Newtonian noise cancellation in tensor gravitational wave detector

Abstract

Terrestrial gravity noise produced by ambient seismic and infrasound fields poses one of the main sensitivity limitations in low-frequency ground-based gravitational-wave (GW) detectors. This noise needs to be suppressed by 3-5 orders of magnitude in the frequency band 10 mHz to 1 Hz, which is extremely challenging. We present a new approach that greatly facilitates cancellation of gravity noise in full-tensor GW detectors. It makes explicit use of the direction of propagation of a GW, and can therefore either be implemented in directional searches for GWs or in observations of known sources. We show that suppression of the Newtonian-noise foreground is greatly facilitated using the extra strain channels in full-tensor GW detectors. Only a modest number of auxiliary, high-sensitivity environmental sensors is required to achieve noise suppression by a few orders of magnitude.

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Newtonian noise cancellation in tensor gravitational wave detector
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2016 J. Phys.: Conf. Ser. 716 012025
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Newtonian noise cancellation in tensor gravitational wave
detector
Ho Jung Paik1 and Jan Harms2
1 Department of Physics, University of Maryland, College Park, MD 20742, USA
2 Università degli studi di Urbino “Carlo Bo” and INFN Sezione di Firenze, Sesto
Fiorentino, I-50019, Italy
hpaik@umd.edu
Abstract. Terrestrial gravity noise produced by ambient seismic and infrasound fields poses
one of the main sensitivity limitations in low-frequency ground-based gravitational-wave
(GW) detectors. This noise needs to be suppressed by 35 orders of magnitude in the
frequency band 10 mHz to 1 Hz, which is extremely challenging. We present a new approach
that greatly facilitates cancellation of gravity noise in full-tensor GW detectors. It makes
explicit use of the direction of propagation of a GW, and can therefore either be implemented
in directional searches for GWs or in observations of known sources. We show that
suppression of the Newtonian-noise foreground is greatly facilitated using the extra strain
channels in full-tensor GW detectors. Only a modest number of auxiliary, high-sensitivity
environmental sensors is required to achieve noise suppression by a few orders of magnitude.
1. Introduction
The Newtonian noise (NN) generated by moving local masses poses a formidable challenge to
approaching the detector noise limit in gravitational-wave (GW) detectors at frequencies below 1 Hz.
At low frequencies, the NN is dominated by Rayleigh waves and infrasound waves. For a laser
interferometer to overcome this noise below 1 Hz, the ground and air motion within tens of kilometers
from the detector must be measured with a large number of seismometers and microphones with
sufficient accuracy, and then the induced NN computed and subtracted from the detector output. The
NN from Rayleigh waves could be canceled up to one part in 103 by using this method [1]. But for
infrasound waves, cancellation works only for waves coming in certain favorable directions.
In contrast, by using its tensor nature, SOGRO can mitigate the NN from both Rayleigh waves and
infrasound waves to one part in 103 for all incident angles. A detailed analysis of NN mitigation for
SOGRO has been published elsewhere [2]. In this paper, we summarize the result and discuss the
possibility of using mini-SOGROs to mitigate NN for advanced laser interferometer GW detectors.
2. Mitigation of NN on SOGRO
Assuming that the interferometer is underground at depth z < 0, the gravitational perturbation of a
single test mass due to a Rayleigh wave incident at an angle

with respect to the sensitive axis x of
the test mass and an infrasound wave incident in direction (

,

) is given [1] by
,sinexp
)(
cossinπ4exp
)(
cosπ2)( 32
0


























z
c
c
iGz
c
GiX
IS
IS
R
R (1)
11th Edoardo Amaldi Conference on Gravitational Waves (AMALDI 11) IOP Publishing
Journal of Physics: Conference Series 716 (2016) 012025 doi:10.1088/1742-6596/716/1/012025
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
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where

(

) and

(

) are the vertical ground displacement and atmospheric density fluctuation
directly above the test mass,

R  0.83 is a factor that accounts for the partial cancellation for the
Rayleigh NN from surface displacement by the sub-surface compressional wave content of the wave
field, cR  3.5 km/s and cIS  330 m/s are the speed of the Rayleigh waves underground and the
infrasound waves, respectively, and

0 is the mean mass density of the ground.
The metric perturbation tensor in the detector coordinates can be shown to be

,
1sincos
sinsinsincos
cossincoscos
)(),()()()( 2
2




















ii
i
i
bahN (2)
where
,exp
π2
)( 0







z
cc
G
a
RR
R




.sinexpsin
π4
),( 2
2













z
c
G
bIS (3)
Consider a GW coming from (

,

) direction in the presence of multiple Rayleigh and infrasound
waves. The full strain tensor in the GW coordinates has the form:














)(')(')('
)(')(')()(')(
)(')(')()(')(
)('
332313
232212
131211




NNN
NNN
NNN
hhh
hhhhh
hhhhh
h, (4)
with


iiiiiN ibah 2
11 ]sincos)[cos()(),()()()('

, (5a)


iiiiiN bah )(sin)(),()()()(' 2
22

, (5b)


iiiiiN ibah 2
33 ]cossin)[cos()(),()()()('

, (5c)


iiiiiiN ibah ]sincos))[cos(sin()(),()()()(' 12

, (5d)


iiiiiiN ibah ]cossin))[cos(sin()(),()()()(' 23

, (5e)

]cossin)[cos(]sincos)[cos()(),()()()(' 13

iibah i
iiiiiN  . (5f)
Due to the transverse nature of the GW, h’13, h’23 and h’33 contain only the NN components. To
recover h+(

) and h(

), the NN could be removed from h’11 and h’12 by correlating them with h’13, h’23
and h’33, and possibly also with some CM channels and subtracting the correlated parts.
Figure 1 shows the residual NN achieved for Rayleigh waves in the absence of infrasound waves
by using h’13, h’23, h’33 and az, plus seven seismometers with signal-to-noise ratio (SNR) of 103 at the
radius of 5 km as the input of the Wiener filter. The NN has been removed to about 103 with
environmental sensors (seismometers) alone. The local channels of SOGRO improve the noise
significantly only near

= /2, where the noise of the DM and CM channels drop out.
Figure 2 is the residual NN achieved for infrasound waves in the absence of Rayleigh waves by
using h’13, h’23, h’33 and 15 microphones of SNR of 104, one at the detector, seven each at the radius of
600 m and 1 km around the detector. With the environmental sensors (microphones) alone, the NN
cannot be mitigated except at

= 0, /2 and . This is because the infrasound waves come from a half
space and the microphones deployed over a surface is insufficient to measure the effect of 3D density
variations of the atmosphere. Thus mitigation of infrasound NN constitutes a formidable challenge for
laser interferometers. In SOGRO, the vertical strain component h’33 largely makes up for this
deficiency. With the aid of the local strain channels, the NN has been rejected to 10-3 for all

.
11th Edoardo Amaldi Conference on Gravitational Waves (AMALDI 11) IOP Publishing
Journal of Physics: Conference Series 716 (2016) 012025 doi:10.1088/1742-6596/716/1/012025
2

3. Mitigation of NN on interferometers with the aid of SOGROs
Since SOGRO is a very sensitive gravity strain gauge, one may be able to employ scaled-down
SOGROs with arm-length  << L, in place of a large array of seismometers, to directly measure and
remove the NN affecting the interferometer test masses. We restrict our discussion to underground
detectors like KAGRA [3] or Einstein Telescope (ET) [4].
The Rayleigh waves are expected to dominate the NN for an underground detector [1]. In the
presence of a GW and Rayleigh waves, the arm-length along the x axis is modulated by
),()(
12
xXxXhLL
RR

(6)
where X
R
(x
i
) is the first term of equation (1) summed over multiple waves for the i-th test mass on the
x axis. At 10 Hz, the Rayleigh wave length becomes

R
~ 350 m << L, causing X
R
(x
1
) and X
R
(x
2
) to be
uncorrelated. Hence we need to measure X
R
(x
i
) for each test mass by using a separate SOGRO co-
located with it, as shown in figure 3.
From equations (1) and (2), we find that the 13-component of the SOGRO output is given by
).()/()( 1313 iRRi xXcihx


(7)
We solve equation (7) for X
R
(x
i
) and substitute it into equation (6) to obtain

.)()(
113213
xx
L
c
i
L
L
h
R




 (8)
The sensitivity required for mini-SOGRO to recover h is then given by
h
cL
R


2
1




. (9)
Figure 1. NN due to Rayleigh waves removed
to ~10

3
by using h’
13
, h’
23
, h’
33
and a
z
(vertical
CM), plus seven seismometers with SNR = 10
3
at the radius of 5 km.
Figure 2. NN due to infrasound removed to 10

3
by using h’
13
, h’
23
, h’
33
and 15 microphones o
f
SNR = 10
4
, one at the detector, seven each at the
radius of 600 m and 1 km.
Figure 3. Four mini-
SOGROs collocated
with four test masses of
a laser interferometer
GW detector.
11th Edoardo Amaldi Conference on Gravitational Waves (AMALDI 11) IOP Publishing
Journal of Physics: Conference Series 716 (2016) 012025 doi:10.1088/1742-6596/716/1/012025
3

Figure 4 shows the sensitivity goals of advanced LIGO (aLIGO) [5] and ET [4]. The shaded
region represents the parameter space dominated by the NN at a shallow depth. A worthy goal would
be rejecting the NN by an order of magnitude to h  10-22 Hz1/2 at 3 Hz and to 1023 Hz-1/2 at 10 Hz.
For ET with L = 10 km, equation (9) yields

 4  10-21 Hz-1/2 at 3 Hz and 1.3  10-21 Hz-1/2 at 10 Hz.
The NN between SOGRO test masses must be highly correlated. According to Beker et al. [6],
,
1
1
2

R
SN
c
C
S

 (10)
where S is the mitigation factor and CSN is the correlation between the test masses. To obtain S = 10 at
10 Hz, we need CSN = 0.995 and   cR/

S = 5.6 m. Mitigating the NN for ground detectors is much
more challenging since the low speed of the Rayleigh waves on the surface, cR  250 m/s, reduces  to
 0.4 m. Such a small SOGRO would hardly have enough sensitivity.
Figure 5 shows the instrument noise spectral density for SOGRO with  = 5 m, M = 1 ton (each test
mass), and Q = 5  108 cooled to 0.1 K and coupled to a dc SQUID with 2 noise. The expected
sensitivity of SOGRO comes to within a factor of 2 from that required for S = 10. The same SOGRO
with Q = 109 coupled to a 1 SQUID would meet the sensitivity requirement, provided all the other
noise could be reduced to below its intrinsic noise limit. Should these sensitivities be achieved,
SOGRO could make it possible to construct ET less deep.
It is interesting to see how a mini-SOGRO two orders of magnitude less sensitive to GWs can help
ET mitigate the NN by an order of magnitude. This is because a SOGRO with  = 5 m is quite
efficient to detect the Rayleigh NN with

R/2 = 56 m and SOGRO employs a highly sensitive
superconducting displacement sensor. Although achieving a test mass Q of 109 and reaching the
quantum limit for the SQUID noise is very challenging, it is worth investigating the SOGRO option
since it has intrinsic advantages over seismometers in that it detects the NN directly and can monitor
the local gravity gradient environment with high sensitivity.
[1] Harms J et al 2013 Phys. Rev. D 88 122003
[2] Harms J and Paik H J 2015 Phys. Rev. D 92 022001
[3] Somiya K 2012 Class. Quantum Grav. 29 124007
[4] ET Science Team 2011 Einstein Gravitational Wave Telescope Conceptual Design Study,
available from European Gravitational Observatory http://www.et-gw.eu/. ET-0106C-10.
[5] LIGO Scientific Collaboration 2009 Rep. Prog. Phys. 72 076901
Figure 5. Instrument noise spectral density o
f
mini-SOGRO of 5-m arm-length cooled to 0.1
K
and coupled to a nearly quantum-limited SQUID
amplifier.
Figure 4. Sensitivity goals of aLIGO and ET.
The shaded region represents the parameter space
dominated by the NN.
[6] Beker M G et al 2011 Gen. Rel. Grav. 43 623
11th Edoardo Amaldi Conference on Gravitational Waves (AMALDI 11) IOP Publishing
Journal of Physics: Conference Series 716 (2016) 012025 doi:10.1088/1742-6596/716/1/012025
4