include the effects described here that areattributable to the large-scale surface topog-raphy. Quantitative analysis of the Clemen-tine thermal infrared imaging experimentcan begin once the instrument calibrationto radiance is completed. Incorporation ofApollo 17 infrared observations (18) willallow interpretation of surface physical prop-erties at selected locations.An important objective of the Clem-

entine program was to investigate the ef-fects of the space radiation environmenton the advanced technologies and light-weight spacecraft components beingflight-tested on board the Clementinespacecraft and the Interstage Adapter sat-ellite. A charged particle telescope (CPT)was built, tested, and integrated on boardthe main Clementine spacecraft to mea-sure the fluxes of energetic electrons andprotons encountered by the spacecraftthroughout its mission. The low-energyelectron channels (25 to 500 keV) haveprovided extensive data on the interactionbetween the moon and the Earth's mag-netotail: While orbiting the moon, theCPT saw the wake created by the moonwhen it blocked the flow of energetic par-ticles along magnetotail field lines. TheCPT has also observed numerous bursts ofenergetic electrons during geomagneticstorms and magnetospheric substorms. Aparticularly important goal of the CPTwas to measure fluxes of energetic protonsin the energy range 3 to 80 MeV, whichare emitted during solar energetic particleevents. A strong solar particle event wasobserved on 20 to 25 February 1994 andwas associated with a very strong inter-planetary shock wave passage at -0900UT on 21 February. The Clementine CPTobserved this particle event and detectedthe precise time and position of the shockpassage. The Clementine data were partic-ularly valuable because they were obtainedconcurrently with measurements from sev-eral other near-Earth spacecraft (GOES-7,SAMPEX, GEOTAIL), thus permitting aremarkable multipoint study of the shockinteraction with geospace (Fig. 8).

REFERENCES AND NOTES

1. A computer with a capacity of 1.7 million instructionsper second (MIPS) used for safemode, attitude con-trol, and housekeeping. A reduced-instruction setcomputer (RISC) 32-bit processor operating at 18MIPS was used for image processing and autono-mous operations. Also incorporated is a state-of-the-art image compression system provided by theFrench Space Agency (CNES). A data handling unitwith its own microcontroller sequenced the cameras,operated the image compression system, and di-rected the data flow. During imaging operations, thedata were stored in a 3-kg, 2-gigabit dynamic solid-state data recorder and later transferred to theground stations using a downlink operating at 128kilobits (kb) per second. The spacecraft was com-manded by a 1-kb/s uplink from the NASA DeepSpace Network and Department of Defense sta-

tions. Demonstration of autonomous navigation, in-cluding autonomous orbit determination, was a ma-jor goal of the Clementine mission. Autonomous op-erations were conducted in lunar orbit. Data com-pression was done on board by the CNEScompression chip. This processing was performedon a completed, framed image before storage on thesolid-state data recorder when the appropriate com-pression flag was set. The compression chip, devel-oped by Matra Marconi (location) under CNESspecifications, could be used in two modes, select-able by an uplink command. The first optimizedroot-mean-square error (for a nominal compres-sion). The second mode (JPEG) provided visualoptimization at a fixed compression rate. In the firstmode, blocks of 8 by 8 pixel 8-bit data are trans-formed to a best-fit cosine series expansion in theorthogonal row and column directions. This algo-rithm tends to preserve high-frequency informationwith less loss than does JPEG at the same com-pression ratio. The nominal amount of compressionwas set by limiting the scene error induced by com-pression to a fraction of the camera's temporalnoises. Analysis of lunar images during the first partof the mission showed that the quantitization matrixused by the chip was optimum for the imagingcameras. The HIRES camera was operated inJPEG mode. The high-frequency information in theHIRES scenes was spurious (it was caused by non-uniformity of the gain of the intensifier tube); elimi-nating high-frequency content allowed higher com-pression without harming the information contentof the scenes. The average compression rate for allimages obtained during the mission was 5.5.

2. P. G. Lucey et al., Science 266, 1855 (1994).3. A. S. McEwen et al., ibid., p. 1858.4. C. M. Pieters et al., ibid., p. 1844.5. E. M. Shoemaker et al., ibid., p. 1851.6. K. Watson, B. C. Murray, H. Brown, J. Geophys.

Res. 66, 3033 (1961); J. R. Arnold, ibid. 84, 5659(1979); A. P. Ingersoll, T. Svitek, B. C. Murray, Icarus100, 40 (1992).

7. P. D. Spudis et al., Science 266,1848 (1994).8. M. T. Zuber et al., ibid., p. 1839.9. B. W. Hapke, /carus 67, 246 (1986).

10. , ibid. 88, 407 (1990).11. , R. M. Nelson, W. D. Smythe, Science 260,

509 (1993).12. D. L. Domingue, B. W. Hapke, G. W. Lockwood, D.

T. Thompson, Icarus 90, 30 (1991).13. Precision is about 1 K at a surface brightness tem-

perature of 400K, 2 K at 300K, and 10K at 210 K.The DN correspondence is 100 DN to about 400 K,25 DN to 300 K, and 2DN to 200 K.

14. D. F. Winter, Radio Sci. 2,229 (1970); J. M. Saari andR. W. Shorthill, Moon 5,161 (1972); R. W. Shorthill,in Thermal Characteristics of the Moon, J. W. Lucas,Ed. (MIT Press, Cambridge, MA, 1972), pp. 3-50.

15. A. E. Wechsler, P. E. Glaser, J. A. Fountain, in Ther-mal Characteristics of the Moon, J. W. Lucas, Ed.(MIT Press, Cambridge, MA, 1972), pp. 215-242; B.M. Jakosky, in preparation.

16. P. G. Lucey, Proc. Lunar Planet. Sci. Conf. 21, 417(1991); D. B. Nash etal.,J. Geophys. Res. 98, 23535(1993).

17. P. E. Johnson, K. J. Vogler, J. P. Gardner, J. Geo-phys. Res. 98, 20825 (1993); K. V. Vogler, P. E.Johnson, R. W. Shorthill, Icarus 92, 80 (1991).

18. W. W. Mendell and F. J. Low, Moon 9, 97 (1974).19. The LWIR images had a space background sub-

tracted and had hot pixels removed by means of amedian filter. A flat field shows variations in pixelsensitivity that are much smaller than the observedgeographic variation; the flat-field variation has notbeen corrected.

16 September 1994; accepted 15 November 1994

The Shape and Internal Structure of theMoon from the Clementine Mission

Maria T. Zuber,* David E. Smith, Frank G. Lemoine,Gregory A. Neumann

Global topographic and gravitational field models derived from data collected by theClementine spacecraft reveal a new picture of the shape and internal structure of themoon. The moon exhibits a 16-kilometer range of elevation, with the greatest topographicexcursions occurring on the far side. Lunar highlands are in a state of near-isostaticcompensation, whereas impact basins display a wide range of compensation states thatdo not correlate simply with basin size or age. A global crustal thickness map revealscrustal thinning under all resolvable lunar basins. The results indicate that the structureand thermal history of the moon are more complex than was previously believed.

Though formed in the same part of thesolar system, the Earth and moon have fol-lowed dramatically different evolutionarypaths in their 4.6-billion-year histories. Ab-solute ages of the lunar surface revealed bythe Apollo missions (1) demonstrate thatvolcanism and tectonism indicative of sub-stantial heat loss from the lunar interioressentially ceased by 2.5 to 3 billion yearsago, in contrast to Earth, which remainsgeologically active to the present day. Thefundamental difference in thermal evolu-tion between the Earth and moon has typ-ically been attributed to the planets' differ-ent size and mass (2)-the moon containedfewer radiogenic heat-producing elements

SCIENCE * VOL. 266 * 16 DECEMBER 1994

because of its smaller volume and cooledfaster because of its higher surface area-to-volume ratio as compared with Earth. Be-yond this basic knowledge, however, under-standing of the thermomechanical evolu-tion of the moon has been elusive, largelybecause of limited knowledge of lunar in-ternal structure.

The Clementine mission, sponsored bythe Ballistic Missile Defense Organization,with participation from NASA, mappedthe moon from late February through earlyMay 1994 (3). Included in the spacecraftinstrument complement were a laser rang-ing device and an S-band microwave tran-sponder from which topographic and grav-

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itational information, respectively, werecollected for most of the moon. These datahold the promise of greatly improving ourunderstanding of the lunar interior. In thisreport, we describe the derivation of topo-graphic and gravitational field modelsfrom the Clementine data and use thisinformation to characterize the shape ofthe moon, define the power spectral prop-erties of the global fields, and map thedistribution of crustal thickness. We alsoaddress preliminary implications of thedata for the understanding of lunar struc-ture and evolution.

The Clementine spacecraft carried a la-ser ranging instrument (LIDAR) that mea-sured the slant range from the spacecraft tothe lunar surface at spacecraft altitudes of640 km or less (3). The instrument collect-ed data for approximately one-half hour per5-hour orbit during the 2-month lunar map-ping mission. For the first month, withspacecraft periapsis at latitude -30°, topo-graphic profiles were obtained in the ap-proximate latitude range -75° to +150,whereas in the second month of mapping,with spacecraft periapsis at latitude +30°,profiles were obtained in the approximaterange -15° to +75°.

To produce a global topographic dataset from the lidar system, we first subtract-ed a precise orbit from the range profiles.We computed these orbits with the GEO-DYN/SOLVE orbital analysis programs(4). We converted the timing of the ar-rival of the laser pulse on the lunar surfaceto selenocentric coordinates by interpolat-ing the spacecraft orbital trajectory to thetime of the laser pulse, which accountedfor the one-way light time to the surface.The observed range from the spacecraft tothe surface was transformed to a radiusmeasurement in a lunar center-of-massreference frame. Our orbits were charac-terized by a formal uncertainty in radialposition of about 10 m and have an accu-racy with respect to the lunar center ofmass of better than 100 m, which is com-parable to the single-shot ranging preci-sion of the lidar (40 m). The radial orbitaccuracy thus determines to first order theaccuracy of the global topographic model.In the topographic data set presented here,

M. T. Zuber, Department of Earth and Planetary Sci-ences, Johns Hopkins University, Baltimore, MD 21218,USA, and Laboratory for Terrestrial Physics, NASA/God-dard Space Flight Center, Greenbelt, MD 20771, USA.D. E. Smith, Laboratory for Terrestrial Physics, NASA/Goddard Space Flight Center, Greenbelt, MD 20771,USA.F. G. Lemoine, Laboratory for Terrestrial Physics, NASA/Goddard Space Flight Center, Greenbelt, MD 20771,USA, and Astronomy Department, University of Mary-land, College Park, MD 20742, USA.G. A. Neumann, Department of Earth and Planetary Sci-ences, Johns Hopkins University, Baltimore, MD 21218,USA.*To whom correspondence should be addressed.

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we did not include a correction for space-craft pointing errors, which were at themilliradian level (5) and are insignificantcompared with the instrument rangingprecision and orbit error.

The LIDAR typically ranged once per0.6 s, expending over half a million lasershots during the 2-month Clementine lunarmapping mission. The instrument detectortriggered on 19% of the shots. To distin-guish valid ranges from noise hits for these-114,000 triggers (6), we applied a Kalmanfilter based on a stochastic model of topo-graphic variance (7). We developed thefilter on the basis of the known power-spectral distribution of the topography ofthe moon (8), which made it possible topredict the likely dynamic range of topo-graphic power over a specified spatial dis-tance such as the along-track or cross-tracklaser shot spacing. Filtering the data yielded-72,300 "valid" ranges.

These data were assembled into a 20 by20 grid in the latitude range from -75° to+ 75°. Figure 1 is a location map that showsthat most major lunar basins were sampledby Clementine altimetry. The elevationswere referenced to a spheroid with a radiusof 1738 km and flattening of 1/3234.93, thelatter corresponding to the C20 sphericalharmonic term we obtained for the lunargravity field (see below). This is the ob-served dynamical flattening of the planetand is greater than the flattening for ahydrostatic ellipsoid. We did a 70th-degreeand -order spherical harmonic expansion(half-wavelength resolution -80 km) ofthe data set to yield the topographic modeldesignated Goddard Lunar TopographyModel 1 (GLTM-1) (Fig. 2A). In this andother maps, the lunar near side (the sidevisible from Earth) is on the right side ofthe figure, and the lunar far side is on theleft.

This topographic model represents thefirst reliable global characterization of sur-face heights for the moon. The moon ex-

hibits a dynamic range of topography ofabout 16 km, which is over 30% greaterthan the range noted in previous reportsbased on Apollo laser measurements andEarth-based radar and limb measurements(8, 9). This difference is due to bettercoverage: The greatest variations in lunartopography are on the far side over a broadband of latitude. Previous topographicmeasurements of the moon's far side werelimited to equatorial swaths covered bythe Apollo laser altimeters (9). WhereApollo and Clementine coverage overlap,measured relative topographic heightsgenerally agree to within -500 m, withthe difference due to our more accurateorbit corrections and to noncoincidenceof laser measurements. As was previouslynoted by the Apollo altimetry (9), Clem-entine topography shows the lava-floodedmare basins to be extremely level, withtypical slopes of less than one part in 103.

The most pronounced topographic fea-ture on the moon is the South Pole-Ait-ken Basin (180'E, 560S). With a diameterof 2500 km and a maximum depth of 8.2km below the reference ellipsoid, thisstructure was first identified in lunar im-ages (10, 11). From Clementine altimetry,we recognize this structure to be the larg-est and deepest impact basin in the solarsystem. Maria Humboltianum, Crisium,and Fecunditatis, all in the longituderange 40'E to 80'E, also constitute dis-tinctive topographic lows. The highest to-pography of 8 km above the referenceellipsoid occurs on the lunar far side in thehighlands north of the Korolev Basin(205'E, 50N), adjacent to the South Pole-Aitken structure that represents the low-est elevation on the moon.

Some structures that were suspectedancient impact basins display distinct to-pographic depressions. A notable feature isthe Mendel-Rydberg Basin (2750E, 520S),just south of Mare Orientale, which hadbeen proposed as an impact basin (1 1), but

Fig. 1. Locations of major lunar basins. Here and in Fig. 2, longitude = 2700 and the western limb of themoon as viewed from Earth is at the center front. The lunar near side is right of center and the lunar far sideis left of center.

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posed impact structure ( 1 2). However, thetopographic map does not show obviouSevidence for a previously proposed mrassive(3200 km in dliameter) nearside OceanusProcellarum basin (1 1 ).

The gravx itational signature of the

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moon waXs determined from velocity per-turbations of the Clementine spacecraft asmeasured from the Doppler shift of theS-band radio tracking signal. Clementinewas tracked by NASA's Deep Space Net-work (D)SN) at Goldstone, California,Canberra, Australia, and Madrid, Spain,as well as bN the Pomonkey, Maryland,tracking station operated by the NavalResearch Laboratory. Data from the DSNsites typically had an accuracy of 0.3s a1at 1 0-s intervals, whereas data fromthe Pomonkey site was accurate to - 3 mms The tracking data were used to deter-mine the Clementine orbit about themioon, as well as the lunar gravity field.

Clementine provided over 361,000 ob-servations, of which 57,000 were atspacecraft altitudes of less than 1000 kim,and these dlatatc now constitute the stron-gest constraint on the long-waxvelength(gravity field of the moon. We combinedthe Clementine data with nearly 294,000historical S-band tracking observationsfrom Lunar Orbiters 2, 3, 4, and 5 andfrom the Apollo 15 subsatellite (13).These spacecraft lacked the global cover-a(Ige of Clementine, but most had lowerperiapsis latitudes and thus provided dis-tributed regions of short-wavelength reso-lution in the vicinity of spacecraft pern-apses (generally +400 latitide).

In developing the grarity model, weapplied an a priori power law constraint ofthe form 15 X 10 '/l', where I is thespherical hari-nonic, degree (14). This con-straint has the effect of bounding the grav-itational powrer in the wavelengths whoseeffect on the signal is at or below the noiselevel. In addition, we judiciously down-weighted some of the low a-clltitLide data to

avoid artificial'1striping" long orbittracks in the field at short wavxelengths.These techniqrues, which we have previ-orusly applied in models of the gravityfields of Earth, Mars, and Venus (15),have the advantage of preserving short-w~cavelength inform-ation in the field,where it is well resolved by the trackingdata. Free-air grvity anomallies from our70th-degree and -order spherical harrmon-ic gravitational field model, designatedGoddard Lunar Gravity Model 1 (GLGM-1), are shown in Fig. 21.

Because of the moon's syNnchronous ro-tation, spacecraft cannot be directly trackedfrom Earth over a large part of the Ilunar farside, so there is no tracking data from 1200to 240° longitude in the ±450 latitudeband. Nonetheless, orbiting spacecraft aresensitive to the positions of gcravity anomna-lies even in areas without direct tracking, ascevidenced by numerouis anomnalies in thisregion that correlate writh maljor impact balsins. However, the magnitudes of gravityanomalies in occulted recions are character-

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details of the structure are obscured be-cause it is largely covered by Orientaleejecta. There is also a circtular depression700 km in diameter in the northwest

Ocecanus Procellaruim (300°E, 40°N), tothe southwest of another recently pro-

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ized by large errors. Gravity anomaly errorsfrom GLGM-1 ranged from 22 milli-Gali-leos (mGal) (0.22 mm s- 2 over the well-tracked near side at low latitudes to 47mGal for the high-latitude far side.We evaluated the global gravitational

field of the moon at the surface, rather thanat spacecraft altitude as done by others ( 13,16, 17). In comparison with the most re-cent pre-Clementine gravity model ofKonopliv and colleagues (13), GLGM-1shows an -10% greater range of anomalieswhen evaluated at an altitude of 100 kmand, in addition, resolves some high-lati-tude farside structures not present in thatmodel.

Figure 2B shows in red the gravityhighs or "mascons" that correlate with themajor nearside basins. The mascons,which were first recognized from LunarOrbiter tracking data (18), are believed tobe a consequence of the gravitational at-traction of lava fill in mare basins (19)and of uplifted mantle beneath the basins(20). The improved short-wavelengthcontrol in our representation of the field,however, reveals that many of the mas-cons are ringed by negative anomalies out-side the basins that suggest flexure of thelunar lithosphere in response to loading bythe fill of mare lavas and uplifted mantledue to the impact process (21). Our modelalso shows gravitational signatures of sev-eral farside basins that have not previouslybeen resolved or well resolved, includingHertzprung (232YE, 1PN), Korolev(203YE, 4CS), Mendeleev (1410E, 60N),Freundlich-Sharonov (1750E, 18'N), andMoscoviense (1470E, 260N).

Figure 2B shows that, as in previouslunar gravity models, the highland terrainsare gravitationally smooth, indicating astate of isostatic compensation. For surfacetopography that is isostatically compensat-ed, pressures caused by the weight of over-lying rock balance at some depth beneaththe surface. Isostatic equilibrium repre-sents the state into which planetary topog-raphy tends to evolve with time and isindicated by a near-zero free-air gravityanomaly. In contrast to the highlands,lunar basins display a broad range of com-pensation states. Nearside mascon basins,which display large free-air positive anom-alies, are distinctly uncompensated. Theirgravitational signature indicates that sur-face topography is supported flexurally anddemonstrates that in the vicinity of theseimpact structures, the lunar lithosphere(that is, the rigid outer shell) has displayedconsiderable strength since the time ofloading (22). In contrast, the South Pole-Aitken Basin on the lunar far side has amodest free-air anomaly for its depth andis approximately 90% compensated. The5-km-deep Mendel-Rydberg Basin shows a

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very small 25-mGal free-air anomaly andis almost fully compensated. Compensa-tion states do not correlate simply withbasin size or age. The range of compensa-tion states of lunar basins indicates thatthe strength of the lunar lithosphere waslikely to have been characterized bymarked spatial variability at the timewhen the major basins formed and weresubsequently flooded with mare basalts,and implies a complex lunar thermal his-tory. Variations in the population of im-pactors (size, incidence angle, and veloci-ty) could also contribute to the variablecompensation states.

Figure 2B shows a marked asymmetry inthe free-air gravitational signature of MareOrientale, the youngest major impact basinon the moon (age, -3.8 billion years) (1 1).This basin exhibits a comparatively modest125-mGal mascon at basin center that issurrounded by a horseshoe-shaped gravitylow with a maximum amplitude of -225mGal centered on the inner and outer Rookrings. In contrast to the nearside basins thatare encircled by negative anomalies outsidethe basins, the discontinuous negative isinside the Orientale Basin, and the basin isbounded by a gravity high centered on theCordillera ring. Earlier studies have recog-nized a "bull's-eye" appearance of Orien-tale's gravity signature (13, 17, 23), butcareful consideration of low-altitude orbitalpasses shows that the asymmetry is a char-acteristic feature of the basin.

To interpret the global topographicand gravitational observations in the con-text of lunar internal structure, we calcu-lated Bouguer gravity anomalies (Fig. 2C),in which the gravitational attraction ofsurface topography (assuming a crustaldensity p, = 2800 kg m- 3) is subtractedfrom the free-air anomaly to reveal thesubsurface density distribution. Bougueranomalies for the moon have previouslybeen calculated both globally (8) and formajor mare basins (17, 24), but detailedanalyses have been limited because of er-rors of 12 to 70 mGal in the Bouguercorrection that are due to the uncertaintyof topographic knowledge. The relativeerrors in Clementine topography are gov-erned by the orbit-to-orbit repeatability, oforder 10 m, which translates to a 5-mGalerror in the Bouguer anomaly, and by theprecision of the altimeter system in bothrange and time, which is of order 10 mGal.In comparison with the errors in the gravityfield discussed above, it is clear that Bouguergravity errors are dominated by gravity error,in contrast to pre-Clementine analyses, inwhich Bouguer gravity error was dominatedby errors in topography.

The simplest plausible interpretation ofthe Bouguer map is that subsurface massdifferences are solely a consequence of

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crustal thickness variations. This interpre-tation is an oversimplification, but it pro-vides a useful first-order indication of thevariability of lunar internal structure. Wehave calculated uncorrected crustal thick-nesses from the Bouguer gravity, assuming areference value of 64 km in order to matchthe thickness of 56 km at the Apollo 12 and14 sites (25). Figure 2D shows a degree 70(80-km half-wavelength) resolution effec-tive crustal thickness map in which weassume a constant-density crust and mantle(Pm = 3300 kg m-3). For our assumedreference value, the crust composes 11% oflunar volume. The attraction of mare fillproduces an error in crustal thickness oforder 20% in flooded basins, and we haveneglected this correction in making theglobal map.

Figure 2C shows that the farside crust is,on average, thicker (68 km) than that onthe near side (60 km). The minimum crust-al thickness is near zero beneath the MareCrisium, with other notable areas of thincrust including the Orientale (4 km),Smythii (15 km), and South Pole-Aitken(20 km) basins. All resolvable lunar basinsexhibit varying degrees of crustal thinning,which is likely the consequence of excava-tion and mantle rebound associated withthe impact process (17, 26). The thickestcrust (107 km) is on the far side in thevicinity of the Korolev Basin (also the re-gion of highest topography), though on the

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nearside southern hemisphere (3OWS, 30WE)the crustal thickness reaches 95 km. Theregion of thick crust on the far side contrib-utes substantially to the moon's center ofmass-center of figure offset (9, 27), whichwe have recomputed from the spherical har-monic power spectra of gravity and topog-raphy and find to be 1.68 km + 50 m in theEarth-moon direction, with the center ofmass closer to Earth.

If the average farside crustal thickness isassumed, the area of anomalously thickcrust on the far side has a volume compa-rable to that of the adjacent South Pole-Aitken Basin. This observation raises theintriguing question of whether the majortopographic variation on the lunar far sideis a consequence solely of enhanced meltingrelated to the lunar magma ocean (to formthe highland) or alternatively due to a com-bination of this process and impact ejectafrom the South Pole-Aitken Basin or otherbasins or both.

Finally, in Fig. 3, we examine the globalspectral properties of the moon by calculat-ing admittance and coherence, which arepower-spectral ratios of geoid (gravitationalpotential) and topography (28) that containinformation about isostatic compensationmechanisms as a function of spatial wave-length. The degree 2 spherical harmonicterms show unusually low coherence relatedto long-wavelength complexities associatedwith the lunar flattening and the SouthPole-Aitken Basin. Between spatial scales of2000 km and 600 km (degrees 3 to 9) thereis significant coherence and decreasing ad-mittance. Features in this range include thelunar highlands and the largest impact ba-sins. The negative admittance at degree 10likely occurs because this wavelength isdominated by mare basins that are charac-terized by geoid highs and topographic lows.For features of spatial scale 500 km andsmaller (degrees greater than 10), the geoidand topography are uncorrelated. In thiswavelength range, most surface topographyis supported by the strength of the lunarlithosphere, and the processes that producedtopography and geoid anomalies do not re-sult in simple global correlations of thesequantities.

Figure 3A also shows the predicted ad-mittance for a model with a linear isostaticresponse (28), with the assumption of com-pensation by an Airy mechanism at depthsof 25, 50, and 100 km. In an Airy mecha-nism, topography is supported at a givendepth by constant density columns of vary-ing thickness (such as crustal thicknessvariations). The poor fit of the observedadmittance to the model indicates that,unlike the case with other terrestrial planets(29, 30), there is no single Airy compensa-tion depth that characterizes any wave-length range on the moon. Even at the

longest wavelengths, which are typicallyAiry-compensated, lunar topography ap-pears to be supported by multiple compen-sation mechanisms. For example, highlandcrust produced by the lunar magma oceanmay be supported by density variations deepin the mantle, whereas some large basinsmay be compensated by shallower crustalthickness variations, and other basins maybe uncompensated and supported by thestrength of the moon's rigid outer shell. Theglobal spectral character of the moon istherefore consistent with the full range ofbasin compensation states discussed above.

Several pre-Clementine studies have ar-gued for a relatively "quiet" lunar stress stateon the basis of the observed range of topog-raphy (31 ) and the power in the gravitation-al potential (29) as compared with Earth.These studies assumed that stresses arisesolely from surface topography and that thegravity field is a consequence of topographythat is Airy-compensated, even at wave-lengths corresponding to major basins. How-ever, we have shown that many of thesebasins are clearly uncompensated. Further,Clementine data have revealed more powerin the lunar topographic and gravitationalfields at long wavelengths and, in addition,show that large subsurface density variationscontribute substantially to the gravity fieldover a range of wavelengths. These resultsindicate that the lunar lithosphere supportsrelatively large elastic stresses. Simple scal-ing relations of the power in the terrestrialand lunar gravity fields would suggest thatthe lunar stress state is much greater thanpreviously thought, though long-wavelengthstresses on Earth are mostly a consequenceof mantle dynamics rather than of subsur-face density variations as on the moon.

Topography and gravity from Clemen-tine thus reveal a richer complexity in lunarstructure and thermal history than had beenpreviously appreciated. Detailed analysis ofthe global shape and modeling of individualfeatures will provide further clarification ofthe nature of lunar evolution.

REFERENCES AND NOTES

1 5. R. Taylor, Planetary Science: A Lunar Perspective(Lunar and Planetary Institute, Houston, TX, 1982).

2. W. M. Kaula, Icarus 26,1 (1975); J. W. Head and S.C. Solomon, Science 213, 62 (1981).

3. S. Nozette et al., Science 266, 1835 (1994).4. B. H. Putney, The National Geodetic Satellite Pro-

gram, General Theory for Dynamic Satellite Geodesy(1977); J. J. McCarthy et al., NASA/Goddard SpaceFlight Center and Hughes/STX contractor report,GEODYN systems descriptions and operationsmanuals (1994). The GEODYN programs numericallyintegrate the spacecraft cartesian state and force-model partial derivatives by use of a high-order pre-dictor-corrector model. The force model includes aspherical harmonic representation of the lunar andterrestrial gravity fields; point mass representationsfor the sun and other planets; lunar tides; and rela-tivistic effects. Solar radiation pressure, tracking sta-tion measurement biases, and the elements of theorbit state are estimated for each data arc.

5. P. A. Regeon, R. J. Chapman, R. Baugh, Int. Acad.Astron. IAA-L-0501, 1 (1994).

6. The LIDAR contained a multistop detector that re-corded the first trigger before and after the rangewindow and up to four triggers inside the window,thus accepting up to four false triggers per shot dueto either electronic instrument noise or backgroundradiation at the laser wavelength.

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8. B. G. Bills and A. J. Ferrari, Icarus 31, 244 (1977).9. W. M. Kaula, G. Schubert, R. E. Lingenfelter, W. L.

Sjogren, W. R. Wollenhaupt, Proc. Lunar Sci. Conf.3, 2189 (1972); ibid. 4, 2811 (1973); Proc. LunarPlanet. Sci. Conf. 5, 3049 (1974).

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11. D. E. Wilhelms, U.S. Geol. Surv. Prof. Pap. 1348(1987).

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13. A. S. Konopliv, W. L. Sjogren, R. N. Wimberly, R. A.Cook, V. Alwar, "A high resolution lunar gravity fieldand predicted orbit behavior," AIM AstrodynamicsSpecialist Conference, Victoria, B.C., Canada, 1993,pp. 93-622.

14. W. M. Kaula, Theory of Satellite Geodesy (Blaisdell,Waltham, MA, 1966).

15. J. G. Marsh, et al., J. Geophys. Res. 95, 22043(1990); D. E. Smith etal., ibid. 98, 20871 (1993); R.S. Nerem, J. McNamee, B. G. Bills, Geophys. Res.Lett. 20, 599 (1993).

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17. S. R. Bratt, S. C. Solomon, J. W. Head, C. H.Thurber, ibid. 90, 3049 (1985).

18. P. M. Muller and W. L. Sjogren, Science 161, 680(1968).

19. R. J. Phillips, J. E. Conel, E. A. Abbot, W. L. Sjogren,J. B. Morton, J. Geophys. Res. 77, 7106 (1972).

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21. A simple calculation for a line load on a linear elasticplate, matching the radial positions of the maximumlow and the transition from positive to negativeanomalies, yields an elastic thickness for Mare im-brium of 35 km.

22. S. C. Solomon and J. W. Head, J. Geophys. Res. 84,1667 (1979); Rev. Geophys. 18,107 (1980).

23. W. L. Sjogren and J. C. Smith, Proc. LunarSci. Cont.3, 2639 (1976).

24. R. J. Phillips and J. Dvorak, Proc. Lunar Planet. Sci.Conf. 12, 91 (1981).

25. Y. Nakamura et al., ibid. 10, 2299 (1979); N. R.Goins, A. M. Dainty, M. N. Toksoz, J. Geophys. Res.86, 5061 (1981).

26. H. J. Melosh, Impact Cratering: A Geologic Process(Oxford Univ. Press, New York, 1989).

27. W. L. Sjogren and W. R. Wollenhaupt, Moon 15,143(1976).

28. B. G. Bills and M. Kobrick, J. Geophys. Res. 90, 827(1985).

29. R. J. Phillips and K. Lambeck, Rev. Geophys. 18, 27(1980).

30. A. B. Kucinskas and D. L. Turcotte, Icarus, in press.31. W. M. Kaula, M. J. Drake, J. W. Head, in Satellites, J.

A. Burns and M. S. Matthews, Eds. (Univ. of ArizonaPress, Tucson, 1986), pp. 581-629.

32. We are grateful to P. Rustan and the Clementinespacecraft, mission operations, and instrument en-gineers for outstanding support during the lunarmapping mission. We also thank 1. Lewis and R.Reisse for assistance in understanding the lidar rang-ing data, D. Rowlands for modifying the GEODYNsoftware for lunar orbiting spacecraft, A. Konoplivand W. Sjogren for providing the raw Lunar Orbitertracking data, and A. Brenner, G. Elman, S. Fricke,and N. Paviis for assistance in processing the track-ing and altimetry data. We also thank B. Bills forhelpful discussions and W. Kaula and S. Solomon forconstructive reviews. The software used in this studywas developed in support of the NASA Mars Observ-er and Mars Global Surveyor projects.25 July 1994; accepted 1 November 1994

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