer located outside of the cave, and KAGRA 2 is the in-cave magnetometer. In addition, we plot the expected correlation given Gaussian noise. In the middle is the same between LIGO Livingston X-arm direction and those stations. In this analysis, LIGO 1 is the X-arm direction magnetometer, and LIGO 2 is the Y-arm direction magnetometer. The correlation between the two LIGO magnetometers is dominated by local noise, which means a Wiener filter using one of these to clean the other may not reduce correlations due to Schumann resonances, but is still useful to include in the filtering because it can increase sensitivity of the target channel by removing local disturbances. On the right is the coherence between Virgo North-South magnetometer and the North-South Poland, North-South Colorado, North-South Patagonia, LIGO Livingston X-arm direction, and LIGO Hanford X-arm direction magnetometers over a week of coincident data. In this analysis, Virgo 1 is the North-South magnetometer, and Virgo 2 is the East-West magnetometer.

Figure 5

Spectrograms (left) and Coherence (right) of colocated and coaligned magnetometers at Virgo at distances of 0.5 m, 1 m, 2 m, 5 m, and 10 m.

Figure 6

On the left is a comparison of spectra from the Virgo low-noise location and the one in Villa Cristina (located about 13 km from Virgo). They are both acquired with a magnetometer MFS-06 by Metronix oriented North-South. On the right is an example of the V-shaped data transient in Virgo magnetometers data.

Figure 7

Ratio of the auto power spectral density before and after Wiener filter subtraction. In the first example, we use one KAGRA magnetometer as the target sensor and use the second KAGRA magnetometer as the witness sensor. In the second example, we compute the ratio of the auto power spectral density before and after Wiener filter subtraction using the Villa Cristina magnetometer as the target sensor. We show subtraction using only the sensor with the highest coherence in each frequency bin as well as using all available sensors as witnesses, which shows improvement.

Figure 8

On the left is the coherence between the KAGRA and the Villa Cristina magnetometer before and after Wiener filter subtraction. For the KAGRA network, one KAGRA magnetometer is used as the target sensor while the second KAGRA magnetometer is the witness sensor. For the Villa Cristina network, we use the Villa Cristina magnetometer as the target sensor and the orthogonal sensor, Poland Hylaty, and Colorado Hugo magnetometers as witness sensors. There is no measurable remaining peak from the Schumann resonances. In the middle is the same between LIGO Livingston and the Villa Cristina magnetometers. For the LIGO Livingston network, we use the orthogonal sensor and Colorado Hugo, while for the Villa Cristina network, we use the orthogonal sensor and Poland Hylaty. Due to the distance from the witness sensors, some coherence remains. On the right is the same between LIGO Hanford and Virgo magnetometers. For the Virgo network, we use the orthogonal sensor, Poland Hylaty, and Patagonia, while for the LIGO Hanford network, we use the orthogonal sensor, LIGO Livingston, and Colorado Hugo.