1.5000264.pdf

Effects of transients in LIGO suspensions on searches for gravitational waves

M. Walker

, T. D. Abbott

, S. M. Aston

, G. González

, D. M. Macleod

, J. McIver

, B. P. Abbott

, R. Abbott

, C.

Adams

, R. X. Adhikari

, S. B. Anderson

, A. Ananyeva

, S. Appert

, K. Arai

, S. W. Ballmer

, D. Barker

, B. Barr

L. Barsotti

, J. Bartlett

, I. Bartos

, J. C. Batch

, A. S. Bell

, J. Betzwieser

, G. Billingsley

, J. Birch

, S. Biscans

, C.

Biwer

, C. D. Blair

, R. Bork

, A. F. Brooks

, G. Ciani

, F. Clara

, S. T. Countryman

, M. J. Cowart

, D. C. Coyne

A. Cumming

, L. Cunningham

, K. Danzmann

, C. F. Da Silva Costa

, E. J. Daw

, D. DeBra

, R. T. DeRosa

, R.

DeSalvo

, K. L. Dooley

, S. Doravari

, J. C. Driggers

, S. E. Dwyer

, A. Effler

, T. Etzel

, M. Evans

, T. M. Evans

M. Factourovich

, H. Fair

, A. Fernández Galiana

, R. P. Fisher

, P. Fritschel

, V. V. Frolov

, P. Fulda

, M. Fyffe

, J.

A. Giaime

, K. D. Giardina

, E. Goetz

, R. Goetz

, S. Gras

, C. Gray

, H. Grote

, K. E. Gushwa

, E. K. Gustafson

R. Gustafson

, E. D. Hall

, G. Hammond

, J. Hanks

, J. Hanson

, T. Hardwick

, G. M. Harry

, M. C. Heintze

A. W. Heptonstall

, J. Hough

, K. Izumi

, R. Jones

, S. Kandhasamy

, S. Karki

, M. Kasprzack

, S. Kaufer

, K.

Kawabe

, N. Kijbunchoo

, E. J. King

, P. J. King

, J. S. Kissel

, W. Z. Korth

, G. Kuehn

, M. Landry

, B. Lantz

, N.

A. Lockerbie

, M. Lormand

, A. P. Lundgren

, M. MacInnis

, S. Márka

, Z. Márka

, A. S. Markosyan

, E. Maros

I. W. Martin

, D. V. Martynov

, K. Mason

, T. J. Massinger

, F. Matichard

, N. Mavalvala

, R. McCarthy

, D. E.

McClelland

, S. McCormick

, G. McIntyre

, G. Mendell

, E. L. Merilh

, P. M. Meyers

, J. Miller

, R. Mittleman

, G.

Moreno

, G. Mueller

, A. Mullavey

, J. Munch

, L. K. Nuttall

, J. Oberling

, M. Oliver

, P. Oppermann

, Richard J.

Oram

, B. O’Reilly

, D. J. Ottaway

, H. Overmier

, J. R. Palamos

, H. R. Paris

, W. Parker

, A. Pele

, S. Penn

, M.

Phelps

, V. Pierro

, I. Pinto

, M. Principe

, L. G. Prokhorov

, O. Puncken

, V. Quetschke

, E. A. Quintero

, F. J.

Raab

, H. Radkins

, P. Raffai

, S. Reid

, D. H. Reitze

, N. A. Robertson

, J. G. Rollins

, V. J. Roma

, J. H. Romie

S. Rowan

, K. Ryan

, T. Sadecki

, E. J. Sanchez

, V. Sandberg

, R. L. Savage

, R. M. S. Schofield

, D. Sellers

, D.

A. Shaddock

, T. J. Shaffer

, B. Shapiro

, P. Shawhan

, D. H. Shoemaker

, D. Sigg

, B. J. J. Slagmolen

, B. Smith

J. R. Smith

, B. Sorazu

, A. Staley

, K. A. Strain

, D. B. Tanner

, R. Taylor

, M. Thomas

, P. Thomas

, K. A. Thorne

E. Thrane

, C. I. Torrie

, G. Traylor

, D. Tuyenbayev

, G. Vajente

, G. Valdes

, A. A. van Veggel

, A. Vecchio

, P. J.

Veitch

, K. Venkateswara

, T. Vo

, C. Vorvick

, R. L. Ward

, J. Warner

, B. Weaver

, R. Weiss

, P. Weßels

, B. Willke

C. C. Wipf

, J. Worden

, G. Wu

, H. Yamamoto

, C. C. Yancey

, Hang Yu

, Haocun Yu

, L. Zhang

, M. E. Zucker

and

J. Zweizig

Citation:

Review of Scientific Instruments

, 124501 (2017);

View online:

https://doi.org/10.1063/1.5000264

View Table of Contents:

http://aip.scitation.org/toc/rsi/88/12

Published by the

American Institute of Physics

REVIEW OF SCIENTIFIC INSTRUMENTS

88

, 124501 (2017)

Effects of transients in LIGO suspensions on searches

for gravitational waves

M. Walker,

1,2

T. D. Abbott,

S. M. Aston,

G. Gonz

alez,

D. M. Macleod,

J. McIver,

B. P. Abbott,

R. Abbott,

C. Adams,

R. X. Adhikari,

S. B. Anderson,

A. Ananyeva,

S. Appert,

K. Arai,

S. W. Ballmer,

D. Barker,

B. Barr,

L. Barsotti,

J. Bartlett,

I. Bartos,

J. C. Batch,

A. S. Bell,

J. Betzwieser,

G. Billingsley,

J. Birch,

S. Biscans,

4,8

C. Biwer,

C. D. Blair,

R. Bork,

A. F. Brooks,

G. Ciani,

F. Clara,

S. T. Countryman,

M. J. Cowart,

D. C. Coyne,

A. Cumming,

L. Cunningham,

K. Danzmann,

12,13

C. F. Da Silva Costa,

E. J. Daw,

D. DeBra,

R. T. DeRosa,

R. DeSalvo,

K. L. Dooley,

S. Doravari,

J. C. Driggers,

S. E. Dwyer,

A. Effler,

T. Etzel,

M. Evans,

T. M. Evans,

M. Factourovich,

H. Fair,

A. Fern

andez Galiana,

R. P. Fisher,

P. Fritschel,

V. V. Frolov,

P. Fulda,

M. Fyffe,

J. A. Giaime,

1,3

K. D. Giardina,

E. Goetz,

R. Goetz,

S. Gras,

C. Gray,

H. Grote,

K. E. Gushwa,

E. K. Gustafson,

R. Gustafson,

E. D. Hall,

G. Hammond,

J. Hanks,

J. Hanson,

T. Hardwick,

G. M. Harry,

M. C. Heintze,

A. W. Heptonstall,

J. Hough,

K. Izumi,

R. Jones,

S. Kandhasamy,

S. Karki,

M. Kasprzack,

S. Kaufer,

K. Kawabe,

N. Kijbunchoo,

E. J. King,

P. J. King,

J. S. Kissel,

W. Z. Korth,

G. Kuehn,

M. Landry,

B. Lantz,

N. A. Lockerbie,

M. Lormand,

A. P. Lundgren,

M. MacInnis,

S. M

arka,

Z. M

arka,

A. S. Markosyan,

E. Maros,

I. W. Martin,

D. V. Martynov,

K. Mason,

T. J. Massinger,

F. Matichard,

4,8

N. Mavalvala,

R. McCarthy,

D. E. McClelland,

S. McCormick,

G. McIntyre,

G. Mendell,

E. L. Merilh,

P. M. Meyers,

J. Miller,

R. Mittleman,

G. Moreno,

G. Mueller,

A. Mullavey,

J. Munch,

L. K. Nuttall,

J. Oberling,

M. Oliver,

P. Oppermann,

Richard J. Oram,

B. O’Reilly,

D. J. Ottaway,

H. Overmier,

J. R. Palamos,

H. R. Paris,

W. Parker,

A. Pele,

S. Penn,

M. Phelps,

V. Pierro,

I. Pinto,

M. Principe,

L. G. Prokhorov,

O. Puncken,

V. Quetschke,

E. A. Quintero,

F. J. Raab,

H. Radkins,

P. Raffai,

S. Reid,

D. H. Reitze,

4,11

N. A. Robertson,

4,7

J. G. Rollins,

V. J. Roma,

J. H. Romie,

S. Rowan,

K. Ryan,

T. Sadecki,

E. J. Sanchez,

V. Sandberg,

R. L. Savage,

R. M. S. Schofield,

D. Sellers,

D. A. Shaddock,

T. J. Shaffer,

B. Shapiro,

P. Shawhan,

D. H. Shoemaker,

D. Sigg,

B. J. J. Slagmolen,

B. Smith,

J. R. Smith,

B. Sorazu,

A. Staley,

K. A. Strain,

D. B. Tanner,

R. Taylor,

M. Thomas,

P. Thomas,

K. A. Thorne,

E. Thrane,

C. I. Torrie,

G. Traylor,

D. Tuyenbayev,

G. Vajente,

G. Valdes,

A. A. van Veggel,

A. Vecchio,

P. J. Veitch,

K. Venkateswara,

T. Vo,

C. Vorvick,

R. L. Ward,

J. Warner,

B. Weaver,

R. Weiss,

P. Weßels,

B. Willke,

12,13

C. C. Wipf,

J. Worden,

G. Wu,

H. Yamamoto,

C. C. Yancey,

Hang Yu,

Haocun Yu,

L. Zhang,

M. E. Zucker,

4,8

and J. Zweizig

Louisiana State University, Baton Rouge, Louisiana 70803, USA

California State University Fullerton, Fullerton, California 92831, USA

LIGO Livingston Observatory, Livingston, Louisiana 70754, USA

LIGO, California Institute of Technology, Pasadena, California 91125, USA

Syracuse University, Syracuse, New York 13244, USA

LIGO Hanford Observatory, Richland, Washington 99352, USA

SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom

LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Columbia University, New York, New York 10027, USA

University of Western Australia, Crawley, Western Australia 6009, Australia

University of Florida, Gainesville, Florida 32611, USA

Leibniz Universit

at Hannover, D-30167 Hannover, Germany

Albert-Einstein-Institut, Max-Planck-Institut f

ur Gravitationsphysik, D-30167 Hannover, Germany

The University of Sheffield, Sheffield S10 2TN, United Kingdom

Stanford University, Stanford, California 94305, USA

University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli,

I-80100 Napoli, Italy

The University of Mississippi, University, Mississippi 38677, USA

University of Michigan, Ann Arbor, Michigan 48109, USA

American University, Washington, D.C. 20016, USA

University of Oregon, Eugene, Oregon 97403, USA

University of Adelaide, Adelaide, South Australia 5005, Australia

SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom

Australian National University, Canberra, Australian Capital Territory 0200, Australia

0034-6748/2017/88(12)/124501/9/

$

30.00

, 124501-1

Published by AIP Publishing.

124501-2

Walker

et al.

Rev. Sci. Instrum.

, 124501 (2017)

University of Minnesota, Minneapolis, Minnesota 55455, USA

Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain

Hobart and William Smith Colleges, Geneva, New York 14456, USA

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA

MTA E

otv

os University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary

SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom

University of Maryland, College Park, Maryland 20742, USA

Monash University, Victoria 3800, Australia

University of Birmingham, Birmingham B15 2TT, United Kingdom

University of Washington, Seattle, Washington 98195, USA

(Received 14 August 2017; accepted 2 November 2017; published online 1 December 2017)

This paper presents an analysis of the transient behavior of the Advanced LIGO (Laser Interferometer

Gravitational-wave Observatory) suspensions used to seismically isolate the optics. We have charac-

terized the transients in the longitudinal motion of the quadruple suspensions during Advanced LIGO’s

first observing run. Propagation of transients between stages is consistent with modeled transfer func-

tions, such that transient motion originating at the top of the suspension chain is significantly reduced

in amplitude at the test mass. We find that there are transients seen by the longitudinal motion mon-

itors of quadruple suspensions, but they are not significantly correlated with transient motion above

the noise floor in the gravitational wave strain data, and therefore do not present a dominant source of

background noise in the searches for transient gravitational wave signals. Using the suspension transfer

functions, we compared the transients in a week of gravitational wave strain data with transients from

a quadruple suspension. Of the strain transients between 10 and 60 Hz, 84% are loud enough that they

would have appeared above the sensor noise in the top stage quadruple suspension monitors if they

had originated at that stage at the same frequencies. We find no significant temporal correlation with

the suspension transients in that stage, so we can rule out suspension motion originating at the top

stage as the cause of those transients. However, only 3.2% of the gravitational wave strain transients

are loud enough that they would have been seen by the second stage suspension sensors, and none of

them are above the sensor noise levels of the penultimate stage. Therefore, we cannot eliminate the

possibility of transient noise in the detectors originating in the intermediate stages of the suspension

below the sensing noise.

Published by AIP Publishing.

https://doi.org/10.1063/1.5000264

I. INTRODUCTION

The Laser Interferometer Gravitational-wave Observatory

(LIGO) was designed to detect gravitational waves from astro-

physical sources.

1,2

After six science runs over the course of

several years, the detectors underwent major upgrades start-

ing in 2010. In September 2015, the newly upgraded Advanced

LIGO detectors began taking data for their first observational

period (

1). Figure 1 shows the basic optical configuration

of Advanced LIGO. With a sensitivity more than three times

better than that of the previous generation,

the detectors had

the astrophysical reach to make the first direct observation

of a gravitational wave signal, GW150914, from the merger

of two black holes,

and later a second unambiguous detec-

tion, GW151226.

These observations have opened a new

field of gravitational-wave astronomy, which will continue

to grow brighter with further improvements to the detector

network.

The main limitation to LIGO’s low-frequency (up to

10 Hz) sensitivity is seismic noise. (At intermediate frequen-

cies, technical noises and thermal noise of the mirror coatings

are the dominant source of noise, and at frequencies higher

than 100 Hz, the detectors are limited by photon shot noise.)

The LIGO detectors are affected by earthquakes from around

the world, windy weather that shakes the buildings housing

the interferometer instrumentation, microseismic vibrations

from ocean waves crashing on the shores of the Pacific Ocean,

Atlantic Ocean, and the Gulf of Mexico, and local anthro-

pogenic activity.

6,7

The study of the effects of seismic activity

was especially important for improving the data quality of tran-

sient gravitational wave searches in the initial LIGO era.

8,9

One of the key improvements from initial to Advanced LIGO

is the implementation of a much more sophisticated seismic

isolation system, which includes stages of active and passive

isolation for all of the cavity optics.

2,10

It is important to verify that this entirely new system pro-

vides the very high isolation expected and that it does not

introduce any new types of transient noise that could add to

the noise background for searches of short-duration gravita-

tional waves, such as signals from black hole mergers and

supernovae. Here we present an investigation of the transient

motion of the Livingston suspension systems as measured

by local sensors on each suspension, specifically looking at

the displacement of the quadruple stage pendulums in the

longitudinal degree of freedom, which is the direction of the

optical path used to sense spacetime strain induced by passing

gravitational waves.

II. ADVANCED LIGO SUSPENSIONS

In Advanced LIGO, all optical cavities use optics sus-

pended from multi-stage pendulums, in order to benefit from

124501-3

Walker

et al.

Rev. Sci. Instrum.

, 124501 (2017)

FIG. 1. Simplified diagram of the Advanced LIGO optical configuration,

adapted from B. P. Abbott

et al.

, “Observation of gravitational waves

from a binary black hole merger,” Phys. Rev. Lett.

116

, 061102 (2016).

tion 3.0 Unported License.

As a gravitational wave impinges upon the

interferometer, it stretches and squeezes the arms of the interferometer,

creating differential cavity length variations that are sensed by the pho-

todetector. To reduce the effects of seismic motion on the measurement

of strain, the mirrors at the input and end of both arms are suspended

from quadruple-stage pendulums, in addition to active seismic isolation

systems.

the lowpassing of seismic motion. The input and end mir-

rors (the optics whose motion most directly contributes to

the gravitational-wave readout signal) are all hung from

quadruple-stage suspensions,

with each stage providing

additional isolation at frequencies above the suspension res-

onances, which range from 0.4 Hz to 14 Hz. The quadruple

pendulum is suspended at the top from maraging steel blade

springs, with two further sets of springs incorporated into

the top two masses, thus providing three stages of enhanced

vertical isolation. The two lower masses of the quadruple

suspension are cylindrical silica masses connected by fused

silica fibers to reduce thermal noise. Another similar quadru-

ple suspension is hung next to the test mass suspension, so the

actuation on lower stages can be done from a similarly isolated

reaction chain. Figure 2 gives an overview of the design of the

Advanced LIGO quadruple suspensions.

The local displacement of the top three stages of the

suspensions is measured using Optical Sensor and Electro-

Magnetic actuators, or OSEMs, which are electromagnetic

sensors and actuators used for damping the suspensions’ res-

onances and controlling the mirrors to keep cavities aligned

and locked.

10,11

The lowest stage on each quadruple suspen-

sion does not have the OSEM sensors, but instead is controlled

by an electrostatic drive.

The OSEMs can sense suspension motion at low frequen-

cies where the displacements are relatively large. At frequen-

cies above 5 Hz, the suspension motion has typically fallen

below the sensitivity level of the OSEMs such that the resulting

spectra are dominated by electronics noise. Multiple OSEMs

on each stage allow the calculation of the mass’s motion in

each degree of freedom using a linear combination of the sen-

sors’ signals. The sensed displacement of the top stage is used

in a feedback loop to actuate on that stage of the suspension in

order to damp the mechanical resonances of the suspension.

The sensors at lower stages are only used as witnesses of the

optics’ displacement for the purposes of diagnosing problems

in the suspensions. The actuators on lower stages use inter-

ferometer and cavity signals to keep various degrees of the

interferometer precisely on resonance.

III. MOTION TRANSIENTS IN SUSPENSIONS

In order to eliminate false positives from the gravitational

wave searches, it is necessary to understand the origins of non-

astrophysical noise transients in the gravitational wave data.

Each subsystem of the detector itself is therefore investigated

in great detail to fully study all potential noise sources.

FIG. 2. Quadruple suspension design. Reprinted with permission from S. M. Aston

et al.

, “Update on quadruple suspension design for advanced LIGO,”

Classical Quantum Gravity

29

The left image shows the suspension systems with the blades, fibers, and

reaction chain. On the right, the whole structure is shown, with the four masses labeled.

124501-4

Walker

et al.

Rev. Sci. Instrum.

, 124501 (2017)

FIG. 3. Typical amplitude spectral density (ASD) for the

Y-arm input test mass suspension (ITMY) longitudinal

motion monitors during the first Advanced LIGO observ-

ing run. The spectra below the suspension resonances are

dominated by seismic motion, and other low frequency

features of the ASDs correspond to the pendulum reso-

nances and the control loops used to damp them. Since

this is during a time when suspension modes were damped

and not excited, not every resonance of the system shows

up in the ASD. For example, the pitch mode near 2.7

Hz is not visible here. The smooth portion of the ASD

above 5 Hz shows where the electronics noise of the sen-

sors dominates the spectrum. Since the penultimate stage

requires a lower actuation force than the top mass, it uses

a more lightweight type of actuator, which has slightly

higher sensing noise floor at higher frequencies.

In this article, we characterize transients in the displace-

ment of the suspensions’ stages as measured by the OSEMs,

the propagation of transients between different stages, and

their effects on the gravitational wave strain data. Specifically,

transients in the longitudinal degree of freedom were studied

in the top three stages of the quadruple suspensions. The angu-

lar motion of the test masses is sensed using optical levers, but

since these sensors do not measure the longitudinal motion,

they are not used in this study.

Motion transients seen by the local displacement sen-

sors have a few potential sources. For example, they could

be caused by motion that is intrinsic to the suspension sys-

tems themselves, from the crackling in the suspension wires or

the steel blades.

12,13

Transients could also come from excess

seismic motion by propagating through each stage of active

seismic isolation and then down through the suspension stages.

Above the suspension’s resonance f

, the seismic transients

should decrease in amplitude by a factor of (f

/

)

at each

stage and be less likely to appear above the sensor noise at

lower stages. Therefore any seismic transients that affect mul-

tiple stages should appear mostly at low frequencies. Another

source of transients seen in the local sensors is the actuation

on the suspensions from the feedback loops used to control the

interferometer.

A. Suspension behavior in Advanced LIGO’s first

observing run

The typical spectrum of the suspension motion monitors is

characterized by several peaks near the low frequency pendu-

lum resonances between 0.4 and 5 Hz, and the smooth noise

above 5 Hz due to the sensors’ electronics noise. The main

resonances in the longitudinal degree of freedom are modeled

for the quadruple suspensions to be at 0.435 Hz, 0.997 Hz,

2.006 Hz, and 3.416 Hz, but coupling from other degrees of

freedom and the active seismic isolation system creates addi-

tional peaks in the spectrum. Figure 3 shows a typical spectrum

of the Y-arm input quadruple suspension (Input Test Mass Y or

ITMY

) motion in O1 along with estimated sensor noise levels.

FIG. 4. The panel on the left shows a 5 min time series from the top stage of the ITMY suspension, with bandpass filters applied between 4 to 5 Hz and 10

to 11 Hz. The distribution of time series amplitude over the same time is shown on the right, with dashed lines to indicate a Gaussian distribution. While the

Gaussian-distributed stationary sensor noise dominates the higher frequency band shown, the time series from 4 to 5 Hz exhibits large excursions from the

average noise level.

124501-5

Walker

et al.

Rev. Sci. Instrum.

, 124501 (2017)

FIG. 5. (Top) The Signal-to-Noise Ratio (SNR) and cen-

tral frequencies of Omicron triggers of the ITMY sus-

pension during one week of O1. (Bottom) Histograms

showing the SNR distributions of the penultimate stage

triggers at three representative frequency ranges (note the

different SNR scales), selected to show how transient

behavior differs across the spectrum. While the distri-

bution of higher frequency triggers fall off much like

Gaussian noise, the lower frequency ranges contain more

outliers.

Ideally, the noise would be stationary and the average

spectrum would statistically characterize the noise level, but

in actuality there are non-stationary disturbances at different

frequencies. To demonstrate this, Fig. 4 shows the time series

of several minutes of data from the top stage of one suspen-

sion with two different bandpass filters applied to select for

4-5 Hz and 10-11 Hz. Above 10 Hz, the sensor noise dom-

inates the signal and the resulting time series is Gaussian

distributed, but the lower frequency shows large non-Gaussian

transients.

Rather than visually inspecting time series, the Omicron

algorithm is used to find transients in the data, producing

trig-

gers

that indicate the time, frequency, amplitude, and signal-

to-noise ratio of the transient noise.

14,15

Figure 5 shows the

distribution in frequency and signal-to-noise ratio of Omicron

triggers for the longitudinal degree of freedom, using data from

the Y-arm input suspension over one week of the observing

run. While stationary noise would produce a background of

low SNR triggers across all frequencies, the actual data from

the suspension monitors show a varying structure in different

frequency bands. This suggests the presence of non-stationary

noise sources.

B. Motion transient propagation

To characterize the effects of short duration disturbances

in the upper stages of the suspensions on the motion lower in

the suspension chain, we need more than just the frequency

domain models usually used to characterize the suspensions

due to the influence of the impulse response of the system. The

MATLAB Simulink toolbox

was used to model the response

of a simple pendulum to a sine-Gaussian input signal. Note

that the input signal is not a pure sine wave at a single fre-

quency, but rather a sine-Gaussian wave characterized by a

peak frequency with a Gaussian amplitude envelope that acts to

truncate the signal in time, giving it broader frequency content.

Therefore, as the pendulum response more strongly attenuates

the higher frequencies of the input signal, the peak frequency

of the resulting motion is a mixture of the driving and the

resonance frequencies, as demonstrated in Fig. 6.

FIG. 6. Modeled transient response of a simple pendu-

lum to a sine-Gaussian injection. Simulink was used to

model a simple pendulum with a resonance at 2 Hz. A

one-second 4 Hz sine-Gaussian signal (top panel) was

used as the input to show the response of the system (mid-

dle panel) compared with the input signal multiplied by

the transfer function of the system at 4 Hz. Local maxima

and minima of the time series can be used to calculate

the frequency for each half-cycle (bottom panel). This

simulation shows that even for this simple model, the

transient response of the system deviates from the steady

state frequency response at 4 Hz.

124501-6

Walker

et al.

Rev. Sci. Instrum.

, 124501 (2017)

FIG. 7. Ratio of amplitudes of injection Omicron trig-

gers at lower stages to the top stage, plotted against the

peak frequency estimated by Omicron for the top stage

motion, compared with the modeled transfer function.

At lower frequencies, the propagation of the transients

is close to the model, but above a few Hz, the motion at

the lower stages is smaller than the sensor noise, and the

amplitude ratio is not as close to the model. There are

fewer Omicron triggers at the penultimate stage since the

motion at that stage is at a lower amplitude and is not

great enough at higher frequencies to be seen above the

sensor noise.

To examine the propagation of transients in Advanced

LIGO suspensions and compare with expected behavior, sine-

Gaussian waveforms were physically injected in the Y-end

quadruple suspension (End Test Mass Y or

ETMY

) in the lon-

gitudinal direction using the top mass actuators, with central

frequencies ranging from 2 to 10 Hz. The Omicron algorithm

was used to characterize the resulting transients caused in the

top stage as well as in lower stages.

Figure 7 shows the ratio of the Omicron trigger amplitudes

of the lower suspension stages to the top stage for different

frequencies, using the Omicron frequency estimate of the top

stage trigger. The solid lines show the frequency response of

the suspensions as predicted by the quadruple suspension mod-

els. One reason for apparent discrepancies from the model is

variation of the transient motion frequency between stages, as

well as the fact that the motion at each stage is not character-

ized by only a single frequency. To analyze this effect, time

series of the injections were examined individually to char-

acterize the frequencies and amplitudes of the signals at each

stage, similar to the process used in analysis of the Simulink

model shown in Fig. 6.

Using a bandpass filter with a 1 Hz window around the

injection frequency and finding the local maxima and minima

of the resulting time series, the peak frequency of the induced

transient motion was estimated with each cycle. Similar to the

simulation performed in Simulink, the suspension’s response

is not exactly at the peak sine-Gaussian frequency, and when

the injection is finished, the suspension’s motion begins to ring

down with a frequency approaching the nearest resonance.

As the motion propagates downwards, the pendulum filter

response attenuates the signal more in the frequency range far-

ther from the resonance, resulting in a slight frequency shift

towards the resonance at the lower stage. Figure 8 shows the

period increasing in the bandpassed time series from one of the

injections. The 1 Hz bandpass filter was chosen to most clearly

show the injected signal in the time series, but results are con-

sistent with the use of other bandpass widths, such as 2 Hz.

The bandpass filter reduces the noise so that the time series

cycles can be clearly determined. The frequency of the result-

ing motion at each stage was then estimated by taking the

mean frequency, weighting each cycle by the amplitude of its

maximum or minimum. The amplitude of motion was calcu-

lated using Omega, a multi-resolution technique for studying

transients related to Omicron.

14,15

Using the weighted aver-

age frequency and the amplitudes calculated by Omega, the

ratio of motion transient amplitudes between suspension stages

for each frequency can be better compared to the suspension

model. Figure 9 displays this comparison for the propaga-

tion of the motion from the top stage to the second and third

stages. Since the transient amplitude is much smaller at higher

frequencies for each successive stage, the higher frequency

injection measurements are farther from the model due to the

sensor noise at the lower stages. In both lower stages, we see a

shift in the frequency away from the frequency at the top stage,

generally closer to the nearest suspension resonance, a pitch

mode at 2.7 Hz.

FIG. 8. Time series from one injection at 4.1 Hz, after

application of a bandpass filter with a window of 1 Hz

around the injection frequency. Similar to the simple pen-

dulum model analysis, the frequency shifts throughout

the time series. The period of the cycles in the top stage

lengthens slightly, from 0.25 s (4.0 Hz) at the peak of the

transient to 0.28 s (3.6 Hz) a few cycles later.