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 [55
, 166
]. For clarity, the two stages of in-vacuum
isolation are shown in Figure 5, whereas the test-mass suspensions are shown separately in
Figure 6.
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, 134
]. However, it is also possible
for this vibrational seismic noise to couple to the suspended optic through the gravitational
field.