Supconducting gavimt calibation by co-locatd gavity obsvations sults fom GWR C25 B. us Dpatmnt of toology and Gophysics, Univsity of Vinna, Althanstass 19, A- 19 Win, Austia. Cospondnc should b addssd to buno.mus@univi.ac.at Abstact Aft a 12 yas obsvation in Vinna (VI), th supconducting gavimt GWR C25 has bn tansfd in autumn 27 to th nw Conad obsvatoy (CO) 6 km SW of Vinna. It is on of fw instumnts which w opatd at diffnt stations. This aspct motivatd a -analysis of all calibation xpimnts pfomd so fa in VI and CO, focusd on th dict impact of dift ffcts and nois. Nois limitd th calibation accuacy achivabl in VI considably. It tuns out that considing th dift vn of absolut gavimts in a common adjustmnt ducs th oot man squa o of th avagd calibation facto ssntially. Futh it is shown that also sping typ gavimts hav som potntial to contibut to th SG calibation facto dtmination. Th -analysis of th calibation xpimnts povs that th calibation facto of GWR C25 did not significantly chang duing th tansf fom VI to CO. Th final calibation facto is calculatd as wightd avag ov in total 9 JILAg and FG5 xpimnts with an accuacy of btt than ±.5. Th calibation facto is tmpoaily stabl with maximum vaiation lss than ±.1. Basd on ths sults th gavity tim sis in VI and CO hav bn analyzd. Th spctiv amplitud factos fo O 1, K 1 and 2 ag almost pfctly at both stations aft cocting fo ocan loading ffcts. Th maximum dviation fom th numbs povidd by th non-hydostatic body tid modls DDW and AT1 is.8 at maximum. Intoduction Cuntly, th supconducting gavimt (SG) is th most pcis instumnt fo invstigating tmpoal gavity vaiations both in th tim and th fquncy domain. SGs xhibit an xtmly small instumntal dift that can b modld by ith a lina o xponntial function of tim [27]. Th supconducting gavimt GWR C25 has bn opating sinc 1995. Fo mo than 12 yas it was installd in an undgound laboatoy in Vinna (Austia) and movd to th nw Conad obsvatoy (CO) 6 km SW of Vinna (VI) in autumn 27 (Fig. 1). Both stations a locatd at th NE magin of th Eastn Alps. VI is situatd at th tansition fom th Eastn Alps to th Vinna Basin at about 19 m altitud, whil CO is locatd within th mountains at 145 m. Th SG sph could b kpt lvitatd duing tanspot. Consquntly only mino -adjustmnt masus w quid, among oths bcaus of th gavity diffnc btwn both sits. Th gavity tim sis in CO cuntly xtnds ov mo than 4 yas and allows now safly compaing th tidal analysis sults fo VI and CO as wll as validating th most cnt body tid modls ([2], [14]). Th accuacy of gavimt calibation is still a limiting facto fo modn godynamical studis basd on gavity tim sis. In paticula, validating diffnt body tid modls quis an accuacy of btt than 1. Fom this viwpoint it is impotant to know th tmpoal stability of th calibation facto and th accuacy achivd und th givn sit nois conditions. Th high sit nois lvl in VI was on of th majo poblms with th SG spons function dtmination. Thfo, big ffots hav bn don in od to claify this qustion. Psntly, th most common mthod of SG calibation is basd on co-locatd gavity obsvation by using absolut gavimts (AG) [8]. In th tim domain, th 1 accuacy lvl can b achivd by monitoing sid by sid duing at last 5 to 7 days
([7], [9]). Th calibation sult dos not dpnd on th spcific AG usd [6]. Actually, th calibation accuacy of SGs opating in th famwok of GGP vais btwn a fw [15]. Taking a high numb of calibation xpimnts into account, th o lvl can b ducd wll blow 1 (.g. [1], [22]). Rcntly, [21] studid th pfomanc of sping gavimts usd in th calibation xpimnt instad of an AG. Expimnts fo calibating a LCR gavimt by co-locatd SG obsvations hav bn potd by [5]. Figu 1: Location of SG sits in Vinna (VI: 48.2489 N, 16.3565 E, 192.74 m a.s.l.) and Conad obsvatoy (CO: 47.9283 N, 15.8598 E, 144.12 m a.s.l.) (maps modifid aft http://commons.wikimdia.og/wiki/catgoy:aps) Th calibation mthod lis on th basic assumption, that obsvation os follow a Gaussian distibution, and that both th SG and AG snso xpinc xactly th sam gavity vaiation. Actually, this assumption is nv pfctly tu, as th signal composition of both snsos diffs du to following asons (.g. [16]): instumntal nois gound nois spons spatial spaation of both snsos tansf function intoducing diffnt tim lags p-pocssing filt spons spons on ai pssu vaiations (.g. non-compnsatd Achimdan focs in sping gavimts) instumntal dift Kon [13] pots on noticabl diffncs btwn Nwtonian mass tanspot signals obsvd by th snsos of a dual sph SG at oxa. Similaly to oxa, VI and CO can b gadd as undgound stations with spct to local hydology. Of cous, th spatial spaation of th snsos involvd in th xpimnts in VI and CO is much lag than that of dual sph SG snsos (Tab. 1). Fo stimating th ffcts xpctd at CO and VI, th gavitational ffct of a wat mass lay (.g. du to ain) spad ov th tain sufac has bn stimatd basd on tain modls with high spatial solution [19]. Tab. 1 psnts th diffncs Δg btwn th gavity signals at th spctiv snso positions causd by 1 cm ain fall. At CO, snsos involvd in th calibation xpimnts would xpinc a signal clos to 4 nms -2, but a maximum diffnc of.5 nms -2 only in this scnaio. A systmatic o aiss whn on o both snsos a influncd by instumntal dift [8]. Synthtic studis show that th calibation facto is systmatically affctd in thos cass and stongly dpnds on th numb of data pais usd in th gssion analysis [16]. Typically, AG dift ats a small and thfo a oftn nglctd. Howv, at last th lina pat of th instumntal AG dift has bn takn into account in sval SG calibation xpimnts (.g. [8], [12] and [25]). This pap addsss again th ol of instumntal dift in calibation xpimnts basd both on AGs and sping gavimts and how th calibation sults impov if dift is considd vn fo AGs.
A pfomanc study by [21] coms to th conclusion, that sping gavimts cannot b usd as stabl fnc fo SG calibation. Thy compad diffnt sping gavimts lik Scintx Ltd. Autogav CG3 and CG5 and icog-lacost gphon. Basd on sval xpimnts pfomd with a convntional Scintx Autogav CG5 gavimt, this poblm is -visitd in this pap. Th qustion whth sping gavimts can liably suppot th calibation of SGs is discussd paticulaly und th aspct of dift dtmination. Finally, all sults achivd so fa fo th SG GWR C25 a discussd. VI CO snso spaation [m] Δg hoizontal vtical [nms -2 ] FG5 2.1.98.186 JILAg 2.1.68.139 CG5 1.2.5.98 FG5 3.4.98.51 JILAg 3.4.68.5 CG5 1.4.5.14 Tab. 1: Spatial spaation of th SG and co-locatd gavimt snsos. Δg is th diffnc btwn th Nwtonian ffcts at th two snso positions causd by 1 cm ain fall. Calibation Fo calibation both diffnt AGs and a wll calibatd Scintx Autogav CG5 hav bn usd. Th calibation facto is calculatd by lina adjustmnt of th gavity data acquid by th SG and th gavimt usd as fnc (ith th AG o th sping gavimt). Acquisition and pocssing pocdus a dscibd in th following chapt. Data acquisition and pocssing Th aw 1s SG data is filtd by convolution with th GGP filt g1s1m (http://www.as.slu.du/ggp/ggpfilts.html) and -sampld to 1 s data. Th filt gain is qual to 1 within tidal fquncis including th quat-diunal band, about.9986 at piods of 1 min and apidly dcass towads shot piods (1.8 x 1-7 at Nyquist fquncy). Howv, gavity signals at ths fquncis xhibit small amplituds compad to th tids. Fo xampl, th amplitud of gavitational ffcts du to shot tm (1 min) atmosphic pocsss is in th od of 1 nms -2. SG/AG compaison: Th mthods a applid in this study. In th fist appoach, ach singl AG dop is usd. Th cosponding SG data is xtactd fom th filtd 1s SG tim sis. Th SG tim lag is takn into account. Outlis a movd by applying ith th 3-cition o th modifid Z-sco mthod [11] on th AG siduals, spaatly fo ach AG dop st. Th final data st consists of th SG-AG data pais, thi acquisition tim and th standad dviation which is assumd to b idntical with th standad dviation of th AG dop st a spcific data pai oiginats fom. Bcaus th nois of th filtd SG data is much small than th AG dop-to-dop scatt, th SG data is assumd to b o-f in th adjustmnt pocss. An altnat pocdu, poposd.g. by [22], uss th AG dop st avag instad of singl dops. Bcaus ach AG dop st sult psnts th gavity avagd ov th st intval (typically up to 6 min), in this study th man of th filtd SG data ov th sam intval is calculatd instad of xtacting just th SG data at th cntal tim of th AG st. Th numb of data pais now quals to th numb of AG dop sts and thus is vy small compad to th fist mthod. This mthod is slightly changd in a thid pocdu. Both SG and AG data is avagd by applying a moving window. Th window lngth cosponds to th duation of on AG dop st. Thn th standad dviation of th AG siduals within ach window is dtmind. Lik in th scond mthod, th scatt of th avagd gavity is dastically
ducd compad with th dop-to-dop scatt, but th numb of data pais nting th adjustmnt mains compaabl with that of th fist mthod. SG/sping mt compaison: In this study, a commcial Scintx CG5 Autogav has bn usd (SN 4236). This instumnt has bn cafully calibatd twic a ya on th Hochka calibation lin (HCL). Th latt is locatd within th Nothn Calcaous Alps of Austia and covs a gavity diffnc of 198 µms -2 [17]. Shot distancs povid apid accss to in total fou stations stablishd along an Alpin oad. Consquntly, th gavimt dift can b accuatly dtmind as on cycl including all stations is compltd within lss than 2 hous. Th gavity at all stations has bn divd fom absolut gavimt obsvations. Absolut gavity masumnts patd in 1995 as wll as gula lativ gavity masumnts in th past dcads povd th HCL calibation lin to b vy stabl and wll suitd fo scal facto dtmination of lativ gavimts with high accuacy [18]. Du to th lag gavity ang, nvionmntal gavity ffcts do not affct th calibation sult svly. HCL is a vtical calibation lin coving an lvation intval of about 95 m. Thus systmatic os causd by buoyancy ffcts may occu in cas of sal failu. Howv, this is not xpctd fo th CG5, bcaus th snso unit is potctd fom ambint tmpatu and atmosphic pssu changs by saling th snso in a tmpatu stabilizd vacuum chamb [23]. Rpatd obsvations on HCL show that th CG5 scal facto vais linaly with tim and dcasd by.5 within 3.5 yas (Fig. 2). Thfo, dtmining th tmpoal CG5 scal facto vaiations on a gula bas is mandatoy. Fotunatly this can b don on a high accuacy lvl clos to.5. Figu 2: Scal facto dtmination of th Scintx Autogav CG5, SN 4236. Th gy and black dots f to sults taking only on spcific gavity diffnc into account; th d tiangls dnot th sults achivd by wightd avaging ov all possibl gavity diffncs along th Hochka calibation lin. Th Scintx Autogav CG5 sampls both gavity and tilt data with 6 Hz duing a slctabl tim intval. Th final gavity ading cosponds to th avag ov this intval (typically 1 o 2 min), automatically coctd fo tilt ffcts. Th filtd 1s SG data is xtactd and avagd ov th sam piod. Optionally th CG5 adings can also b coctd fo th tids. Howv, th CG5 acquisition softwa stos all sults with a limitd solution of 1 nms -2. Round off os a poducd lat on, whn th tids a stod, and affct th calibation sult systmatically. Thfo, this option is not commndabl fo SG calibation. In this study, gavity masumnts w pfomd in th auto-pat mod with 2 min duation duing a fw months. Adjustmnt pocdu: Calibation facto and dift function a dtmind in a common adjustmnt pocss as poposd by.g. [8] and [5]. Fo that pupos, th following schm is implmntd. Lt g b th tu gavity signal, g AG th AG obsvation, g SG th un-calibatd SG signal, d AG and d SG th instumntal dift of th AG and SG spctivly, and a th calibation facto, thn
a gsg () t g() t dsg () t g () t g() t d () t a g () t d () t d () t AG AG SG AG SG (1) Th diffntial dift signal on th.h.s. of q. (1) is modld as polynomial function of dg n. Thn, q. 2 dscibs a modl which is lina with spct to n +2 unknown paamts a j, j=,,n +1: n1 j 1 AG() SG() j j1 g t a g t a t (2) This gnal lina last squas poblm can b solvd by dfining th mit function (.g. [2]) 2 N i 1 2 n1 j 1 AG, i SG, i j j 1 g a g a t i wh i stands fo th i-th of in total N AG-SG data pais, and i dnots th standad dviation of g AG,i. Accuacy limit Th AG dop-to-dop scatt of f fall obsvations dpnds on th typical sit nois and consquntly limits th calibation accuacy. Dpnding on th mico-sismic activity, th standad dviation of th AG sidual typically vais btwn 5 and 3 nms -2. Th lag gound nois in Vinna (VI) hamps achiving a calibation accuacy btt than 2 fo a singl xpimnt. Howv, gtting a liabl calibation facto fo th VI tim sis is cucial fo compaing tidal analysis sults. Evn in cas of andom nois, th calibation facto dos not ncssaily convg o dos not convg to th coct numb vn whn a high amount of data pais is availabl. This is shown by th following study. W us synthtic body tids as fnc and compa with an idntical tim sis to which Gaussian nois has bn addd. Th nois standad dviation was dfind by multiplying th AG dop st standad dviations takn fom a al calibation xpimnt by th factos.1, 1, 3 and 5, sulting to a nois sigma btwn 1 and 6 nms -2. 25 data sts with diffnt andom nois modls hav bn compild fo ach multiplication facto. Similaly as in th calibation xpimnts, th 3 sigma cition has bn applid to mov outlis bfo th lina adjustmnt. Fig. 3 (lft panl) dmonstats that th coct facto (dviation <.2 ) is obtaind only whn th nois lvl is vy low (.g. about 1 nms -2 ). With high nois standad dviation, th gssion facto gnally convgs aft 1 to 2 data pais, i.. 5 to 7 days of obsvation a quid. This xactly confims th sult potd by [7] and [6]. Howv, th convgnc lvl can dviat fom th xpctd on by up to 1 %. (3) Figu 3: Lft: Rgssion facto fo synthtic data sts which combin synthtic tids without and with andom nois of diffnt standad dviation. Fo ach nois standad dviation, 25 data sts hav bn compild. Without nois, th gssion facto would b qual to 1 as xpctd. This is
not shown on th viw gaph fo simplicity. Right: aximum dviation of th sulting gssion cofficints fom th valu xpctd fo nois-f data in dpndnc on th nois standad dviation and on th numb of data pais nting th adjustmnt. This bhavio is du to th fact, that th vn ath lag numb of data pais still violats th law of lag numbs pincipl of statistics. Consquntly, it obviously happns in som cass, that th nois is wakly colatd with th tidal signal. Th o ang (maximum of th absolut dviation fom xpctation) incass almost linaly with th nois standad dviation (Fig. 3, ight panl). It has to b pointd out, that th nois standad dviation of all modls applid h dos not vay with tim lik at sits wh industial o taffic nois causs typical day-night cycls in th nois amplitud. Of cous, non-andom nois dtioats th calibation sult futh. Calibation Rsults SG/AG compaison: Absolut gavimts a obviously not f fom systmatic os du to instumntal asons. Th dop st sults gnally should b andomly distibutd, but oftn a sytmatic tnd is visibl in th siduals obtaind by subtacting th tids and atmosphic ffcts whil almost no tnd is dtctabl in th SG cod. Fig. 4 psnts typical xampls of calibation xpimnts pfomd with SG GWR C25 and JILAg o FG5 typ absolut gavimts in Dcmb 28 and Jun 211 spctivly at Conad obsvatoy. Duing th Dcmb 28 xpimnt, about 2 singl dops hav bn obsvd within a 5 days intval, whil fo th Jun 211 xpimnt about 238 singl dops gathd in 219 sts duing 8 days could b valuatd. In both cass, th SG sidual shows vy small vaiation, whil a distinct, pdominantly lina dift is supposd to th AG sidual. Th obsvd AG tnd is most likly of instumntal oigin. At CO, th stimats psntd in Tab. 1 indicat that both snsos xpinc almost th sam hydological signal. Additionally, th was no pcipitation vnt duing both calibation xpimnts. Figu 4: Gavity sidual (unning avag) of SG (d) and AG (blu) duing th calibation xpimnt at Conad obsvatoy in Dcmb 28 (GWR C25/JILAg-6, lft panl) and in Jun 211 (GWR C25/FG5 242, ight panl). Th diffnc (gn) is usd to modl th dift (dashd lin). Dift ffcts lik thos psntd in Fig. 4 hav to b considd in th lina adjustmnt pocdu. Othwis th calibation facto might b systmatically affctd. Fig. 5 shows th lina adjustmnt sult of th xpimnts shown in Fig. 4 fo diffnt dift modls and in dpndnc on th numb of data pais usd. If th AG dift signal is nglctd, th calibation facto dos not convg but oscillats aound a ctain lvl (black lins in Fig. 5, lft, upp and low panl). Additionally, th calibation facto stongly dpnds on th numb of data pais usd. This ffct is makably ducd whn a lina dift is adjustd togth with th calibation facto (d lins in Fig. 5). It is also impotant to not, that th lvl to which th calibation factos convg can diff by mo than 1 fom th sult obtaind by zo dift assumption. Th application of th lina dift modl actually impovs th oot man squa o of th adjustmnt slightly (Fig. 5, ight, upp and low panl) whil high dg polynomials do not povid
futh o duction. Th calibation facto vais with th polynomial dg and only somtims xcds th 1 o ang (gy box in Fig. 5). Bsids, it is woth mntioning that th calibation sults do not dpnd on th pocssing mthod (singl dop vs. st man) with xcpt of th standad dviation stimat. Figu 5: SG/AG compaison xpimnt at Conad obsvatoy in Dcmb 28 (upp panls) and Jun 211 (low panls). Lft: Calibation facto plottd against th numb of data pais usd in th lina adjustmnt. No (black) o lina (d) dift has bn adjustd. Right: Calibation facto (black) and RS of th sidual (gy) plottd against th polynomial dg slctd fo AG dift adjustmnt. Th 1 o ang is displayd as gy box. SG/sping mt compaison: Th situation is compltly diffnt fo sping gavimts bcaus of thi much stong and igula dift, which cannot b appoximatd simply by lina functions. In th following th calibation xpimnt pfomd at Conad obsvatoy btwn July 13, 21 and Sptmb 22, 21 is discussd, whn th SG GWR C25 monitod sit by sit with a Scintx Autogav CG5. Fig. 6 displays th calibation sults that again dpnd on th adjustd dift modl and on th numb of data pais takn into account. If high dg dift polynomials a adjustd, th calibation factos convg fast, and diff by lss than.1 (Fig. 6, lft). Howv, a piod as long as mo than 1 month is quid to achiv convgnc. Th oot man squa o of th siduals obtaind fom q. (2) aft th adjustmnt dcass makably with incasing polynomial dg and mains constant byond a ctain polynomial dg (Fig. 6, ight). Th sam holds fo th calibation facto which gts stabl byond th sam polynomial dg. This finding as wll as inspcting th gavity siduals has bn usd as cition fo slcting th appopiat dift modl. Sinc th SG GWRC25 has bn opating in VI and CO, numous calibation xpimnts hav bn pfomd, involving JILAg and FG5 absolut gavimts as wll as th Scintx Autogav CG5 SN 4236. All sults a psntd in Fig. 7. With xcpt of th JILAg-6 in VI and th fist two CG5 xpimnts at CO, all calibation factos plot within th ang of ±1, povidd th AG dift is poply adjustd. Th scatt incass considably if zo dift is adoptd (dak gy dots in Fig. 7) whil th man calibation facto dos not significantly chang as long as a sufficintly lag st of xpimnts is availabl.
Figu 6: SG/CG5 compaison xpimnt at Conad obsvatoy (July 13, 21 to Sptmb 22, 21). Lft: Calibation facto plottd against th numb of data pais usd in th adjustmnt and fo diffnt dift polynomials. As bst choic, a dift polynomial of dg 8 has bn slctd (dashd d lin). Right: Calibation facto (black) and RS of th sidual (gy) plottd against th polynomial dg slctd fo AG dift adjustmnt. Th 1 o ang is displayd as gy box. Figu 7: Calibation factos dtmind by adjusting co-locatd gavity obsvations with SG GWR C25 and FG5 (d dots), JILAg-6 (gn dots) and Scintx Autogav CG5 SN 4236 (blu dots). Th diffntial dift of th fnc gavimt has bn adjustd by polynomial functions. Dak gy dots indicat th sults obtaind fo th zo dift assumption. Th 1 o ang is displayd as gy box. Th dottd lins indicat th calibation factos sulting fom th CG5 (779.1628 nms 2 /V, blu) and AG (779.1628 nms 2 /V, d) xpimnts. Lft: All calibation xpimnts pfomd in Vinna (VI) and Conad obsvatoy (CO). Right: Zoom of th xpimnts pfomd at Conad obsvatoy (CO). Du to th high nois lvl at th VI station th calibation xpimnts using th JILAg typ absolut gavimt a much lss accuat than thos using FG5s in 25 and 26. Und low nois lvl conditions lik at CO, both AG typs povid a compaabl accuacy. Tab. 2 and 3 compa th calibation sults of th xpimnts pfomd in Vinna and at Conad obsvatoy with spct to th applid pocssing mthods. Both tabls psnt th wightd avag of th calibation facto a obtaind by applying diffnt pocssing mthods, its o and th ms dviation of th singl sults fom th avag by using q. (4): wa i, i a, i a i 1 1 i 1 a wi 1/ w 2 i i 1 1 w i i 1 i 2 (4) wh is th standad dviation of th i-th of calibation xpimnts. i Th diffnc btwn th man calibation factos obtaind with and without common AG dift adjustmnt amounts to about.6 at CO. Also th ms dviation, which chaactizs th scatt of singl calibation sults with spct to th avag a, is ducd by a facto of 3 whn th AG dift is poply adjustd togth with th
calibation facto. Th o flcts th accuacy, which is psntly achivabl with FG5 absolut gavimts, as stongly dpnds on th dop-to-dop scatt. Th diffnc btwn th man calibation facto obtaind whn AG dift is o is not takn into account is in th sam od of magnitud, i.. th impovmnt by a common dift adjustmnt is just at th o limit. Nvthlss, basd on th sults psntd h, considing th AG dift is commndd. This is potntially mo impotant in futu povidd futh instumntal impovmnts duc th AG dop-to-dop scatt, o vn psntly at stations with vy low nois lvl. Th man calibation factos divd fom diffnt pocssing mthods, which dtmin both calibation facto and AG dift in a common adjustmnt, diff by.5 (CO). Vinna Vinna Conad obsvatoy Conad obs. mthod Singl dop Outli dtction 3 cition modifid Z-sco mthod a [nms 2 /V] [nms 2 a /V] [nms 2 /V] [nms 2 /V] [nms 2 /V] [ ] [ ] [nms 2 /V] [ ] [ ] FG5 + JILAg with AG dift adjustmnt -779.5978.5272 2.38.5278 2.4234-779.6254.68 2.95.68 3.11 FG5 + JILAg no AG dift adjustmnt -779.6828.5272.68 2.8414 3.64-779.7127.5278.68 thod St man Running avag 2.8677 3.68 Outli dtction modifid Z-sco mthod modifid Z-sco mthod a a [nms 2 /V] [nms 2 /V] [nms 2 /V] [nms 2 /V] [nms 2 /V] [nms [ ] [ ] 2 /V] [ ] [ ] FG5 + JILAg with AG dift adjustmnt -779.7295 7.139 9. thod 2.382 3.5 Singl dop -779.5454.5297.68 2.7151 3.48 Outli dtction 3 cition modifid Z-sco mthod a [nms 2 /V] [nms 2 a /V] [nms 2 /V] [nms 2 /V] [nms 2 /V] [ ] [ ] [nms 2 /V] [ ] [ ] CG5-779.1628.2295.5392.29.69 FG5 + JILAg with AG dift adjustmnt -779.4676.1774.5268.1746.3721-779.4566.23.68.22.48 FG5 + JILAg no AG dift adjustmnt -779.6434.1774.23 1.58 1.29-779.623.1746.22 thod St man Running avag.989 1.27 Outli dtction modifid Z-sco mthod modifid Z-sco mthod a a [nms 2 /V] [nms 2 /V] [nms 2 /V] [nms 2 /V] [nms 2 /V] [nms [ ] [ ] 2 /V] [ ] [ ] FG5 + JILAg with AG dift adjustmnt -779.4982 1.987 2.45.3584.46-779.462.1756.23.3875.5 1 6 6 1 6 1 7 7 1 7 Tab. 2: Wightd avag a of th calibation facto obtaind by th calibation xpimnts in Vinna btwn 1996 and 27 and at Conad obsvatoy btwn 28 and 212. Eq. (4) was applid fo calculations. Th diffnc btwn th sults (modifid Z-sco mthod) obtaind in Vinna and at Conad obsvatoy is.22. This numb is about 3 tims small than th fomal o of th wightd avag in Vinna, i.. th is no statistically significant chang of th calibation facto associatd with th tansf of th SG fom Vinna to Conad obsvatoy. This finding is vn mo convincingly confimd by considing xclusivly th xpimnts with FG5s involvd. In this cas, th wightd avags diff only by.16. Bcaus of th lag scatt of th xpimnts with JILAg typ absolut gavimts in Vinna, th final calibation facto fo SG GWR C25 is calculatd taking into account only th FG5 xpimnts in Vinna and all FG5 and JILAg xpimnts at Conad obsvatoy spctivly. Th final sult is compild in Tab. 3.
VI + CO thod Singl dop Outli dtction 3 cition modifid Z-sco mthod a [nms 2 /V] [nms 2 a /V] [nms 2 /V] [nms 2 /V] [nms 2 /V] [ ] [ ] [nms 2 /V] [ ] [ ] FG5 + JILAg sinc 25 with AG dift adjustmnt -779.4537.1692.5432.1667.4476-779.4458.22.7.21.57 FG5 + JILAg sinc 25 no AG dift adjustmnt -779.6221.1692.22.9255 1.19-779.655.1667.21.9161 1.18 1 9 9 Tab. 3: Wightd avag a of th calibation facto obtaind by th calibation xpimnts in Vinna and at Conad obsvatoy btwn 25 and 212. Eq. (4) was applid fo calculations. Th sults obtaind by co-locatd obsvation with th Scintx Autogav CG5 SN 4236 fit vy wll to thos obtaind by AGs (diffnc:.38 ). In paticula, thy do not indicat a significant chang of th calibation facto, which might b causd by th tansf fom VI to CO. Th sult shows also, that vn sping gavimts can suppot valuabl infomation on th SG calibation facto povidd thy a cafully calibatd and thi igula dift is poply modld in th adjustmnt pocss. Th SG phas calibation has bn pfomd by applying th stp spons mthod [28]. Th tim lag has changd sval tims du to had- and softwa upgads. Th sults a psntd in Tab. 4. Th fomal os indicat that th o of th tidal phass causd by onous tim lag dtmination is xpctd to b lss than.6 fo smi-diunal and.3 fo diunal wavs. sit VI CO dat 1995 8 1997 9 1999 12 24 4 27 11 tim lag [s] 16.995 9.345 1.4 9.131 8.72 o [s].5.27.47.66.26 Tab. 4: Tim lag of th SG GWR C25 at stations VI and CO. Tidal analysis Bfo tidal analysis, spiks and shot-tm distubancs psnt in th 1 Hz aw SG data (.g. du to athquaks o maintnanc) w cafully movd by applying th softwa packags ETERNA v3.4 [29] and TSOFT [26]. Offsts du to tchnical asons o maintnanc hav bn coctd individually. ETERNA v3.4 [29] has also bn applid fo tidal analyss taking Tamua's [24] tidal potntial into account. Ocan loading coctions hav bn pfomd basd on load vctos povidd by [1] fo 7 diffnt ocan modls. Tab. 5 shows th coctd tidal paamts fo O 1 and 2. Th coctd amplitud factos at both sits diff by.4 (O 1 ) and.8 ( 2 ) only and do also confim that th calibation facto did not significantly chang duing th tanspot of th SG fom VI to CO. As both stations li clos togth, th amplitud facto coctions fo ocan loading a almost idntical. Actually, th agmnt btwn th amplitud factos gts slightly wos, whil th phass com clos togth aft th ocan load coction. Intstingly, th diffncs of th phass in VI and CO a about -.6 fo both main tidal wavs whil th phass itslf ang btwn -.15 and +.23. This is two ods of magnitud high than th fomal os of th phas lag dtmination. Th avagd amplitud factos (VI, CO) fo O 1, K 1 and 2 a in full agmnt with th numbs obtaind fo th Wst Euopan ntwok (WEN) [3], [4]. Th avagd amplitud factos ath fit btt to th non-hydostatic modls DDW/NHi [2] o AT1/NH [14] with slight pfnc to th latt. Th dviation fom th inlastic DDW [2] modl is about.8 (O 1 ),.5 (K 1 ) and.1 ( 2 ) spctivly. Th cosponding numbs fo th AT1/NH modl [14] a.5 (O 1 ),.2 (K 1 ) and.4 ( 2 ) (Tab. 6).
ocan modl no co. CO VI diffnc CO-VI δ(o 1 ) κ(o 1 ) [ ] δ(o 1 ) κ(o 1 ) [ ] Δδ(O 1 ) Δκ(O 1 ) [ ] 1.14981.6.189.28 1.14979.3.1158.14.2 -.69 CSR4. 1.15319 -.186 1.15315 -.131.4 -.55 DTU1 1.15322 -.217 1.15316 -.149.6 -.68 EOT11a 1.1533 -.219 1.15324 -.151.6 -.68 FES24 1.15369 -.4 1.15364.29.5 -.69 GOT.2 1.15341 -.139 1.15338 -.81.3 -.58 HATIDE 1.15359 -.12 1.15354 -.54.5 -.66 TPXO.7.2 1.15347 -.98 1.15343 -.5.4 -.48 av 1.15341 -.146 1.15336 -.84.5 -.62 stddv.19.66.19.66.1.8 max-min.5.179.49.18.3.21 ocan modl no co. CO VI diffnc CO-VI δ( 2 ) κ( 2 ) [ ] δ( 2 ) κ( 2 ) [ ] Δδ( 2 ) Δκ( 2 ) [ ] 1.18351.3 1.156.12 1.18345.1 1.778.7.6.278 CSR4. 1.16224.256 1.16217.334.7 -.78 DTU1 1.16193.244 1.16187.294.6 -.5 EOT11a 1.16212.74 1.1625.123.7 -.49 FES24 1.1631.43 1.1631.469.9 -.66 GOT.2 1.16192.125 1.16182.194.1 -.69 HATIDE 1.1626.41 1.16195.11.11 -.69 TPXO.7.2 1.16174.3 1.16161.128.13 -.98 av 1.16216.168 1.1627.236.9 -.68 stddv.45.138.45.135.3.17 max-min.136.373.14.359.7.49 Tab. 5: Tidal analysis sults of th VI and CO gavity tim sis coctd fo ocan load basd on load vctos povidd by [1]. DDW/H [2] DDW/NHi [2] AT1/NH [14] WEN [3], [4] av (CO,VI) Dv DDW/H Dv DDW/NHi Dv AT1/NH δ(o 1 ) 1.1528 1.1543 1.154 1.1534 1.1534.6 -.9 -.6 δ(k 1 ) 1.1324 1.1345 1.1349 1.1353 1.1351.27.6.2 δ( 2 ) 1.165 1.162 1.1616 1.1621 1.1621.16.1.5 Tab. 6: Compaison of th coctd amplitud facto (avag ov all ocan modls applid at VI and CO) with th DDW [2] and AT [14] body tid modls. Dviations a calculatd as obsvd minus modl amplitud factos. Tmpoal stability of th calibation facto Th scatt of th calibation factos divd fom singl xpimnts (Fig. 7) dos not pmit studying th tmpoal stability of th SG calibation. Thfo th tim sis was spaatd into ovlapping 1-ya intvals, which thn w subjctd to tidal analysis. Fig. 8 (lft) displays th sults aft applying th ocan load coction [1] basd on th TPXO.7.2 modl. Fig. 8 (lft) also allows fo dict compaison of th tidal paamt obtaind fom th VI and CO tim sis and psnts additionally th ai pssu to gavity admittanc facto calculatd in th diunal and smi-diunal tidal fquncy band. Th ai pssu admittanc facto is systmatically high at CO (-3.35 nms -2 /hpa) than in VI (-3.54 nms -2 /hpa). Bcaus th distanc btwn both stations is small (about 6 km), th dfomation pat is xpctd to b simila at both sits. Howv, th
Nwtonian pat is diffnt, as both stations a locatd in diffnt altituds (VI: 19 m, CO: 145 m). Th admittanc factos diff by.19 nms -2 /hpa oughly. This numb matchs faily wll th Nwtonian ffct du to th lvation diffnc calculatd in flat appoximation fo a hydostatic atmosph. Figu 8: Lft: tidal analysis sults fom ovlapping 1-ya intvals (black dots: amplitud facto, blu dots: phas). Ocan load coction [1] basd on th TPXO.7.2 modl has bn applid. Hoizontal lins indicat th analysis sult obtaind fom th nti gavity tim sis. Right: Colation btwn th O 1 and 2 tidal paamts. Only th phass a colatd significantly (black dots: VI, blu dots: CO). Th amplitud factos of O 1 and 2 do not vay consistntly, i.. th colation is not significant on th 95% confidnc lvl. Th ovall vaiation is as small as lss than.2. In contast, th phass of O 1 and 2 show a statistically significant colation (Fig. 8, ight panls). Accoding to th slop of th gssion lin, th ang of th 2 phas vaiation (.2 ) is twic that of th O 1 phas vaiation, indicating a link to tim with os of up to 2.4 s. As tim kping is basd on GPS, this suggsts instumntal tim lag vaiations. Howv, only th main tidal constitunts a considd h. Thfo, in od to study th tmpoal stability of th SG calibation facto, thotical body tids hav bn calculatd basd on th individual tidal paamt sts obtaind fom th analysis of ach 1-ya intval. Ths synthtic tim sis a thn adjustd to synthtic tids using tidal paamts obtaind fom th analysis of th nti obsvation piod in VI and CO spctivly (Fig. 9). Figu 9: Tmpoal vaiation of th gssion facto and th tim lag obtaind by adjusting synthtic tids basd on tidal paamts obtaind fom 1-ya intval analyss to synthtic body tids using tidal paamts obtaind fom analyzing th nti tim sis.
By this way, tim dpndant gssion factos and tim lags a obtaind that can b intptd as tmpoal calibation facto vaiation povidd th tidal paamts a assumd not to chang with tim. Of cous, this is not ncssaily a valid assumption. Fig. 9 dmonstats that all vaiations gnally a wll blow.1. Tim lag vaiations tun out to b in th ang of 1 s which cosponds to a phas vaiation of about.8 fo 2. A wakly significant anti-colation (.55) btwn calibation facto and tim lag vaiations xists. Conclusions Fo sping typ gavimts it is mandatoy to consid th igula dift in th adjustmnt of th calibation facto. Th calibation xpimnts pfomd in VI and CO show, that vn th dift of th AG should b considd in a common adjustmnt of th calibation facto. Though th systmatic ffct is small, th oot man squa o of th avagd calibation facto is ssntially ducd. Calibation sults a biasd not only by dift ffcts, but also by vn andom nois which limits th accuacy of th calibation xpimnt. Thfo th calibation xpimnt should b patd sval tims. Sping typ gavimts hav som potntial to contibut to th SG calibation facto dtmination povidd th dift is cafully modld,.g. by high dg polynomial functions, and th sping gavimt is accuatly calibatd. Th dpndnc of th oot man squa o of th adjustmnt on th polynomial dg of th dift function may sv as slction cition fo an appopiat dift modl. Th -analysis of th calibation xpimnts pfomd in VI and CO povs that th calibation facto of GWR C25 maind unchangd duing th tansf fom VI to CO. Th SG/CG5 xpimnts fully suppot this statmnt and tun out to b a valuabl xtnsion to th SG/AG compaisons. A final calibation facto has bn calculatd as wightd avag ov in total 9 JILAg and FG5 xpimnts. Basd on th oot man squa dviation fom th avag, th accuacy stimat amounts to.5, whil th fomal o of th calibation facto is vn small (.2 ). Th calibation facto tuns out to b tmpoaily stabl. A gssion analysis shows that tmpoal vaiations, if psnt, a blow ±.1. Th -analysis of th calibation xpimnts nabls a dict compaison of th tidal paamts obtaind in VI and CO. Th amplitud factos O 1, K 1 and 2 ag almost pfctly aft cocting fo ocan loading ffcts and fit closly to th non-hydostatic body tid modls calculatd by [2] and [14]. Th maximum dviation fom th numbs povidd by th non-hydostatic DDW body tid modl [2] is.8, th fit to AT1/NH [14] is vn small (.5 ). Additionally, th amplitud factos diff fom th sults of th Wst Euopan ntwok ([3], [4]) by lss than.1. Acknowldgmnt Clos co-opation with ZAG (Austia), th own of Conad obsvatoy and th GWR C25, is gatfully acknowldgd as wll as all th ffots of th opatos of th JILAg and FG5 absolut gavimts D. Russ, Ch. Ullich (both BEV, Vinna), O. Fancis (Univsity of Luxmboug) and V. Pálinkáš (Rsach Institut of Godsy, Topogaphy and Catogaphy, Dpatmnt of Godsy and Godynamics). Two anonymous viws mad valuabl suggstions impoving th pap. Th autho of th manuscipt has no dict financial lations with th commcial idntitis mntiond in th pap that might lad to a conflict of intst fo th autho. Rfncs [1] Bos,.S. and Schnck, H.G.: http://fost.oso.chalms.s/loading/, f ocan tid loading povid. [2] Dhant V., Dfaign P., Wah J., 1999: Tids fo a convctiv Eath. J. Goph. Rs., 14, B1, 135-158.
[3] Ducam, B., 29: Limitations of High Pcision Tidal Pdiction. In: Poc. Nw Challngs in Eath Dynamics (ETS28), Bulltin d'infomations aés Tsts, 145, 11663-11677. [4] Ducam, B., Rosat, S., Vandcoildn, L., Xu, J.Q., Sun, H.P., 29: Euopan Tidal Gavity Obsvations: Compaison With Eath Tid odls And Estimation Of Th F Co Nutation (FCN). In: Sidis,.G. (Ed.): Obsving ou Changing Eath: Pocdings of th 27 IAG Gnal Assmbly, Pugia, Italy, July 2-13, 27. Intnational Association of Godsy, Symposia, vol. 133, 523-532. [5] Fancis, O. and Hndickx,., 21: Calibation of th LaCost-Rombg 96 by Compaison with th Supconducting Gavimt C21 in mbach (Blgium), Jou. God. Soc. Japan, 47, 1, 16-21. [6] Fancis, O. and Van Dam, T., 22: Evaluation of th pcision of using absolut gavimts to calibat supconducting gavimts, tologia, 39, 485 488. [7] Fancis, O., Nibau, T.., Sasagawa, G., Klopping, F. and Gschwind, J., 1998: Calibation of a supconducting gavimt by compaison with an absolut gavimt FG5 in Bould, Gophys. Rs. Ltt., 25, 175-178. [8] Hind J., Flosch, N., akinn, J., Lgos, H., Fall, J.F., 1991: On th calibation of a supconducting gavimt using absolut gavity masumnts, Gophys. J. Int., 1991, 16, 491-497. [9] Hind, J., Amalvict,., Fancis, O. and äkinn, J., 1998: On th calibation of supconducting gavimts with th hlp of absolut gavity masumnts, In: Ducam, B. and P. Pâqut (ds.) (1998): Poc. 13 th Int. Symp. Eath Tids, Bussls, July 22-25, 1997, 557-564. [1] Hind, J., Cossly, D. and Wabuton, R.J., 29: Gavimtic thods Supconducting Gavity ts, In: Schubt, G. (d.): Tatis on Gophysics, Hing, T. (d.): Vol. 3: Godsy, 65-122. [11] Iglwicz, B., Hoaglin, D.C., 1993: How to dtct and handl outlis. Vol. 16 in: ykytka, E.F. (d.): Th ASQC Basic Rfncs in Quality Contol: Statistical Tchniqus, Amican Socity fo Quality Contol (ASQC), Statistics Division, ASQC Quality Pss, ilwauk, WI. [12] Imanishi, Y., Higashi, T. and Fukuda, Y., 22: Calibation of th supconducting gavimt T11 by paalll obsvation with th absolut gavimt FG5 #21 a Baysian appoach. Gophys. J. Int., 151, 867 878. [13] Kon, C., 26: Hydological signals in th SG cods at oxa - a follow-up. Bulltin d'infomations aés Tsts, 142, 11353-11358. [14] athws, P.., 21: Lov numbs and gavimtic facto fo diunal tids. Poc. 14th Int. Symp. on Eath Tids, Jounal of th Godtic Socity of Japan, 47, 1, 253-259. [15] us, B., 21: Supconducting gavimty in gophysical sach today, J. God. Soc. Japan. 47, 3 37. [16] us, B., 22: Aspcts of gavimt calibation by tim domain compaison of gavity cods, Bulltin d'infomations aés Tsts, 135, 1643 165. [17] us, B. and Russ, D., 1985: Eichtung in nun Gavimt-Eichlini am Hochka. ÖZfVuPh, 73, 3, 175-183. [18] us, B. and Russ, D., 21: Gavity masumnts at th Hochka calibation lin (HCL). 8 th Int. ting on Alpin Gavimty, Lobn 2, Öst. Bit. t. Goph., 26, 29-215. [19] us, B., Van Camp,., Ptmans, T., 27: Cocting supconducting gavity tim-sis using ainfall modlling at th Vinna and mbach stations and application to Eath tid analysis, Jounal of Godsy, 81, 11, 73 712, DOI -
1.17/s19-7-137-1, http://www.spinglink.com/contnt/t6282688375w57. [2] Pss, W.H., Tukolsky, S.A., Vttling, W.T. and Flanny, B.P., 1992: Numical Rcips in Fotan, Th At of Scintific Computing, Scond Edition, Cambidg Univsity Pss, pp. 933. [21] Riccadi, U., Rosat, S. and Hind, J., 211: On th Accuacy of th Calibation of Supconducting Gavimts Using Absolut and Sping Snsos: a Citical Compaison, Pu Appl. Gophys., DOI 1.17/s24-11-398-8. [22] Rosat, S., Boy, J.-P., Fhat, G., Hind, J., Amalvict,., Ggout, P. and Luck, B., 29: Analysis of a tn-ya (1997-27) cod of tim-vaying gavity in Stasboug using absolut and supconducting gavimts: nw sults on th calibation and compaison with GPS hight changs and hydology, Jounal of Godynamics, 48, 36-365, doi:1.116/j.jog.29.9.26. [23] SCINTREX Limitd, 26: CG5 Scintx Autogav systm opation manual, pat # 8677 Rv. 1, pp. 312. [24] Tamua, Y., 1987: A hamonic dvlopmnt of th tid-gnating potntial. Bulltin d'infomations aés Tsts, 99, 6813-6855. [25] Tamua,Y., Sato, T., Fukuda, Y. and Higashi, T., 25: Scal facto calibation of a supconducting gavimt at Esashi Station, Japan, using absolut gavity masumnts. Jounal of Godsy, 78: 481 488, DOI 1.17/s19-4-415-. [26] Van Camp,. and Vautin, P., 25: Tsoft: gaphical and intactiv softwa fo th analysis of tim sis and Eath tids, Computs & Goscincs, 31(5) 631-64. [27] Van Camp,. and Fancis, O., 26: Is th instumntal dift of supconducting gavimts a lina o xponntial function of tim?, J. God., 81, 5, 337-344, doi: 1.17/s19-6-11-4. [28] Wnzl, H.G., 1991: Pcis instumntal phas lag dtmination by th stp spons mthod, Bulltin d'infomations aés Tsts, 111, 832-852. [29] Wnzl, H.-G., 1996: Th nanogal softwa: Eath tid data pocssing packag ETERNA 3.3. Bulltin d'infomations aés Tsts, 124, 9425-9439.