SSEISMIC NOISE MEASURES FOR UNDERGROUNDGRAVITATIONAL WAVE DETECTORS
SOMLAI L. , AND GRÁCZER Z. , LÉVAI P. , VASÚTH M. ,WÉBER Z. , VÁN P. , , Abstract.
The selection of sites for underground gravitational wave detec-tors based on spectral and cumulative characterisation of the low frequencyseismic noise. The evaluation of the collected long term seismological data inthe Mátra Gravitational and Geophysical Laboratory revealed several draw-backs of the previously established characteristics. Here we demonstrate theproblematic aspects of the recent measures and suggest more robust and morereliable methodology. In particular, we show, that the mode of the data isnoisy, sensitive to the discretization and intrinsic averaging, and the rms Hz is burdened by irrelevant information and not adapted to the technologicalchanges. Therefore the use of median of the data instead of the mode and alsothe modification of the frequency limits of the rms is preferable. Introduction
The improved sensitivity of future third generation gravitational wave (GW) de-tectors requires various technological developments. One of the plans is to optimizethe facility for underground operation, in order to reduce the noise between thefrequencies from 1 Hz to 10 Hz. According to the related sensitivity calculationsthe seismic and Newtonian noises represent the most important noise contribu-tions in this frequency range [1, 2]. During the preparatory studies of the so-calledEinstein Telescope (ET), the European initiative, several short term seismic mea-surements were performed in various locations [3, 4, 6]. Based on these studies twoperformance measures were established: a spectral and a cumulative one. Accord-ing to the spectral recommendation the average horizontal acceleration AmplitudeSpectral Density should be smaller than the A BF limit,(1) A BF = 2 · − m/s √ Hz , in the region Hz ≤ f ≤ Hz.
This is the so-called Black Forest line, named after one of the investigated sites.This spectral criterion corresponds to a cumulative value, the square root of thedisplacement Power Spectral Density integrated from the Nyquist frequency downto Hz , this is the rms Hz and its value for the Black Forest line is . nm .In the ET survey the three best sites that fulfilled these requirements are theLSC Canfranc laboratory in Spain ( rms Hz = 0 . nm ), the Sos Enattos mine inSardinia, Italy ( . nm ) and the Gyöngyösoroszi mine in Hungary ( . nm and . nm in depths m and m respectively). The data collection was performedup to a week at most in the various sites. In spite of the similar cumulative rms Hz values, the spectra of these sites is far from being uniform: the contributions of a r X i v : . [ a s t r o - ph . I M ] O c t SOMLAI L. , AND GRÁCZER Z. , LÉVAI P. , VASÚTH M. , WÉBER Z. , VÁN P. , , civilization noise, oceanic and sea waves appear in different frequency ranges andwith different weights.The Mátra Gravitational and Geophysical Laboratory (MGGL) has been operat-ing since March 2016 with the purpose to evaluate and survey the Mátra mountainrange as a possible ET candidate site. The primary goal of the laboratory is tocollect seismic noise data for long period and evaluate them from the points ofview of ET [7]. The laboratory is located at the coordinates (399 MAMSL, 47 ◦ ◦
51’ 57.77392" OGPSH 2007 (ETRS89)), along a horizontal tunnel ofthe mine, 1280 m from the entrance, 88 m depth from the surface. It is situated nearto the less deep location of the above mentioned former short term measurementsand it is prepared for long term data collection in a telemetric operation mode. Inthe laboratory a Guralp CMG-3T seismometer (hereafter referred as ET1H) wasinstalled and has been operating continuously except shut downs which happens atstrongly interfering mine activities (e.g. explosions). There is an ongoing reclama-tion activity in the mine and therefore the human activity is not negligible in recentyears. The regular operation of the mine railway, the continuously working largewater pumps in the vicinity of the laboratory and the related technical service andconstruction activities are producing industrial noise. These instruments will notbe present in the future, especially during gravitational wave detection.The ET related analysis of long term noise data revealed some particular as-pects, that are not apparent in short term measurements, and could influence theoperational conditions and detection possibilities of GWs in an underground loca-tion. Therefore we need to expose these effects for the optimal operation of thedetector facilities. These are in particular the presence of various short term seis-mic disturbances with large amplitudes and the methodology of long term dataevaluation.The short time, large amplitude disturbances are unpredictable, unavoidable andmust be left out to obtain reliable estimation of the average low noise level. How-ever, any particular truncation or cutting process generates biases on the spectraland also the cumulative noise measures.
To avoid these biases we suggest to usethe percentiles of the complete data.
The percentiles select the highest and lowestvalues, this selection is relative, and based on the intrinsic feature of the data set.Any long term analysis and the evaluation of spectra and rms may require someintermediate averaging over the basic averaging length of the Fourier transforma-tion. For this purpose here we suggest two different averaging steps:(a) calculate short time averages (STA) to get manageable size of the data setsand to use the optimal time-scales of the planned detector.(b) calculate intermediate – for whole day, night or working periods i.e. natu-ral periodicity of the data – percentiles and analyse the averages of themto study daily, annual, etc. variations. In the following we will call thisintermediate or long time averaging as intrinsic averages (INA).In particular the averaged daily percentiles of the complete data set can be used toestimate the spectral and cumulative variation of the data and the averaged dailymedian – the th percentile – values for the comparison with the Black Forest line.If the data collection period is longer than half year, then it is practical to use INA.The paper is organized as follows. First we shortly survey the evaluation pro-cedure including its pitfalls, like the usage of mode for rms calculation. Then weanalyse the effect of averaging on spectral and cumulative measures established by EISMIC NOISE MEASURES FOR UNDERGROUND GRAVITATIONAL WAVE DETECTORS 3
Beker et al [4]. After that the utility of INA is studied and we examine rms valueswith different frequency interval. Finally we conclude our experiences of calculationprocess and measurements and suggest further quantities to compare sites.2.
Data and data analysis
The new seismological data for our recent analysis were collected by a GuralpCMG 3T low noise, broadband seismometer, which is sensitive to ground vibrationswith flat velocity response in the frequency range 0,008-50Hz. The self noise of theseismometer is below the New Low Noise Model of Peterson in the region . Hz to Hz [5]. In this paper we study data collected by one instrument (ET1H).This station was permanently installed in the MGGL. The seismometer is deployedon a concrete pier which is connected to the bedrock. Between the pier and theseismometer a granite plate has been placed. The data collection period for ET1Hhas been started on 2016-03-01. In this paper we focus on methodology restrictingthe studied data period from 2017-01-01 until 2017-12-15 (349 days).In our analysis we followed the data processing method of [4], e.g. the so-calledNuttal-window was applied with / overlap. In this section we recall the basicdefinitions. The Power Spectral Density (PSD) for the velocity is defined as(2) P ( v ) = 2 f s · N · W | V k | , where f s is the sampling rate, N is the length of the analysed data sample, and W = N (cid:80) Nn =1 w [ n ] with the Nuttall window function w [ n ] . The coefficients V k = F ( w [ n ] · ( v [ n ] − (cid:104) v (cid:105) ) , represent the Fourier transform F of the deviationof raw velocity data v [ n ] from its average value (cid:104) v (cid:105) . In our analysis PSDs werecalculated with s data samples. The choice of this sample length for Fouriertransformation is a compromise between the frequency resolution of the spectraand the detectability of short noisy events. The resulted . Hz resolution seemsto be reasonably fine and we can reliably identify less than a second long seismicevents. We did not use the advantage of fast Fourier algorithm on the expense ofincreasing the lowest frequency value . Before further processing, raw data werehighpass-filtered with f HP = 0 . Hz .Our STA is chosen to be s . As we have mentioned above, the basic Fourierlength is influenced by the sampling rate of the instrument. On the other handfor long term data the analysis can be easily adapted to the natural human andindustrial noise periods. In the previous studies STA was s , which is naturalwith the basic s Fourier length, considering the overlap. With our choice ofSTA, the comparison of the two analysis is with minimal bias, simply because × s = 1800 s ≈ × s .The Amplitude Spectral Density (ASD) for the velocity can be calculated fromPSD via A ( v ) = √ P ( v ) . Both amplitude and power spectral densities can be ex-pressed also as either acceleration ( a ) or displacement ( d ) by multiplying or dividingby ω = 2 · π · f or the square of it respectively. For example, A ( d ) = A ( v ) /ω . There-fore the mentioned ET comparison level, (1), can be transferred easily to other Other instruments, the Trillium seismometer of the previous study, work with Hz sam-pling rate. Then the s interval is convenient for fast Fourier calculation, but hourly or dailyspectra require truncations. SOMLAI L. , AND GRÁCZER Z. , LÉVAI P. , VASÚTH M. , WÉBER Z. , VÁN P. , , Figure 1.
Illustration of rms at a displacement PSD spectrum(blue line) together with the Black Forest line (solid black) and theNew Low Noise Model of Peterson (dashed black). The filled arearepresents rms Hz .spectral densities, e.g. for the Black Forest line:(3) P ( a ) BF = ( A ( a ) BF ) = 4 · − m /s Hz or P ( d ) BF = (cid:18) A BF ω (cid:19) = 4 · − ω − m Hz It is convenient to characterize sites in terms of acceleration ASD spectra andits variation and also by displacement rms as a single cumulative property. Thedisplacement rms is the square root of the integral of displacement PSD betweentwo frequency values(4) rms ( d ) = (cid:118)(cid:117)(cid:117)(cid:116) T N/ (cid:88) k = l P ( d ) k , where l is the cutoff index, T = Nf s . The usual choice is Hz for comparing ETcandidate sites [4]. The displacement power spectral density of the daily average of2017-10-22 of ET1H station, East direction is shown on Figure 1. The Black Forestline is the solid straight line, the New Low Noise Model of Peterson (NLNM) [8] isthe dashed one. The rms Hz is the square of the area of the shaded region.For the comparison of various spectra of ET sites it is worth to show the BlackForest line, Eq. (1) and to recall the corresponding rms ( d ) = 0 . nm value at 2Hz: rms ( d )2 Hz = (cid:115)(cid:90) f s / P ( a ) BF π ) f df = A BF (2 π ) (cid:115)(cid:90) f s / f df ≈ A BF (2 π ) (cid:113) [ f − / ( − ∞ ≈ . nm, (5) EISMIC NOISE MEASURES FOR UNDERGROUND GRAVITATIONAL WAVE DETECTORS 5 where we considered that the displacement PSD values decrease significantly athigher frequencies and expanded the domain of BF line to the infinity with thesame value. See Figure 1 as an illustration, where it is obvious that in some caseshigher frequencies can contribute significantly to the rms value. For the particulardata shown in Figure 1 the rms Hz = 0 . nm , the rms − Hz = 0 . nm andtheir ratio is . .In the following only displacement rms will be used so the ( d ) superscript isomitted. Furthermore, two more rms will be considered: the rms − Hz and the rms − Hz . For the Black Forest line they are: rms − Hz = (cid:115)(cid:90) P ( a ) BF π ) f df ≈ . nm, (6) rms − Hz = (cid:115)(cid:90) P ( a ) BF π ) f df ≈ . nm. (7)In Section 5 we will show how both values can specify new information about thesite. 3. Mode vs. median
In Beker et al . [4] the mode of the STA was used to characterize the typical noiselevel. Here we show that for long term data analysis the mode strongly dependson the discretization of the spectrum. In order to illustrate the differences, we usethe same method as Beker [4] to determine modes. Only 7 days of data, between2017-01-01 and 2017-01-07, was chosen for the recent analysis. The modes areshown together with the th , th and th percentiles of the half-hour averageson Figure 2 between Hz and Hz , with dB and . dB bins. It is clear thefluctuation of the mode is discretisation dependent and larger than the fluctuationof the median. It is remarkable that the rms − Hz -s are . nm , . nm and . nm for the median, mode dB and . dB respectively.Our next step is to illustrate the advantage of median when considering differentshort time averaging (STA) lengths. A "well-behaving" characterization is expectedto keep its profile for different STAs, in order to avoid process dependent artifacts.As it was mentioned, the STA is 300s in our case. In Beker’s site selection study[4] approximately half-hour ( s ) STA was chosen. The differences between theexpected values are illustrated in Figure 3. The mode is noisier than the median.The median is slightly increasing above Hz with increasing STA.For the median there is no need for noise level discretization and it is not sensi-tive to noise level distribution. In general it is a more stable quantity. The followingsimple example demonstrates this. Let us consider the half-hour PSD-s calculatedfor one-week interval. Then we have about 350 samples. Then a PSD bin with0.1dB, and an 10dB difference between the 10th, 90th percentiles, we obtain 100bins for calculating the mode. With a sufficiently uniform noise level distribution ata given frequency only 4 PSD values could define the mode. Then it is understand-able, hat with several noise peaks with varying strength the mode can fluctuateviolently. On the other hand the median characterizes the best/worst
50 % of thedata, it is not sensitive of the form of the distribution and does not require powerdiscretisation. Therefore, in the following analysis the use of median is preferred . SOMLAI L. , AND GRÁCZER Z. , LÉVAI P. , VASÚTH M. , WÉBER Z. , VÁN P. , , Figure 2.
In this figure the median (solid blue line) and themodes (dashed and dotted lines) with dB and . dB bins arecompared. The solid black horizontal line represents the BlackForest line and the blue area indicates the 10th-90th percentiles.4. The effect of intrinsic averaging
To study long term – annual and seasonal – seismic noise variation and investigatesite properties for the planned detector the use of intrinsic averages can also benecessary. Considering one year of data implies days × ST A ≈
100 000 datapoint so the th percentile is defined by the
10 000 worst STAs. It could be aproblem that one has not get any information about the density distribution: the th percentile is defined by just few noisy months or by three hours every day.Therefore intrinsic averaging (INA) is suggested to handle this difficulty and it canalso be use to optimize the process whether discretization is omitted or not. Thenatural periodicity of the noise data indicates the use of daily averaging.To illustrate it, we defined night period (00:00 - 2:00 and 20:00 - 24:00 UTC) –in order to reduce the effect of human activity and focus on the noise changes –and calculated the percentiles with and without INA in Figure 4. As it can be seenthe medians have almost the same values for the whole interval, but either th or th percentiles show slightly different properties of the site. In general the use ofintrinsic averaging shows small differences when compared to the evaluation withoutINA. The spectrum is slightly noisier with INA, therefore we cannot underestimatethe noise level using that. On the other hand for large amount of data the analysisand the calculations are more convenient with INA. EISMIC NOISE MEASURES FOR UNDERGROUND GRAVITATIONAL WAVE DETECTORS 7
Figure 3.
Upper figure displays the median with different shorttime averaging lengths. Lower figure shows the mode of the samedata with the same different STA lengths. The Black Forest lineis solid black. The data is from the first week of January in 2017.
SOMLAI L. , AND GRÁCZER Z. , LÉVAI P. , VASÚTH M. , WÉBER Z. , VÁN P. , , Figure 4.
Here the differences of spectra with and without intrin-sic averaging (INA) are shown. Red curves belong to no INA andgreen ones to the averages of night percentiles – averages of 10th,and 90th percentiles are the upper and lower limits of the shadedarea. The median is shown with green and red lines in the middle.5.
The frequency range and cumulative statistics
Beker’s original rms Hz compare sites with the help of a single parameter , usinga particular frequency range from Hz to the upper frequency determined by thespeed of the data acquisition. However, the noise budget of the low frequency partof ET is more frequency dependent.The term "seismic noise" covers two different aspects: the "original" seismicnoise – the movement of Earth shakes the mirrors – and the Newtonian noise, orgravity gradient – the seismic activity causes perturbation in the local gravity field.The first one can be damped by passive filtering (e.g. by a suspension system) butthe second one cannot, thus active filtering is necessary [2, 9]. The seismic noiseis relevant until − Hz and the Newtonian, or gravity gradient noise is relevantabove that frequency up ot Hz according to ET low frequency sensitivity budget[3]. The exact values depend on the suspension system and the efficiency of theapplied filtering methods.Therefore it is reasonable to consider the modification of the frequency rangefor cumulative characterisation of ET sites. There are two aspects that influenceour choice. First, the rare very noisy events at high frequencies, above Hz , are Beker originally defined sigma _ ET also to distinguish the distributions of PSDs. In thispaper we do not want to explore this quantity but focus only to the rms . EISMIC NOISE MEASURES FOR UNDERGROUND GRAVITATIONAL WAVE DETECTORS 9 collected in rms Hz . This can be seen in Figure 5. Noises from this region eventuateirrelevant properties of the site, therefore high frequency cutoff is reasonable.Also the low frequency limit is worth consideration. The recent cutoff at Hz wasdetermined by the properties of the planned mirror suspensions. If one expects thatmirror technology enables and science requires observations down to 1Hz, then thedifference in the spectral properties of various sites must be characterized accord-ingly. Therefore we suggest to introduce suitable quantities and use also rms − Hz and rms − Hz for further site selection information. The referential Black Forestline values are given in Eqs. (7). To illustrate it in Figure 6 the normalized valuesof rms -s and they ratio are plotted. The figure indicates that there is a qualita-tive difference in the noisiness when lower frequencies are considered, otherwise onewould expect an approximately constant ratio.6. Conclusions
In the previous sections we have studied and characterised the specific aspects oflong term low frequency seismological data evaluation in order to find the best sitecharacterisation measures for Einstein Telescope. Our general observation is, thatthere are several sensitive aspects in the spectral and cumulative characteristicsand in their calculation methods. The differences may become significant when thenoise spectra are different and also, these performance measures are not the samefrom the point of view of potential ET requirements.In order to reduce this sensitivity we suggest the following improvements in sitecharacterisation measures(1) Use median instead of mode. Then we can omit the discretization andtherefore its uncertainties and avoid STA sensitivity. Also the mode isunstable if the distribution of the data contains new peaks, a phenomenonobserved several times in our data. The use of median provides a selection.(2) Use optimal STAs and INAs. That is advantageous for handling largeamount of data. Moreover, the chosen interval length can be related directlyto operational conditions and requirements of the low frequency part of theET .(3) Use both rms − Hz and rms − Hz . The upper limit in the frequencyrange removes the information from the rms which is irrelevant for the lowfrequency operation. The − Hz frequency range enhances the lowerfrequency properties of the site.The suggested new rms measures are different because of the mode-median dif-ference and the change of the frequency range. We illustrate the differences in Table1, where the first row shows the reference values from the Black Forest line andthe second row contains the values calculated from the 2017 data (349 days) of theET1H station in the MGGL. Here the first column is calculated from the modeand the other columns from the median of the data. The mode related and medianrelated values calculated from the same data are different. Usually the median islarger, but not necessarily. A detailed evaluation of the MGGL data is shown in[10]. The planned detection length of GW signals could reach 1-10ks. It could be reasonable to usea more suitable – less than the order of expected detection length – than the 14x128s averagingof Beker et al [4]. Furthermore the STA makes the overlapping much easier to handle. , AND GRÁCZER Z. , LÉVAI P. , VASÚTH M. , WÉBER Z. , VÁN P. , , Figure 5.
The upper figure displays the daily rms Hz (blue)toghether with rms − Hz (red). The lower figure shows the ratioof the rms Hz and rms − Hz . The data is calculated from dailyaverages at the North direction of each day in 2017. EISMIC NOISE MEASURES FOR UNDERGROUND GRAVITATIONAL WAVE DETECTORS11
Figure 6.
The upper figure displays the normalized rms − Hz (blue) and rms − Hz values (red) of the daily averages in 2017in the North direction. The lover figure shows the ratio of thesame normalized rms − Hz and rms − Hz . In both cases thenormalization is made by the Black Forest values. , AND GRÁCZER Z. , LÉVAI P. , VASÚTH M. , WÉBER Z. , VÁN P. , , rms Hz (mode) rms Hz rms − Hz rms − Hz Black Forest line [nm] 0.1 0.1 0.1 0.29ET1H 2017 [nm] 0.136 0.153 0.152 0.502
Table 1.
The various suggested rms values for the Black Forestline and calculated from the 2017 data of the ET1H station.It is also remarkable that the expected duration of gravitational wave signalscan be considered already in site selection. For example it may be reasonable tochoose the STA periods according to observational requirements. If one expects,that a continuous observation of a minimal length (e.g. 128s for a black holemerger) is suitable, then the percentiles of low level averaging directly characterizethe observation capabilities of the particular site.We have seen that several seemingly minor aspects of the noise measures (e.g. thewidth of the noise levels in the mode calculations) may introduce different numbersand spectra, emphasizing different properties of the overall noisiness. Long periodsare more sensitive to these aspects than short ones.7.
Acknowledgement
The work was supported by the grants National Research, Development andInnovation Office – NKFIH 116197(116375) NKFIH 124366(124508) and NKFIH123815. The support of the PHAROS (CA16214) and G2net (CA17137) COSTActions is also acknowledged. The authors thank Géza Huba for the constantsupport and help, for Zoltán Zimborás and Jan Harms for important remarks.Also the help and support of the Nitrokémia Zrt and GEO-FABER Zrt. is greatlyacknowledged.
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EISMIC NOISE MEASURES FOR UNDERGROUND GRAVITATIONAL WAVE DETECTORS13 MTA Wigner Research Centre for Physics, Institute of Particle and NuclearPhysics, 1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary;, University ofPécs, Faculty of Sciences, H-7624 Pécs, Ifjúság út 6, Hungary;, MTA ResearchCentre for Astronomy and Earth Sciences, Geodetic and Geophysical Institute, H-9400, Sopron, Csatkai E. u. 6-8, Hungary;, Budapest University of Technology andEconomics, Department of Energy Engineering, 1111 Budapest, Bertalan Lajos u.4-6, Hungary;,5