Overview of KAGRA: Calibration, detector characterization, physical environmental monitors, and the geophysics interferometer

KAGRA is a newly built gravitational wave observatory, a laser interferometer with a 3 km arm length, located in Kamioka, Gifu, Japan. In this series of articles, we present an overview of the baseline KAGRA, for which we finished installing the designed configuration in 2019. This article describes the method of calibration (CAL) used for reconstructing gravitational wave signals from the detector outputs, as well as the characterization of the detector (DET). We also review the physical environmental monitors (PEM) system and the geophysics interferometer (GIF). Both are used for characterizing and evaluating the data quality of the gravitational wave channel. They play important roles in utilizing the detector output for gravitational wave searches. These characterization investigations will be even more important in the near future, once gravitational wave detection has been achieved, and in using KAGRA in the gravitational wave astronomy era.


Introduction
Gravitational wave (GW) astronomy is becoming one of the most exciting research fields in physics and related disciplines.Since the first direct detection of GWs from a binary black hole merger [4], many GW signals have been detected by the LIGO [5] and Virgo [6] interferometers.Moreover, the first detection of a GW signal from a binary neutron star merger in 2017 [7] has opened the era of multi-messenger astronomy [8].
KAGRA [9] is a GW interferometer located in Japan.It is termed a 2.5 th -generation GW interferometer because it is constructed underground [10] and operate at cryogenic temperatures (20K) [11] Underground construction and cryogenic operation are essential techniques for the next-generation detectors [45,46].By April of 2019, the installation work was mostly completed, and the interferometer was commissioned [1].At the end of August 2019, the first lock of the Fabry-Perot Michelson interferometer (FPMI) configuration was established, and by the end of January 2020, a power-recycled Fabry-Perot Michelson interferometer (PRFPMI) configuration had been established.Finally, the GEO600 [12] and KAGRA interferometers conducted a joint two-week observation run, called "O3GK", in April 2020.Preparation of the calibration instruments and understanding the characterization of the interferometer play important roles in the accurate reconstruction of GW strain.Reducing the systematic errors in GW signal reconstruction with lower bias leads to precise GW parameter estimation.Precise mass evaluation from compact binary coalescence (CBC) provides information about the origin of the binary and the evolution of the universe.Precise spatial identification of a GW source in the sky (sky localization) provides a wealth of knowledge for multi-messenger astronomy and may lead to a solution for the origins of gamma-ray bursts.
Detector characterization plays an essential role in distinguishing a GW signal from detector noise.During the O1 and O2 observations [13], only GWs from CBCs were successfully detected.Understanding the origin of detector noise is critical for data analysis of GWs searches and parameter estimation; detection of GW signals from NEW sources may significantly expand our knowledge.To identify noise due to disturbances external to the detector, physical environmental monitors (PEMs) are essential.
A geophysics interferometer (GIF) was constructed in the KAGRA X-arm tunnel and has been operating continuously since 2016.The 1,500m GIF provides precise measurements of ground motions in the underground environment, which also can be used in the KAGRA arm-length-compensation system.
Section 2 summarizes the history of the KAGRA calibration activity.Section 3 discusses the data acquisition/quality and transient noise identification.Section 4 describes the introduction history of the KAGRA PEMs and highlights some of their controbutions.Section 5 provides a description of the geophysics interferometer and its installation and discusses some recent topic.Section 6 summarizes this paper. 6/31

Calibration 2.1. Introduction
The main purpose of the calibration study is to provide the GW strain and its error [15,21].Development of the calibration instruments and reconstruction pipelines is essential for precise calibration of the detector.In this process, we need to consider the relationship between the GW strain and a model of the GW detector.The time series (h(t)) of GW strain is given by where L 0 is the effective length of a KAGRA arm (3,000 m) and ∆L ext (t) = L x (t) − L y (t) is the difference between the x-and y-arm lengths caused by external sources; the strain h(t) is not directly available from the interferometer output.The KAGRA interferometer is controlled by digital feedback loops.Four length-control loops -the Michelson differential length (MICH), power-recycling cavity length (PRCL), common-mode arm cavity length (CARM) and differential arm length (DARM)-were used for control during O3GK [32].A model diagram of the KAGRA DARM feedback loop is shown in Fig. 1.In this diagram, the model consists of a real-time interferometer-control part and a reconstruction-pipeline part.Real-time interferometer control is based on sensing and actuation functions, together with digital filter.The sensing function corresponds to the optical response of the interferometer and its readout, and the actuation function corresponds to the efficiency of the coil-magnet actuator on the end test mass.The digital-filter is a component of the real-time control system.This model enables us to use an analytic formula to calculate the transfer functions.However, the sensing and actuation functions include time-dependent parts [16].A set of measurements of the sensing and actuation functions is thus necessary to complete the DARM model.The external displacement, ∆L ext (t), is calculated from the digital signals d err (t) and d ctrl (t).Using Fig. 1, we obtain ∆L ctrl (t) = A * d ctrl (t).
(4) By combining with above equations, the external excitation is obtained as where the convolution operation is defined by t) is a timedomain filter, and G(t) is a digital signal.Precise calibration is required to measure the actuation and sensing functions accurately.

Calibration instruments
We have developed both a photon calibrator (PCAL) [18] and a gravity field calibrator (GCAL) [22] for precise calibration of the GW detector.They allow us to determine the actuation and sensing functions and complete our DARM model.To calibrate the sensing and actuation functions, a displacement has to be applied to produce a differential change in the arm length.Classically, the free-swinging Michelson method has been used to calibrate displacements.It uses the wavelength of a laser as the length standard.However, photon pressure or gravity fields are the modern methods used today.Figure 2 shows an overview of the KAGRA calibration instruments.The PCAL was used as the main calibrator of the KAGRA observatory during O3GK.The KAGRA PCAL was placed 36 m away from the end test mass, and a stabilized laser beam was injected onto the mirror surface to produce a displacement.We also plan to install gravity-field calibrators at the front of the end test masses [29,30,38].A gravity-field calibrator generates a gravity-field gradient around the end test mass.By calculating the force exerted by a quadrupole mass distribution, we can determine the motion of the test mass very accurately.

Photon calibrator.
The PCAL was originally developed at the GEO600 and Glasgow 10 m interferometers and is regarded as a 1 st -generation photon calibrators [35,36].By using photon pressure, the investigators succeeded in actuating the mirror surface.However, they reported elastic deformations at the injection points, which were the centers of mass of mirrors [14].To avoid elastic deformations, LIGO developed a 2 nd -generation PCAL system that uses two-point injections [18], which move the node of the drum-head mode to mitigate elastic deformations [15].An optical-follower servo was also developed to reduce laser noise and higher harmonics.In this paper, we discuss a 3 rd generation PCAL for KAGRA, which was developed by a collaboration between KAGRA and LIGO.To understand the highfrequency response, a 20 W continuous-wave laser is used with an optical-follower servo, and the operating power was increased to be 10 times larger than that of a 2 nd generation system.An independent beam-control system was also employed to characterize the response of the test-mass pendulums.Monitoring of the beam position is also necessary to characterize 8/31 rotation and elastic deformations.The response from the detector is converted into power using a laser-power standard calibrated by the National Institute of Standards and Technology (NIST) [37].We calibrate the PCAL response every month.The relative uncertainty in laser power obtained from the laser-power standard measurement is 0.32 %.However, the absolute laser power has a 3 % uncertainty, because it is determined by the absolute power measurement based on the NIST power standard, and the power standard of each country has a variance of 3 %.
2.2.2.Gravity-field calibrator.The GCAL is a new type of calibrator for absolute calibration.When we calibrate the interferometer response using the PCAL, the absolute error in laser power is propagated directly into the uncertainty in the gravitational-wave strain.To avoid this problem, we have newly developed a gravity field calibrator system for KAGRA.
The original design for this calibrator is based on the CLAB experiment at KEK and the University of Tokyo [23][24][25][26][27]. We took over the system design of the previous experiment and improved it with current technology; the original design was tested 40 years ago.We replaced the motor, encoder, and vacuum seal with state-of-the-art designs.Virgo developed the same concept independently, which they called a "Newtonian calibrat"or [33].Virgo performed a demonstration to measure the displacement due to gravitational wave strain.We will employ the mew system for collaborative worldwide observations.The KAGRA gravity-field calibrator system consists of four subsystems.As shown in Fig. 2, the gravity-field calibrators are placed at the left and right sides of the chambers for symmetry.The left and right calibrators cancel the systematic errors due to rotation.Large and small calibrators are used for consistency checks of the displacement.To verify the model uncertainty, we cross-check the expected response of the mirror using both large and small rotors.Four rotors are synchronized using a rotary encoder and its readout system.By monitoring the rotation, we can determine the expected displacement.At the same time, we need to monitor the absolute distance between the center of the GCAL and the position of the end test mass.By using the hexapole distribution of the rotor, we can cancel systematic errors in the absolute distance measurement.

DARM model
The calibration instruments provide the parameter information needed to determine the DARM model precisely through the response function R [21], which is defined as follows: where the open loop gain is G = C * D * Ã.The response function is thus given by the following equation: where Ã(f, t) and C(f, t) are models of the actuation and sensing functions.These function is defined as: 9/31 To complete the calibration model, the parameter set θ = {H c , f c , τ c , H a } is measured using a swept-sine injection test, where H c , f c , and τ c correspond to the optical efficiency, cavity pole frequency, and time delay of the sensing function, and H (i) a and τ (i) a are the actuation efficiency and time delay from the i-th suspension mass, respectively.The Markov-Chain Monte Carlo (MCMC) method is used to determine θ based on the swept sine measurements from the coil magnet actureator and photon calibrator.The MCMC algorithm provides posterior probability distributions of the model parameters, with a likelihood L(M, d| θ) and an assumed prior distribution.The likelihood is defined using least-squares minimization between the model M and the measured data d.The parameters so-determined are also used in each reconstruction pipeline.

Reconstruction pipelines
Three types of pipelines have been developed to calculate the GW strains, called the C00, C10, and C20 pipelines.Each pipeline has its own characteristics.The purpose of each pipeline is explained below.ET M X , ∆L 0 ET M Y and ∆L 0 res , are used as inputs.They are filtered by the FIR correction filters in the actuation and inverse sensing paths, added together, and then divided by L to give the strain signal h(t).
2.4.1.C00: The online pipeline.The main purpose of the C00 pipeline is to monitor h(t) during the operation of the interferometer.It is a front-end calibration pipeline that employs infinite-impulse response (IIR) filtering techniques.Using the output of the front-end system, we multiply the actuation and sensing function models by the IIR filters.We update these parameters every week.We neglect the time dependence in this pipeline.By using the IIR filter, we approximate the high-frequency response as a time delay effect.
2.4.2.C10: Low-latency pipeline.The main purpose of the C10 pipeline is for low latency analysis.This pipeline receives DARM loop signals that are partially calibrated with the IIR in the C00 pipeline as shown in Fig. 3.The time dependent factors are also monitored with calibration lines.The C10 reconstruction filters are calculated with appropriate finiteimpulse response (FIR) filters using a GStreamer-based pipeline known as "gstlal" [34].This pipeline generates h(t) with a latency less than 10 seconds.By using an FIR filter and the demodulation signals from the calibration lines, the uncertainty in h(t) can be reduced below that of obtained from C00 [16].This h(t) is used for event-search analysis, for which C10 pipeline generates information about the calibration status, providing calibration flags at the same time.We also update these parameters every week.
2.4.3.C20: High-latency pipeline.The C20 calibration pipeline is also based on the gstlal.It produces h(t) with offline raw data on a high-latency server.The high-latency pipeline produces data several months after the acquisition of raw data.The time dependence from the PCAL is also applied in this process. 11/31

Error estimation
Error estimation for the response functions is one of the most challenging topics, because the reconstruction process is non-linear.Even if we attempt to fit the data, it is sometimes mismatched under the linear regression [21].Gaussian-process regression (GPR) is the method of Bayesian model estimation for a non-linear system.In a Gaussian process, the set of data is modeled as a simple Gaussian distribution N [m(f ), σ(f )].The GPR results vield a distribution function around the mean of the data, which provides an uncertainty estimate at the same time.To apply the GPR method, we determine the residual response function as follows: δ where Rmodel (f ) and Rmeas (f ) based on the parameters determined with the MCMC method and the measured response function.The frequency-domain response-function δR is proportional to the GW strain error δh, as shown in eq. ( 9).We can also define the corresponding uncertainties σ R and σ h as in eq. ( 10) The response function must therefore be characterized in order to perform the calibration.Finally, we obtained the mean and uncertainty of the response function and determine the time-dependent errors.By using the DARM-model parameters parameters and timedependent correction factors from the reconstruction pipeline, we estimate the uncertainty with a Monte Carlo simulation.The PCAL uncertainty, based on the power calibration of the read-back signal, is also included in the error estimation.

Data acquisition
KAGRA is composed of nineteen suspended mirrors and many optical components [1].All mirrors and optics are controlled by a digital control system.The data-acquisition system is integrated into this digital control system, and it records more than 100,000 channels.The recorded channels contain not only the main interferometer signals but also signals from physical environmental sensors, many test points in the control loop of the main interferometer, local control signals from all the suspended mirrors, and so on.All data are recorded as discrete time-series signals with various sampling intervals.The total data rate reached 12 MB/s during the O3GK observing run on KAGRA.This data set was obtained at the Kamioka site and was transferred to KAGRA's main data center at Kashiwa.The KAGRA data is distributed from Kashiwa to many computer centers located both in Japan and at overseas sites, including the computer centers of LIGO and Virgo.Details of the data transfer from KAGRA are discussed in [2] By using these signals, the recorded data are classified into two categories.One is used for scientific purposes such as searching for GWs and determining the parameters of GW sources.The other is used solely for evaluating the detector and its noise status.For realtime GW searches, it is difficult to analyze all channels due to limited computer resources.
12/31 However, analyzing auxiliary channels can tell us whether the quality of the interferometer signals is sufficient for GW searches.For this reason, basic criteria are set for many auxiliary channels.Some indicators, called "data-quality state vectors", are provided if these criteria are satisfied.This process is performed by the digital control system and the vectors are recorded in bit-string format.The process of data-quality evaluation is also performed offline in order to correct for mistakes and errors in the real-time process.Because amount of data reaches 1PB/yr for each detector, it's difficult to transfer all data between overseas.From the view point of the data storage, there is no enough storage for keeping all KAGRA, LIGO and Virgo's data.Therefore only some important channels are shared with oversea.In order to reduce the amount of data, only the main interferometer signals and the data-quality state vector are shared with LIGO and Virgo.In addition, a list of GPS times that define "science segments" in which the data can be used for searching is provided.This "segment" information is provided to indicate the noise status in order to evaluate the status of the interferometer.To search for GWs reliably, it is important to reject false events from among the GW candidate events.Each GW search pipeline evaluates false alarm probability from the background noise behavior of the GW channel.Other auxiliary channels are not usually used in the GW search pipelines; instead, they are analyzed using "glitch pipelines" and other noise-evaluation methods.Glitch pipelines are tools in order to detect transient signals.
They are applied not only to GW channels but also many auxiliary channels.Detected transient signals in the GW channel and auxiliary channels are evaluates their coincidence and used as one of information to remove fake events from GW event candidates.Data quality is assessed not only for reliable detection, but also for improving the sensitivity and stability of the detector.Comparison between the current and past interferometer status often helps in finding the reason why data has been flagged as "bad condition".A data-monitoring system is provided as a web interface called "SummaryPages," which is used to check interferometer stability and to detect changes in the interferometer status.Various plots of the main interferometer signals and many auxiliary channels are provided and archived every day.Figure 4 shows an example of the SummaryPages, which displays the latest detector sensitivity, inspiral ranges that indicate the detectable distance of GWs from binary neutron stars, and some data-quality flags.The plots on the SummaryPages are updated every 15 minute and are also used for daily check from the remote sites.

Data-Quality State Vector
Interferometer status is evaluated from many auxiliary channels.Because this evaluation result is used in many cases such as the decision of interferometer control strategy, interferometer noise evaluation, various GW searches, etc., status evaluation is performed as a real-time process in automatically and its results are recorded as a simple indicator such as "OK" or "Not OK".In order to satisfy the various situations, several types of indicators were prepared during O3GK.These indicators are merged as one bit-string named as "Data Quality (DQ) state vector".This DQ state vector helps us to use same criteria for each search pipelines and to reduce CPU costs for re-evaluation.The definition of DQ state vector is shown in Table 1.The most important flag is the science-mode flag, because GW searches are performed only for data indicated to be science-mode data.The science mode does not include any periods in which (1) a calibrated strain signal is not available, due to 13/31 Fig. 4 Example of the SummaryPages.They are used to monitor the interferometer status by on-site team members and for daily checks from remote sites.some reason such as a hang-up of the calibration process, (2) interferometer control setting are not nominal, or (3) there are signal injections or excitation.Periods in which saturation of analog-to-digital converters (ADCs) or digital-to-analog converters (DACs) occurs are provided as auxiliary segment information.
KAGRA's digital control system makes it easy to change the configuration, as compared with analog control systems in general.On the other hand, managing the definition of the control settings is more significant.Operating the interferometer with any different configuration changes the stability and sensitivity to GWs.Such a change affects background estimation in each GW-search pipeline.All of the interferometer control configurations were well defined as nominal settings during interferometer commissioning.If the interferometer status change due to time variations or some trouble, the nominal settings are set again after human validation.Unexpected differences between the latest configuration and the nominal configuration can be detected through KAGRA's digital control system.Any period with at least one setting different from the nominal one is flagged as a non-science mode.
The data-quality state vector also inclues injection flags.Signal injections are performed in order to measure the interferometer response to GWs, investigate sources of detector noise that limit the sensitivity to GWs, and check the calibrated strain signals and GWsearch pipelines.For those purposes, signals are injected from coil-magnet actuators on the suspended mirrors or from the photon calibrators through the digital control system.Measuring the response of the interferometer is performed by using sine, swept-sine, and sine-Gaussian waveforms.Various theoretical GW waveforms are used to check calibrated strain signals and test the GW-search pipelines.Because signals due to these injections must be excluded from candidate events, any periods with injections are flagged.Five injection flags are provided to indicate the type of waveform being injected.As shown in Table 1, there are five different kinds of injection flags for the different waveforms.

Data-Quality Segment
Segment information is generated to indicate multiple data periods that are suitable for use in gravitational wave searches.One segment is recorded between the two GPS times when a science mode starts and ends.In addition to the science mode, segment information is provided about overflow periods and various types of noise status.Such information is generated every 15 minutes, based on the data-quality state vector, which is recorded as timeseries data with bit information at a 16 Hz sampling rate.KAGRA's segment information is sent to a database server called "DQSEGDB" [39] at the California Institute of Technology (CIT) and is stored together with segment information from LIGO, Virgo and GEO.Some search pipelines use such segment information from multiple detectors to perform coincidence and coherence searches.For future observing runs, we plan to create not only information indicating whether or not a segment is in science mode, but also information containing various noise conditions caused by earthquakes, loud microseismic disturbances, and so on.

Transient-noise identification
While gravitational-wave search pipelines usually use only the gravitational-wave channel data, the quality state vector, and segment information, other auxiliary channels help with noise investigations to reduce false candidate events caused by noise transients.Especially for burst searches, in which theoretical waveforms are not assumed, removing false events by using the auxiliary signals is one of the most important tasks for the reliable detection of gravitational wave events.Coincidence investigations of transient signals with the gravitational-wave channel and auxiliary channels are often performed to provide veto analysis for candidate transient gravitational wave events.The method is called "Hierarchichal Veto (hveto)" [40,41].hveto rejects fake events by using the significance of coincident events between the GW channel and auxiliary channels.In order to detect coincident events on the GW channel and auxiliary channels, Omicron pipeline was used during O3GK for around 200 auxiliary channels.Omicron pipeline is one of tools to detect transient events, which is based on the constant Q-transform method [42][43][44].This method provides an epoch time, central frequency, and Q-value for every transient event in the gravitational-wave channel and auxiliary channels.The hveto analysis vetoes the gravitational wave candidate events caused by noise transients on auxiliary channels.
Veto analysis using hveto was conducted offline during O3GK.On the other hand, an event list of noise transients was provided every 15minuts as input to hveto.For future observing runs, online veto analysis is also required.Data transfer for online searchesincluding calibration, h(t) generation, and the durations of data files-takes less than one minute to the main data centers at Kashiwa and overseas sites such as CIT [2].Depending on the computing time in the search pipeline itself, the veto process can be started within a 10 -20 minute delay, which is necessary to provide breaking news of GW-event alerts.In the future, we also aim to reduce the time spent both in data transfer and om tje GW search itself.Great improvements in data transfer and GW searches in future observation will also require improvements in noise-transient investigation.

Physical environmental monitors 4.1. Introduction
Because the typical amplitudes of GWs are extremely small, strains on the order of 10 −21 , anything can produce noise-source contamination that reduces the sensitivity.To evaluate the noise sources, about 100,000 auxiliary channels are recorded by the KAGRA digital system.Major noise sources include environmental disturbances caused by earthquakes, effects from magnetic and acoustic fields, temperature fluctuations, and so on.
The three main purposes of physical environmental monitors are the following: The first use of PEMs is to identify noise sources and understand their couplings to detector sensitivity so that noise-hunting measures can be applied.The second purpose is to collect environmental information that can be used in evaluating the data quality of the GW channel and in trying to distinguish GW signals from any pseudo signals caused by noise.The details are described in Sec.3.4.The third purpose is for R&D studies directed toward the development of 3 rd -generation GW interferometers.As described above, the KAGRA interferometer has two unique features: the underground site and cryogenic technology.Both features will be essential for 3rd-generation detectors.Understanding the influences of these new technologies on GW detectors is attracting great attention from the international LIGO and Virgo collaborations.

Installation protocols for the KAGRA PEM sensors
To evaluate the environmental noise, we have installed many PEM sensors in the KAGRA experimental site (including outside the tunnel).Detailed information about the sensors used for the O3GK observation is summarized in Table 2, including the sensor type, product name, operating frequency, and number of sensors, and in Fig. 5   The PEM sensors are installed for the following protocols in KAGRA: 4.2.1.Monitors for vibration, sound, and the voltage at the optical tables.Monitoring and controlling the auxiliary optics is important for interferometer operation.Such auxiliary optics are used for many purposes, such as laser-source stabilization, mode matching, sensing for the interferometer controls, and control of the photon calibrator.For sensing and stabilization, multiple optical tables are installed in several places.Optical parts like photo-diodes and periscopes are fixed onto the table, so they are directly affected by their environments.We placed at least one accelerometer, microphone, and voltage monitor to monitor the ground between each optical table and its ADC.By monitoring those signals, we can identify stationary interferometer noise, narrow band frequency noise (line noise), and glitch noise caused by the environment.
4.2.2.Monitors for ground motions in the underground facility.We placed three seismometers at the center, X-end, and Y-end areas and positioned one GIF along the X-arm (the GIF details are described in Section.5) to monitor the ground motions caused by Earth tides, earthquakes, ocean waves, and human activities.An important point is that the seismometers are placed on the 2nd floor of each area; the four cryogenic mirrors that comprise the Fabry-Perot cavities, are hung from the 2nd floor.They are used not only ground motions but also for sensor corrections [50], controlling the suspensions with multiple sensors.[47]).This map is available at [48].
In addition, we installed three compact seismometers on the 1st floor of the center area: (1) near the input-mode cleaner (IMC), to monitor local ground motions at the pre-stablized laser (PSL) room, the IMC, and the input mode-matching telescope, (2) near the beam splitter (BS), to monitor local ground motions at the power-recycled mirror chambers, the BS chambers, and the signal-recycled mirror chambers, and (3) near the input test mass X (ITMX), to monitor local ground motions at the cryostat and to compare differences between the 1st and 2nd floors.4.2.3.Monitors for magnetic fields in the underground facility.Magnetic-field noise is an important environmental noise for a GW detector, because it can cause electrical noise due to mirror motions.At LIGO, the identification and mitigation of narrow spectral artifacts -due to power lines and magnetic fields to/from suspensions or electrical circuits-played important roles in O1 and O2 [49].It is even more important for KAGRA to monitor the magnetic fields in the experimental site, because coil-magnet actuators are used to control the suspensions instead of the electro-static drivers used in LIGO.
We placed three 3-axis magnetometers near the BS chamber, X-end cryo-chamber, and Y-end cryo-chamber to monitor the magnetic fields coming from various instruments (e.g, cryo-coolers, power lines, and digital devices) or due to natural phenomena (e.g, lightning strikes, magnetic storms, and Schumann resonances [52]).
18/31 4.2.4.Monitors for room temperature and humidity in the underground facility.Even though the temperature of the underground site is stable, the KAGRA suspensions are extremely sensitive to the surrounding temperature.Because many delicate analog circuits are used, monitoring the humidity is also important.The temperature and humidity vary as instruments are turned on and off (e.g, vacuum pumps and fans).We placed a number of thermo-hygrometers on all the electrical racks, in the clean booths, near the chambers, and near the air conditioners [55].4.2.5.Monitors for weather conditions outside the tunnel.To monitor the environment outside the KAGRA tunnel, a weather station was set up in front of the tunnel entrance.It monitors the temperature, humidity, air pressure, rainfall, wind speed, and wind direction.In addition, a lightning sensor was installed as a part of the Blitzortung.orgnetwork [51] to monitor the time and position of lightning strikes.

Development of a portable PEM system
Besides the regular PEM sensors at various fixed locations, we are also utilizing so-called 'Portable PEMs' in addition to the regular PEM sensors to assess various unknown noise sources, to make characterization of the KAGRA instruments easier, and to understand the noise-coupling paths.There are two types of portable PEMs: One is a combination of an analog output sensor and the KAGRA digital system, as with the regular PEM sensors.Some versatile ADC channels are reserved for this purpose in each area.Since the digital system is available, it is possible to carry out data analyses with other channels; e.g, to provide real-time coherent analyses.The other one is a combination of a USB sensor and a Chromebook R PC (ASUS Flip C101PA), as shown in Fig. 6.Since this PC has USB-A and USB-C ports, and since Android R applications are available, a real-time spectrogram from a USB sensor (microphone, accelerometer, and magnetometer) can be displayed.Using this system, we can work free from any limitation due to cabling, power supply, ADC port, etc.This system enables us to investigate environmental noise very effectively.Detailed information about the portable PEM system will be described in a future paper.
where Ỹinj (f ) and Ỹ (f ) are the amplitude spectral density of the GW strain channel with and without PEM injections, respectively, and Xinj (f ) and X(f ) are the amplitude spectral density of the PEM sensor signal.The effect of environmental noise on the sensitivity is given by These formulas are also used by LIGO and Virgo.
Figure 7 shows the results of an acoustic-injection test performed during FPMI commissioning in December 2019 as one example of a PEM injection into KAGRA [53].The several peaks in this figure can be identified with acoustic noise sources around the optical tables.More detailed studies with the PRFPMI configuration were performed before and after the O3GK observation, and a paper describing the results is in preparation.[53].Strain sensitivity without PEM injection (black), with projected acoustic noise (orange, incoherent; red, coherent), and the 3σ upper limit to the acoustic noise (green).

Noise hunting using PEMs
We succeeded in hunting down several noise sources that affected the interferometer sensitivity.Representative noise-hunting are summarized below.with the optical levers that monitor the motions of the test masses, at the signal-recycling mirrors.We found that the fan filter unit (FFU), which is used to keep the booth at a given clean level, generated the vibration.The resonant frequency of the framework of the clean booth turned out to be 17.2 Hz.When the FFU was turned off, the noise vanished.• 44 Hz noise hunting by portable PEM system Noise was detected at 44 Hz in the frequency noise of the auxiliary lasers that support arm-length stabilization for interferometer-lock acquisition [54].When we evaluated the coherence with the power of those auxiliary lasers using the PEMs, we found that the accelerometers placed in the PSL room exhibited large coherence.Using a portable PEM with Chromebook, the large vibration at 44 Hz was identified to be the mechanical vibration of a 24V DC power supply used for the laser shutter.We changed the position of the power supply, and this noise disappeared.• 160, 280 and 360 Hz noise hunting using PEM injection The bumps around 160, 280, and 360 Hz in Fig7 were identified as ambient acoustic noise in the FPMI configuration; similar results were observed in the PRFPMI configuration before the O3GK run.By using a hammering test we found that they came from the bellows at the IMC output (most likely scattered-light noise).We suppressed these noise sources by reducing the sound sources and adding sound proofing.

Summary
To evaluate and reduce the effects of environmental noise, various PEMs were installed and portable PEMs were prepared.Following the installation protocols, seismometers, accelerometers, microphones, magnetometers, voltage monitors, and weather monitors were installed around the interferometer.As a result, environmental noises which are 17.2 Hz, 44 Hz, and 160, 280, and 360 Hz, were identified and removed.
Because the KAGRA interferometer has the unique features of being located in an underground site and using cryogenic techniques -features that are key for the development of 3rd generation GW interferometers-environmental noise from those features must be understood.They have accordingly attracted gread attention also from the international LIGO and Virgo collaborations.

Introduction
The GIF is one of KAGRA's unique features.It is a pair of Michelson laser interferometers specifically designed to measure ground motions (strains) along the KAGRA arms.The GIF covers a wide frequency range, which includes effects such as tidal motions, microseismic motions, coseismic steps, Earths free oscillations, slow earthquakes, and so on.These events themselves are of interest for geophysical studies, and in addition, the ground motions detected by the GIF can be used to compensate for changes in the KAGRA baseline lengths in order to improve its stability.The first GIF strainmeter was constructed in the KAGRA X-arm tunnel in 2016, and it has been in operation since then.See Fig. 8 for its location.

The GIF system
The basic design of the GIF strainmeter is an asymmetric Michelson interferometer with 1.5 km-and 0.5 m-long arms.The interferometer optics consist of two retroreflectors, a BS, a quarter-wave plate (QWP), and a wedge plate, as shown in Fig. 9.The optics are housed in vacuum chambers located at both ends of the main arm.They are separated by 1.5 km and are connected by a vacuum tube.The vacuum pressure in the optical path is maintained lower than 10 −2 Pa to suppress optical-path-length fluctuations due to variations in the refractive index of the residual gas.The 0.5 m-long reference arm consists of the BS and one of the retroreflectors, both mounted on a single Super Invar plate for thermal stability.The other reflector is installed in another vacuum chamber, and together with the BS, it forms the main arm, the displacement of which is detected by the interferometer.The optical components are rigidly connected to bedrock, and since no length control is applied to them, they follow the exact ground displacements.
A frequency-doubled Nd:YAG laser is used as the light source.The laser frequency is stabilized to an absorption line of iodine (I 2 ) gas via the saturated-absorption technique.Frequency fluctuations directly cause displacement noise due to the asymmetry of the interferometer [57].The fundamental limit to the strain resolution of this instrument is set by the stability of the laser frequency.The actual frequency-noise level is estimated to be better than 10 −11 over a 10 second period by comparison with an identical stabilized laser.
The laser beam is introduced into the input optical system through a polarizationmaintaining fiber.The input optics consists of a pair of lenses and a flat and a concave mirror, which form a folded mode-matching telescope.This arrangement optimizes the beam profile so that the beam waist is located at the end reflector, and the return beams from the two arms overlap adequately on the BS.The diameters of the beam waist and the return beam from the main arm (on the BS) were calculated to be 32 mm and 45 mm respectively [58].The input beam is aligned with the main arm remotely over the internet by tilting the concave mirror with piezo linear actuators (Picomotors, Newport Inc.).A similar optical system is installed along the input telescope to form an output telescope that focuses the return beam onto the photodetectors (PDs).The input and output optics are mounted on two optical tables separated by 5 m, and the optical path between them is doubly covered by PVC pipes and by an enclosure with aluminum-plate walls in order to prevent contamination and airflow that causes alignment fluctuations.
A quadrature-detection technique is used to obtain the phase changes of the interferometric fringes that represent the ground displacements, including their directions.Combined with the absence of length control, this configuration enables a very wide (ideally infinite) observation range.The QWP inserted in the reference arm makes this technique possible by creating two linearly-polarized components that are 90 degrees out of phase, and they are detected by two PDs at the output port after being separated by a polarized beam splitter.
We developed a data acquisition (DAQ) and automatic control system for laser stabilization based on a commercial modular controller (PXI system, National Instruments Inc.).It records the interferometer signals, i.e., the fringe signals and other monitoring signals (50k samples per second), together with environmental-monitoring signals (200 samples per second).The controller sets the status of the laser-frequency stabilization system, which is implemented with analog circuits, in the lock-acquisition or lock-maintaining mode.

Details of implementation, installation, and operation
The GIF is constructed in the KAGRA tunnel in a severe environment, with water dripping frequently from bare rock surfaces, and the atmosphere is very humid and dusty.In order to protect the interferometer optics and the laser system from contamination, we built clean booths with clear PVC walls around the vacuum chambers and the optical tables prior to their installations.
The long baseline length of the GIF is advantageous for achieving better strain resolution, but due to beam divergence it requires larger optics than shorter interferometers.This introduced difficulties in the production of some optical components, such as the retroreflectors (which require 15-inch clear apertures) and the BS.The parallelism and flatness of their surfaces strongly affect the fringe visibility of the interferometer.For the retroreflectors, we made a simple two-dimensional model to determine the requirements for surface flatness necessary to realize the desired fringe visibility.However, technical limitations in their production prevented us from meeting these requirements fully, so the reflectors were made using best efforts.After their production, we recalculated the expected visibility to be 0.  degradation imposed by other components, the actual visibility was reduced to 0.1, but this is still sufficient to extract the necessary phase information.A similar problem occurred in manufacturing the BS.In the initial design we had planned to make it from a single glass plate, expecting better parallelism, which is important for achieving a uniform wavefront (i.e., better visibility).However, it turned out that a single plate large enough to cover both the input and output beams was too large for the fabrication facility of the manufacturer.We therefore decided instead to make two separate plates, one each for the input and output beams.This "compromise" actually allows us to adjust their angles independently by inserting thin spacers into their mounts, coarsely correcting the wavefront distortion of the returning beams from the main and reference arms (Fig. 10).Additional wavefront correction was applied by inserting a glass wedge plate between the BS and the main arm reflector (Fig. 11) to compensate for residual wavefront mismatch.
The lock status of the laser-frequency stabilization is continuously monitored by the DAQ system.In order to maximize the observation time, it starts the relocking process immediately after a loss of lock is detected.Due to the automatic relocking system and the stable environment of the underground site, the GIF requires little human effort to maintain its operation.We use monthly realignment of the input beam to compensate for its drift in tilt (supposedly caused by plastic deformations of the springs used in the flat mirror mount of the input telescope).The beam path in the saturated-absorption optics needs realignment only a few times a year.These realignments can be done remotely without disturbing the site environment.We regularly check the status of the vacuum system, inspect the facility, and fix problems -for instance, by installing shields for the vacuum components to protect them from water drops -in order to maintain stable operation.

Recent topics
5.4.1.A study of barometric effects.Ground strains at low frequencies are subject to variations in the air pressure [59].Figure 12 shows the spectra of ground strains observed by the GIF and of the local air pressure measured at the front and end chambers of the GIF.Strains in 10 −4 − 10 −3 -Hz region have a spectral shape similar to that of the air pressure, 24/31 and their temporal variations also are highly correlated with the temporal variations in air pressure.
The barometric admittance to strain, in terms of a coefficient of strain response to air pressure, is estimated to be ∼ 0.55 × 10 −9 / hPa, which is consistent with typical values [59].Air pressures at the front and the end chamber, which are separated by 1.5 km in the tunnel, are almost identical (within 10 % difference) below ∼ 3 mHz, while they are uncorrelated above ∼ 10 mHz (Fig. 13).Correcting the ground strain with the measured air pressure in the 10 −4 10 −3 -Hz region, however, reduces the background strain only by ∼ 1/3 at best (Fig. 14).It should be noted that the reduction is still limited even in the period of bad weather when amplitudes of the background strain increase in proportion to air pressure.Therefore, it is suggested that the background strain is not determined simply by the local air pressure but also is affected by the regional air pressures which will have similar amplitudes but may have different correlations to the local air pressure.Baseline corrections of the GW detector based on in-situ measurements of ground strains are effective, especially in the 10 −4 10 −3 -Hz region (see the following section), where local measurements of air-pressure data and seismometer data are insufficient due to limitations in the spatial distributions and instrumental noise, respectively.

Baseline-length compensation in KAGRA.
The duty cycle of a GW detector is usually limited by seismic noise below 1 Hz, produced by earthquakes, microseisms, tidal motions, etc. [60].Active vibration isolation systems based on seismometers have been used to improve the detectors duty cycle by suppressing the effect of those noise sources [61].However, seismometers have a fundamental problem, that is they cannot distinguish horizontal acceleration -which is the signal needed for active isolation -from gravity acceleration introduced by ground tilt.This makes it difficult to provide sufficiently high feedback gain in the low-frequency range for active isolation systems.
Tidal effects can be removed by applying a global tide model [62], but other noise sources are intrinsically unpredictable, such as the air-pressure effect described in the previous section.Therefore it is crucial to use the actual ground motions observed at the GW detector  site in order to build an effective baseline-compensation system.The degradation of the duty cycle due to low-frequency seismic noise can be mitigated by implementing a compensation system using the GIF, a sensor that can measure the actual change in baseline length with sufficient sensitivity all the way down to DC.We have demonstrated such a baseline length compensation system for the KAGRA X-arm, using the strain signal measured by the GIF 26/31 Fig. 14 Ground-strain spectra before (blue) and after (red) correction using the measured air pressure.The background strain is reduced by ∼ 1/3 at best in the in 10 −4 10 −3 -Hz region (within the dashed red circle).This limited reduction suggests that the background strain is not determined simply by the local air pressure but also is affected by the regional air pressures which may have different correlations to the local air pressure.in October 2019 [58].In our control system, the change in the baseline length was measured accurately by the GIF, and that signal was fed forward to the actuators installed at the suspension point of the end test mass in order to suppress the change in the arm length of the cavity.
Figure 15 shows the change in baseline length observed by the GIF (top) and the length change of the arm cavity (bottom).The constant drift in the top window corresponds to tidal motion at that time.The arm cavity was locked in resonance by controlling the laser frequency without applying any mechanical control, and the change in cavity length was derived from the control signal to the laser.Length compensation was turned on at the point indicated by On in the bottom panel.There are two noticeable effects in the cavitylength signal after the control was introduced.The first effect is that the length change caused by the tidal motion was reduced to a few µm.At least a one-order-of-magnitude reduction is estimated by comparing this number to the typical amplitude of tidal motion (several tens of µm RMS ).The second effect is about a 50 % suppression in the amplitude of the higher-frequency fluctuations.This was further studied in the frequency domain, and the spectra of cavity-length changes together with their RMS amplitudes with and without compensation are plotted in Fig. 16.The RMS amplitude was dominated by a microseismic peak around 200 mHz, and it was halved by the feedforward control.

Summary
The GIF strainmeter was designed to monitor ground motions over the 1.5 km baseline in the KAGRA tunnel, and it has been operating with a high duty cycle of 99.4 % (average in 2019).The strainmeter constantly observes tidal and microseismic motions and other occasional events, including near and far earthquakes as well as small coseismic steps originating from 27/31 Fig. 16 Spectra of cavity-length changes of the KAGRA X-arm, before and after applying baseline-length compensation, black and red solid lines, respectively.The RMS motion (dashed lines in corresponding colors) was reduced by factor of ∼ 2. distant earthquakes.The strain resolution of the GIF was estimated to be better than 10 −12 in the 2 20 mHz range and 10 −11 in the 1 mHz 10 Hz range, based on the observed background noise (the lowest value among laser strainmeters), which corresponds to ambient seismic motions or to laser-frequency noise, depending on frequencies [56].We are currently working to improve the laser-frequency noise.

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A strong correlation between air pressure and strain was observed in the frequency range 10 −4 − 10 −3 -Hz.The small improvement achieved by correcting the strain using just the local air pressure record indicates the effect of regional air pressure onto the ground strain.This result also suggests that the use of actual strain data is crucial for baseline compensation.
The main disturbance to the continuous operation of KAGRA is seismic noise at low frequencies (below 1 Hz) [3].The GIF can accurately observe ground motions in that frequency range, and its signal is useful for baseline-length compensation to enhance the duty cycle of KAGRA.We have successfully demonstrated reductions in the cavity-length change in the frequency ranges of both tides and microseismic motions.

Conclusion
KAGRA is a GW interferometer in Japan.In April 2019, the installation work was mostly completed, and two-week observation run called O3GK was performed in April 2020.To publish the staunch results, the accuracy of the calibration and detector characterization play an Calibration accuracy and detector characterization both play important roles in obtaining definitive results.To evaluate the quality of the interferometer and the GW data, and to understand the interferometer environment, physical-environment monitors and the geophysics interferometer play important roles.
For accurate calibration, two calibration instruments, PCAL and GCAL, are planned to install, with PCAL being used for calibration during the O3GK observations.For reconstructing the h(t) strain, a calibration model was constructed and the calibration parameters measured.Three types of reconstruction pipelines were developed: online, low-latency, and high-latency pipelines.Error estimation is also important for evaluating the reconstruction pipelines and performing data analysis.The details will appear in future publications.
The data-acquisition system is integrated with the KAGRA digital control system, and more than 100,000 auxiliary channels were recorded with GW signals.To evaluate the detector health and noise status, a data-quality state vector was prepared and used to identify appropriate science segment.The KAGRA science segments were shared with other international interferometers via DQSEGDB in a data server at CIT. SummaryPages were also prepared to help identify the reason why data were flagged as"bad" (i.e., unsuitable for GW searches).To investigate and veto transient signals in the gravitational wave channel and auxiliary channels, we implemented the hveto analysis technique.This technique is used in un-modeled GW searches (burst searches).
In one auxiliary channel, various types of physical environment monitors were installed before the O3GK observations.They have helped to identify noise sources and to understand their couplings to the detector sensitivity.Several noises sources have already been hunted down and identified.
The GIF is a unique feature of KAGRA.It is used to evaluate ground motions that limit the stability of the GW detector in the low-frequency region.It has been observing the actual ground motions in the KAGRA tunnel below 1 Hz with good resolution virtually continuously, with a 99.4 % duty cycle.A strong correlation between ground motions and air pressure was found by the GIF in 10 −4 − 10 −3 Hz frequency range, which cannot be estimated accurately from global models.A baseline-length compensation system for KAGRA has been successfully demonstrated using the GIF data.

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In this article, we focused on the introduction and history of the KAGRA calibration, detector characterization, physical-environment monitors, and the geophysics interferometer.Detailed results for the O3GK observations will appear in subsequent articles.

Fig. 1
Fig. 1 Diagram of the DARM control loop and the reconstruction pipeline.The DARM model consists of actuation and sensing parts.The actuator part corresponds to the transfer function from a digital-to-analog converter (DAC) to the displacement of the mirror.The sensing part is a combination of interferometer and photo-detector responses.The quantities d err and d ctrl are error and control signals, which are outputs from the interferometer.Using this DARM model, we can construct actuator part and sensing part for reconstructing the signal.Red arrows show injections from outside the feedback loop.

Fig. 2
Fig. 2 Schematic view of the KAGRA calibration instruments.The photon calibrator is placed 36 m from the end test mass.Beams from the transmitter module are injected onto the mirror surface to it.The expected displacement is monitored by using a read-back signal at the receiver module.The gravity-field calibrators are installed around the end test mass.The gradient of the gravity field changes the position from the test mass.The expected displacement is calculated from the masses of the rotors and the geometry.

Fig. 3
Fig. 3 Conceptual diagram of the low-latency calibration pipeline.The partially-calibrated outputs of the front-end calibration pipeline, ∆L 0 ET M X , ∆L 0 ET M Y and ∆L 0 res , are used as inputs.They are filtered by the FIR correction filters in the actuation and inverse sensing paths, added together, and then divided by L to give the strain signal h(t).
with a location map.Signals from the fast sensors (seismometers, accelerometers, microphones, magnetometer, and voltmeter) are acquired by the KAGRA digital system together with the interferometer signals and suspension signals.The slow sensors (thermohygrometers and weather station) have their 16/31 own data loggers, and the signals are also merged into the KAGRA data through the EPICS 1 channel.

1Fig. 5
Fig.5Location map of the KAGRA PEM sensors for the O3GK observation (the design is based on LIGO[47]).This map is available at[48].

Fig. 6
Fig. 6 Photograph of a Chromebook with a USB accelerometer.The real-time spectrum and a spectrogram generated by free software are displayed.

Fig. 7
Fig.7Result of an acoustic-injection test performed during FPMI commissioning in December 2019[53].Strain sensitivity without PEM injection (black), with projected acoustic noise (orange, incoherent; red, coherent), and the 3σ upper limit to the acoustic noise (green).

•
17.2 Hz noise hunting using installed PEM sensors Noise was detected at 17.2 Hz in the interferometer control signal.It was largely coherent 20/31

Fig. 8
Fig.8Location of the GIF 1500-m laser strainmeter in the KAGRA X-arm tunnel and surrounding area.Adopted from reference[56]

Fig. 9
Fig. 9 Optical configuration of the GIF.The interferometer arms are located in vacuum.The input and output telescopes are placed in the atmosphere but are covered by hard enclosures.
53, based on the surface-flatness distribution measured by the manufacturer.Due to additional 23/31

Fig. 10
Fig. 10 Progress of wavefront correction.(A) Five or six fringe stripes/cm were observed without correction, which resulted in insufficient visibility to obtain phase information.(B) That number was reduced to 1 stripe/cm by adjusting the angle of the BS plate, enabling phase determination.(C) Further correction was achieved by inserting a wedge plate in the main arm to improve the visibility.

Fig. 11
Fig. 11 Inside the front vacuum chamber.The BS and retroreflector are mounted on a Super Invar platform to form a 0.5 m reference arm.The wedge plate provides wavefront correction.

Fig. 12
Fig. 12 Spectra of ground strains observed by the GIF and of local air pressure measured at the front and end chambers of the GIF.Strains in the 10 −4 10 −3 -Hz region (within the dashed red circle) have a spectral shape similar to the air pressure.The barometric admittance to the strain is estimated to be ∼ 0.55 × 10 −9 / hPa.Different datasets are shown in different colors to see the repeatability and the fluctuation.

Fig. 13
Fig. 13 Relative differences in air pressure between the front and end chambers.Both air pressures are almost identical (within 10 % difference) below ∼ 3 mHz and they are uncorrelated above ∼ 10 mHz.Different datasets are shown in different colors to see the repeatability and the fluctuation.

Fig. 15
Fig. 15 Baseline motions observed by the GIF (top) and the change in length of the KAGRA X-arm cavity (bottom).Baseline-length compensation was turned on at 12 minutes (indicated by the On arrow).

Table 1
Definition of KAGRA data-quality state vector

Table 2
Summary of the KAGRA PEM sensors installed for the O3GK observation.