Improving the Robustness of the Advanced LIGO Detectors to Earthquakes
Eyal Schwartz, A Pele, J Warner, B Lantz, J Betzwieser, K L Dooley, S Biscans, M Coughlin, N Mukund, R Abbott, C Adams, R X Adhikari, A Ananyeva, S Appert, K Arai, J S Areeda, Y Asali, S M Aston, C Austin, A M Baer, M Ball, S W Ballmer, S Banagiri, D Barker, L Barsotti, J Bartlett, B K Berger, D Bhattacharjee, G Billingsley, C D Blair, R M Blair, N Bode, P Booker, R Bork, A Bramley, A F Brooks, D D Brown, A Buikema, C Cahillane, K C Cannon, X Chen, A A Ciobanu, F Clara, S J Cooper, K R Corley, S T Countryman, P B Covas, D C Coyne, L E H Datrier, D Davis, C Di Fronzo, J C Driggers, P Dupej, S E Dwyer, A Effler, T Etze, M Evans, T M Evans, J Feicht, A Fernandez-Galiana, P Fritschel, V V Frolov, P Fulda, M Fyffe, J A Giaime, K D Giardina, P Godwin, E Goetz, S Gras, C Gray, R Gray, A C Green, Anchal Gupta, E K Gustafson, R Gustafson, J Hanks, J Hanson, T Hardwick, R K Hasskew, M C Heintze, A F Helmling-Cornell, N A Holland, J D Jones, S Kandhasamy, S Karki, M Kasprzack, K Kawabe, N Kijbunchoo, P J King, J S Kissel, Rahul Kumar, M Landry, B B Lane, M Laxen, Y K Lecoeuche, J Leviton, J Liu, M Lormand, A P Lundgren, R Macas, et al. (99 additional authors not shown)
IImproving the Robustness of the Advanced LIGO Detectors to Earthquakes
E Schwartz , , A Pele , J Warner , B Lantz , J Betzwieser , K L Dooley , , S Biscans , , M Coughlin ,N Mukund , R Abbott , C Adams , R X Adhikari , A Ananyeva , S Appert , K Arai , J S Areeda , Y Asali ,S M Aston , C Austin , A M Baer , M Ball , S W Ballmer , S Banagiri , D Barker , L Barsotti , J Bartlett ,B K Berger , D Bhattacharjee , G Billingsley , C D Blair , R M Blair , N Bode , , P Booker , , R Bork ,A Bramley , A F Brooks , D D Brown , A Buikema , C Cahillane , K C Cannon , X Chen , A A Ciobanu ,F Clara , S J Cooper , K R Corley , S T Countryman , P B Covas , D C Coyne , L E H Datrier , D Davis ,C Di Fronzo , J C Driggers , P Dupej , S E Dwyer , A Effler , T Etzel , M Evans , T M Evans , J Feicht ,A Fernandez-Galiana , P Fritschel , V V Frolov , P Fulda , M Fyffe , J A Giaime , , K D Giardina ,P Godwin , E Goetz , , S Gras , C Gray , R Gray , A C Green , Anchal Gupta , E K Gustafson ,R Gustafson , J Hanks , J Hanson , T Hardwick , R K Hasskew , M C Heintze , A F Helmling-Cornell ,N A Holland , J D Jones , S Kandhasamy , S Karki , M Kasprzack , K Kawabe , N Kijbunchoo , P J King ,J S Kissel , Rahul Kumar , M Landry , B B Lane , M Laxen , Y K Lecoeuche , J Leviton , J Liu , ,M Lormand , A P Lundgren , R Macas , M MacInnis , D M Macleod , G L Mansell , , S M´arka , Z M´arka ,D V Martynov , K Mason , T J Massinger , F Matichard , , N Mavalvala , R McCarthy , D E McClelland ,S McCormick , L McCuller , J McIver , T McRae , G Mendell , K Merfeld , E L Merilh , F Meylahn , ,T Mistry , R Mittleman , G Moreno , C M Mow-Lowry , S Mozzon , A Mullavey , T J N Nelson , P Nguyen ,L K Nuttall , J Oberling , Richard J Oram , C Osthelder , D J Ottaway , H Overmier , J R Palamos ,W Parker , , E Payne , C J Perez , M Pirello , H Radkins , K E Ramirez , J W Richardson , K Riles ,N A Robertson , , J G Rollins , C L Romel , J H Romie , M P Ross , K Ryan , T Sadecki , E J Sanchez ,L E Sanchez , T R Saravanan , R L Savage , D Schaetzl , R Schnabel , R M S Schofield , D Sellers ,T Shaffer , D Sigg , B J J Slagmolen , J R Smith , S Soni , B Sorazu , A P Spencer , K A Strain , L Sun ,M J Szczepa´nczyk , M Thomas , P Thomas , K A Thorne , K Toland , C I Torrie , G Traylor , M Tse ,A L Urban , G Vajente , G Valdes , D C Vander-Hyde , P J Veitch , K Venkateswara , G Venugopalan ,A D Viets , T Vo , C Vorvick , M Wade , R L Ward , B Weaver , R Weiss , C Whittle , B Willke , ,C C Wipf , L Xiao , H Yamamoto , Hang Yu , Haocun Yu , L Zhang , M E Zucker , , and J Zweizig LIGO Livingston Observatory, Livingston, LA 70754, USA LIGO Hanford Observatory, Richland, WA 99352, USA Stanford University, Stanford, CA 94305, USA The University of Mississippi, University, MS 38677, USA Cardiff University, Cardiff CF24 3AA, UK LIGO, California Institute of Technology, Pasadena, CA 91125, USA University of Minnesota, Minneapolis, MN 55455, USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany California State University Fullerton, Fullerton, CA 92831, USA Columbia University, New York, NY 10027, USA Louisiana State University, Baton Rouge, LA 70803, USA Christopher Newport University, Newport News, VA 23606, USA University of Oregon, Eugene, OR 97403, USA Syracuse University, Syracuse, NY 13244, USA LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Missouri University of Science and Technology, Rolla, MO 65409, USA Leibniz Universit¨at Hannover, D-30167 Hannover, Germany OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia RESCEU, University of Tokyo, Tokyo, 113-0033, Japan. OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia University of Birmingham, Birmingham B15 2TT, UK Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain SUPA, University of Glasgow, Glasgow G12 8QQ, UK University of Florida, Gainesville, FL 32611, USA The Pennsylvania State University, University Park, PA 16802, USA University of Michigan, Ann Arbor, MI 48109, USA OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India University of Portsmouth, Portsmouth, PO1 3FX, UK The University of Sheffield, Sheffield S10 2TN, UK Southern University and A&M College, Baton Rouge, LA 70813, USA a r X i v : . [ phy s i c s . i n s - d e t ] J u l OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA University of Washington, Seattle, WA 98195, USA Universit¨at Hamburg, D-22761 Hamburg, Germany Concordia University Wisconsin, 2800 N Lake Shore Dr, Mequon, WI 53097, USA and Kenyon College, Gambier, OH 43022, USA
Teleseismic, or distant, earthquakes regularly disrupt the operation of ground–based gravitationalwave detectors such as Advanced LIGO. Here, we present
EQ mode , a new global control scheme,consisting of an automated sequence of optimized control filters that reduces and coordinates themotion of the seismic isolation platforms during earthquakes. This, in turn, suppresses the differ-ential motion of the interferometer arms with respect to one another, resulting in a reduction ofDARM signal at frequencies below 100 mHz. Our method greatly improved the interferometers’capability to remain operational during earthquakes, with ground velocities up to 3.9 µ m/s rms inthe beam direction, setting a new record for both detectors. This sets a milestone in seismic controlsof the Advanced LIGO detectors’ ability to manage high ground motion induced by earthquakes,opening a path for further robust operation in other extreme environmental conditions. Keywords : LIGO, earthquakes, control, seismic
INTRODUCTION
The detection of gravitational waves (GWs) by the Advanced Laser Interferometer Gravitational Wave Observatory(LIGO), include dozens of detections in recent years from binary black hole and neutron star mergers [1–3], whichwere facilitated by the use of unparalleled seismic isolation systems. At their core, the GW detectors are modifiedkm-scale Michelson interferometers with Fabry-Perot cavities in each arm, whose mirrors must approximate inertialtest masses in order to act as markers of space-time coordinates. A passing gravitational wave induces a strain inspace-time, which modulates the separation of the mirrors in an arm, typically by less than 10 − m around 100 Hz.To measure such small displacements, the optical cavities are held on resonance [4] with highly-stabilized laser lightin order to both build up laser power and to ensure a linear response to the GWs. Typical ground motion of 10 − mrms requires state of the art seismic isolation to reach the small enough relative mirror motion needed to detect GWs.The high level of isolation of the mirrors from the ground, 10 orders of magnitude at 30 Hz and an order ofmagnitude at 150 mHz, is achieved through the use of a series of passive and active control techniques [5]. Themirrors are suspended as pendula, which, in turn, are mounted on actively isolated platforms that rely on both feed–forward and feed–back control from sensors on the ground and the platform, respectively. Despite such phenomenallevels of isolation, particularly large seismic vibrations nonetheless remain responsible for about 5% of the unplanneddowntime (out of 25-30%) at both the LIGO Hanford and LIGO Livingston Observatories (LHO and LLO) duringtheir first observing runs, O1 and O2, from 2015 to 2017. Produced by ocean waves, wind, human activity, and,most dramatically, earthquakes, seismic vibrations can cause a loss of resonance of the Fabry-Perot arms, known asa lock loss, when the input motion to the seismic control system exceeds its design capabilities. Excessive actuationto the isolation platforms exacerbates problems arising from imperfect decoupling of degrees of freedom, both onthe platform itself as well as further downstream in the optical control of the cavities. After a lock loss, it takes aminimum of 30 minutes to reacquire the locked state of the detector, thus severely hindering its duty cycle.Two fundamental types of seismic waves are generated by an earthquake: body and surface waves. Body waves prop-agate within a body of rock and are subdivided into the faster Primary wave (P-wave), or longitudinal–compressionalwave, and the slower Secondary wave (S-wave), or shear wave.When shallow earthquakes occur (at depths of several km below the surface), coupled P–S waves known as Rayleighwaves are generated and particularly affect GW detectors because their motion is restricted to near the surface ofthe ground. Rayleigh waves [6, 7] have periods of anywhere from 3–60 s with the majority occurring at 15–20 s,corresponding to frequencies of about 50–60 mHz. The surface waves from a large earthquake can be measuredaround the world. These teleseismic waves impact Advanced LIGO operations when they are larger than about1 µ m/s at the observatories, which happens several times per week on average.This paper focuses on the design and implementation of a novel set of techniques to reduce the detrimental effectof earthquakes on the GW detectors. Section describes the active seismic isolation system used for each core mirrorand highlights the problem of how the primary ground motion frequency that is amplified by earthquakes, 50 mHz,also gets amplified by the seismic control system when in its nominal configuration. Section presents the solutionwhich consists of two independent, yet complementary, modifications to the seismic control system to reduce the inputsignal at 50 mHz and its amplification. Section presents the results of implementing the new EQ mode at LLO andLHO during observing run 3 (O3). Finally, Section discusses the major accomplishments of this work and providesan outlook for the future.
ADVANCED LIGO SEISMIC CONTROLS
The Advanced LIGO mirrors are suspended from isolation platforms. These platforms fulfil several roles. Theyprovide active positioning from DC to about 30 Hz, active isolation from ground motion from around 100 mHz to 30Hz, and passive isolation above a few Hz. The multi-stage mirror suspensions provide additional passive isolation,active damping, and control for the optics.The actively isolated platforms make up part of the Internal Seismic Isolation (ISI) system, in which a number ofsensors on the ground and on the platform are used for feed–forward and feed–back control. Each platform’s motionis reduced to 10 − m/ √ Hz at 10 Hz, several orders of magnitude below ground motion. Details about the design,operation and performance of the ISI platforms can be found in [8–10].FIG. 1: Illustration of the BSC–ISI Stage 1 seismic controls. Sensors on the ground and on the ST1 platform arecombined to act as a witness of the platform’s inertial motion. Control signals are derived and sent to actuators onthe platform. Note that multiple sensors (not drawn) of each type are used to provide control in all three Cartesiandegrees of freedom.Two types of ISI systems are used at the observatories. The HAM-ISIs are single–stage platforms which supportthe power and signal recycling mirrors, as well as auxiliary optics, and are located in small vacuum chambers calledhorizontal access modules (HAMs). The BSC-ISIs are two–stage platforms for the beam-splitter and the four mirrorsof the arm cavities and are located in large vacuum tanks called basic symmetric chambers (BSCs) [8]. In this paperwe will focus on the first stage of the BSC–ISI. It is from this Stage 1 (ST1) platform that a second platform issuspended, from which the mirrors in turn are suspended.A schematic of the active seismic control for ST1 of the BSC–ISI is depicted in Figure 1. An absolute inertialmeasurement of the platform motion, X P , is constructed across a broad band of frequencies from a combination ofsensors on the ground and on the platform. The sensed motion is used to generate a feed–back control signal, F P ,which is applied to the platform via actuators to reduce the overall motion.Information about the platform’s motion above 100 mHz is provided by two types of inertial sensors located onthe platform: the Trillium 240 (T240) & the Sercel L–4C geophone [11–13]. Information below 100 mHz is providedby displacement sensors on the platform, the Microsense Capacitive Position Sensors (CPS), and a tilt-correctedStreckeisen STS-2 seismometer located on the floor near the BSC [11, 14].The CPS measures the relative position between the ground and the ST1 platform. In order to use the CPS asan inertial sensor of the platform’s motion, information about the ground’s absolute motion is needed. A schemedenoted as sensor correction (SC), in which the signal from the STS-2 is first high–pass–filtered and then added tothe CPS signal turns the CPS into a virtual inertial sensor at frequencies above 50 mHz [15]. The filtering of theSTS-2 signal, using a filter called the sensor correction filter , is necessary because at frequencies below ∼
50 mHz, theSTS-2 measurements of ground motion are contaminated both by sensor noise and by unresolved tilt of the grounddue to the fact that conventional seismometers cannot differentiate between horizontal displacement and ground tilt[16]. Ground tilt that can be measured is removed from the STS-2 signal through a scheme called
STS–tilt correction ,which uses a beam rotation sensor (BRS) that measures the tilt of the ground near the STS-2 [16].FIG. 2: Block diagram of the control servo up to 500 mHz for one degree of freedom of a BSC–ISI ST1 platform.The L-4C is not depicted because it only contributes to the control above ∼ η BRS , η ST S , η T and η CP S ) and actual ground ( X G ) andplatform ( X P ) motion are shown on the left and the resulting inertial motion of the platform on the right. The tilt–corrected ground motion is given by (cid:101) X G = X G + Θ ST S − Θ BRS + η ST S + η BRS , where Θ
ST S and Θ
BRS is the groundtilt sensed by the STS–2 and the BRS correspondingly. These two tilt contributions cancel each other out, therefore (cid:101) X G becomes limited by the noise from one of the two instruments, η ST S or η BRS . The CPS signal by definition is X P − X G + η CP S . The sensor–corrected CPS signal is low–pass–filtered ( L ) and blended with the high–pass–filtered( H ) inertial sensors. P S and P G are the plant transfer functions, describing how the platform reacts to the actuationand ground motion, respectively. The control filter, C , is designed such that the open loop gain is unity at ∼
30 Hz,and is very large at low frequencies [17].When feed–back is engaged, the expected inertial motion of the platform below ∼ X P = P G X G + ( X G − (cid:101) X G · SC) · L · C · P S C · P S − η BRS · SC · L · C · P S C · P S − ( η CP S · L + η T · H ) · C · P S C · P S , (1)which can be simplified to X PC · P S (cid:29) = X G · (1 − SC) · L − η BRS · SC · L − ( η CP S · L + η T · H ) (2)given the very large gain ( C · P S (cid:29)
1) at frequencies below 1 Hz and that L + H = 1 by construction. We furtherassume that (cid:101) X G ≈ X G + η BRS because tilt cancels out (i.e. Θ
ST S = Θ
BRS ) and η ST S is negligible with respect to η BRS at frequencies below 1 Hz .This nominal configuration of the seismic controls is regularly used and enables operation during the majority ofthe varying environmental conditions, including different microseismic states, wind and small earthquakes ( < µ m/s).To operate through larger earthquakes, this configuration was altered in order to confront the impact of high groundmotion on the stability of the detectors. EARTHQUAKE MODE
The goal of a seismic control configuration specifically designed for use during earthquakes is to maintain theoptimized performance of the seismic isolation system at frequencies above 100 mHz while limiting gain peaking inthe 50 −
60 mHz frequency band [5]. The result should be a reduction of the fluctuations of the length of each arm,as well as a reduction of the differential motion of the arms with respect to one another. The latter is the degree offreedom known as DARM (differential arm) which dictates the sensitivity of the detector to GWs.
EQ mode consistsof two distinct modifications to the ISI controls: 1) a change to the SC filter; and 2) a change to the input of the SCfilter.
The sensor correction filter
The SC filter is a high pass filter designed to maximize the seismic isolation at 100 −
300 mHz, where the groundmotion is dominated by the secondary microseism caused by storms in the ocean [18], while suppressing any BRSnoise or residual tilt below 100 mHz. The trade off for good isolation above 100 mHz is amplification of the groundmotion at the cut-off frequency of the high pass filter SC. We call gain peaking the maximum amplification in thefrequency band where the suppression function (1-SC) is greater than unity. .The nominal SC filter results in gain peaking at 50 mHz, as shown in Figure 3a. Figure 3a also plots the groundmotion measured by the STS-2 during a quiet time and during a magnitude 5.9 earthquake in Indonesia (2019-10-1422:23:54 UTC, depth 19.0 km), clearly showing that the frequency of the gain peaking coincides with the frequencyof the peak energy of the earthquake. When the nominal SC filter is used during an earthquake, the amplified excessmotion in the 50 −
60 mHz frequency band often results in a lock loss of the interferometer.A modification to the SC filter that shifts the gain peaking to lower frequencies is the first of two components thatcomprise the new
EQ mode scheme. Figure 3b shows the SC filter designed for
EQ mode , which has a gain peakshifted down to 20 mHz. The expected isolation (1 − SC) is also plotted, highlighting how the SC filter for
EQ mode provides nearly an order of magnitude more isolation at 50 mHz compared to the nominal filter, while maintainingthe requirements for frequencies above 100 mHz.The shifted gain peaking has the effect of introducing excess motion below 30 mHz compared to the nominal SCfilter. Tilt motion of the ground and sensor noise of the BRS dominate the motion below 30 mHz under normalconditions, therefore restricting our ability to use the modified SC filter all the time. The
EQ mode
SC filter can beused during an earthquake, however, because the character of the ground motion is different than during seismicallyquiet times. During an earthquake, translational motion of the ground, rather than tilt, dominates at frequenciesbelow 50 mHz.
A global control scheme
During earthquakes, using the large local ground motion as input to the sensor correction scheme can be problematic.Attempting to keep each ISI platform inertially isolated can saturate the actuators, compromising cavity stability andresulting in a lock loss. The ground motion along the length of an arm during an earthquake is largely coherent,however, and leads to the second modification that comprises
EQ mode : the removal of the common motion along an The Bode Integral theorem, or ‘waterbed theorem’ shows that, for non–trivial real time control systems, improved performance at somefrequencies results in degraded performance at other frequencies.[19] (a) (b)
FIG. 3: (a) Ground motion during an earthquake (black) and quiet times (red) as measured by an STS-2. Thenominal SC filter (solid blue) has gain peaking at 50 mHz so that SC (cid:28) − SC, is shown in dashed blue. (b) The SC filter for
EQ mode has a gain peakingshifted out of the earthquake band down to 20 mHz. This is made possible by the decreased false signals at thesefrequencies during earthquakes.FIG. 4: Global automatic seismic sensing and control of an arm cavity for one degree of freedom. The localdifferential is used as an input to the sensor correction of the CPS on the ST1 platform of each station during
EQmode .arm from the input to the SC filter. An analysis of the 134 earthquakes detected at LLO during O3a shows that duringFIG. 5: Block diagram depicting how the local differential signal is created. During earthquakes, the localdifferential signal rather than the local ground motion is used as input to the sensor correction (see Figure 2). Theaverage of the BRS noise from the two stations of the arm is given by η BRSCM .earthquakes the common motion of the ground from one end of an arm to the other dominates the differential motionby a factor of 5 − X IG + X EG ) /
2, and differential–modeas DM = ( X IG − X EG ) /
2, where I and E represent the corner and end stations, respectively, the ground motion ateach station can be represented as a linear combination of DM and CM. Because the differential motion is muchsmaller than the common motion during an earthquake, removing the common motion component from the input toa platform’s control system yields a control signal that falls within the maximum range of the actuators.We therefore introduced a novel global control scheme which is illustrated in Figure 4. The STS-2 signals at thecorner and end stations are used to calculate the CM motion along the arms. This is in turn subtracted from thelocal ground motion at each station, thus creating a local differential signal, which is used as the input to the SCfilter during earthquakes. By allowing the platforms to sway together, while isolating solely against the differentialmotion, we create a more stable interferometer.Figure 5 shows the modification to the sensor correction path for EQ mode . The CM of an arm is filtered bya low–pass filter, L CM , which is designed to reject the secondary microseism (100-300 mHz) while preserving themagnitude and phase of the common mode signal in the earthquake band, below 100 mHz. The filtered CM signal isthen subtracted from the local ground motion thus giving the local differential signal, which serves as input to thesensor correction during an earthquake. Removal of the CM below 100 mHz is intended to reduce the platform drivewhen large ground motion occurs. Without the filtering of the CM signal, the secondary microseism would add inquadrature with the local signal, as typically uncorrelated from one end to the other, and would be detrimental forthe isolation performance in this band. (a) (b) FIG. 6: (a) The L CM filter (solid) with the expected CM suppression (dashed). (b) Spectra of ground motion(black) vs. local differential motion (red) created using the CM filter shown in (a).In Figure 6a we present L CM along with the expected reduction of CM motion. Figure 6b shows the local groundmotion and the resultant local differential motion after L CM is applied. Here we see one of the impacts of the new EQ mode control approach: Up to 50 mHz the input to SC during an earthquake is reduced by a factor of 2. As seenboth in Figure 6a and Figure 6b, there is a small increase in noise near 100 mHz, however the overall reduction ininput motion significantly improves the stability of the interferometer. The EQ mode model
Our complete model of the ST1 platform motion for the nominal and
EQ mode configurations is given by: X nomP = [ X G · (1 − SC nom ) − η BRS · SC nom + γ X ⊥ · SC nom ] · L (3a) − ( η CP S · L + η T · H ) X EQP = [ X G · (1 − SC EQ ) + CM · L CM · SC EQ + γ X ⊥ · SC EQ (3b) − ( η BRS − η BRSCM ) · SC EQ ] · L − ( η CP S · L + η T · H ) . Eq. 3a describes the nominal ST1 platform motion and is identical to Eq. 2, except for the introduction of anadditional linear term, γ X ⊥ · SC · L , which describes a residual horizontal motion of the platform that correlatesstrongly with the platform’s vertical motion, X ⊥ . The importance of the coupling term for producing a realisticmodel is apparent in Figure 8, though the source of the coupling is not yet understood and remains and active areaof investigation. The platform motion when EQ mode is engaged is given by Eq. 3b. Eq. 3b includes the vertical–to–horizontal coupling term in addition to the change in the SC filter and the common–mode subtraction.The model proves to be a powerful tool for optimizing the design of
EQ mode because the transfer function fromST1 to the optics can be approximated as unity below the first resonant mode frequency of the pendula (400 mHz).We can therefore infer how the optical cavities will react in the earthquake band frequencies by simply modeling thebehavior of the platforms.To analyze the expected and actual performance of
EQ mode , we focus on the extent to which both the lengthfluctuations of a single arm cavity and DARM are reduced during an earthquake when
EQ mode is engaged comparedto times when it is not engaged.We can estimate the length fluctuations of an arm cavity by calculating the differential motion of the platforms ofthe arm along the beam direction. This is given by:∆ P = ∆ G · (1 − SC) · L − η ∆ BRS · SC · L + γ ∆ ∆ ⊥ · SC · L + O ( noises ) (4)where ∆ = − and O ( noises ) is the sum of all sensor noises. Importantly, ∆ P does not include any CM contributions,yet it does rely on the SC filter. We can thus use this model to optimize the EQ mode
SC filter design to minimizelength fluctuations of the arm during an earthquake.Likewise, an estimate of DARM at frequencies below 100 mHz can be made from the models for platform motion inEq. 3. DARM is defined as (ETMX X -ITMX X )-(ETMY Y -ITMY Y ) Where ITM is Input Test Mass and ETM is EndTest Mass, thus giving:DARM CPS = (CPS
ETMXX − CPS
ITMXX ) − (CPS ETMYY − CPS
ITMYY ) (5)= X DARM G [(1 − SC) · L −
1] + [ γ DARM X DARM ⊥ − η DARM
BRS ] · SC · L..
With these sets of equations, we can predict the motion of a single optic as well as various degrees of freedom ofthe whole interferometer, allowing us to optimize the design of the seismic isolation system to achieve the best opticalperformance of the detector during earthquakes.
Implementation and automatic switching of
EQ mode
Due to the complexity of changing the detector configuration both globally and locally in lock, a change in con-figuration always has the risk of contaminating the observation data or causing a lock loss. It is therefore essentialto switch to
EQ mode only when a problematic earthquake arrives at the site and not at other unnecessary times.For that, an early alert system named
Seismon , which uses publicly available data acquired from a global networkof seismic observatories compiled by USGS, was developed and installed at the observatories [20, 21]. Based on amachine learning algorithm,
Seismon predicts the arrival times and velocities of the P and S body waves and, mostimportantly, the Rayleigh surface waves of an earthquake with a notification latency of several minutes for earthquakesmore than 2000 km away. Using this information and the current state of the interferometer, a decision can be madeabout whether to engage
EQ mode .Both interferometers are governed by a state machine called
Guardian [22] which consists of automation nodescapable of automatic handling of control changes. We designed a Guardian sub–system (see Figure 4) which monitors
Seismon alerts together with the local ground motion in all degrees of freedom to initiate the change in configurationto
EQ mode when the necessary trigger levels are reached. When the earthquake has passed and the ground motion isbelow the nominal thresholds, the guardian transfers the seismic platform controls back to the nominal configuration.These changes of state only require a few minutes, as it is possible to switch the filters without having to turn off theseismic isolation loops, and thus keep the interferometer locked. The threshold that we have chosen to trigger
EQmode is for earthquakes that produce Rayleigh waves larger than 1 µ m/s at LLO and 0.5 µ m/s for LHO. Our nominalconfiguration is capable of handling smaller earthquakes.When engaging EQ mode , we change the seismic control configuration for not only all of the ST1 platforms in theBSC chambers, but also for the single platforms of the HAM chambers. The core optics for the power and signalrecycling cavities, crucial components of the design of the GW detectors, are located in both the HAM and BSCchambers. The change to the HAM–ISI controls during
EQ mode follows the same concepts as the changes for theST1 platform of the BSC-ISI.
RESULTS
A month–long break in the third observing run separates O3 into 2 parts, named O3a and O3b.
EQ mode wasfirst implemented at LHO at the start of O3a and at LLO at the start of O3b. We studied the performance of theisolation platforms at LLO during several earthquakes at the end of O3a and beginning of O3b. We verified that themodel for the nominal seismic configuration fits well with the data and then used the model to optimize the design of
EQ mode . Here, we present the reduction we achieved in local platform motion, single arm motion and DARM when
EQ mode was engaged during two of the earthquakes studied. This in turn enabled the interferometer to stay lockedduring the high ground motion. Lastly, we give a statistical analysis of the detectors’ performance before and afterthe implementation of
EQ mode . Local platform and single arm motion
At LLO, one of the times
EQ mode was engaged was during a magnitude 6.3 earthquake, 102 km WNW of Kirakira,Solomon Islands (2020-01-27 05:02:01 UTC, depth of 21 km). The interferometer managed to stay locked with groundrms velocities up to 3.9 µ m/s for the horizontal direction and 2.5 µ m/s for the vertical, a new record for the detectors(with the nominal configuration, the maximum achieved was 2 µ m/s for horizontal and 1 µ m/s for the vertical directionduring an earthquake). Plotted in Figure 7 (a) is the modeled and measured single platform horizontal motion ofITMX, X P , for the nominal configuration and EQ mode during the Solomon islands earthquake. The
EQ mode modelfits well with the data, thus demonstrating it is a trustworthy tool for further optimizations. At the earthquake peakfrequency of 50 mHz we get a factor 2.6 reduction in both local platform motion and drive, when switching fromnominal configuration to
EQ mode . In Figure 7 (b) we show the modeled contributions for
EQ mode displacementmodel, as from Eq. 3b. From Figure 7 (b), we see that at 50 mHz, the biggest contribution to the single platformmotion is the common–mode motion and the vertical coupling. Therefore the removal of common-mode was the mainreason of the reduction in the single platform drive and motion.In Figure 8(a), we present the arm length fluctuations of the x–arm, as witnessed by the T240 inertial sensorslocated on each platform of the arm. We also plot our models (Eq.4) for the nominal configuration and for
EQmode . Furthermore, we show the model without the addition of the coupling term, to demonstrate the substantialcontribution the coupling term has on the differential motion of the arm. The coupling coefficient per platform, γ ,was empirically determined so that the model optimally fits the data in 30-300 mHz band. On average, γ ≈ .
2, butdoes differ between platforms at the different stations. At 50 mHz we observe a factor 2.5 reduction of arm lengthfluctuations between the nominal and
EQ mode configurations. In Figure 8 (b) as in Figure 7 (b), we show the0 (a) (b)
FIG. 7: (a) Predicted ITMX ST1 platform motion during an earthquake for nominal configuration (blue) and
EQmode (red). Data (black) for the platform motion (T240) was acquired when the
EQ mode was engaged. (b)modeled contributions to the ST1 platform motion that are used to construct the
EQ mode model in (a) as fromEq. 3b. Legend in (b) contains - Local ground: X G · (1 − SC EQ ) · L , Common mode: CM · L CM · SC EQ · L , Ver-Horcoupling: γ X ⊥ · SC EQ · L and dashed line is the sum of all sensor noise contributions. (a) (b) FIG. 8: (a) Predicted differential ST1 platform motion along the X-arm for Nominal (blue) and
EQ mode (red)during an earthquake. (b) The same as in Figure 7 (b), detailing the arm length fluctuations model. Legend in (b)contains - Local ground: ∆ G · (1 − SC) · L , Ver-Hor coupling: γ ∆ ∆ ⊥ · SC · L and dashed line is the sum of all sensornoise contributions.modeled contributions constructing the EQ mode model in (a) as in Eq.4. We see that the vertical coupling term isthe dominant contribution to the single arm differential motion.1
DARM
To assess the performance of DARM during earthquakes, when either nominal configuration or
EQ mode is engaged,we transitioned between these two configurations in the middle of an earthquake to allow close comparison for the sameground conditions and detector optical state (alignment parameters, drift in laser power and gain and optimum opticalstates change constantly thus affecting performance as well). The data presented is of a 6.1 magnitude earthquakein the Southern East Pacific Rise (2019-12-25 20:20:12 UTC, depth 10.0 km). The maximum rms ground velocitiesreached 2.3 µ m/s for horizontal motion and 1.3 µ m/s for vertical motion. (a) (b) FIG. 9: (a) Seismic DARM signal. Measured data in solid lines and our model (equation 5) as dashed lines. (b)Optical DARM signal motion. In both sub figures we normalize the plots by the ground motion and blue is nominalconfiguration while red is
EQ mode .To track the optical signals, we observed the DARM control signal used as input to the ETMX quadruple suspension,which is used to push, or drive, the test mass in order to compensate for the differential arm motion and keepthe interferometer locked. Only the top and upper intermediate (UIM) masses had significant and comparablecontributions to the total control signal, while the penultimate (PUM) and bottom test mass (TST) were negligible(for LHO, it is the UIM and PUM that contribute to the DARM signal). We calibrated this DARM control signal forsub Hertz frequencies in displacement units .In Figure 9a, we show the seismic DARM signal together with our with our model (Eq. 5). In Figure 9b, we plotthe optical DARM signal. Both plots are normalized by the ground motion. In this example we get a factor of 4reduction between the nominal configuration and EQ mode at 50 mHz. From the figure we can see that the opticalDARM signal follows the seismic DARM signal, and in turn, our models, in the earthquake band. By this, we showthat we can optimize DARM performance during an earthquake by observing the seismic behavior of the platformsand use our models to tune the SC filter and the input to it, and infer from that how the optical cavity will react.
Statistical analysis
We studied the probability of the LLO and LHO detectors to maintain lock during earthquakes for each observationrun starting from O1. The results are presented in Figure 10. We looked at the maximum sustained ground velocities We used a calibration based on the maximum displacement range at DC per OSEM, per our maximum digital to analog converter rangeof 18 bits for M0, L1 and L2 [24]
EQ mode versus staying in the nominal configuration during an earthquake. The probability for the interferometerto stay locked during ground velocities above 1000 nm/s for LLO and 500 nm/s for LHO has much increased. Forsmaller earthquakes, we attribute the improvement to other configuration upgrades carried out. The two bottomfigures show the ground velocity distributions for both the horizontal and vertical directions for
EQ mode and thenominal configuration, during O3 for LHO and O3b for LLO (as in the the top figures). It should be noted that duringO3b, the high microseism (100 mHz–1 Hz) posed a significant limitation to the performance at both sites, which alsolimited the use and effectiveness of
EQ mode .In Table I we summarize the LLO and LHO detectors’ performance before (in white) and after (in gray) incorporating
EQ mode . For LLO, the probability of the detector to stay locked during earthquakes increased significantly from38% in O3a to 71% during O3b when
EQ mode was introduced. Equivalently for LHO, the increase in probabilitywas from 64% during O2 to 72% during O3.FIG. 10: Top: The probabilities during each observing run for the LHO and LLO interferometers to stay locked as afunction of ground velocity.
EQ mode was first implemented at LHO in O3a and at LLO in O3b. Bottom:Distribution of ground velocities for the two control modes engaged during earthquakes for which the detectorsremained locked during O3 (LHO - left) & O3b (LLO - right).Lastly, in Figure 11 we present a statistical analysis of the LHO and LLO DARM signals (similar to Figure 9b) forO3 and O3b correspondingly. We averaged the calibrated DARM signal, normalized by the ground motion, over allthe earthquakes for which the interferometers remained locked, as presented in Table ?? , separated to each seismic3TABLE I: LLO & LHO performance during earthquakes. White rows are data for pre- EQ mode (LLO - O3a, LHO -O2 while gray rows are for post implementation of
EQ mode . The threshold for earthquakes is 200 nm/s on the30-100 mHz band limited rms signal of vertical STS-2 at all stations. Total earthquakes relates to all teleseismicevents when the detector was in lock just prior to the arrival and managed to stay locked until the end of the event. (a) (b)
FIG. 11: Averaged DARM signal normalized by ground motion during earthquakes for which the detector remainedlocked as given in Table 1 for (a) LHO - O3 and (b) LLO - O3b. Nominal configuration presented in blue and
EQmode in red. Gray area is the 95% confidence interval of the mean for each configuration.configuration (
EQ mode is in red while nominal configuration is in blue). The shaded gray area per configuration isthe 95% confidence interval of the mean. This allows us to see that at 50 mHz, we get a reduction factor betweennominal configuration and
EQ mode of 3.4 ± ± CONCLUSIONS
Earthquakes are one of the major disturbances detrimental to the performance of ground-based GW observatories,limiting their duty cycle and the amount of useful data for GW detection. In this paper we describe the design andimplementation of
EQ mode , a modification to the nominal seismic control scheme, which includes a global controlscheme to isolate against the differential motion of the detector arms, along with a change to local sensor correctionfilters used to decouple the isolation platforms from ground motion. We combined
EQ mode with a new automatedsystem that receives alerts about incoming earthquakes and switches the detector seismic configuration to handle suchevents. We improved the ability of the detectors to maintain lock during ground velocities up to 3.9 µ m/s rms, whichis a new record for the detectors.Our seismic models predict the behavior of the local platform, the single arm differential motion and most impor-tantly the DARM optical signal, which allows us to optimize the performance of the detector at frequencies below1 Hz during an earthquake.Analysis of the averaged optical DARM signal during an earthquakes shows a clear reduction in DARM motion4at frequencies below 100 mHz upon switching from nominal configuration to EQ mode . Furthermore, our modelincorporates a newly discovered cross-coupling between the platform vertical and horizontal motions, yielding arealistic model that matches well to the experimental data.DARM performance in very low frequencies is of great importance since it directly affects the interferometer stability.Moreover, due to different processes such as light scattering from the optics, undesirable sub-hertz signals get up-converted to higher frequencies (30-100 Hz), and contaminate the data where the detector is most sensitive to detectgravitational waves.
EQ mode , as an automated global control scheme, sets a milestone in seismic controls of theAdvanced LIGO detectors, significantly reducing DARM motion at sub-Hertz frequencies during earthquakes, thuscontributing to sustaining the data quality and stability of the interferometers in extreme environmental conditions.
Acknowledgments
The authors thank the LIGO Scientific Collaboration for access to the data and gratefully acknowledge the supportof the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratoryand Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, andthe Max Planck Society (MPS) for support of the construction of Advanced LIGO. Additional support for AdvancedLIGO was provided by the Australian Research Council. This project was supported by NSF grants: PHY-1708006and 1608922. ES acknowledge the LSC fellows program for supporting his research at LIGO Livingston Observatory.LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology withfunding from the National Science Foundation and operates under cooperative agreement PHY-1764464 . This papercarries LIGO Document Number LIGO-P2000072.
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