Hsui Borehole Measurement of the Newtonian Gravitational Constant

7/28/2019 Hsui Borehole Measurement of the Newtonian Gravitational Constant

1/4

Borehole Measurement of the Newtonian Gravitational ConstantAuthor(s): Albert T. HsuiSource: Science, New Series, Vol. 237, No. 4817 (Aug. 21, 1987), pp. 881-883Published by: American Association for the Advancement of ScienceStable URL: http://www.jstor.org/stable/1699892 .

Accessed: 16/04/2013 10:33

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

American Association for the Advancement of Science is collaborating with JSTOR to digitize, preserve and

extend access to Science.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=aaashttp://www.jstor.org/stable/1699892?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/1699892?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=aaas


2/4

Borehole Measurement of the NewtonianGravitational ConstantALBERT T. HsuI*It has been reported that the geophysically determined Newtonian gravitationalconstant is consistently larger than the laboratory value by 1 to 2% on the basis ofgravity measurements in Australian mines. This discrepancy may have strong implica-tions for the physics of gravitation. To test whether similar results can be observed in adifferent geological environment, gravity measurements in a Michigan borehole havebeen examined. Although these results cannot be taken as conclusive, owing to thelarge uncertainties involved in mass determination on a geophysical scale, thesemeasurements are generally consistent with those of the Australian experiment.

RECISE DETERMINATION OF THENewtonian gravitational constant Ghas been attempted by many investi-gators, both in the field and in laboratories.Because of the deficiencies associated withthe instruments in the past, the geophysical-ly determined values did not have the accu-racy to match that obtained in laboratories.Consequently, the accepted value for thegravitational constant up to the present isdetermined in laboratories. During the late1970s and the early 1980s, Stacey and hiscolleagues revived the earlierAiry approach(1) and attempted to determine the Newto-nian gravitationalconstant by means of geo-physical measurements. They have carriedout numerous measurements in Australianmines, and reported their researchresults inseveralarticles (2-7). Generally, their resultsindicate that the geophysically determinedgravitationalconstants areconsistently high-er by about 1 to 1.5% than the acceptedlaboratoryvalue. On the basis of their obser-vations, Stacey and his colleaguLes ave pro-posed a possible correction to the inversesquare law of gravitation and have speculat-ed on the existence of an intermediate-rangeforce (sometimes known as the "fifth" orce)(2). Since both the defect of the inversesquare law and the possible existence of a

fifth force have been independently pro-posed (8, 9), and if the validity of theobservations by Stacey and his colleaguescan be confidently established, its implica-tion for the laws of fundamentalphvsicswill

be profound. To test if similar results can beobserved in a different geological environ-ment, a gravimetricmeasurement in a bore-hole within the Michigan Basin has beenexamined to determine an inferredvalue forthe Newtonian gravitationalconstant.During September 1983, a gravity surveywas carried out in the State Burch #1-20well in Manistee County, Michigan, by ED-CON, Inc. The borehole is located about300 km northwest of the center of theMichigan Basin (Fig. 1) and was drilledto adepth of approximately 2 km, mostlythrough Devonian and Silurian sediments.The well is about 100 m from a small reefformation which domes upward slightly at adepth of about 1.4 km. Other than this reefstructure, stratigraphic boundaries of thearea are generally parallel with very littledipping as revealed by a three-dimensionalsurfaceseismic survey and some offset verti-cal seismic profiling studies (10). Thus,within a radius of about 2 km of the bore-hole, strata above the reef can be approxi-mated by flat layers for all practical pur-poses. The gravity meter used for the surveyis a LaCoste-Romberg instrument of slim-hole design. It is housed in a 213-cm-longtool with a diameter of about 10.5 cm.Precision of the gravity survey is reported tobe within 10 microgal (11) (1 gal =1 cmsec2). Positions of the stations downholeare determined by an optical encoder whichis clamped onto the logging wireline andprovidesa resolution of about 0.3 cm. How-ever, the borehole deviates from the truevertical. There is an offset of about 40 m atthe bottom of the hole. Most of the devi-ation occurs beneath 1-km depth. Takingthis effect into consideration, the maximumuncertaintyin position determination is esti-mated to be less than 0.2%. Spacings be-

tween stations are variable since the surveywas designed for a somewhat different pur-pose; there is a higher than average densityof coverage between the depths of 1200 to1500 m. Station spacings can be as small as20 m within this interval, and the spacingsgradually increase towards the surface. Nearthe surface, station spacings can be as largeas 150 m. Gravitvreadings in many stationshave been repeated, not only for the purposeof instrument drift corrections, but also toensure data reliability.A theory for the variation of gravity with-in the Earth has been formulated that incor-porates the effects of Earth's rotation andthat assumes a layered Earth near its surface[equation 7 of (2)]. In principle, givengravity measurements at two stations alongthe same vertical and knowing the total masssandwiched between these two stations, wecan compute the Newtonian gravitationalconstant. For the Michigan borehole, gravi-ty has been measured at various depths.After the standard corrections for instru-ment drift, tidal, and terrain effects, data ofgravity differences from the referencesurfacevalue are shown in Fig. 2. The referencesurface value, however, does not coincidewith the surface gravity value at the bore-hole site because the gravity tool was cali-brated at a Gulf Coast location for economicreasons. As a result, the gravity difference atthe surfacein Fig. 2 will not vanish. Figure 2shows that gravity increases with depth fol-lowing an almost lineartrend. At about 1.5-km depth, a small deviation from the lineartrend is noticeable. This is due to the anom-alous density associatedwith the nearby reefformation. It should be noted that both thegravity and the depth can be determined tosuch a high precision that the error bars ofthe data are within the data points them-selves in this scale. Since gravity within theborehole has been surveyed at variousdepths, G can be calculated with different

Fig. 1. Location of the State Burch #1-20 bore-hole in Michigan. Its position is at 44?10'N and8606'W.

U.S. Air Force Geophvsics Laboratory, Ilanscom AirForce Base, Bedford, MA 01731, and Earth ResoturcesLaboratorv, Department of Earth, Atmospheric, andPlanetarySciences, MassachtisettsInstituLtef Techniolo-gy, Cambridge, MA 02142.*Permanent address: Department of Geology, Universi-tv of Illinois, Urbana, IL 61801.21 AUGUST 1987 REPORTS 881

This content downloaded from 140.209.2.26 on Tue, 16 Apr 2013 10:33:04 AMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp


3/4

500

~'1,000 K

1,500

2,000OQ950 1,050 1,150

Ag (mgal)Fig. 2. Correctedgravitydiffcrence rom therefercnce urface alue (979.5609 gal) as a ftunc-tionof depth.

station separations. Choosing the upper-most station at about 43-m depth as the topstation, the averaged gravity gradient resultsare tabulated in Table 1. All error boundsgiven in this table are estimated assumingthe largest possible uncertaintiesfor all vari-ables. For the purpose of computing thegravitational constant, there should be aslittle lateralvariation as possible in geologi-cal stnictures. Therefore, stations choscn forthis study are those located above 1.3-kmdepth such that the effects of the rcef arenegligible. The effects of the reef on. thegravity measurements can be estimatedquantitatively.It produces a maximumverti-cal gravity anomaly of no more than 1 mgal.Consequently, the maximum uncertainty ingravity measuremenlt s no more than onepart in a thousand throujghout the entiresection of the borehole. For the stationsabove the reef, accuracy is expected to bemuch better.Estimation of rock masses sandwichedbetween surveying stations is carried out

based oni the density information obtainedfrom a gamma-gamma density log throughthe strata of interest. The gammna-gammadensitv instrument carriesboth a source anda detector of gamma ravs. Rock elementsinteract with gamma rays mainlv throughCompton scattering and to a lcsser degreethrough photoelectric absorption. There-fore, by measuring the intensity of gaInmaraysreceived bv the detector after they havetravcledthrough the formnation,we can esti-matc the density of the rock formation. Thieinstrument is quite insensitive to boreholefluids and the formation pore fluids. Formost of sedimentary rocks, the detectedgamma-rav ntensity is directly proportionalto the formationldensitN (12). If carefullyvcalibrated,it is a reliable instrument for themneasurement of rock-formation density.Unforttunately, gamma ravs are not able topenetrate very deeplv into rock formations.Their maximum penetration depth is nomore than 20 cm. As a result, densitiesdetermined by the gamma-gamnmadensitylog represent those of the rocks immediatelyadjacent to the borehole. The precision ofthis logging tool varies with borehole condi-tions. Density comparisons between a gam-ma-gamma log and a core sample analysisfrom another borehole (12) indicate thatover 75% of the gamma-gamma densitydeterminations are within 1% of those de-termined through core analyses. For theMichigan hole, core samples are unfortu-nately not available. In order to core a hole,the cost will be at least an order of magni-tude higher. Since the tool has been careful-ly calibrated, the gamma-gamma log is ex-pected to yield formation density to within2%. In addition to density, the gamma-gamma log, together with other borcholedata, provides detailed information aboutthe lithology of the area.Thus, by integrat-ing the gamma-gamma density togetherwitl the lithological thicknesses of individ-ual stratum [see equation 7 of (2)], the massintegral between stations can be evaluated(Table 1).Once these quantities aredetermined, theNewtonian gravitational constant can becalculated. The values associated with differ-ent station separationsare listed in Table 1.

It is evident that the gravitationialconstantdceterminedon the basis of this boreholemeasurement is higher than the laboratoryvalue (6.672 ? 0.004 x 10--" m3 kg-'-sec~-) (13). Thlese values are in generalagreement with those reported by Stacev'sgroup. Although station separationsfor thistabuLlationange from about 250 m to 1.2km, all values calculatedfor the Newtoniiangravitational constant arc within 0.2% ofeach other. There appears no apparcentlength scale dependence in G, over thisrange.To establish the validity, of this value forG, it is necessarv to examine the errorbounds of all the measurementsinvolved. Asdiscussed earlier, all gravity and positiondeterminations can be estimated to betterthan 1%. Therefore, the observed small de-viation in G cannot be accounted for bv theerrors associated with the gravity and theposition determinations. However, the samething cannot be said for the mass determina-tions. Although a carefully calibratedgam-ma-gamma density log is generally acceptedwith a high level of confidence by profes-sionals, a quantitativeaccuracyhas vet to beestablished. Even if such a density log canachieve a precision to within 1% as claimed(12), questions remain as to how repre-sentative the densitv surroundinga boreholeis of the large-scale ormation density. Thereexists no simple answer to this question.One way to prove or disprove whether asmall variation in the Newtoniani gravita-tional constan-t s real is to exanmine largenumber of data sets to see if such a consis-tently small positive deviation can be statisti-cally established. Although the G value re-ported here should not be considered con-clusive, it is intriguing to note that theresults derived from this study andthat fromthe Australianiexperiments converge to asimilarconclusion, despite the different geo-logical environments where the experimentsare carried out and despite the differenitinstrumentsused for the experimenits.

Table 1. Values for the averaged gravity gradient, the layer mass, and the calculated Newtoniangravitational constant.GravitationalStation Avcragcdtation Averaged Laycr mass coinstantseparation dgldz 2Cp.lratlOtl ~(mgal mll- (IOt' kg ml OW(1 tm'3 kg- 'sec 2)

264.5 ? 0.5 0.11640 ? 0.0080 0.69366 ? 0.014 6.6901 ? 0.0668585.5 ? 0.5 0.10226 ? 0.0036 1.52710 + 0.030 6.6837 + 0.0650886.5 + 0.5 0.09509 ? 0.0024 2.34150 + 0.050 6.6848 ? 0.06501163.5 ? 0.5 0.09456 + 0.0018 3.04620 ? 0.060 6.7000 ? 0.0650

REFERENCES AND NOTES1. CT. . Airn, Philos. Trans. R. Soc.Londoni146, 297

(1856).2. F. D. Stacey, G. J. Tuck, S. C. Holding, A. R.Malher,D. Morris, Pbvs.Rev. D 23, 1683 (1981).3. F. D. Stacey and G. J. Tuck, Natnre (London) 292,230 (1981).4. F. D. Stacev, in Proceedingsfthe WorkshopnScience

Undergronnd,Los Alamlos,NM, 1982, M. M. Nietoet al., Eds. (American Iinstitrtieof Physics Confer-ence Proceecdings 6, Americani nistittrte f Physics,New York, 1982).5. S. C. I-Inliiig and G. J. Tuick,Nature (London)307,714 (1984).6. F. D. Staccv and G. J. Tutck,in Natl. BUr. Stand.(U.S.) Spec.Phibl.No. 617, B. N. Taylor and W. D.Phillips, Eds. (U.S. Dept. of Commcrce, Washing-toIn, DC, 1984).7. S. C. Holdinig, F. D. Staceyr,C. J.Tuck, IPhets.eip.D33, 3487 (1986).

882 SCIENCE, VOL. 237



4/4

8. J.O'Hanldn,Phvs.Rev.Lett.29, 137 (1972).9. E. Fischbach,D. Sudarsky, . Szafer,C. Talmadge,S. H. Aronson, bid.56, 3 (1986).10. D. Daniels,C. Monash,G. Omnes,Resmvoir elin-eation FinalReportforState Burch #1-20 Well (Com-pagnie Generalede Geophvsique,Denver, CO,1985).11. A. J. Black,BoreholeGravitySurvev n thieState Burch#1-20 Well EDCON, Inc.,Denver,CO, 1983).12. J.Tittmanand J. S. Wahl, n GammaRay,Neutronand Densit Lo,ging, B. L. Lawson, W. A. Hover, G.R. Pickett,Eds. (Societyof ProfessionalWell LogAnalvsts,Houston,TX, 1978).13. G.G.Luther ndW. R. Towler,Phvs.Rev.Lett.48,121 (1982).14. I thankD. H. Eckhardtorstimulatingmy interest

in this problem.This work would not have beenpossiblewithout he dataprovided vthe followingindividuals:R. Turpening f the EarthResourcesLaboratorvERL)of the Massachusettsnstitute fTechnology MIT)andA. Black f EDCON,Inc.Ialso have benefited rom discussionswith D. H.Eckhardt,T. P. Roonev, C. Jekeli, and A. R.Lazarewiczf theAir ForceGeophvsicsLaboratory(AFGL),andC. H. Cheng,R. Wilkens,C. Black-wav,andJ.Mendelson f ERL/MIT.Support romtheAirForceOffice f ScientificResearchhroughresidentacultyellowship ndhospitalitiesxtendedto mebyboththeAFGLand heERL aregratefullyacknowledged.23 March1987; accepted 6 May 1987

Possible Tornado-Like Tracks on MarsJOHN A. GRANTAND PETER H. SCHULTZDistinct atmosphericconditions suggest that dark, ephemeral, filamentary ineationson the martian surface may be formed during the passage of intense atmosphericvortices.

V IKINGORBITER IMAGESREVEALwell-defined,dark filamentary in-eations in numerous ocationsonthe martianurface.Althoughsimilarmark-ings were previously nterpretedas linearseif dunes (1) or joint patterns 2), newlyrecognized haracteristics,ncludinga morecompleterecognition of their spatial andtemporaldistribution,makethese interpre-tations unlikely.The occurrence of suchlineations is controlledmore strongly byseasonal atmosphericconditions than bysurface r boundaryayerprocesses.Conse-quently, formation by tornadic-intensityvorticesmay provide he closest analogy.The filamentaryineationsare from2 kmto at least 75 km long and less than 1 kmwide. Most are straight o curvilinear, ndsome haveobvious nontopographicallvni-tiatedgaps in theirpath (Fig. 1, a and b).The lineationsare sharplydefinedand donot have resolvablerelief.Althoughsomecrosscraterwalls andother scarps, hey arenot initiatedor terminatedby such obsta-cles.Manycrisscross t relativelyow angles,and they generallyhave a similar averageorientation:east to west in the southernhemisphere,and both northeast o south-westand east to west in the northernhemi-sphere. The lineations occur on smoothintercrater lains and the floors of somecraterswhere the surfacesgenerallyappearpartiallytrippedof sedimentcover.Although he lineationsare foundat lati-tudes from about65?Sto 75?N andalmostalllongitudes Fig.2), most occur n severaldistinct locations in the southern hemi-sphere.Poorlydefined lineationswere de-

tectedonlyin isolated ocations n the northwith a generalabsence in equatorial ati-tudes.A high-resolutionmageof lineationsbetweenArgyreandHellasPlanitia Fig. 1,a and b) revealsa densityof 55 to 60 perthousand quarekilometers,probably ypi-calof the density n most areas.The occurrenceof both the lineationsobserved n this study and those observedduringMariner9 (2) depends stronglyonseason: in the southern hemisphere heywere visible only from midsummer ntoearly all.After formation heywererapidlymodified and were no longer visible bymidfall.In the northernhemisphere inea-tions appear rom earlyto midsummer.By

late summerthese lineationsalso becamesmearedand faint;subsequently,hey wentundetected.The occurrence f lineations nthe lower latitudesappears ess seasonallydependent han those at higher atitudes.Althoughgroupsof lineations ecordedn1972 by Mariner (2) redevelopedn gen,-erally he sameareas n 1976-1977, suchasbetweenArgyreand HellasPlanitia Fig.2),thespecificocationandorientation f indi-vidual ineations hanged Fig. 3). The highconcentrationof lineations near ElysiumMonsin 1972 (2) contrastswiththepaucityof lineationsobserved here n 1976-1977.The seemingly arge ractionof lineationsatlow latitudesduringMariner9 (2) reflectsthe existence f largegaps n high-resolutionimagecoveragebetween45?Sand55?S(3),where most of the lineationsduring theVikingmissionwere detected.Dark ilamentaryineationswere firstob-served 1) in a largecrater n Hellespontus(Fig. 3) and interpreted s linearseif dunesassociatedwith an adjacentdune field.Ve-verka(2) concludedthat such an analogywasunreasonable ecause he lineations i)are highly variable n time, (ii) typicallyshow a crisscrosspattern,and (iii) crosscraterwalls.He suggested hat helineationswere most consistent with an origin bypreferred rosion of, or depositionwithin,joints. We believe that this suggestion isunlikelybecause he markings i) crossfea-tures, local structuraltrends, and topo-graphicobstacleswithout deflection (Fig.1); (ii) varyin locationfrom year to year(Fig. 3); (iii) are insensitiveto regionalstructural rain; (iv) are largerthan mostterrestrial oints; (v) have grossly similarorientationson a hemisphericto global

? bsK m R,? ,ro t , +~~~-71,ICFig. 1. (a) Filan cntary lincartiOnsbcltwcn Arpgrcaindi1-iclias l iliti l .t I \\! 4'S. (b) Tclrran mapot the area Omtlincd iTl ( I) ineUtiOns cross ctraterlvalls in the di-iglt- cAtcLlportioln ot the im11age.Note the stri ppi apparanccpp t the plaints (SPl)suirroundinlg t[ic lincittions. \Viking image;541A76.Department f GeologicalSciences,BrownUniversitv,Providence, I 02912.

21 AUGUST 1987 REPORTs 883


Hsui Borehole Measurement of the Newtonian Gravitational Constant

Documents

Transcript of Hsui Borehole Measurement of the Newtonian Gravitational Constant