4.1 Seismic noise

Seismic noise at a reasonably quiet site on the Earth follows a spectrum in all three dimensions close to 10–7f–2 m/Hz1/2 (where here and elsewhere we measure f in Hz) and thus if the disturbance to each test mass must be less than 3 × 10–20 m/Hz1/2 at, for example, 30 Hz, then the reduction of seismic noise required at that frequency in the horizontal direction is greater than 109. Since there is liable to be some coupling of vertical noise through to the horizontal axis, along which the gravitational-wave–induced strains are to be sensed, a significant level of isolation has to be provided in the vertical direction also. Isolation can be provided in a relatively simple way by making use of the fact that, for a simple pendulum system, the transfer function to the pendulum mass of the horizontal motion of the suspension point falls off as 1/(frequency)2 above the pendulum resonance. In a similar way isolation can be achieved in the vertical direction by suspending a mass on a spring. In the case of the Virgo detector system the design allows operation to below 10 Hz and here a seven-stage horizontal pendulum arrangement is adopted with six of the upper stages being suspended with cantilever springs to provide vertical isolation [99], with similar systems developed in Australia [194] and at Caltech [127]. For the GEO600 detector, where operation down to 50 Hz was planned, a triple pendulum system is used with the first two stages being hung from cantilever springs to provide the vertical isolation necessary to achieve the desired performance. This arrangement is then hung from a plate mounted on passive ‘rubber’ isolation mounts and on an active (electro-mechanical) anti-vibration system [257, 298]. The upgraded seismic isolation for Advanced LIGO will also adopt a variety of active and passive isolation stages. The total isolation will be provided by one external stage (hydraulics), two stages of in-vacuum active isolation, and being completed by the test mass suspensions [55Jump To The Next Citation Point, 166Jump To The Next Citation Point]. For clarity, the two stages of in-vacuum isolation are shown in Figure 5View Image, whereas the test-mass suspensions are shown separately in Figure 6View Image.
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Figure 5: Internal stages of the large chamber seismic isolation system for Advanced LIGO (image is inverted for clarity).
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Figure 6: CAD drawing of quad suspension system for Advanced LIGO, showing the mirror test mass at the bottom and where the uppermost section is attached to the third stage platform of the large chamber seismic isolation system shown in Figure 5View Image.

In order to cut down motion at the pendulum frequencies, active damping of the pendulum modes has to be incorporated, and to reduce excess motion at low frequencies around the micro-seismic peak, low-frequency isolators have to be incorporated. These low-frequency isolators can take different forms – tall inverted pendulums in the horizontal direction and cantilever springs whose stiffness is reduced by means of attractive forces between magnets for the vertical direction in the case of the Virgo system [220], Scott Russell mechanical linkages in the horizontal and torsion bar arrangements in the vertical for an Australian design [322], and a seismometer/actuator (active) system as shown here for Advanced LIGO [55] and also used in GEO600 [256]. Such schemes can provide sufficiently-large reduction in the direct mechanical coupling of seismic noise through to the suspended mirror optic to allow operation down to 3 Hz [98, 134Jump To The Next Citation Point]. However, it is also possible for this vibrational seismic noise to couple to the suspended optic through the gravitational field.

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