4.2 Gravity gradient (Newtonian) noise

Gravity gradients, caused by direct gravitational coupling of mass density fluctuations to the suspended mirrors, were identified as a potential source of noise in ground-based gravitational-wave detectors in 1972 [313Jump To The Next Citation Point]. The noise associated with gravity gradients was first formulated by Saulson [275] and Spero [291], with later developments by Hughes and Thorne [184Jump To The Next Citation Point] and Cella and Cuoco [93]. These studies suggest that the dominant source of gravity gradients arise from seismic surface waves, where density fluctuations of the Earth’s surface are produced near the location of the individual interferometer test masses, as shown in Figure 7View Image.
View Image

Figure 7: Time-lapsed schematic illustrating the fluctuating gravitational force on a suspended mass by the propagation of a surface wave through the ground.

The magnitude of the rms motion of the interferometer test masses, &tidle;x(ω), can be shown to be [184]

&tidle;x(ω) = 4-πG-ρβ(ω ) &tidle;W (ω), (2 ) ω2
where ρ is the Earth’s density near the test mass, G is Newton’s constant, ω is the angular frequency of the seismic spectrum, β(ω) is a dimensionless reduced transfer function that takes into account the correlated motion of the interferometer test masses in addition to the reduction due to the separation between the test mass and the Earth’s surface, and W&tidle; (ω) is the displacement rms-averaged over 3-dimensional directions. In order to eliminate noise arising from gravity gradients, a detector would have to be operated far from these density fluctuations, that is, in space. Proposed space missions are discussed in Section 7.

However, there are two proposed approaches for reducing the level of gravity-gradient noise in future ground-based detectors. A monitor and subtraction method can be used, where an array of seismometers can be distributed strategically around each test mass to monitor the relevant ground motion (and ground compression) that would be expected to couple through local gravity. A subtraction signal may be developed from knowing how the observed density fluctuations couple to the motion of each test mass, and can potentially allow a significant reduction in gravity-gradient noise.

Another approach is to choose a very quiet location, or better still, to also go underground, as is already going ahead for LCGT [234Jump To The Next Citation Point]. Since the dominant source of gravity-gradient noise is expected to arise from surface waves on the Earth, the observed gravity-gradient noise will decrease with depth into the Earth. Current estimates suggest that gravity-gradient noise can be suppressed down to around 1 Hz by careful site selection and going ∼ 150 m underground [94]. The most promising approach (or likely only approach) to detecting gravitational waves whose frequency is below 1 Hz is to build an interferometer in space.

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