tle vibrator ground force 090801

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960 The Leading Edge August 2009

V

br ur ar t rnal nnmulv urud n land m xlratn. av an mrvd

mag f t uburfa wt gr aura and bttrrlutn, t nar t tak t tru grund fr a trfrn n alulatng t r-rrlatn funtn wt tfar-fild data ntad f ung t trtal rfrn gnal.T tru grund fr dfind a t ttal mrv frxrtd b t Eart un t vbratr balat. Trtall,t an b alulatd b ntgratng t mrv tr vrt urfa ara tat ntat t balat. In rat t vr dffi ult t quantf t tru grund fr auratl.

A t vbratr ak n gl varabl urfa u adrt and dun, t vbratr wll gnrat mr armndtrtn. At t am tm, t balat wll flx and rk.

T rult n r ratablt f ur gnatur. Tman tat t tru grund fr var frm la t laand bm mbl t dtrmn.

T vbratr grund fr an b arxmatd b u-ng a “wgtd um” f alratn f t ratn maand t balat. T mtd bad un a rgd bd aumtn fr bt t ratn ma and t balat. Un-frtunatl, t balat ubjt t flxural mtn du tt lw rgdt. Dffrnt latn wtn t balat avdffrnt mtn tat t alratn rrdd b tngl balat alrmtr annt rrnt t balatmtn. Trfr, t valdt f t wgtd-um grundfr bm qutnabl. Lad ll an rvd a tru

maurmnt f t vbratr fr utut but ar nt t r-but nug fr rutn u. Dgnng t vbratr balat

wt uffi nt tffn t rbtv. A mbnatn f t rlatvl tffr balat and t dtrmnatn f tbalat alrmtr tn mgt rvd a gnfiantl bttr tmatn fr t tru grund fr.

Vibrator baseplate flexure and weighted-sum ground force

A mdrn m vbratr ntall a drman-al tm drvn b a rvvalv ambl tat ntrlldltrnall. Fgur 1 dt a r tn f an ION(rvul I/O) AHV-IV vbratr. T tn rgdl n-

ntd t a t r and a bttm r. T t r andt bttm r ar firml jnd wt fur t rd tatar manall ntgratd wt a balat ad. T tn,t t r, t bttm r and t t rd ar lnkdtgtr and alld t balat tlt trutur. T vbratrbalat frmd b a balat ad and t balat tlttrutur. T tn mv n a lndral br nd tratn ma and dvd t lndr nt an ur ambrand a lwr ambr. T g-rur draul l flwut f t rvvalv ambl and fd altrnatl nt tur and lwr ambr t drv t ratn ma u anddwn. T fr atng n t ratn ma quall and

How good is the weighted-sum estimate of the vibrator

ground force?

ACQUISITION/PROCESSING

Z HOUHONG W EI , ION Geophysical Corporation

tl ald t t tn. Evntuall, t fr mt-td nt t grund b t vbratr balat. In gnral, t

vbratr balat funtnall at lk a tranmttr, brad-atng a draul fr nt t Eart.

Alrmtr ar tratgall muntd n t vbra-tr trutur t rrd alratn f t balat and tratn ma. Fr an AHV-IV vbratr, t balat al-rmtr muntd n t t r and t ratn maalrmtr ntalld n t t f t ratn ma adtd n Fgur 1. Salla (1984) rntd a wgtd-um mtd t arxmat t tru grund fr (F

g). T

mtd aum tat t balat at a a rgd bd, anda full ulng f t balat and t grund avd.Undr t aumtn, t wgtd-um grund fr btand b ummng wgtd balat and ratn ma

alratn. In t a,

F g = M

r A

r + M

b A

b(1)

wr Mr, M

b, A

r, and A

bar t ma f t ratn ma,

t ma f t balat, t ratn ma alratn, andt balat alratn, rtvl.

Du t t lw rgdt, t balat ubjt t flxuralvbratn at gr frqun. T md f t flxural v-bratn ar dvr and dnd n grund ndtn. Wnt balat n vr unvn urfa, t flxural vbratnan b drbd a t balat wbblng and jumng u

Figure 1. Te schematic model of an AHV-IV vibrator.

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August 2009 The Leading Edge 961


and dwn. Oftn t flxural vbratn lad t full du-lng r vr artal dulng, and t vbratr rfr-man gnfiantl dgradd. Wn t balat n aflat urfa, t flxural vbratn an b drbd a a brdflang t wng. In t tuatn, t artal dulng

wll ur, but t dulng ara mall. Fr an AHV-IV vbratr, t draul fr mr nntratd n t

ntral ara f t balat ad tan t d ara f tbalat wn t balat ud dwnward. In ta, t rtn f t balat at t fur rnr mvuward t t t dwnward drtn f t fr.

Wn t balat ulld uward, t balat dfrmn t a f an ar wt t ntr f t balat at tt f t ar. A artal dulng ur at t ntralara. Gnrall, dffrnt latn wtn t balat wllrdu dffrnt mtn. Plang alrmtr n dffrntla n t balat wll maur dffrnt alratn. It vr dffi ult t dtrmn t xat vrtal alratnf t balat ung a ngl alrmtr. It al bmdffi ult t dtrmn w mu balat ma artatn t vrtal mtn.

T vbratr grund fr an b tmatd b ung a“wgtd um” f alratn f t ratn ma and tbalat. Bau f t flxng f t balat ad and vr mlatd rkng f t balat tlt trutur at grfrqun, t wgtd-um mtd an arxmat ttru grund fr nl n a narrw frqun band. In gn-ral, t wgtd-um arxmatn vrtmat t a-tual fr utut f t vbratr. Man rarr av vr-fid t b makng marn btwn t wgtd-umgrund fr and t drt-fr maurmnt ung ladll (Salla t al., 1985; Batn and Strjb, 1988; Batn

and Zlkk, 1990). Fgur 2 w an xrmntal tu.T AHV-IV vbratr t n lad ll. T lad ll a n-r tat an drtl maur t tru grund fr. Egtlad ll ar firml muntd n nrt and lad vnl undr t balat. Tr ar tw f rubbr ad nt t f a lad ll t rtt t lad ll frm mtal-t-mtal ntat. Undr t ladng ndtn, t balat wll uld wt t lad ll. Hwvr, t ntat ara mall. Obvul, a vr dulng frmd btwnt balat and t nrt. Fgur 3 dt a t vw f t balat ad wr magnt alrmtr ar -tnd. T latn ar grud n t drvr’ d (A,B, E, H, and J) and angr’ d (D, C, G, I, and K) wt

nr F n t mddl. T tn f A, D, J, and K ar 6n awa frm t rnr n t X and Y drtn. B, C,H, and I ar n t b at t lg tub tn. T -tn f E and G ar latd n t ntrln n t X dr-tn and mdwa btwn t dg and tlt tub. F at tntr f t balat ad. Sx magnt alrmtr arud t maur t mtn f t balat ad. T wrlad n drvr’ d firt t rrd alratn f t ba-lat ad, and tn t wr mvd t t angr’ d trrd alratn f t balat ad. In gnral, t datafrm t drvr’ and angr’ d ar vr mlar. Tu,

w nl rnt t drvr d’ data r.

mar t wgtd-um grund fr and t trugrund fr, a lnar w wt a lngt f 20 frm 1 Hzt 201 Hz wa ud t run t vbratr. T targt fr t

at 70% f ld-dwn wgt (60,000 lb). Fgur 2 wt xrmntal tu. T balat tlt trutur f tvbratr abut 6 n rtr tan tat f t rdu-tn AHV-IV vbratr. Fgur 4 w t frqun rnf t wgtd-um grund fr agant t tru grundfr. T wgtd-um grund fr wr alulatd b u-ng dffrnt balat alratn rrdd wt magntalrmtr n dffrnt tn, and t tru grundfr wa maurd b lad-ll nr. T magntudrat and a tra wr lttd b ung t lad-llgrund fr a t nut and t wgtd-um grund fra t utut. Trtall, t magntud rat trumand t a trum uld rman ntant at 0 dB and

0°, rtvl, f t wgtd-um and maurd grundfr ar qual. Fgur 4 larl dmntrat tat nn f

wgtd-um grund fr ar n agrmnt wt t lad-ll grund fr n t 200-Hz frqun rang. T brknln markd a FBK n Fgur 4 t wgtd-um grundfr alulatd b ung t Pltn alrmtr agantt tru grund fr. T Pltn balat alrmtr ftn lad n t t r f t balat tlt trutur.

T maurmnt frm tn F and H ar xtrml anmalu. T grund fr tmatd b t wgtd-um mtd frm t tn ar mltl dffrnttan t tru grund fr. T trnd f t dran n-

Figure 2. Te vibrator is on load cells.

Figure 3. Magnetic accelerometer positions on the baseplate pad.




962 The Leading Edge August 2009


dat tat t ntral ara f t balat a xrndvr artal dulng fr a ubtantal amunt f t tm.Cnvrl, t grund fr tmatd b t wgtd-ummtd ung alratn n t tn f A, B, E, and

J agr t t tru grund fr n t frqun rang b-lw 50 Hz. Fr frqun abv 50 Hz, t maurmntdmntrat tat t wgtd-um mtd n lngr vald

t arxmat t vbratr tru grund fr utut. Tfindng al ald fr t FBK a. Atuall, t abn brvd a wll n tr t f vbratr b Salla tal. (1985) and Alln t al. (1998).

Fgur 5 w n xaml f wr-trum dn-t t mar t wgtd-um grund fr and t trugrund fr. T xrmnt ud a 20- lnar w n tfrqun rang f 5–105 Hz. T wgtd-um grundfr mutd b ung t Pltn balat alrm-tr data. A tatd arlr, t Pltn balat alrm-tr muntd n t t r f t tlt trutur. T

wgtd-um grund fr wn n blu, and t grundfr maurd b lad ll wn n grn. Bt fr

ar n gd agrmnt blw 50 Hz, but at 50 Hz t frtart t dvrg. A t frqun g u, t dran b-m largr. Obvul, t wgtd-um grund fr annt full rrnt t tru grund fr. It undrtmatt tru grund fr n t a. Fgur 6 w antrxaml f wr-trum dnt marn btwn t

wgtd-um grund fr and t tru grund fr. Ttt wa run ung a 20- lnar w n t frqun rangf 1–201 Hz. On agan t wgtd-um grund fr alulatd b ung t Pltn balat alrmtr data.

A n Fgur 5, t wgtd-um grund fr wn nblu and t grund fr maurd b lad ll wn ngrn. In t frqun rang blw 100 Hz, Fgur 6 wmlar bavr t Fgur 5. Wn t frqun g abv80 Hz, t wgtd-um grund fr a r tmatnf t tru grund fr and t vrtmat t tru grundfr. radtnall, mt f t dran ar attrbutdt t balat flxural vbratn. Hwvr, t mlxt nrad b t rlatn btwn t wgtd-umgrund fr and t tru grund fr, w varabldu t dffrnt grund-ulng ndtn. In rat,t grund fr nt knwn xatl and var frm lat la. Fr t a f t AHV-IV vbratr n lad ll,t wgtd-um arxmatn undrtmat t atualfr utut f t vbratr btwn 50 and 100 Hz, but t

vrtmat t atual fr utut f t vbratr bnd100 Hz. Drt fr maurmnt u a ung lad ll ndd t maur t ral grund fr, but lad ll ar ntt rbut nug fr rutn u.

New stiffer baseplate and weighted-sum ground force

T wgtd-um f t alratn f t balat andt ratn ma rvd a man fr maurng t trugrund fr. T advantag f t mtd tat t nl rqur maurng alratn f t balat and ra-tn ma. In rat, t alrmtr a t ntall,mantan, and trublt. T dadvantag f t mt-d tat t aum t balat bav a a rgd bd

Figure 4. Comparison in frequency response of weighted-sum ground force versus load-cell force in frequency range from 1 to 201 Hz.

Figure 5. Comparison in power-spectrum density of weighted-sum ground force versus load-cell force in frequency range from 5 to 105 Hz.

Figure 6. Comparison in power-spectrum density of weighted-sum ground force versus load-cell force in frequency range from 1 to 201Hz.






and tat t balat full uld wt t grund. Inral wrld alatn, w knw t mbl t ava rgd-bd balat. Full ulng an nvr b avdtr bau t grund nvr flat. A tatd arlr anddmntratd n Fgur 4 and Fgur 5, t balat nta rgd bd and ubjt t flxural vbratn. Plang a-lrmtr n dffrnt tn wtn t balat wll

maur dffrnt alratn. Wgtd-um grund fr- frmd b ung t balat alratn agr wtt grund fr maurd b lad ll n a vr narrw-frqun bandwdt. Wn t frqun g abv 50Hz, t dran ur and grw largr. Evntuall, tdran au t valdt f t wgtd-um grundfr t bm qutnabl.

T naura n t wgtd-um grund fr t-matn, tmmng frm bt balat flxur and t lm-tatn f alrmtr lamnt n t balat, all frmrvmnt n vbratr dgn. Trtall, t flxuralvbratn f t balat an b rdud b tffnng tbalat trutur. T rultant rdutn n flxur allwt dnam mtn f t balat t b mlfid andaratrzd mr auratl. Havng aratrzd t ba-lat mtn auratl, an tmal latn r “wt t”an tn b fund fr t alrmtr lamnt wr tvrtal mtn f t balat and grund an b maurdmr rl. T tw-fld ara allw t wgtd-um grund fr tmat t b far mr rrntatv f t tru grund fr.

Stffn t rtan f an lat bd t dfrmatnb an ald fr. It a matral rrt and xtnvl ntrlld b bt t Yung’ mdulu f t matral andt gmtr f t lat bd. Fr mdrn m vbra-

tr, t balat mad f tl. Enanng t tffn b ung matral wt a g Yung’ mdulu (u a m-t matral) wll gnfiantl nra atal t f tvbratr. T nl tn lft t ang t gmtr f t balat. Trug xrmntal tt and fint-lmntmdlng and anal, a nw tffr balat wa dgnd.T nw balat dgn nvlvd xtnvl angng ttrutural a f t manal mnnt. Exrmntalrult w tat t nw dgn gnfiantl nra ttffn f t balat and dramatall rdu t flxur.T nw balat 2.5 tm tffr tan t tandard ba-lat but a nl an 8% nra n wgt. Wt t nw balat, t ulng f t balat and t grund

mrvd undr varu ladng ndtn, and t vbratrrfrm rbutl. In gnral, t vrtal mtn f t ba-lat an tll b drbd a a brd flang t wng. Fr tnw tffr balat, an tmal t wa fund t u a tbalat alrmtr latn.

Fgur 7 mar t wgtd-um grund fr andt lad-ll grund fr n t wr trum dnt nblu and rd, rtvl. A 20- lnar w frm 5 t 105Hz wa n fr t xrmnt. T wgtd-um grundfr mutd ung t tmal latn balat a-lrmtr data. Fgur 7 w tat bt fr ar n vr gd agrmnt trugut t ntr frqun band. Onl

Figure 7. Comparison in power-spectrum density of weighted-sum ground force versus load cell force in frequency range from 5 to 105 Hz.

Figure 8. Comparison in power-spectrum density of weighted-sum ground force versus load-cell force in frequency range from 1 to 201Hz.

a lgt dran brvd btwn 90 and 100 Hz. T wgtd-um grund fr alulatd ung t balat a-lratn n t tmal latn tmat t tru grundfr vr wll. Fgur 8 w antr marn n wr-trum dnt. In t a, t xrmnt wa rfrmdung a 20- lnar w frm 1 t 201 Hz. On agan t

wgtd-um grund fr alulatd ung t tmallatn balat alratn. Fgur 8 dmntrat tatt wgtd-um grund fr vrla t tru grundfr vr wll u t 120 Hz. Fr t frqun abv 120Hz, t wgtd-um grund fr lgtl vrtmat f t tru grund fr. Hwvr, mard t Fgur 6 t

wgtd-um grund fr tmatd ung t balat a-lratn n t tmal latn a gnfiant mrv-mnt.

Fgur 9 mar grund fr maurd b lad ll.Grn rrnt t tru grund fr utut frm t tan-dard balat and rd rrnt t tru grund fr utut






frm t nw tffr balat. T lad-ll grund fr wr rntd n Fgur 6 and Fgur 7. T nw tffr ba-lat rvd mr grund-fr nrg tan t tandardbalat d n rgn 1 frm 5 t 10 Hz and rgn 2 frm40 t 105 Hz. T bau t nw tffr balat rdut balat rkng and flxural vbratn tat t frl mnmzd. Bt lad-ll fr dln at gr fr-

qun. T grund fr at t g frqun ndattat tr ar m lmtatn n t vbratr draul andmanal tm; fr xaml t wgt f t balat,t lmt f t trqu mtr urrnt n t lt rvvalv,and t draul ul rur. T lmtatn vntu-all rvnt t vbratr frm avng t targt fr.

Fgur 10 w t rat f t grund fr frqun rn alulatd b t wgtd-um mtd agant tgrund fr maurd b lad-ll nr, n mlar mannrt Fgur 4. T marn wa mad btwn t nw tff-r balat and t tandard balat. T dad blu ln

Figure 9. Comparison in power-spectrum density of load-cell forces in frequency range from 5 to 201 Hz.

Figure 10. Comparison in frequency response of weighted-sum ground force versus load-cell force in frequency range from 1 to 201 Hz.

u t nw tffr balat wt t balat alrmtrn t tmal latn. T ld grn ln, wvr, umaurmnt frm t tandard balat wt t balatalrmtr muntd n t t r f t tlt trutur.

A zr-dB and zr-a rn wll b n n t grundfr frqun rn lt f t balat atng a argd bd and t balat alrmtr rrd t vrt-

al mtn f t lat and t grund. A llutratd n Fg-ur 10, t wgtd-um grund fr rvdd b t nw balat rvd a mr aurat dtn f t wgtd-um grund fr wn mard t t tru grund frxrnd b t lad ll. Fgur 10 al w tat t

wgtd-um grund fr undr t tandard balat anarxmat t grund fr maurd b lad ll blw 40 Hz. Wt t nw balat, t wgtd-um mtdan auratl tmat t maurd grund fr u t 160Hz.

Conclusions

Idall, a vbratr ud n vbr data aqutn uldrdu grund fr a a knwn atal l-nvarant wavltu tat an varatn n rftn data an b attrbutd tvaratn n glg. In ralt, w dn’t vn knw t trugrund fr bng utut b t vbratr. Exrmntal dataw tat t ular mtd f wgtd-um nl wrkn a narrw-frqun band n urrnt rdutn vbratr.

Wt t nw tffr balat and t tmal latn frt balat alrmtr, t wgtd-um grund fran b ud t arxmat t tru grund fr and wllrman vald u t 160 Hz. Manwl, mr grund frnrg rdud b t nw tffr balat brvd.

Suggested reading. “Sm vbratr ntrl and t dwn-gng P-wav” b Salla (Geophysics, 1984). “Grund frntrl f a P-wav vbratr” b Salla t al. (SEG 1985 -m fild tnqu wrk). “Wav fild f a vbratr na lard alfa: tr and rat” b Batn t al. (SEG1988 Expanded Abstracts ). Te Vibroseis Source b Batn andZlkwk (Elvr, 1990). “Hg-fidlt vbratr m(HFVS) mtd fr aqurng m data” b Alln t al. (SEG1998 Expanded Abstracts ).

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tle vibrator ground force 090801

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