Final report. Absolute gravimeter Intercomparison

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1 Federal Department of Justce and Polce FDJP Federal Offce of Metrology METAS Baumann Henr Fnal report Absolute gravmeter Intercomparson EURAMET Project no Coordnator of the comparson Henr Baumann - METAS Co-author Olver Francs Unversty of Luxembourg, Mchel Van Camp - Royal Observatory of Belgum 1/7

2 1. Introducton From May 19 th to May 1 st 008, a comparson between the absolute gravmeters of the European Center for Geodynamcs and Sesmology (ECGS, the Royal Observatory of Belgum and the Federal Offce for Metrology METAS was hosted n the Underground Laboratory for Geodynamcs n Walferdange. All three absolute gravmeters have been manufactured by Mcrog-Lacoste and are workng on the same prncple [1] even f ther constructon concepts dffer from each other. The am of the project was to ensure that there s good agreement between these three test facltes. The partcpant persons n EURAMET 1093 have been: Dr. Henr Baumann henr.baumann@metas.ch Prof. Olver Francs Olver.francs@un.lu Dr. Mchel Van Camp mvc@oma.be Federal Offce for Metrology METAS (plot Unversty of Luxembourg/ECGS Royal Observatory of Belgum. Instrument descrpton The nstruments used n the context of ths project are ballstc free fall absolute gravmeters provded by Mcrog-Lacoste. The absolute gravmeter of the Royal Observatory of Belgum, FG5 #0, s n operaton snce 1996 and the two other one, from the ECGS, FG5 #16, and from METAS FG5 #09, snce 001. FG5 #0, ROB FG5 #16, ECGS FG5 #09, METAS Fgure.1: Absolute gravmeters used durng ths comparson As t can be seen n Fgure.1, even f all three gravmeters have the same workng prncple ther desgn n the constructon s slghtly dfferent. The man dfference les n the ntegraton of the laser. If for more recent gravmeters, #16, #09, the lasers are mechancally separated from nterferometer t s not the case for the gravmeter #0 where the laser s ntegrated n the nterferometer. /7

3 3. Test procedure The test procedure appled durng ths comparson s quet smple. From May 19 th 008 to May 1 st 008, each gravmeter was placed alternatvely on the reference statons B3 and B4 of the Underground Laboratory for Geodynamcs n Walferdange. For each staton the absolute value of gravty was measured by each gravmeter for 4 hours. 4. Measurement results The results obtaned durng the comparson at the staton B3 and B4 by the three gravmeters are summarzed n Table 4.1. The values are gven n µgal (µgal = 10-8 ms -. ROB (#0 METAS (#09 UL (#16 Statons g-g offset u g-g offset u g-g offset u (µgal (µgal (µgal (µgal (µgal (µgal B B Table 4.1: Gravty value measured by the three gravmeters at statons B3 and B4 (g offset = µgal The uncertanty gven n the Table 4.1 corresponds to the square root of the quadratc sum of the typcal uncertanty of an FG5, and the ste dependant uncertanty [3]. The gravty values measured by each gravmeter at each staton are graphcally represented n the Fgure 4.1. Fgure 4.1: Gravty value measured by the three gravmeters at the tow statons B3 and B4. The contnues lne represents the reference value, and the dot lnes ts uncertanty. 3/7

4 5. Evaluaton of the measurement results 5.1 Compatblty ndex En The compatblty ndex E n beng defned by, E n x x j = (8 U ( x + U ( x j defnes the rato between the dfference of two estmated values and the expanded uncertanty (k= of the dfference. An E n factor larger than one means, that the dfference between the values can not be covered by the uncertanty. Wth a perfectly repeatable transfer standard, ths mples that ether at least one of the two values s corrupted, or the clamed uncertantes are too small. For the measured values at the two staton B3 and B4, the E n factors are lsted n Table 5.1. B3 B4 #0 #09 #16 #0 #09 #16 # # # # # # Table 5.1: E n factors at the gravty statons B3 and B4 evaluated wth the extended uncertanty. The values of the E n factors, gven n table 5.1 shows that all measures are n equvalence. 5. Evaluaton of the reference values As descrbed by M. G. Cox [], the reference values at each gravty staton are determned by the weghted mean y. x u ( x 1 + L+ xn u ( xn ( x + L u ( x 1 y = 1 u 1 +1 N (9 u 1 ( y u ( x u ( x 1 1 = (10 1 N where: y : weghted mean value for the gravty value at the staton u(y : uncertanty of the weghted mean value for the gravty value at the staton x j : estmated gravty value by the gravmeter j at the staton u j : uncertanty of the gravmeter j at the staton 4/7

5 The evaluated reference values for each staton are gven n Table 5.. Weghted mean Statons g ref -g offset u ugal ugal B B Table 5.: Reference gravty value at the statons B3 and B4 (g offset = µgal To be able to dentfy systematc errors, t s useful to carry out a statstcal test lke a descrbed by M. G. Cox []. χ as ( x 1 y u ( x ( xn y u ( x = + L+ obs 1 N χ (11 where: χ obs : ch-squared value for the staton : weghted mean value for the staton y x j u j : estmated gravty value by the gravmeter j at the staton : uncertanty of the gravmeter j at the staton To evaluate whether the data are consstent the ch-square test has been performed to demonstrate consstency of the data. Pr χ ν χ < 0. The consstency check passes when : ( { } 05 > obs Wth ν = N - 1 and N s the number of partcpatng labs for the ch-square test. The ch-squared test s summarzed n Table 5.3 #0 #09 #16 Statons Ch Ch Ch Ch Ch 95 from table B B Table 5.3: Analyss overvew of the ch-squared test The ch-squared test (Table 5.3 s satsfed for both statons B3 and B Degree of equvalence For all three gravmeters, the degree of equvalence of the measured gravty values has been evaluated. Equvalence between nsttute and the reference value The degree of equvalence between the nsttute and the reference value s gven by: d = x x (1 ref U d = u( d u ( d = u ( x u ( x (13 ( ref 5/7

6 The obtaned values are gven n table 5.4: ORB METAS UL d 0 U(d 0 d 09 U(d 09 d 16 U(d 16 µgal µgal µgal µgal µgal µgal Table 5.4: Degree of equvalence between the dfferent ntuts and the reference value Equvalence between nsttute and nsttute j The degree of equvalence between the nsttute and the reference value s gven by: d j = x x (14 j U d = u( d u ( d = u ( x + u ( x (15 ( j j j j The obtaned values are gven n table 5.5 for the staton B3 and n table 5.6 for the staton B4: B3 #0 #09 #16 d 0 U(d 0 d 09 U(d 09 d 16 U(d 16 #0 d 0j #09 d 09j #16 d 16j Table 5.5: Degree of equvalence between the gravmeter at staton B3 B4 #0 #09 #16 d 0 U(d 0 d 09 U(d 09 d 16 U(d 16 #0 d 0j #09 d 09j #16 d 16j Table 5.6: Degree of equvalence between the gravmeter at staton B4 6/7

7 6. Lnk to Walferdange 007 (Euramet 1030 To lnk the comparson to the Euramet project 1030 the mean value of the dfference to the respectve reference values has been estmated for all three gravmeters. The obtaned mean dfferences have then been compared wth the results estmated durng the comparson 1030 for whch, due to geophyscal changes of the local gravty feld, another reference value was estmated. These results are graphcally represented n Fgure 6.1. Lnk Walferdange Dfference to the reference value FG5#101 FG5# FG5#0 FG5#06 FG5#11 FG5#15 FG5#16 FG5#18 FG5#0 FG5#1 FG5#6 FG5#8 FG5#9 FG5#30 FG5#3 FG5#33 Gravmeters (# FG5#34 IMGC# Jlag-6 FG5#0 FG5#16 FG5#09 Fgure 6.1: Dfference to the reference value. : dfference to the reference value 07, : dfference to the reference value 008. It demonstrates that the dfference to the reference values estmated n 007 and 008 are coherent. Based on ths, we can consder that the lnk between these two comparsons s acceptable. (The results of the comparson 1030 have been publshed and presented n 008 [5]. The draft B from the comparson 1030 wll be publshed 7. Concluson The analyss done n secton 5 ndcates that the gravty values measured by the three gravmeters, #0, #09 and #16 are n agreement. In Fgure 6.1, we reported the present results wth the ones obtaned durng the European Comparson of 19 absolute gravmeters held n Walferdange n November Lterature [1] Nebauer T M, Sasagawa G S, Faller J E, Hlt R and Kloppng F 1995 Metrologa [] Cox, M.G., The evaluaton of key comparson data, Metrologa, 00, 39, [3] Results of the Seventh Internatonal Comparson of Absolute Gravmeters ICAG-005 at the Bureau Internatonal des Pods et Mesures, Sèvres, GGEO-008. [4] Pearson, E. A., Hartley, H. O., Bometrka Tables for Statstcans, Vol , table 8, [5] Francs O et al 008, Results of the European Comparson of Absolute Gravmeters n Walferdange (Luxembourg of November 007. IAG Internatonal Symposum Gravty, Geod and Earth Observaton 008, Chana, Greece, 3-7 June /7