1. Seismic noise and vibration isolation
Kazuhiro Yamamoto
Department of Physics, Faculty of Science,
University of Toyama
Ok, let’s start ! In the second half of this lecture, I will explain seismic noise and quantum noise.
Lecture about gravitational wave detector for fresh persons
12 July 2017
@Gofuku campus, University of Toyama, Toyama, Japan

2. 0.Abstract
I would like to explain … (1) Seismic motion Investigation for silent site selection. (2) Vibration isolation How to suppress seicmic noise ?
This is abstract. I would like to explain seismic motion at first, especially, investigation for silent site selection. At second, I will introduce quantum noise, for example, reduction of shot noise, observation of radiation pressure noise, beyond radiation pressure noise.

3. Contents Introduction Seismic motion Vibration isolation Summary
This is the contents. At first, I would like to talk about seismic noise, quantum noise, and summary

4. 1. Introduction Vibration of ground shakes mirrors.
OK, let’s start review of seismic noise. This is the example of sensitivity. Seismic noise is here. Below 10 Hz, the sensitivity is limited by this seismic noise.
Seismic noise limits
sensitivity below 10 Hz.
Sensitivity wall in low frequency region

5. 1. Seismic noise How can we reduce seismic noise ?
(1) Small seismic motion site
(2) Excellent vibration isolation system
So, how can we reduce seismic noise ? There are two methods. The first one is that we put interferometer on the site with small seismic motion. The second one is good vibration isolation system. Since I am not familiar with isolation system, I introduce the isolation system shortly at first. Next, I will explain the seismic motion.

6. 2. Seismic noise What is seismic motion ?
If ground is perfectly equivalent to inertial frame, it implies no seismic noise (mirrors must be on inertial frame).
Seismic motion is acceleration. Accelerometer is necessary for measurement.
We often show power spectrum density of displacement, not acceleration. Acceleration spectrum is divided by (2pf)2 to convert acceleration to displacement.
So, how can we reduce seismic noise ? There are two methods. The first one is that we put interferometer on the site with small seismic motion. The second one is good vibration isolation system. Since I am not familiar with isolation system, I introduce the isolation system shortly at first. Next, I will explain the seismic motion.

7. 2. Seismic noise Site selection is essential !
How do we measure seismic motion ?
It is not easy even if seismic motion is typical one …
(a) Excellent (not usual !) commercial accelerometer
(b) Sensor made by ourselves …
One example : Michelson interferometer
So, I would like to explain the small seismic motion site. Site selection is essential for interferometer project. But, how do we measure seismic motion ? In fact, it is not so easy even if seismic motion has typical amplitude. We have two choice. The first one is we buy excellent commercial accelerometer. It must be noted that usual commercial accelerometer can not measure seismic motion. The second choice is that we make sensor by ourselves. For example, Michelson interferometer as like this. Laser, beam splitter, suspended mirror, fix mirror, photo detector. The seismic motion cause the relative motion between this plate and suspended mirror. Michelson interferometer can measure this relative motion. Anyway, we must prepare excellent sensor. But it is possible. So, we can measure the seismic motion.
A. Araya et al.,
Review of Scientific Instrument
64 (1993) 1337.

8. 2. Seismic noise Typical seismic motion 10-7[m/rtHz](1Hz/f) 2
(above 1Hz)
OK, but where is silent site ? It is famous that underground site has small seismic motion. This is seismic motions at various sites. The horizontal axis is frequency. This red line is the seismic motion at GEO site. This is the typical seismic vibration. Other lines represent the seismic motion at underground sites. Yes, obviously, underground is silent. Although many underground sites all over the world, here, I will show the results which came from Kamioka mine.
K. Arai, master thesis
(1997)

9. 2. Seismic noise Typical seismic motion Micro seismic peak
(around 0.2 Hz)
due to sea waves
near coast.
Amplitude strongly
depends on weather.
OK, but where is silent site ? It is famous that underground site has small seismic motion. This is seismic motions at various sites. The horizontal axis is frequency. This red line is the seismic motion at GEO site. This is the typical seismic vibration. Other lines represent the seismic motion at underground sites. Yes, obviously, underground is silent. Although many underground sites all over the world, here, I will show the results which came from Kamioka mine.
K. Arai, master thesis
(1997)

10. 2. Seismic noise Measurement around center of Kamioka mine (CLIO)
OK, but where is silent site ? It is famous that underground site has small seismic motion. This is seismic motions at various sites. The horizontal axis is frequency. This red line is the seismic motion at GEO site. This is the typical seismic vibration. Other lines represent the seismic motion at underground sites. Yes, obviously, underground is silent. Although many underground sites all over the world, here, I will show the results which came from Kamioka mine.
T.Sekiguchi,
JGW-T

11. 2. Seismic noise Under ground site has two orders of magnitudes
smaller seismic motion.
R. X. Adhikari
Reviews of Modern Physics,
86(2014)121.
OK, but where is silent site ? It is famous that underground site has small seismic motion. This is seismic motions at various sites. The horizontal axis is frequency. This red line is the seismic motion at GEO site. This is the typical seismic vibration. Other lines represent the seismic motion at underground sites. Yes, obviously, underground is silent. Although many underground sites all over the world, here, I will show the results which came from Kamioka mine.

12. 1. Seismic noise (1) Small seismic motion site
Under ground site has two orders of magnitudes
smaller seismic motion.
R. X. Adhikari
Reviews of Modern Physics,
86(2014)121.
OK, but where is silent site ? It is famous that underground site has small seismic motion. This is seismic motions at various sites. The horizontal axis is frequency. This red line is the seismic motion at GEO site. This is the typical seismic vibration. Other lines represent the seismic motion at underground sites. Yes, obviously, underground is silent. Although many underground sites all over the world, here, I will show the results which came from Kamioka mine.

13. 2. Seismic noise Where is Kamioka mine ?
Where is Kamioka mine ? It is in Japan. This is the map of Japan. This is Tokyo, capital city of Japan. Kamioka mine is here. The distance between Tokyo and Kamioka is about 220 km. It is comparable with the distance between Milano and Padova.

14. Location of LCGT
LCGT is planed to be built underground at Kamioka, where the prototype CLIO detector is placed.
By K. Kuroda (2009 May Fujihara seminar)
This is the bird view photograph of Kamioka mine. In this area, population is small. This is the mountain, whose name is Ikenoyama. There are rivers around there. This is the mine entrance. The horizontal distance between mine entrance and center of mine is about 2 km. The vertical distance between center of mine and top of mountain is about 1000 m.

15. 2. Seismic noise Many people measured seismic motion in Kamioka mine.
100 times smaller
seismic motion
at center of
Kamioka mine.
Many people measured seismic motion in Kamioka mine. Their results are consistent with each other. This is the one example. This black line is seismic motion at center of Kamioka mine. This redline is the seismic motion at Kashiwa, suburb of Tokyo. So, seismic motion in Kamioka mine is 100 times smaller. However …
However …
K. Yamamoto,
JGW-G , G

16. 2. Seismic noise All measurement was at center of mine.
Mirror must be far from center !
This is the map of Kamioka mine. This blue parts show the rivers. This part is mountain. As I said, many people measured seismic motion in Kamioka mine. The locations where the seismic motion was measured are shown in this map. There is a problem. They measured seismic motion around center of mine. Since LCGT interferometer is huge, the mirrors can not be the center of mine. Is the seismic motion far from center is sufficiently small? That’s a question. So, we tried to investigate the location dependence of seismic motion.
K. Yamamoto,
JGW-G , G

17. 2. Seismic noise Measurement outside of mine and shaft K. Yamamoto,
The red circles in this map show where we measured seismic motion. We measured seismic motion at CLIO site, the center of mine and outside of mine. Moreover, we investigated the seismic motion along Mozumi shaft in order to investigate the depth dependence of seismic motion. In usual, we use Atotsu shaft not Mozumi shaft.
K. Yamamoto,
JGW-G , G

18. 2. Seismic noise Measurement at Atotsu office K. Yamamoto,
Here is the Atotsu office. This office is on the entrance of mine. This small sensor is commercial accelerometer. So, at this moment, we measure the seismic motion outside of mine.
Measurement at Atotsu office
K. Yamamoto,
JGW-G , G

19. 2. Seismic noise Exit of Mozumi shaft Mozumi office
This is also seismic motion measurement outside mine. This is another mine entrance, Mozumi entrance. So this is exit of Mozumi shaft. This is the Mozumi office.
K. Yamamoto,
JGW-G , G
Outside of Mozumi office

20. 2. Seismic noise Measurement apparatus K. Yamamoto,
This is the experimental apparatus when we investigate seismic motion in Mozumi shaft. This is the spectrum analyzer. This is the logger. These are battery because there is no power supply in mine. Moreover, batteries provide DC voltage. But, analyzer and logger need AC voltage. So, this is the DC-AC converter.
Measurement apparatus
K. Yamamoto,
JGW-G , G

21. 2. Seismic noise K. Yamamoto, Truck JGW-G0500217, G0500218
Yes, these are measurement apparatus. People ride on this truck when we move in mine.
K. Yamamoto,
JGW-G , G
Truck

22. 2. Seismic noise Electric locomotive K. Yamamoto,
This electric locomotive carries the experimental apparatus and human beings.
Electric locomotive
K. Yamamoto,
JGW-G , G

23. 2. Seismic noise Fixed accelerometer in Mozumi shaft 10 cm
This photograph shows the fixed accelerometer in Mozumi shaft. This rock is hardest in Japan.
K. Yamamoto,
JGW-G , G

24. 2. Seismic noise Outside of mine <1 Hz (Outside of mine)
=(Center of mine)
>1 Hz
>(Center of mine)
Vertical motion is similar
to horizontal one.
Results of other locations
are similar.
These are results of outside of mine. These red and green lines are seismic motion mine entrance. This black line is seismic motion at center of mine. This blue line is the seismic motion at Kashiwa, suburb of Tokyo. Below 1 Hz, the seismic motion of outside is similar as that at mine center. But, above 1 Hz, outside motion is larger. Especially, above 10 Hz, the outside seismic motion is comparable with that near Tokyo. This graph shows the horizontal motion. But, the vertical motion is similar. Moreover, other place outside mine is also similar. So, the keyword, “underground” is essential.
K. Yamamoto, JGW-G , G

25. 2. Seismic noise Inside of mine > 50 m Silent sufficiently !
Main mirrors
50 m from ground
So, let us discuss the measurement inside mine, along Mozumi shaft. This black dashed line is the seismic motion at entrance. This black solid line is the seismic motion at mine center. The blue, green, red lines are seismic motion at place 50m, 100m, 800m far from the entrance. Even at 50m, the seismic motion is enough small. This results show that the mirror must be more than 50m underground.
K. Yamamoto, JGW-G , G

26. 2. Seismic noise Mirror displacement around 10Hz must be
below m/rtHz.
Seismic motion around
10Hz is m/rtHz
even at Kamoka.
At least 8 (in typical, 10)
orders of magnitude
vibration isolation
is necessary !
So, let us discuss the measurement inside mine, along Mozumi shaft. This black dashed line is the seismic motion at entrance. This black solid line is the seismic motion at mine center. The blue, green, red lines are seismic motion at place 50m, 100m, 800m far from the entrance. Even at 50m, the seismic motion is enough small. This results show that the mirror must be more than 50m underground.

27. 2. Seismic noise Mirror displacement around 10Hz must be
below m/rtHz.
Seismic motion around
10Hz is m/rtHz
even at Kamoka !
At least 8 (in typical, 10)
orders of magnitude
vibration isolation
is necessary !
No silver bullet ! We need many tricks !
R. X. Adhikari
Reviews of Modern Physics,
86(2014)121.
So, let us discuss the measurement inside mine, along Mozumi shaft. This black dashed line is the seismic motion at entrance. This black solid line is the seismic motion at mine center. The blue, green, red lines are seismic motion at place 50m, 100m, 800m far from the entrance. Even at 50m, the seismic motion is enough small. This results show that the mirror must be more than 50m underground.

28. 3. Vibration isolation
Mirrors must be suspended because they should act
as like free mass.
Otherwise, transfer function from gravitational wave
to detector output is too small.
“Suspended” mirror is also isolated from seismic motion.
So, let’s consider the vibration isolation system. But, how does this system cut seismic motion ? As I said, the mirrors in interferometer are suspended. In fact, this pendulum itself is vibration isolation system. This is the schematic views which show how pendulum works as vibration isolation system. We grasp the support point of pendulum here. If we move our hand slowly, mirror follows motion of support point. On the contrary, if we move our hand rapidly, mirror can not follow the motion of support.

29. 3. Vibration isolation Mirrors are suspended. Slow motion Rapid motion
So, let’s consider the vibration isolation system. But, how does this system cut seismic motion ? As I said, the mirrors in interferometer are suspended. In fact, this pendulum itself is vibration isolation system. This is the schematic views which show how pendulum works as vibration isolation system. We grasp the support point of pendulum here. If we move our hand slowly, mirror follows motion of support point. On the contrary, if we move our hand rapidly, mirror can not follow the motion of support.
Slow motion
Mirror follows
motion of support point.
Rapid motion
Mirror can not follow
motion of support point.

30. 3. Vibration isolation
Transfer function : (Motion of mirror)/(Motion of support)
Motion of support f0
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Motion of mirror

31. 3. Vibration isolation
Transfer function : (Motion of mirror)/(Motion of support) f0
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Typical resonant frequency
25cm pendulum, 1Hz

32. 1. Seismic noise
Transfer function : (Motion of mirror)/(Motion of support) f0
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Not enough …

33. 3. Vibration isolation How to improve isolation ratio ?
Softer spring (Lower resonant frequency) f0
10 times
smaller
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
100 times
smaller
M. Ando,
JGW-G

34. 3. Vibration isolation How to improve isolation ratio ?
Softer spring (Lower resonant frequency) f0
10 times
smaller
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Pendulum
f0 ~ l-1/2
(l is length.)
1Hz : 25cm
0.1Hz : 25m !
100 times
smaller

35. 3. Vibration isolation How to improve isolation ratio ?
Soft pendulum with reasonable size
Inverted pendulum
Elasticity : Positive spring constant
Gravity : Negative spring constant
Both spring constants cancel each other.
30mHz resonance is feasible.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
A. Takamori, LCGT design document (2004)

36. 3. Vibration isolation How to improve isolation ratio ?
Soft pendulum with reasonable size
Inverted pendulum
Elasticity : Positive spring constant
Gravity : Negative spring constant
Both spring constants cancel each other.
30mHz resonance is feasible.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
A. Takamori, LCGT design document (2004)

37. 3. Vibration isolation How to improve isolation ratio ?
Soft pendulum with reasonable size
Inverted pendulum
Elasticity : Positive spring constant
Gravity : Negative spring constant
Both spring constants cancel each other.
30mHz resonance is feasible.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
A. Takamori, LCGT design document (2004)

38. 3. Vibration isolation How to improve isolation ratio ?
Soft pendulum with reasonable size
Inverted pendulum
Elasticity : Positive spring constant
Gravity : Negative spring constant
Both spring constants cancel each other.
30mHz resonance is feasible.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
A. Takamori, LCGT design document (2004)

39. 3. Vibration isolation How to improve isolation ratio ?
Soft pendulum with reasonable size
Inverted pendulum
Drawbacks
(1)Soft spring can be broken easily (tilt..).
Control system or limiter are necessary.
(2)Elasticity depends on temperature.
Small temperature change causes
drastic change of resonant frequency.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
A. Takamori, LCGT design document (2004)

40. 3. Vibration isolation How to improve isolation ratio ?
VIRGO: Super Attenuator
How to improve isolation ratio ?
Multiple pendulum
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Mirror
M. Punturo, GWDAW Rome 2010

41. 3. Vibration isolation How to improve isolation ratio ?
Double pendulum as example of multiple pendulum
Upper mass
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Mirror
Mirror
K. Arai, master thesis(1997)

42. 3. Vibration isolation How to improve isolation ratio ?
Double pendulum as example of multiple pendulum
K. Arai, master thesis(1997)
N-stages
(f0/f)2N
(f0/f)2
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
(f0/f)4
20dB=10
40dB=100

43. 3. Vibration isolation How to improve isolation ratio ?
Double pendulum as example of multiple pendulum
Two peaks
N-stages
N peaks
One peak
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
K. Arai, master thesis(1997)

44. 3. Vibration isolation
We are interested with gravitational wave above 10Hz.
Do we need NOT to take care of vibration below 10 Hz ?
R. X. Adhikari
Reviews of Modern Physics,
86(2014)121.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

45. 3. Vibration isolation
We are interested with gravitational wave above 10Hz.
Do we need NOT to take care of vibration below 10 Hz ?
Contribution from this low frequency region dominates root mean square of vibration.
Root mean square (RMS) is integral of power spectrum in all frequency region.
In typical case, RMS is on the order of mm. Even at Kamioka, it is several times 10 nm.
Dynamic range for interferometer (detector) is about 1 nm.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

46. 3. Vibration isolation
Dynamic range of interferometer (detector) is about 1 nm.
Control and damping is necessary. Since they could be noise sources, we have to design carefully (weaker effect of control or damping is better).
For example …
Double pendulum
with eddy current damping
Magnets
Upper mass
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Mirror
K. Arai, master thesis(1997)

47. 3. Vibration isolation Eddy current damping
Wikipedia Eddy current
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
Magnets (metal) move near metal (magnets). Eddy current occurs. This electric current in resisitance is dissipation .

48. 3. Vibration isolation Resonant peaks are suppressed.
K. Arai, master thesis(1997)
Resonant peaks
are suppressed.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

49. 3. Vibration isolation Magnet is fixed on ground. So, this damping
introduce
seismic motion.
K. Arai, master thesis(1997)
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

50. 3. Vibration isolation Magnet is also suspended. So, seismic motion
can not be introduced.
K. Arai, master thesis(1997)
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

51. 3. Vibration isolation
Control (or damping) have to work only around resonant frequency (about 1 Hz).
Otherwise, noise by this system contaminates observation band (above 10 Hz).
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

52. 3. Vibration isolation
Only upper mass is applied eddy current damping.
It can suppress resonant motion because both masses move.
On the other hand, noise by
damping can not be transferred
to mirror because stage
between upper mass
and mirror act
as vibration isolation.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
K. Arai, master thesis(1997)

53. 3. Vibration isolation Passive vs Active
Eddy current damping -> Passive (without any power supply)
Active (with power supply) : For example, monitors and actuators. Active system is more complicate. On the other hand, we can use some tricks.
However, points for design are same; Control (or damping) works only around resonant frequency (about 1 Hz).
On the contrary, we have to stop it in observation band
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

54. 3. Vibration isolation Vertical vibration isolation
Is it problem ? Yes, due to curvature of Earth !
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
q~ 0.2mrad

55. 1. Seismic noise Vertical vibration isolation
Imperfection of suspension (differences between wires …) make coupling between vertical and horizontal motion. In other words, vertical seismic motion causes not only vertical motion of mirror, but also horizontal one.
Roughly speaking, the ratio is 1/100 or 1/1000.
In the case of KAGRA, baseline has 1/300 gradient to drain water.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

56. 3. Vibration isolation Vertical vibration isolation
Spring constant k (resonant frequency) of vertical motion is higher than that of horizontal motion in usual.
Typical resonant frequency
Horizontal 1 Hz, Vertical 10 Hz
Summary
(1)Vertical-horizontal coupling
(2)Higher vertical resonant frequency
->Vertical motion effect is larger.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

57. 3. Vibration isolation Vertical vibration isolation
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.
A. Takamori, LCGT design document (2004)

58. 3. Vibration isolation Vertical vibration isolation
Softer vertical spring has larger stretch from natural length.
Vertical resonant frequency is proportional to k1/2.
Stretch from natural length is proportional to k.
Resonant frequency Stretch from natural length
10 Hz mm
1 Hz cm
0.1Hz m
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

59. 3. Vibration isolation Vertical vibration isolation
Soft vertical spring with reasonable size
KAGRA adopts Geometrical Anti Spring (GAS).
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.

60. 3. Vibration isolation Vertical vibration isolation
Soft vertical spring with reasonable size
Geometrical Anti Spring (GAS)
Elasticity : Positive spring constant
Compression : Negative spring constant
Both spring constants cancel each other.
0.2 Hz resonance is feasible.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better. 60
A. Takamori, LCGT design document (2004)

61. 3. Vibration isolation Vertical vibration isolation
Soft vertical spring with reasonable size
Geometrical Anti Spring (GAS)
Elasticity : Positive spring constant
Compression : Negative spring constant
Both spring constants cancel each other.
0.2 Hz resonance is feasible.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better. 61
A. Takamori, LCGT design document (2004)

62. 3. Vibration isolation Vertical vibration isolation
Soft vertical spring with reasonable size
Geometrical Anti Spring (GAS)
Elasticity : Positive spring constant
Compression : Negative spring constant
Both spring constants cancel each other.
0.2 Hz resonance is feasible.
Same drawbacks
of inverted pendulum …
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better. 62
A. Takamori, LCGT design document (2004)

63. 4. Summary Summary of seismic motion Typical seismic motion :
10-7[m/rtHz](1Hz/f)2 (above 1Hz)
Microseismic peak is around 0.2 Hz.
Underground site is excellent.
100 times smaller seismic motion
I would like to show the short summary about seismic noise. We need excellent and huge vibration isolation system. Underground site is excellent. Because seismic motion is 100 times smaller than typical one. Depth of mirror must be more than 50 m. If not so, seismic motion is not so small even if the site is country side.
Depth of mirror must be more than 50 m.
If not so, seismic motion is not so small even if
the site is country side …

64. 4. Summary Summary of vibration isolation
At least 8 (in typical, 10) orders of magnitude
vibration isolation is necessary.
Not only horizontal but also vertical motion must be supressed.
Soft vibration isolation with reasonable size
Cancel of positive and negative spring constant
Multiple pendulum to enhance vibration isolation ratio
I would like to repeat the short summary about seismic noise. We need excellent and huge vibration isolation system. Underground site is excellent. Because seismic motion is 100 times smaller than typical one. Depth of mirror must be more than 50 m. If not so, seismic motion is not so small even if the site is country side.
Control and damping to suppress resonant motion is necessary. But they have to work only around resonant frequency (about 1 Hz). Otherwise, noise by this system contaminates observation band (above 10 Hz).

65. Thank you for your attention !
That’s all. Thank you for your attention.

66. 1. Seismic noise (1) Small seismic motion site Where is silent sites ?
Underground !
Kamioka mine
M. Punturo,
GWDAW Rome 2010
OK, but where is silent site ? It is famous that underground site has small seismic motion. This is seismic motions at various sites. The horizontal axis is frequency. This red line is the seismic motion at GEO site. This is the typical seismic vibration. Other lines represent the seismic motion at underground sites. Yes, obviously, underground is silent. Although many underground sites all over the world, here, I will show the results which came from Kamioka mine.
BFO (Black Forest Observatory): -162m
BRG (Berggieshübel seism Observatory): -36m
GRFO (Graefenberg borehole station): -116m
Kamioka (Kamioka mine): -1000m

67. 1. Seismic noise (2) Good vibration isolation system
VIRGO: Super Attenuator
(2) Good vibration isolation system
Unfortunately, single pendulum
does not have enough isolation for
gravitational wave detection.
We need multi stage isolation system.
Unfortunately, single pendulum does not have enough isolation for gravitational wave detection. We need multi stage isolation system. This is an example. Super attenuator of VIRGO project. There are many stages. At the bottom, there is a mirror. The height is 8 m.
Mirror
M. Punturo, GWDAW Rome 2010

68. 3. Vibration isolation Vertical vibration isolation
Stack : rubber and spring.
This graph show the transfer function, which is the ratio of motion of mirror to motion of support. This horizontal axis is frequency. This is the resonance peak of pendulum. Below the resonant frequency, in short, motion is slow, transfer function is unity. So mirror perfectly follows the support point. Above the resonant frequency, in short, the motion is fast, transfer function is less than unity. So, mirror is isolated from the motion of support point. At the higher frequency, isolation ratio is better.