SEAFLOOR TECTONIC FABRIC FROM SATELLITE ALTIMETRY 1

P1: ARK/ary P2: ARK/dat QC: ARK

March 5, 1998 4:35 Annual Reviews AR055-19

Annu. Rev. Earth Planet. Sci. 1998. 26:697–738

SEAFLOOR TECTONIC FABRICFROM SATELLITE ALTIMETRY1

Walter H. F. SmithLaboratory for Satellite Altimetry, National Oceanic and Atmospheric Administration,Silver Spring, Maryland 20910; e-mail: [email protected]

KEY WORDS: gravity anomalies, seafloor spreading rate, seamount, roughness, global

ABSTRACT

Ocean floor structures with horizontal scales of 10 to a few hundred kilometers andvertical scales of 100 m or more generate sea surface gravity anomalies observ-able with satellite altimetry. Prior to 1990, altimeter data resolved only tectoniclineaments, some seamounts, and some aspects of mid-ocean ridge structure.New altimeter data available since mid-1995 resolve 10-km–scale structures overnearly all the world’s oceans. These data are the basis of new global bathymetricmaps and have been interpreted as exhibiting complexities in the sea floor spread-ing process including ridge jumps, propagating rifts, and variations in magmasupply. This chapter reviews the satellite altimetry technique and its resolution oftectonic structures, gives examples of intriguing tectonic phenomena, and showsthat structures as small as abyssal hills are partially resolved. A new result ob-tained here is that the amplitude of the fine-scale (10–80 km) roughness of oldocean floor is spreading-rate dependent in the same way that it is at mid-oceanridges, suggesting that fine-scale tectonic fabric is generated nearly exclusivelyby ridge-axis processes.

INTRODUCTION

A variety of tectonic processes create, modify, and recycle the oceanic crustand lithosphere, generating topography on the ocean floor and lateral densityvariations below the sea floor at a variety of spatial scales. This topographyand structure can produce small (10−6 to 10−4) anomalies in the magnitudeand direction of Earth’s gravity field at the sea surface. Gravity anomalies

1The US Government has the right to retain a nonexclusive, royalty-free license in and to anycopyright covering this paper.

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are manifest in ocean surface topography because the ocean surface closely(typically within 2%) follows a surface of constant gravitational potential energycalled the geoid. The ocean surface topography can be measured by Earth-orbiting spacecraft in a technique known as satellite altimetry.

Correlation between seafloor tectonic fabric and sea surface gravity anoma-lies is expected only over a limited wavelength band: Phenomena termedupward continuation and isostatic equilibrium limit the correlation to wave-lengths not shorter than a few times the average water depth in a region and notlonger than a few times the typical lithosphere thickness, respectively. Longer-wavelength anomalies are ascribed to sublithospheric processes such as man-tle convection, and while these processes might be considered tectonic, inter-pretation of these anomalies is not straightforward, as there are a variety oftemperature and viscosity variations that might produce them. Under typicalconditions, 20 km is the shortest wavelength resolvable by altimetry, whichmeans that structures of a 10-km scale (half the wavelength) can be seen. Forthe purpose of this paper, I define the “tectonic fabric band” as wavelengthsfrom 20 km to a few hundred kilometers.

Geophysical survey data collected by ships while they are underway usuallyinclude not only gravity measurements but also depth and other observable vari-ables, many of which resolve structural scales smaller than 10 km. However,the existing ship data are of variable quality and are irregularly and sparselydistributed (Wessel & Watts 1988, Smith 1993), with gaps of hundreds of kilo-meters between surveys. The peer review system’s emphasis on hypothesistesting has the effect of encouraging the deployment of vessels to previouslysurveyed areas, with the result that hypotheses are based on a limited set of local-ities. The value of satellite altimeter data for tectonic studies is not the claritywith which individual structures are imaged, but the fact that the techniqueprovides nearly global coverage with essentially uniform resolution. Satellitealtimetry can reveal the global distribution of many phenomena and thus iden-tify particular localities where hypotheses may be put to the strongest tests. Arecent example is the use of altimetry for reconnaissance of mid-ocean ridges inthe Southern Ocean to select sites for testing hypotheses that were initially de-veloped from data acquired along the Mid-Atlantic Ridge and East Pacific Rise(see abstracts in sessions T11A, T12A, and T22E of the 1995 Fall Meeting ofthe American Geophysical Union). While a state-of-the-art ship survey cover-ing the oceans would take 125 years and cost 109 dollars (Brown et al 1995), analtimeter satellite can survey the entire ocean at sufficient resolution to resolvethe tectonic band in about 1 year; these satellite programs typically last 5 yearsand cost a few times 107 dollars. Therefore I expect that satellite altimeter datawill have enormous reconnaissance value in marine tectonic studies.

Altimeter data available prior to late 1986 offered only partial resolution ofthe tectonic band. Profiles along satellite ground tracks resolved wavelengths

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SEAFLOOR TECTONIC FABRIC 699

exceeding 50–80 km, and the track spacing limited the resolution betweenprofiles to 160 km; applications were restricted to studies of the isostatic com-pensation of large structures, recognition of major tectonic lineaments, andthe discovery of seamounts large enough and close enough to profiles to bedetectable. Since late 1986, altimeter data have yielded high-resolution (20-to 30-km wavelength) profiles, but unfortunately (from the tectonic point ofview), these have been acquired primarily in “exact repeat” orbits that period-ically resurvey a limited set of widely spaced (80–315 km) tracks. When alldata are combined, gaps of 40 km by 100 km remain, leaving an anisotropicsituation with excellent “along-track” resolution and poor “across-track” reso-lution. Sandwell (1991) reported on geophysical applications of altimeter datapublished in the 1987–1990 period.

Two altimeters have flown in “geodetic” orbits that yield a dense network ofprofiles sufficient for essentially isotropic resolution of the entire tectonic fabricband: the 1985–1986 “Geodetic Mission” (GM) of the US Navy’s GEOSATspacecraft and the 1994–1995 “Geodetic Phases I and II” of the EuropeanSpace Agency’s (ESA) ERS-1 satellite. The GM data were originally classifiedas secret because of their military value; data south of 60◦S latitude weredeclassified in late 1990, and data south of 30◦S in late 1992. However, theentire GM data set was not released until July 1995, after ERS-1 had completedits unclassified mapping in March of that year. Future altimeter missions areplanned, but these will follow their predecessors’ exact repeat orbits, so allforeseeable geodetic altimeter data are now available. Figure 1 shows theprofile networks obtained from the geodetic missions and related exact repeatmissions.

Gravity fields developed after the 60◦S declassification (Sandwell 1992,Marks & McAdoo 1992) and again after the 30◦S declassification (Sandwell &Smith 1992, Marks et al 1993) had a wavelength resolution (in the area of densedata) of 26 km with a precision of 7 mGal (Neumann et al 1993) [1 milli-Galileo(mGal)= 10−5 m/s2, or 10−6 of average gravity], which is adequate for recog-nition of many new features, including abyssal hills and variations in crustalstructure generated by transient, episodic, and/or chaotic or unstable phenomenaat mid-ocean ridges. Examples are shown in Figures 2–5 and discussed furtherlater in this article. Interpretation of these anomalies was initially hampered bythe fact that many of the conventional shipboard data available in the SouthernOcean are of poor quality and very sparsely distributed (Smith 1993). However,propagating rifts (Phipps Morgan & Sandwell 1994) and nontransform offsets(Lonsdale 1994), ridge-hotspot interactions (Small 1995), disorganized back-arc spreading (Livermore et al 1994), small (20 km) ridge jumps (Marks &Stock 1995), and small-scale (25 km) spreading-rate–dependent tectonic fabric(Small & Sandwell 1994, Marks & Stock 1994, Phipps Morgan & Parmentier1995, Sahabi et al 1996) were described. Phipps Morgan & Parmentier (1995)

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https://www.researchgate.net/publication/223721668_Scotia_Sea_tectonics_from_high-resolution_satellite_gravity?el=1_x_8&enrichId=rgreq-19473f35-1773-48cd-ae37-dd3902546da4&enrichSource=Y292ZXJQYWdlOzIyODgwODg5MDtBUzoxMDY1MDYzODUxMDA4MDlAMTQwMjQwNDUwOTg4OA==

https://www.researchgate.net/publication/248794321_On_the_Accuracy_of_Digital_Bathymetric_Data?el=1_x_8&enrichId=rgreq-19473f35-1773-48cd-ae37-dd3902546da4&enrichSource=Y292ZXJQYWdlOzIyODgwODg5MDtBUzoxMDY1MDYzODUxMDA4MDlAMTQwMjQwNDUwOTg4OA==

https://www.researchgate.net/publication/248794881_Geomorphology_and_structural_segmentation_of_the_crest_of_the_southern_(Pacific-Antarctic)_East_Pacific_Rise?el=1_x_8&enrichId=rgreq-19473f35-1773-48cd-ae37-dd3902546da4&enrichSource=Y292ZXJQYWdlOzIyODgwODg5MDtBUzoxMDY1MDYzODUxMDA4MDlAMTQwMjQwNDUwOTg4OA==

https://www.researchgate.net/publication/259049541_Observation_of_ridge-hotspot_interactions_in_the_Southern_Ocean?el=1_x_8&enrichId=rgreq-19473f35-1773-48cd-ae37-dd3902546da4&enrichSource=Y292ZXJQYWdlOzIyODgwODg5MDtBUzoxMDY1MDYzODUxMDA4MDlAMTQwMjQwNDUwOTg4OA==



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Figure 1 Example of the ground track coverage available from the GEOSAT and ERS-1 satellitesin the vicinity of the Hawaiian Islands, after Sandwell & Smith (1997). Each orbit pattern is shownindividually in swaths of 2.5◦ latitude for clarity, although all are combined globally to form asolution. Top to bottom: GEOSAT ERM, GEOSAT GM, ERS-1 Geodetic Phases I and II, ERS-135-day repeat orbit. Data are missing near coasts because of loss of track (discussed in text); theloss is extended further off the coast by along-track filters used in processing.

interpret a new fabric they call crenulated seafloor as evidence for stationaryand/or migratory localized centers of upwelling magma beneath ridges. A to-pographic map of the Southern Ocean was synthesized from a combinationof shipboard depth soundings and altimeter data (Smith & Sandwell 1994a,b).New oceanographic explorations were stimulated and/or aided by these gravityand topography images (Lonsdale 1994, Macario et al 1994, West et al 1994,Devey et al 1995, Geli et al 1996, Sahabi et al 1996).

When geodetic data became globally available in mid-1995, a new gravityfield combining all GEOSAT and ERS-1 data was produced (Smith & Sandwell1995a) using an optimized filtering and processing scheme (Smith et al 1993,Yale et al 1995, Sandwell & Smith 1997). A digital data file and map images areavailable over the Internet (http://topex.ucsd.edu/marinegrav/margrav.html),and a printed map is also available (Sandwell & Smith 1995). Synthetic seafloortopography has also been estimated (Smith & Sandwell 1997b) by a methodthat improves upon the earlier technique (Smith & Sandwell 1994a), a map hasbeen printed (Smith & Sandwell 1997a), and data and images are also available

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Figure 2 Three views of the Pacific Antarctic Ridge from satellite gravity.Top: Gravity anomaliesderived from SEASAT data by Haxby (1987).Middle: Gravity anomalies derived from GEOSATand ERS-1 data by Sandwell & Smith (1997).Bottom: Vertical gravity gradient∂g/∂z of the datain themiddle panelenhances imaging of tectonic fabric.

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Figure 3 Three views of seafloor depth in the same area as Figure 2.Top: Traditional bathymetriccontours (solid lines) and track control (dashed lines) from the General Bathymetric Chart of theOceans (GEBCO) (Jones et al 1997).Middle: ETOPO-5 depth estimates at grid values interpolatedfrom contour charts by the US Navy (National Geophysical Data Center 1988).Bottom: Depthestimates obtained by combining satellite altimetry with shipboard sounding data (Sandwell &Smith 1994a).

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Figure 4 Three characterizations of seafloor tectonic fabric for the area of Figures 2 and 3.Top:Lineations selected and digitized by Gahagan et al (1988) from SEASAT and GEOSAT ERM data.Middle: Structural highs found by paintingblack the areas where∂g/∂z> 5 Eotvos in Figure 2.Bottom: Structural lows found in the same way by paintingblackareas where∂g/∂z<−5 Eotvos.

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Figure 5 Key to new kinds of tectonic fabric recently recognized in altimeter data. Pacific-Antarctic Ridge runs fromupper rightto lower left, with a small propagating rift trace seen in thestructural low map at P. The Hollister Ridge, a shallow, narrow, linear, active volcanic ridge, is atH near the intersection of the Pacific-Antarctic Ridge with the Heezen and Tharp Fracture Zonesof the Eltanin Fracture Zone system. Chaotically wandering structures are found at C.Inside thegray area, ridge axis offsets are few and fabric is smooth, although perhaps regularly crenulated,with few fracture zones or other traces of axial offsets, whereasoutside the gray area, the oppositeis true; this transition has propagated southwest along the ridge.

(http://topex.ucsd.edu/marinetopo/martopo.html). Both the gravity (Marks1996, Sandwell & Smith 1997) and the topography (Smith & Sandwell 1997b)have been verified by comparison with shipboard data. The gravity field hasa precision of 3–6 mGal and a nearly isotropic resolution to wavelengths ofapproximately 22 km, so that it reveals virtually all seafloor tectonic featureswith a horizontal scale of 10 km to a few hundred kilometers. The derivedtopography is similarly limited to a 10-km resolution with a precision of 250 min worst-case areas. Both data types show that the new tectonic fabric previouslydescribed in the Southern Ocean can be found globally.

Because these satellite altimeter data are so new, published interpretationsof this fabric are few and some are speculative. A review and synthesis ofpublished literature would be premature at this time. I hope that many morescientists will investigate the tectonic fabric revealed in the altimeter data. Thisarticle is intended to equip the reader with the concepts, definitions of terms, andtechnical overview necessary to make judicious quantitative use of these data.From the many papers on satellite altimetry in the oceanographic, geodetic,and aerospace engineering literature, I distill a tutorial that explains the issuesgoverning the resolution of tectonic fabric. I also explain why the techniques

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that are most successful in mapping tectonic fabric are different in key respectsfrom those developed for classical geodesy. More general introductions toaltimetry can be found in Stewart (1985) and Zlotnicki (1994). The literatureinterpreting marine gravity anomalies is also extensive but more familiar, so Ionly briefly review how upward continuation and isostasy limit the extent of thetectonic fabric band and how they suggest filtering strategies to isolate gravitysignals in that band. I then demonstrate that the global variation of tectonic-band gravity amplitudes has the same variation with seafloor spreading ratethat was earlier observed for anomalies over ridge axes (Small & Sandwell1989). From this observation, I conjecture that most of the structure in thetectonic band is generated by axial processes. Finally, I tour through a fewareas and topics of research interest, reviewing the history of their explorationby altimetry and demonstrating the new details that are now revealed. In thecourse of this discussion, I refer to gravity anomalies by names that are strictlydefined on the basis of bathymetric data, e.g. “fracture zone”; I trust that puristswill indulge this lapse.

THE ELLIPSOID, GEOID, ANOMALOUS GRAVITYFIELD, DYNAMIC HEIGHT, AND OTHER SEASURFACE HEIGHT SIGNALS

Geoid and EllipsoidIf there were no Sun and Moon producing tides, and if the fluid masses in theatmosphere and oceans were to cease their motions over the solid Earth andcome to rest so that the entire mass of the Earth rotated uniformly, equilibriumwould require that surfaces of constant pressure in the fluids coincide withsurfaces of constant gravitational potential energy. The surface at the interfacebetween the atmosphere and the ocean (“sea level”) would lie upon a particulargravity equipotential called the geoid. If the entire Earth were a uniformlyrotating fluid of uniform density, then one possible shape for the geoid wouldbe an oblate ellipsoid of revolution. A reference field (Moritz 1980) defines anexpected ellipsoidal shape and gravity field for the Earth, including the expecteddirection of gravity (normal to the ellipsoid at its surface) and the expectedmagnitude of gravity on the ellipsoidal surface,γ, which is approximately9.8 m/s2 but varies with latitude by a few parts per thousand.

Anomalous Gravity FieldEarth’s actual gravity field differs from that of the reference field. The geoidis displaced from the ellipsoid by an amountN that is variously called thegeoid undulation, geoid height, or geoid anomaly.N has extremes of±100 mand a root-mean-square (rms) average value over the Earth’s surface of 36 m

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(equation 5-14 of Kaula 1966), or 5 parts per million of the Earth’s radius. Theamplitude spectrum of the geoid is “red”; amplitudes increase as wavelengthsincrease and, at long wavelengths, are approximately proportional to the squareof the wavelength (equation 5-15 of Kaula 1966). The magnitude of actualgravity on the geoid (i.e. at sea level) differs fromγ by an amountg knownas the gravity anomaly;g has extremes of±400 mGal and an rms of 35 mGal(Kaula 1959). The actual direction of gravity is perpendicular to the geoid, notthe ellipsoid, and the angular difference of these two directions has componentsη in the east direction andξ in the north direction, which are called deflectionsof the vertical. These are conveniently measured in microradians [1µrad =10−6 radians (rad), or 1 mm change in geoid height over 1 km of horizontaldistance]. A negativeη indicates a slope of the geoid upward to the east, anda negativeξ indicates a slope of the geoid upward to the north (Heiskanen &Moritz 1967, section 2.13). Below I suggest that the rms ofη andξ may be onthe order of 25µrad.

Dynamic TopographyOver time scales longer than a week and length scales longer than 30 km,ocean currents are in a quasigeostrophic balance with a “dynamic topography,”ζ (Nerem & Koblinsky 1994).ζ is a displacement of the sea surface from thegeoid, and surface current velocities are both proportional and perpendicular tothe gradient ofζ to the first order; the proportionality factor depends on latitudethrough the Coriolis parameter. (At the Equator, the Coriolis parameter is zero,but the balance holds if expressed to the second order.) The peak-to-peakvariation inζ is about±1 m, and gradients inζ are largest across the mostenergetic western boundary currents, whereζ can change by 1 m over a distanceof approximately 100 km.

A long-term (1 year or more, to remove seasonal variation) average ofζ iscalled a mean dynamic height,ζ . ζ can be estimated from a history of oceantemperature and salinity (Levitus 1982); it has an rms of 60–80 cm (Engelis1987) and a spectrum parallel to the geoid spectrum (Wagner 1979), so thatthe amplitude ofζ is 45–60 times smaller thanN at all wavelengths. Therelationship betweenζ andN is less easily evaluated because the strength ofboth signals varies spatially; the amplitude ofζ is less thanN at all wavelengthsgreater than the limiting resolution of the altimeter, but the spectrum ofζ maybe less red than that ofN (Wagner 1979, Brown et al 1983, Marks & Sailor1986, Sandwell & McAdoo 1990, Yale et al 1995).

Other Sea Surface Height SignalsThe tides in the open ocean are small (20–40 cm) and long wavelength (20,000km), but in some shallow seas and near-shore areas, their amplitudes can exceed

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10 m and they can vary significantly over scales of 100 km. The tidal signal inaltimeter data includes the solid Earth’s response to the attractions of the Sunand Moon and to loading by the water tide, the hydrodynamic interaction of thewater and the solid Earth, and the tide’s effect on the satellite’s orbit; modelsfor these effects agree with tide gauge measurements of sea level to an rms of3 cm (Andersen et al 1995).

The response of the sea surface to atmospheric pressure variations is compli-cated (Ponte et al 1991) but is often assumed to be an instantaneous and localone, so that the ocean surface acts as an “inverted barometer.” In this approx-imation, pressure variations produce sea level changes on the order of 50 cmover 1000-km scales, with larger values over shorter distances in severe storms.

SATELLITE ALTIMETER MEASUREMENTSOF SEA SURFACE HEIGHT

The Altimeter Sea Surface HeightSatellite altimeters measure the sea surface height above the ellipsoid, which isthe sum ofN, ζ , and the barometric and tidal responses of the ocean. At wave-lengths shorter than 2000 km or so, geoid heights determined independently ofaltimetry are not accurate enough to allow separation ofN fromζ in the altimeterdata (Nerem et al 1995). BecauseN is essentially constant, satellites operatedin “exact repeat” orbits allow oceanographers to observe temporal variationsin ζ without knowledge ofN. For tectonic fabric studies, variations inN overthe wavelengths in the tectonic band are needed, and the other sources of seasurface height are potential sources of error. What is “signal” in one context is“noise” in the other.

History of AltimetryA program of geodesy and oceanography utilitizing altimeter satellites wasarticulated for the US National Aeronautics and Space Administration (NASA)by Kaula et al (1970). Initial tests were made on board NASA’s Skylab (Leitao& McGoogan 1975, Marsh et al 1975, McGoogan et al 1975). NASA thenoperated GEOS-3 (1975–1978), which carried an altimeter capable of 20- to40-cm precision (Stanley1979a, Tapley et al 1982). Stanley (1979b) collectedpapers giving some scientific results of that mission. NASA followed GEOS-3with SEASAT (1978), which had an 8- to 10-cm altimeter (Lame & Born 1982).Although SEASAT failed prematurely after only 3 months in orbit, many resultswere obtained; collected papers can be found in Bernstein (1982) and Kirwanet al (1983).

Later missions all have carried or will carry altimeters capable of 2- to 3-cmprecision. The US Navy launched GEOSAT into its classified GM (1985–1986)

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to map the geoid for defense purposes; upon completion of the GM, the orbitwas adjusted to permit an exact repeat mission (ERM) (1986–1989), which wasunclassified because it resurveyed SEASAT profiles. Some results are collectedin Douglas & Cheney (1990). The European Space Agency (ESA) operatedits ERS-1 satellite (1991–1996) in a variety of geodetic and exact repeat orbitsfor various purposes; some results are collected in Kaldeich (1993, 1994).ESA launched ERS-2 in 1995 into an orbit that resurveys the 35-day repeatorbit of ERS-1. NASA and the French National Center for Space Studies(CNES) combined forces to launch TOPEX/POSEIDON in 1992; this is onespacecraft with two altimeters, the NASA TOPEX and CNES POSEIDONinstruments. Some results are collected Fu et al (1994) and Cheney (1995).TOPEX/POSEIDON and ERS-2 continue to operate. The GFO satellite (forGEOSAT-follow-on) was launched in February 1998, and missions to followTOPEX/POSEIDON and ERS-2, called JASON and ENVISAT, respectively,are planned as early as 1999.

Altimeter Surface Tracking and Sea State BiasA radar altimeter measures the two-way travel time of a microwave radar pulsebetween the spacecraft’s antenna and the patch of ocean surface that reflectsthe pulse, which is called the footprint. Constraints on power consumptionand on antenna size and orientation accuracy require a “pulse-limited” “pulse-compression” design (Rapley 1992), in which a “tracker” estimates the timeof returned wave forms by comparing them against a parametric model of thereflecting characteristics of the sea surface (Chelton et al 1989). The diameterof the footprint is between 2.5 and 12 km and increases with increasing waveheight; wind speed also affects the surface reflectivity. Thousands of pulsesare transmitted per second, and the tracker averages hundreds of returns toestimate travel time, wave height, and wind speed; altimeter precisions givenabove in centimeters refer to the travel time precision that can be achieved withaverages taken over 1 s, travel time scaled into distance by the speed of light.The scattering of radar energy from the ocean surface is more complicated thanis assumed in the tracker’s parametric model, which causes various wind- andwave-dependent errors in the tracker’s travel time estimate that are collectivelycalled the sea-state bias (Witter & Chelton 1991). The effect of these is tooverestimate the distance by an amount usually a few percent of the typicalwave height; as waves can be on the order of 10 m, the sea-state bias error canbe a few centimeters. A correction can be empirically determined (Born et al1982, Zlotnicki et al 1989, Gaspar et al 1994).

The tracker is designed to follow ocean surfaces, and its estimate will be inerror if the reflections come from falling rain, land, or ice-covered surfaces.After flying over these, the tracker can take a few seconds to acquire “lock”

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on an ocean surface; thus data can be lost near shorelines. By “retracking”individual wave forms, the data may be recovered in some circumstances, and,in sea ice–covered ocean areas, gravity anomalies can be approximated fromretracked data (Laxon & McAdoo 1994, McAdoo & Laxon 1997). Retrackingis a laborious process and is only employed in small areas; global marine gravitysolutions (e.g. Sandwell & Smith 1997) are derived from the onboard trackerdata. Tracker estimates of extreme wind and wave parameters are used to editunreliable data (e.g. Rapp 1979).

Propagation CorrectionsThe radar energy travels at less than the speed of light in a vacuum because ofcharged particles in the ionosphere and gas molecules (water, most importantly)in the atmosphere. To convert the travel time to a distance, the integrated effectof these propagation delays must be known. Spatial and temporal variations inthis effect on the order of 50 cm of distance occur (Cheney et al 1991). Delaysmay be estimated from models (Randel et al 1996, Bilitza 1997) or measuredby devices on the spacecraft. A recent re-analysis of 40 years of climatic data(Kalnay et al 1996) allows for state-of-the-art estimation of the delays in olderaltimeter data.

Orbit Ephemeris, Timing Bias, and Center of GravityThe orbit ephemeris, which is a time series of latitude, longitude, and heightabove the ellipsoid of the center of mass of the spacecraft, is estimated byingesting various tracking data that are observed at tracking stations into a dy-namic model of the forces on the satellite. Uncertainties in the orbital height aredominantly at frequencies of once and twice per revolution; in the early days,these had an rms of 1.5 m (Rapp 1983), but today, orbits (even for the oldermissions) can be calculated with 3- to 10-cm rms height errors (Williamson &Nerem 1994). Ephemeris time and altimeter time are synchronized by aligningthe large once- and twice-per-revolution signals caused by the ellipticities of theorbit and the Earth (Marsh & Williamson 1982, Schutz et al 1982). Synchro-nization errors that are called timing biases are of the order of 0.5 microseconds(µs), corresponding to 1 cm of distance. The distance from the spacecraft’scenter of mass to its antenna must be calibrated, as this changes when fuel isconsumed.

Orbital Ground Track Pattern and Data CoverageIf a satellite records data continuously, its spatial and temporal sampling patternis limited only by its orbit. All altimeters after GEOS-3 have used tape recordersto store acquired data continuously until they can be down-linked to groundstations. GEOS-3 had no tape recorder, so its data were acquired only alongarcs near ground stations, some of which were moved to various sites during

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710 SMITH

the mission. Seasat’s coverage was limited because it operated only duringan Austral winter, when sea ice obscured much of the area south of 65◦S. Theorbital inclination limits the highest latitudes covered to 65◦ for GEOS-3, 72◦ forSEASAT and GEOSAT, 81.5◦ for ERS-1 and 2, and 66◦ for TOPEX/Poseidon.A network of tracks has diamond-shaped holes (Figure 1), and the east-westdimension of these is widest at the Equator and approaches zero at the highestlatitudes reached. The speed of satellites over their ground tracks dependsprimarily on the altitude of their orbits, with a secondary effect due to therotation of the Earth (Sandwell 1992). TOPEX/Poseidon is at an altitude of1336 km, has an orbital period of 112.4 min, and covers its ground track at5.8 km/s; all the other altimeter satellites have/had altitudes typically around800 km, periods around 100 min, and speeds around 6.8 km/s.

Orbits change with time because of various perturbing factors (Kaula 1966),and onboard fuel may be used occasionally to maintain a desired configuration.In general, the ground track pattern will drift randomly around the Earth, but forcertain combinations of orbital parameters, a “repeat” will occur in which thesatellite retraces approximately the same path after everyR revolutions andD“synodic days,” i.e. rotations of the Earth with respect to the slowly precessingorbital plane. An “exact repeat” retraces ground tracks within 1 km. Many suchorbits are possible, and the choice among them is a trade-off of several factors,including how the orbit will sample tidal signals (Parke et al 1987). SEASATinitially had a near repeat withR/Dof 244/17, but in its last month, it repeatedwithin 3 km, with R/D of 43/3. GEOSAT’s GM orbit nearly repeated every23 days but drifted slowly, so that by the end of the 18-month mission, therewas a dense ground track network with an average spacing of 5.1 km at theEquator. GEOSAT’s ERM was the first “exact” repeat; it overflew the previousSEASAT 244/17 orbit. ERS-1 has flown in 43/3 and 501/35 exact repeats, andERS-2 uses the same 501/35 orbit. ERS-1’s Geodetic Phases were designedas 2411/168 patterns; after the first 168 days, the orbit was shifted so that thesecond phase would interlace with the first, so that the ultimate spacing was8.3 km at the Equator. TOPEX/Poseidon is in a 127/10 exact repeat orbit.

Across-Track ResolutionThe across-track resolution of a ground track pattern is characterized in theliterature by applying the Nyquist theorem (e.g. Hamming 1977) to the east-west spacing of the tracks along the Equator. The theorem states that if a signalis sampled every1x distance units, then the shortest wavelength that can beresolved is 21x. Since there are two Equator crossings for every revolution,the across-track resolution of an exact repeat orbit is 40,030 km/Ror 931, 315,164, and 80 km for the 3-, 10-, 17-, and 35-day repeats above. When all ofthese tracks are combined, the resulting network has gaps of 40 km (Smith

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& Sandwell 1994a) limiting the resolution to an 80-km wavelength. In earlierdays, combining GEOS-3 and SEASAT data left gaps of 80 km (Sandwell 1984,Craig & Sandwell 1988), limiting the resolution to 160 km.

Along-Track ResolutionThe along-track resolution of altimeters is assessed by analyzing the cross-spectral coherency (Bendat & Piersol 1986, chapter 6) of repeat profiles. Co-herency measures the mean-square linear correlation between two time series orthe portion of the variance of both that can be explained by a linear relationshipbetween them. The coherency is always between zero (no correlation) and one(perfect correlation); the wavelength at which the coherency equals one half istaken as the along-track resolution limit. If each series has the same signal-to-noise ratio (SNR) as a function of frequency, then the SNR= 1 when thecoherency= 0.5. Estimated resolutions are 76 km and 50 km for GEOS-3 andSEASAT, respectively (Marks & Sailor 1986); 31 km for GEOSAT (Sandwell& McAdoo 1990); and 38, 43, and 37 km for GEOSAT, ERS-1, and TOPEX,respectively (Yale et al 1995). For a given altimeter, the estimated resolutionvaries regionally (Sandwell & McAdoo 1990, Yale et al 1995), depending onthe relative magnitudes of temporal variability inζ (Sandwell & Zhang 1989)and signal strength ofN, because some of the “noise” is actually real temporalchange inζ . Experience with the characteristic SNRs of these altimeters hasbeen used to design optimal filters (Smith et al 1993, Yale et al 1995, Sandwell& Smith 1997). Note that only the geodetic orbits have across-track resolutionsequal to or better than these along-track resolutions.

Stacking of Repeat PassesThe preceding along-track resolution applies to individual profiles. Exact repeatdata can be “stacked,” or time averaged, to yield mean sea surface profiles withreduced noise and time-variable component ofζ . Averaging many (8, 22, or31) repeats together improves the resolution to 20–25 km (Sandwell & McAdoo1990, Yale et al 1995). Note that the resolution improvement of stacking, from30–40 km to 20–25 km, is less than a factor of two, although a data redundancyof 10- to 30-fold has been averaged. This observation was used by Sandwell &Smith (1997) to suggest that an effort to collect more geodetic data would haveto be very extensive in order to have any effect toward improving the resolution.

Precision in Sea Surface HeightErrors in the estimated sea surface height are larger than the altimeter errorsbecause of the errors in the ephemeris, the bias and propagation corrections, andthe atmospheric and tidal responses (if these are modeled and removed). Theoverall error is usually estimated by comparing differences in tide-correctedheight at track crossing points or along repeat profiles. The rms crossover

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712 SMITH

error for all internal crossovers generated during a 10-day TOPEX repeat cycleis about 8 cm (Tai & Kuhn 1995), whereas a state-of-the-art reprocessing ofthe GEOSAT data (http://ibis.grdl.noaa.gov/SAT/gdrs/geosathandbook) gives13 cm for the 17- and 23-day ERM and GM cycles. Real temporal variation ofζ should account for some of this and cause a 20-day value to be larger than a10-day value. It appears that the overall resolution in state-of-the-art altimetryis something under 10 cm. In older data, the rms errors were 1 m but werereduced to 25–30 cm by adjusting for orbit and tide model error (Rapp 1983).

ESTIMATION OF GRAVITY ANOMALIESFROM ALTIMETER DATA

Remove-Restore ProceduresThe very long wavelength (>1500 km) anomalies in the Earth’s gravity field arewell resolved because their perturbing effect on the orbits of satellites (Kaula1966) is seen in tracking data, and these observations are used to develop mod-els of the long-wavelength components of the gravity field (Nerem et al 1995,Tapley et al 1996). Altimetry is useful at shorter wavelengths. To recover a com-plete gravity anomaly field, a “remove-restore procedure” is usually employed,in which a model of the long-wavelength field is used to generate geoid heightsand gravity anomalies. The model geoid is removed from the altimeter heightdata, and various calculations are then performed on the residual heights, whicheventually result in an estimate of residual gravity. If only the local variationsin gravity are of interest, these residuals may suffice, but by restoring (adding)the long-wavelength model gravity the entire field (in principle) is obtained.Such an estimate of the complete field can then be compared with gravity mea-surements made independently by ships (Wessel & Watts 1988, Neumann et al1993, Smith & Sandwell 1995c, Marks 1996, Sandwell & Smith 1997).

The “Flat Earth” Description of AnomalousGravity Field QuantitiesThe tectonic fabric scales are small compared with the radius of the Earth andwith the distances over whichγ changes significantly, and so it is convenient toadopt a Cartesianx, y, zcoordinate system, withzin the direction of the expected(not deflected) vertical andz = 0 at the surface of the Earth. Formulae relatinganomalous gravity components then have a simple description in terms of theirFourier transforms, which I call the flat Earth description. Sandwell (1982)showed that the error caused by ignoring the curvature of the Earth is negligibleat wavelengths shorter than about 1500 km, that is, those wavelengths that arenot well resolved by the models used for the remove-restore procedure. Wiener(1933) and Parker (1973) discussed some of the fine points of the theory of

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Fourier transforms that are not of concern here. Schwartz et al (1990) reviewedthe geodetic applications, and Sandwell & Smith (1997, appendix A) outlinedthe elements they used to derive short-wavelength gravity anomalies from al-timetry. Here I develop the relations and error scaling arguments that are neededto discuss the limiting precision of altimetry and of different mapping methods.I caution the reader about two things: First, the literature does not use a consis-tent definition of the Fourier transform, and thus vigilance for mislaid factorsof 2π is neccessary; see Bracewell’s (1965) chapter 2 for discussion. Second,some early papers on geologic modeling of geoid anomalies (e.g. Ockendon& Turcotte 1977, Haxby & Turcotte 1978) used “flat Earth approximation” ina much narrower sense, meaning a model in isostatic equilibrium intended toapproximate long-wavelength geoid anomalies.

Let x = [x, y] denote position in thex, y plane, f (x) a function in the plane,andf (x, z) a function extended beyond the plane into space. The gravity ano-maly g(x) is associated with an anomalous potentialT (x, z) through

g(x) = −∂T(x, 0)∂z

. (1)

T is the difference between the actual potential and the potential of the referencefield (Heiskanen & Moritz 1967), and in the geodetic literature, it is called thedisturbing potential. I prefer “anomalous potential” because in the celestialmechanics literature, a “disturbing potential” is any nonradial potential. Thegeoid height is related toT through Bruns’ formula (Bruns 1878; Heiskanen &Moritz 1967, equations 2–144)

N(x) = T(x, 0)γ

, (2)

whereγ is now taken to be constant:γ = 9.8 m/s2. The deflections of thevertical are

η(x) ∼= tanη(x) = −∂N(x)∂x

, ξ(x) ∼= tanξ(x) = −∂N(x)∂y

, (3)

if x is in the east andy in the north direction. Becauseξ andη are small, thesmall-angle approximationu = tanu is made, so thatξ andη correspond toslopes of the geoid. Solutions are assumed to be sought outside of volumescontaining masses that are sources of the anomalous gravity field, so thatTsatisfies Laplace’s equation,

∂2T

∂x2+ ∂

2T

∂y2+ ∂

2T

∂z2= 0; (4)

or, substituting Equations 2, 3, and 4 into 5,

∂g

∂z

∣∣∣∣z=0

= −γ[∂η

∂x+ ∂ξ∂y

]. (5)

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714 SMITH

Thus, the vertical gravity gradient∂g/∂z can be obtained from the horizontalderivatives of the deflections of the vertical and, hence, from the curvatureof the geoid. Vertical gravity gradients are conveniently measured in Eötvos(1 E = 10−9 s−2, or 0.1 mGal/km).

When Laplace’s Equation 4 is solved by the method known as separation ofthe variables (Menke & Abbott 1990, section 5.19), the solution has the form

T(x, y, z) = 1

4π2

∫ ∫T(kx, ky) exp[i (xkx + yky)]

× exp[−z√

k2x + k2

y

]dkx dky, (6)

whereT may be any suitably chosen function; this form leads to the use ofFourier transforms. Letk = [kx, ky] denote position in the wavenumber plane,with kx = 2π/λx, ky = 2π/λy, andλx andλy as wavelengths. Define thetwo-dimensional forward Fourier transform of a functionf (x) by

f (k) =∫ ∫

f (x) exp[−i k · x] dx dy, (7)

and the inverse Fourier transform by

f (x) = 1

4π2

∫ ∫f (k) exp[i k · x] dkx dky. (8)

Then ifT (x) denotes the value ofT in thez = 0 plane, andT(k) is the Fouriertransform ofT (x), Equation 6 takes the form

T(x, z) = =−1{T(k) exp[−kz]}, (9)

where=−1{} denotes the inverse Fourier transform, andk = |k|. Combiningall these equations gives both

g(k) = γ kN(k) (10)

and

g(k) = −γk

[ikxη(k)+ ikyξ (k)], (11)

so thatg may be estimated either fromN or fromη andξ . Equations similar toEquations 5 and 11 were obtained by Haxby et al (1983); Parker (1973) usedsomething similar to Equation 10.

Root-Mean-Square Amplitudes, Scaling Arguments,and Special SymmetryFrom Equations 3, 10, and 11, the following relation can be obtained amongthe mean square values:

γ−2∫ ∫|g(k)|2 dk =

∫ ∫|η(k)|2 dk +

∫ ∫|ξ (k)|2 dk. (12)

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If N is isotropic, so thatη andξ have the same mean-square spectra, and therms amplitude ofg is 35 mGal, then Equation 12 says that the rms amplitudesof η or ξ should each be (35 mGal)[γ (2)0.5]−1 = 25µrad. Sandwell (1984)found an rms amplitude of 15µrad in altimeter data from an area of smoothgeoid in the South Pacific.

If N is lineated (constant) in they direction (so thatξ = 0), then Equation11 reduces so thatη andg are related by a Hilbert transform:

g(kx) = −γ [i sgn(kx)η(kx)]. (13)

A deflection of the vertical on the order of 1µrad is seen to be associated witha gravity anomaly on the order of 1 mGal (Equation 13), or 20.5 mGal (Equa-tion 12).

Altimeter Limitation on PrecisionBecause the tracker averages thousands of wave forms, its errors should havea Gaussian distribution, and altimeter precision values should be 1-σ errors.Assume that two successive 1-s averages of height are statistically independent,since the distance traveled along the ground track in this time is approximatelyequal to the footprint diameter. If the altimeter precision were the only sourceof error in the geoid height, the rms error in the geoid slope over this distance(the along-track component of the deflection of the vertical) would be 20.5timesthe altimeter precision divided by the distance traveled; for altimeters of 20- to40-, 8- to 10-, and 2- to 3-cm precision, we get 42- to 83-, 17- to 21-, and 4- to6-µrad rms slope errors. McAdoo & Sandwell (1988) found that stacking canreduce the rms slope variations to as low as 1µrad in areas of lowζ variability.Using the scaling arguments (Equations 12 and 13) leads to the assumption thatin the absence of data redundancy, the gravity precision would be no better than5 mGal, whereas it could be better if redundant data were available.

Maps for Tectonic PurposesClassical geodesy endeavors to map the entire spectrum of the gravity fieldand therefore must be concerned with the entire error budget involved in theestimation of geoid anomalies by satellite altimetry and particularly with thefact that altimetry measuresN+ ζ rather thanN alone. The study of tectonicfabric requires only relative changes in geoid height over spatial scales withinthe tectonic fabric band; thus only sources of error at these scales need be ofconcern. Altimeter data processing and map interpolation schemes developedfor tectonic purposes therefore differ from techniques developed for geodeticpurposes. Methods were pioneered in the early days when orbit errors werelarge and the data were sparse and had anisotropic resolution.

Because orbit errors are of very long wavelength, they can be removed byhigh-pass filtering or removing a polynomial trend designed to minimize errors

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716 SMITH

at crossing tracks. A mapping method developed by Rapp (1979, 1983, 1986)used trend adjustment to produce estimates of height anomalies. Dixon & Parke(1983) and Haxby & Weissel (1986) used band-pass filters to make maps ofshort-wavelength height anomalies for tectonic purposes. Haxby et al (1983)developed an anisotropic interpolation scheme to capture linear trends in heightthat could be correlated across widely spaced parallel profiles. Had they notdone so, a sharp lineament such as a fracture zone anomaly could have lookedlike a string of beads or an uncooked lasagne noodle viewed edge-on.

If the heights are interpolated to a grid that will be converted to a gravityanomaly using Equation 10, then crossing adjustment is required because iftwo tracks have a height disagreement of a few centimeters, the implied slope,and hence the gravity anomaly, becomes infinite as the two disagreeing pointsapproach one another. With dense geodetic orbit data, the number of crossingsbecomes very large, and since the crossings are only 3–4 km apart and theadjustments are on the order of 3–4 cm, the adjustments introduce ad hocslopes of 10µrad, or 10-mGal noise in the resulting maps (Sandwell 1992,Olgiati et al 1995).

An alternative approach developed by Sandwell and his colleagues (Sandwell1984, 1991, 1992, Sandwell & McAdoo 1988, 1990, Sandwell & Zhang 1989,Sandwell & Smith 1997) operates on slopes rather than heights, and it turnsout to be ideally suited to dense geodetic data. Olgiati et al (1995) comparedvarious mapping methods and found that the slope technique does the best jobof error suppression. The along-track sea surface slopes from two or moretrack directions (i.e. satellite data from one or more orbital inclinations) arevectorially projected into north and east slopes, and these are used as estimatesof η andξ in Equation 11 to estimate gravity anomalies (Sandwell 1984, 1992).No crossing adjustment is required because crossing profiles measure differentdirections of the height gradient. Another advantage is due to the fact thatthe error sources in the estimation ofN, apart from the altimeter precision,generally all have long length scales of correlation, so that the slopes of theseerrors are nearly zero (Sandwell 1991). In fact, this is true even of some of thecorrections, such as the propagation delays, and thus these corrections do notneed to be made when slopes are used. (The sea state bias slope is negligibleexcept in severe storms, where the data would be edited for excessive waveheight anyway.) Whereas the height profiles differ from the true sea surfaceheight by 10 cm and from the geoid by 1 m or so, theslope of the heightprofile differs from the slope of the geoid by something on the order of 1µrador less. The slope of the open ocean tide is under 0.1µrad (Sandwell 1991),but it can be much larger in wide shallow seas, such as the North Sea and thePatagonian Shelf (Smith & Sandwell 1995b, Sandwell & Smith 1997), and thusthe modeled tide height (e.g. Eanes & Bettadpur 1995) does need to be removed

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from the data. Even with geodetic data, a small anisotropy in resolution existsthat is due to the fact that the holes between tracks are not square but diamondshaped:ξ is better determined thanη at low latitudes and the opposite is true athigh latitudes. Sandwell & Smith (1997) separately filterη andξ in a latitude-dependent manner to adjust for this.

Dynamic Topography ErrorThe slope method obtains the slopes ofN+ ζ rather thanN. A map combininggeodetic orbit data blends profiles collected over a year and longer [the recentSmith & Sandwell (1995a) and Sandwell & Smith (1995, 1997) maps alsoinclude multi-year stacked data], so I estimate that the global rms average errordue to dynamic topography is 0.7 mGal. This value is simply rmsζ , divided byrmsN times rmsg, which works becauseζ andN have the same spectral shape(Wagner 1979). One expects larger errors in local areas. The fastest (1 m/s)western boundary currents, such as the Kuroshio and the Gulf Stream, produceslopes inζ with peak amplitudes of 10µrad and non-negligible slopes confinedto a width generally less than 100 km. Over time, these currents usually meanderover∼3 times their characteristic width, so that the slope ofζ in these areasis 3µrad; however, in some localities they follow bottom contours and remainspatially fixed. The appropriate error scale estimate for these is the lineatedfield model (Equation 13) because the currents flow as linear jets. Thus, thereshould be errors of the order of 10 mGal confined to widths of 100 km whereboundary currents are stationary and errors of 3 mGal over 300 km where theymeander. Differences between gravity estimated from altimetry by the slopemethod and gravity measured by ships show the expected error offshore ofFlorida where the Gulf Stream remains fixed (Smith & Sandwell 1995c). TheHilbert transform of these differences should be proportional to the surfacecurrent velocity.

Coherency with Ship DataCurrently, common practice has been to assess the resolution of altimeter-derived gravity anomaly maps by comparing them with ship gravity survey datathat use the same cross-spectral coherency technique used on repeat altimeterprofiles (Neumann et al 1993, Smith & Sandwell 1995c, Marks 1996, Sandwell& Smith 1997). The “resolution” is again taken to be the wavelength at whichthe coherency is 0.5, but this no longer has a simple interpretation in terms ofthe SNR, as the noise processes of the two data types are different. Some cross-spectral comparisons are careful to use linear profiles, while others merelyuse the cumulative distance along a zig-zagging ship survey path. I do notrecommend this, as the distance coordinate determines the wavelength in thecross-spectrum. The mean value and trend of ship data are not accurate (Wessel

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718 SMITH

& Watts 1988), and so rms differences are estimated after removing a lineartrend from the differences. Ship data may be corrected by comparison with thealtimeter data (Smith & Sandwell 1995c). For the new solution combining allGEOSAT and ERS-1 data, Marks (1996) and Sandwell & Smith (1997) foundresolutions of 23–30 km and rms differences of 3–9 mGal, which are consistentwith the precision and resolution estimates above. The numbers vary dependingon the location, the quality of the ship data, and the proximity of the ship surveyto a stacked exact repeat profile.

THE GRAVITY FIELD OF SEAFLOORTOPOGRAPHY

Let the sea surface be at the planez = 0, and leth(x) represent the topographyof the seafloor, measured positive upwards from the planez = −d below thesea surface. Then if the sea water has densityρw and the material belowh hasdensityρh, the gravity anomaly at the sea surfaceg is related to the topographyh by

g(k) = 2πG(ρh − ρw) exp[−kd]∞∑

n=1

k(n−1)

n!={[h(x)]n} (14)

(Parker 1973), whereG is the Newtonian gravitational constant 6.6732× 10−11

Nt-m2/kg2. Equation 14 is in the rather inconvenient form of the Fourier trans-form of a Taylor series expansion. Convergence is most rapid when the largestmagnitude ofh is much smaller thand. The one-term approximation of theseries (Equation 14)

g(k) = 2πG(ρh − ρw) exp[−kd]h(k) (15)

has the convenient form

g(k) = f (k) h(k), (16)

which represents an isotropic, spatially invariant, linear system withh as inputandg as output. It is isotropic because the relationship depends onk and notk.It is spatially invariant because the relationshipf (k) betweenh(x) andg(x) isindependent ofx. There is a vast body of literature on linear systems theory, andin linear systems, complex behavior may be synthesized from a superpositionof elementary responses, which facilitates analysis. The actual relationship(Equation 14) is nonlinear, since it involves powers of the topography. It alsorequires thatd andρh be constant, and over large distances in the ocean, theserequirements may be inconvenient. Again, flat Earth approximations are usefulfor local descriptions only.

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Upward ContinuationThe constant term in Equation 15, 2πG (ρh − ρw), is sometimes called theBouguer constant, after the formula for the gravity attributable to a horizontalslab of material [Bouguer 1749 (his section 7.4), Turcotte & Schubert 1982 (seetheir section 5.7)]. Forρh = 2800 kg/m3 andρw = 1030 kg/m3, this factoris approximately 75 mGal per kilometer of topography. The factor exp[−kd]accomplishes an operation known as upward continuation. It is a consequenceof Equation 9, and therefore all constituents of the gravity field are subject tothis phenomenon, not justg. In upward continuation through a distanced, anyconstituent ofT with characteristic horizontal scalesλx andλy is attenuated byan amount exp[−2πd/λ], whereλ−1 = (λ−2

x + λ−2y )0.5. Shorter wavelengths

are more strongly attenuated than longer ones, and if an object is elongated,the attenuation depends more strongly on the shorter of its two characteristicwavelengths,λx andλy. Topography with a wavelength ofλ = 2πdwill have itsgravity effect attenuated by an amount 1/e∼= 0.37; ifd = 4 km, this wavelengthis about 25 km, and ifd increases with sea floor age (e.g. Parsons & Sclater1977), then the 1/e wavelength will be greater than 20 km for all ages greaterthan about 2 Ma. This attenuation due to water depth is one of the factorslimiting the resolution of seafloor tectonic fabric by sea surface gravity data.

Isostatic CompensationA long history of geophysical investigations (reviewed by Heiskanen & VeningMeinesz 1958) has shown that large-scale topographic features on the Earthare isostatically compensated. Studies of isostasy in the oceans have foundthat a “flexural isostatic model” usually characterizes the relationship betweeng andh. Flexural isostasy is a generalization of an isostatic model given byAiry (1855). In Airy’s model, the topography floats on the mantle; the flexu-ral model adds a term representing the mechanical strength of the lithosphereto the buoyant support that Airy proposed. Flexure was proposed in a se-ries of papers by Barrell (1914–1915), applied to pendulum gravity measure-ments in the ocean by Vening Meinesz (1941), and refined by Gunn (1943) andWalcott (1970, 1976). Dorman & Lewis (1970) and Banks et al (1977) devel-oped the linear system approach to isostasy, and Mackenzie & Bowin (1976),Watts (1978, 1979), McNutt (1979), Watts et al (1980), and many subse-quent others investigated flexure of the ocean lithosphere. Watts (1983) gave areview.

In Airy’s model, the mass excess represented by positive topographyh isbalanced by a mass deficit caused by negative (downward) displacements ofthe Mohorovicic discontinuity (Moho). Ifw measures the displacement of theMoho from where it would be ifh were zero, then balancing the deviatoric

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720 SMITH

vertical normal stresses caused byh andw leads to

(ρh − ρw)γh+ (ρm − ρh)γw = 0, (17)

whereρm is the density of the mantle beneath the Moho, from which it followsthat

w = −[(ρh − ρw)(ρm − ρh)

]h. (18)

If we apply the approximation from Equation 15 twice to calculate the combinedgravity effects ofh andw, with w given fromh by Equation 18, we obtain anequation of the form of Equation 16 with

f (k) = 2πG(ρh − ρw) exp[−kd]{1− exp[−kc]}, (19)

wherec is the distance between theh = 0 andw = 0 planes, that is, themean crustal thickness. Now in addition to the upward continuation effect ofEquation 15, we also have attenuation of long wavelengths (long with respectto c), which are due to the last term in Equation 19. In this case,g is nonzeroonly in a band of wavelengths longer than a few timesd and shorter than a fewtimesd+ c.

Flexural isostasy adds to Equation 17 an additional deviatoric stressσzz termthat represents the lithosphere’s resistance to deformation into the shapew. Theresistance is characterized by a parameterD, the “flexural rigidity.” The stressbalance becomes

(ρh − ρw)γh+ (ρm − ρh)γw + D∇4w = 0 (20)

in which ∇4 is the biharmonic operator. [Some authors, e.g. Watts & Ribe(1984), generalize Equation 20 to include spatially varyingD or the effect ofmaterial of another density filling flexural depressions, but these generalizationsprevent the use of the Fourier transform to obtain a spatially invariant linearsystem.] Employing Fourier transforms leads to

w(k) = −[(ρh − ρw)(ρm − ρh)

]8(k)h(k) (21)

where

8(k) =[

1

(1+ (λ f k)4)

](22)

is a “flexural isostatic filter” with a wavelength of half-amplitude

λ f = 2π

[D

γ (ρm − ρh)

]1/4

, (23)

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which I call the flexural wavelength. Other definitions in the literature differfrom mine by absorbing various constant factors intoλ f . Using Equation 21instead of Equation 18 and proceeding as before, a relationship is obtained inthe form of Equation 16, with

f (k) = 2πG(ρh − ρw) exp[−kd]{1− exp[−kc]8(k)}. (24)

Airy isostasy may be viewed as a special case of flexural isostasy, for whenD = 0, the flexure equations reduce to the Airy equations. In the literature,further generalizations of Equation 24 are obtained by assuming that the oceaniccrust has two or more layers, each of which has constant thickness and densityand flexes into the same shapew under the loadh (Watts 1978, Ribe & Watts1982, Muller & Smith 1993). Under these assumptions, anf (k) is obtainedwith values very similar to those of the simpler Equation 24.

The function f (k) is often characterized by a parameterH that is called theeffective elastic thickness of the lithosphere. From a theory for the flexure of athin elastic membrane whenH¿ λ f andw¿ H, the following is obtained:

D = E H3

12(1− ν2), (25)

in which E is Young’s modulus andν is Poisson’s ratio. The literature is notconsistent in the values used in Equations 23 and 25 to relateH and8; valuesare found in the ranges of 0.8–1.0× 1011 Pa forE, 0.22–0.25 forν, 3330–3400kg/m3 for ρm, and 2600–2800 kg/m3 for ρh; I useE = 1.0× 1011 Pa,ν =0.25,ρm = 3330 kg/m3, andρh andρw as defined above in this paper.

H varies in a complicated way in the oceans. Early studies ofH at seamountsalong the Hawaiian-Emperor chain concluded thatH does not change system-atically with seamount age (Watts & Cochran 1974) but thatH increases withthe square root of the age difference between the seafloor age and the seamountage, which is the age of the seafloor when the topographic load formed (Watts1978). Watts et al (1980) suggested thatH is approximately one third of theseismic thickness of the lithosphere and is given approximately by the depthto the 450◦C isotherm if the lithosphere cools as in the model of Parsons &Sclater (1977). If some process limits the ultimate thickness of the lithosphere(Parsons & Sclater 1977), thenH would range between 0 and 40 km (Smith &Sandwell 1994a). Later studies (McNutt & Menard 1982, McNutt 1984,Calmant & Cazenave 1987, Smith et al 1989) foundH values that did notfollow Watts’s rule. Wessel (1992) reviewed these and proposed that thermalcooling stresses complicate the situation. However, the flexural model, withHprobably in the range of 0–40 km, is successful enough that it can be used toillustrate the basic relationship betweeng andh.

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722 SMITH

Figure 6a shows f (k) values obtained from Equation 24 using the abovedensities,d = 4 km, and variousH values. Thedotted lineis the case of noisostatic compensation (Equation 15), which can also be viewed as infiniteH.Figure 6b shows the same curves obtained again withd = 4 km (dotted), andalsod = 2.5 km (solid). Figure 6cshows how wavelength bands and transitionsbetween them might be defined based on these curves. Thesolid line is theratio of f5(k)/ f∞(k), and thedotted lineis the ratio f40(k)/ f∞(k), where thesubscript forf indicates theH value used in thatf. I have chosenH = 5 ratherthanH = 0 because in practice, the lithosphere has greater than zero strength.Watts et al (1980) usedH = 5 km for features formed on a ridge axis (i.e. atzero age), and Cochran (1979) foundH values of 2–6 km at the East Pacific Riseand 7–13 km at the Mid-Atlantic Ridge. The area between the two curves inFigure 6c shows the range of wavelengths over which the gravity/topographyratio is sensitive toH; this has been called the diagnostic waveband of flexuralresponse by Watts & Ribe (1984) (or the “diagnostic band”). Because nearbytopography features may have formed at different ages, each feature can haveits own f (k) (Watts et al 1980). According to the flexural isostasy model,wavelengths of topography larger than the diagnostic band are supported byAiry flotation; various other support mechanisms can be described, each withits own f (k) (see Sandwell 1982). Thus the correlation between sea surfacegravity and seafloor topography is easily understood only at wavelengths lessthan the diagnostic band of flexure, and this limits the tectonic fabric band.

High-Pass Filters for the Tectonic BandBecause the gravity field has a red spectrum, long-wavelength signals in itmay dominate a gravity map, and for tectonic purposes, it is useful to use afilter to enhance the shorter wavelengths. Smith & Sandwell (1994a) used thefunction f5(k)/ f∞(k) (actually a Gaussian approximation of it that was fasterto compute) as a high-pass filter to isolate the portion of the gravity field thatis expected to be most strongly correlated with topography, and within whichit is not necessary to knowH in order to interpret the anomalies. They alsoused the converse low-pass filter on interpolated bathymetry in order to forma regional depth map. The half-amplitude transition of these filters is at awavelength of 160 km. They “downward continued” (multiplied by exp[+kd])the high-pass–filtered gravity field to various levelsd and then interpolated thedownward-continuedg solutions onto the low-pass–filtered regional depth, ineffect “draping” the high-pass–filteredg over the long-wavelength variationsin d. Downward continuation is unstable at short wavelengths (largek), andso Smith & Sandwell (1994a) used the SNR information from repeat trackaltimetry to design a stabilizing filter that minimizes the mean square error ofdownward continuation. I have used the same process here (Figure 7), so that

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0.0

0.5

1.0

f rat

io

25102050100200500100020005000

Wavelength (km)

C

0

25

50

75

f(k)

(m

Gal

/km

)

B

0

25

50

75f(

k) (

mG

al/k

m)

40

20

10

5

0

A

Figure 6 Topography-to-gravity transfer functionf (k) from Equation 24.Top: For water depthd = 4 km. Numbers indicate effective elastic lithosphere thicknessH. Dotted lineindicates uncom-pensated situation (Equation 15).Middle: Comparison ofd = 4 km (dotted lines) andd = 2.5 km(solid lines). Bottom: Ratios f5(k)/ f∞(k) (solid) and f40(k)/ f∞(k) (dotted) illustrate partitioningof wavebands;tectonic fabric scalelies to theright of thesolid curve.

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724 SMITH

0˚0˚

60˚

60˚

120˚

120˚

180˚

180˚

240˚

240˚

300˚

300˚

0˚0˚

-60˚

-60˚

-30˚

-30˚

0˚0˚

30˚

30˚

60˚

60˚

Fig

ure

7G

ravi

tyfie

ldis

show

nhi

gh-p

ass

filte

red

and

dow

nwar

dco

ntin

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tore

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alde

pth

valu

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variations in the amplitude ofg in the tectonic fabric band may be comparedbetween areas that lie at different depths.

Much simpler filters will work just as well to illustrate tectonic fabric ingravity field data. For example, the vertical gravity gradient∂g/∂z suppresseslong wavelengths because its Fourier transform is equal tokg(k). PhippsMorgan & Sandwell (1994) used∂g/∂z to illustrate fine-scale ridge axis fabric,and Wessel & Lyons (1997) used it to facilitate a search for seamounts. I showit in Figures 2, 4, 11, 12, 14, and 16.

Correlation Betweeng andhThe topography generated by tectonic processes at mid-ocean ridges graduallybecomes buried under sediment. If the sediment cover is sufficiently thick,the seafloor may be flat. Gravity anomalies at tectonic wavelengths will stillbe seen, although with diminished amplitude; these come from the basementtopography, and Equation 14 can describe them as well, if the density contrastbetween the basement rock and the sediment is used. Because this contrast isgenerally much less than the density contrast between seafloor materials andseawater,g is usually correlated with sea floor topography wherever the seafloor is not flat. A complicated and nonlinear correlation is expected whenthe basement topography is partially buried, with structural highs exposed andtroughs filled with sediment. Smith & Sandwell (1994a, 1997b) computed thecorrelation between high-pass–filtered ship surveys of depth and high-pass–filtered and downward-continued gravity in order to determine the correlationand proportion between these two quantities, which they exploited in order toestimate detailed bathymetry from altimeter-derived gravity. High correlations(Figure 8) occur in most areas except over very smooth seafloor, such as overabyssal plains. Liu et al (1982) gave an interesting example of a gravity anomalydue to a tectonic structure buried under flat sea floor.

THE RMS AMPLITUDE OF TECTONIC FABRICANOMALIES MAY SUGGEST AN ORIGININ RIDGE-AXIS PROCESSES

The morphology of mid-ocean ridge axes seems to vary with spreading rate, atleast to first order: The fast-spreading East Pacific Rise is characterized by anaxial topographic high and a>+10 mGal gravity anomaly, whereas the slow-spreading Mid-Atlantic Ridge has an axial topographic valley flanked by highsand a similar pattern in gravity anomalies at the 30-mGal level (Menard 1967,Cochran 1979, McDonald 1986, Small & Sandwell 1989, 1992). Axis segmentlengths and offset lengths also differ between the two (Abbott 1986). A numberof models have been proposed to explain these two types of ridge systems

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726 SMITH

0˚0˚

60˚

60˚

120˚

120˚

180˚

180˚

240˚

240˚

300˚

300˚

0˚0˚

-60˚

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-30˚

-30˚

0˚0˚

30˚

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60˚

0.0

0.2

0.4

0.6

0.8

1.0

Cor

rela

tion

Coe

ffic

ient

Fig

ure

8C

orre

latio

nbe

twee

nfil

tere

dgr

avity

(Fig

ure

7)an

dse

afloo

rto

pogr

aphy

.

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in terms of spreading-rate–dependent material strength and the transience orpermanence of magma supply (Sleep 1969, Tapponier & Francheteau 1978,Phipps Morgan et al 1987). Chen & Morgan (1990a, 1990b) and Phipps Morgan& Chen (1992, 1993) advanced a model that produces an abrupt transition inaxial morphology at a half spreading rate of 38 mm/year. Small & Sandwell(1989, 1992) used the rms roughness of high-pass–filtered sea surface slopesalong GEOSAT ERM profiles to characterize how gravity roughness varieswith spreading rate over the global mid-ocean ridge system, and they foundan abrupt transition at a similar spreading rate. This contradicted the findingof Malinverno (1991) that the roughness of axial bathymetric soundings variessmoothly in a manner inversely proportional to the square root of spreadingrate.

Although Small & Sandwell (1992) presented maps of their gravity roughnessestimate, they did not account for the upward continuation effect produced bythe greater depths off-axis, and so they restricted their quantitative analysis toridge axes. Here I extend this work beyond the ridge axes by calculating therms amplitude of the filtered gravity field (Figure 7) in a square window that is160 km on a side (Figure 9). Halftone and page-size limitations do not permitfull illustration of the interesting variations in this quantity, so a verbal summarywill have to suffice. I found that in areas of flat sea floor where the correlationwith depth (Figure 8) is low, the rms is 6–8 mGal over deep abyssal plainsand 4–6 mGal over shallow continental platforms. These values suggest thateither genuine differences in geology produce these different values, or elsethe stabilization of downward continuation is imperfect and noise is slightlyamplified at great depths. I observed clear variations in rms values over ridgeflanks: Amplitudes in the 4- to 6-mGal range are confined to the flanks ofthe East Pacific Rise near to and immediately south of the Galapagos TripleJunction, as well as on a section of the Pacific Antarctic Ridge that is south ofthe Udintsev Fracture Zone, in an area associated with a prominent propagatingrift (Sahabi et al 1996) (gray area in Figure 5). The 6- to 8- and 8- to 10-mGal ranges are common throughout the eastern Pacific and the southeasternIndian oceans, except along fracture zones where the rms increases to 10–30mGal. The Mid-Atlantic Ridge is characterized by flank rms in the 10- to20-mGal range, with axial rms in the 20- to 40-mGal range, and a few majorfracture zones exceeding 40 mGal. The South West Indian Ridge has an rmsexceeding 40 mGal along the axial valleys, with values of 20–40 mGal alongthe flanks. Some areas, notably the Pacific Antarctic Ridge between 190◦Eand the Udintsev Fracture Zone, as well as much of the Atlantic, show verydifferent values near the axis than on the older flanks, which suggests a changein spreading rate or magma supply, or both. I calculated how much ocean areafalls in intervals of 1-mm/year half spreading rate and 1-mGal rms, as shown

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728 SMITH

0˚0˚

60˚

60˚

120˚

120˚

180˚

180˚

240˚

240˚

300˚

300˚

0˚0˚

-60˚

-60˚

-30˚

-30˚

0˚0˚

30˚

30˚

60˚

60˚

06

812

2032

5

rms

ampl

itude

(m

Gal

)

Fig

ure

9A

mpl

itude

ofth

efil

tere

dgr

avity

field

(Fig

ure

7)sh

ows

vari

atio

nsin

tect

onic

fabr

icst

reng

thal

ong

ridg

eax

esan

dat

vari

ous

ages

onri

dge

flank

s.

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0

20

40

60G

ravi

ty A

mpl

itude

(m

Gal

)

0 20 40 60 80 100

Half Spreading Rate (mm/yr)

0.0 4.0 4.5 5.0 5.5 6.0

Log10 Area (km2)

Figure 10 Area of the seafloor summed in intervals of 1 mGal of gravity amplitude and 1-mm/yearhalf spreading rate. Note that amplitudes less than 3 mGal are rare, large amplitudes are uncommonat half rates greater than 50 mm/year, and the largest amplitudes are found at spreading rates lessthan 20 mm/year.

in Figure 10. The results agree with those that Small & Sandwell (1989, theirfigure 7; 1992, their figure 6) obtained over mid-ocean ridges, which supports arate-dependent morphology. I conjecture that much of the tectonic fabric we seein altimetry over old seafloor is due to structures generated at or near ridge axes.

A TOUR OF SOME HISTORICAL AND CURRENTRESEARCH AREAS AND TOPICS

The Pacific Antarctic Ridge Area; Fabric StylesWhen the GEOSAT GM data were declassified south of 30◦S, the tectonic de-tails of the ridges of the Southern Ocean became visible, and it was immediatelyclear that these intermediate rate ridges exhibit a variety of new and complexfabrics and abrupt, sometimes propagating transitions between them. Fig-ures 2–5 exhibit nearly all of these, and space does not permit a complete dis-cussion. I note a few features and refer the reader to the literature cited hereand in the introduction for more details.

One exciting feature that was first clearly imaged in the altimeter data is theHollister Ridge. One old survey track by the R/V Vema had crossed it andreported depths within a few hundred meters of sea level, but these were notbelieved and so it was never shown on hand-drawn contour charts. After the

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730 SMITH

altimeter data appeared and the site was recognized to be seismically active(Talandier & Okal 1996), several oceanographic expeditions tried to reach thisarea but were driven away by severe weather. Finally, a French expeditionsucceeded and found an extensive area within 100 m of sea level, from whichzero-age rocks were dredged (Geli et al 1996). A new model for the motion ofthe Pacific plate over the hotspots (Wessel & Kroenke 1997) suggests that thisis the site of the Louisville Ridge hotspot, which was previously thought to lienorth of the Eltanin Fracture Zone system (Lonsdale 1988, Watts et al 1988).

The images of Figures 2–5 show areas of well-organized seafloor spreadingwith clear ridge axes and linear and parallel fracture zones. Within these areas,the axial morphology sometimes changes abruptly across a fracture zone fromaxial high to axial valley (Marks & Stock 1994). But there also are areas wherethe ridge is offset by many small discontinuities and where the trace of these off-sets on the flanks is not parallel with the fracture zones. In some cases, thesetraces are persistently oblique to both the trends of the ridge and the fracturezones, in the manner of propagating rifts (Phipps Morgan & Sandwell 1994),whereas in other instances, they seem to meander chaotically, although withthe trace on each flank having symmetry across the axis. Phipps Morgan &Parmentier (1995) have also noted regularly spaced lineations in the spreadingdirection that have a wavelength of 40–70 km, which they attributed to stationarycenters of nontransform discontinuities in the spreading system, at slow andintermediate spreading ridges. Sahabi et al (1996) confirmed with a recent shipstudy what can be seen in the altimeter data: Transitions among these types ofbehavior occur abruptly across sharp lines, such as the boundary of thegrayregion in Figure 5, and these transitions can migrate with time (1000 km over30 Ma shown in Figure 5). Sahabi et al suggested a spreading-rate–dependentprocess with a sharp threshold of transition that also depends on a secondaryvariable such as temperature to explain the fact that fabric of both types canbe found at the same spreading rate. Further work is required to understandthis process, but it may turn out that these large propagation structures recordtransient thermal anomalies moving across the ridge system.

Bathymetric Expressions of FabricFabric representations from bathymetry (Figure 3) show a number of limita-tions. The traditional hand-drawn contour charts, the General BathymetricCharts of the Oceans (GEBCO) (GEBCO Guiding Committee 1982, Jones et al1997), show considerable geological vision and artistic license applied to a verylimited distribution of control survey lines (dashed linesin Figure 3top). Notethat between 200◦ and 210◦ longitude and north of 60◦S, a large-age-offset frac-ture zone is implied by the large zig-zag of bathymetric contours (solid lines),although there are no data upon which to base this conjecture. From the

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contours, it appears that there is an increase in the bathymetric roughness andthe number of seamounts south of 60◦S, but this is not the case; the area north of60◦S was contoured by one bathymetrist and the area south of 60◦S was drawnby two others, and they had very different interpretive styles (D Monahan,Canadian Hydrographic Service, personal communication, 1997).

Many geophysicists rely on a 5-arc-minute (arc-min) grid of estimated ba-thymetry produced by the US Navy from hand-drawn contours like these.This 5-arc-min data set was originally called DBDB-5 for “digital bathymetricdatabase at 5 min,” and after land elevations were added, it was distributedunder the name ETOPO-5, for “Earth topography at 5 min” (National Geo-physical Data Center 1988). The ETOPO-5 bathymetry in this area is shown inthemiddle panelof Figure 3. The bathymetry that Smith & Sandwell (1994a)estimated by combining altimeter data with shipboard sounding data is shownin thebottom panelof Figure 3. Note that both GEBCO and ETOPO-5 do notclearly locate the ridge in the southwesternmost part of the area shown, theyfail to show the Hollister Ridge, and they overestimate the areal extent of aseamount at around 60◦S, 230◦E. Other errors in ETOPO-5 are discussed bySmith (1993).

Some Features of the Atlantic, Including Abyssal HillsFigures 11–15 show tectonic fabric in the Atlantic basin. The Southern Mid-Atlantic Ridge (Figure 11) exhibits sharp linear and parallel fracture zones, butthe corridors within these fracture zones show propagating rift wakes, crenu-lations, and more chaotic wandering structures. The Equatorial Atlantic Basin(fabric shown in Figure 12) shows the same phenomena generated in the last 70million years (Figure 13) and a much smoother fabric prior to that time whenthe spreading rate was faster. Also of tectonic interest in this area is the mergingpattern of fracture zones south of the Cape Verde Islands, which may help toconstrain the relative motions of North America, South America, and Africaduring the opening of the Atlantic. This area is difficult to decipher because thecombination of the north-south orientation of the ridge axis and the magneticEquator passing through the area makes the magnetic anomalies due to seafloorspreading invisible (Müller & Smith 1993).

Another interesting feature in this area is the group of large east-west–trending anomalies that are immediately east of the trench, which are asso-ciated with the Lesser Antilles Arc. Müller & Smith (1993) interpreted theseas indications of buckling of the plate, caused by relative motion between thetwo American continents, and recent Global Positioning System surveys finda similar motion (Dixon & Mao 1997). Müller & Smith corrected the grav-ity in this area for seafloor topography using ship data, and then, out of theinfinite number of Moho configurations that could give a reasonable fit to the

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Figure 11 Structural lows (same definition as in Figure 4) along the Southern Mid-Atlantic Ridge.

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Figure 14 Detail of Figure 12 showing propagating rifts, crenulations, and chaotic fabric.

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Figure 15 Top: Detail of Figure 14 in area where Goff et al (1995) have studied the fabric witha multibeam acoustic survey.Bottom, right to left: Synthetic model of abyssal hill topography inthis area. Hills are elongate, with characteristic wavelengths (as defined by Goff & Jordon 1988)10 km by 30 km. Also shown are sea surface gravity effects of this model topography and the seasurface gravity effect averaged in grid cells that are the size of the altimeter solution shown attop[grid cells are the same size as those of the Sandwell & Smith (1997) gravity field]. The grid-cellaveraging has no effect on the resolution.

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residual gravity, they found the unique one that minimizes the curvature ofthe Moho surface. They showed that this curvature was so large that the platecould not support it elastically, and hence the plate had yielded. Other tightlycurved subduction zones also exhibit similar structures that have not yet beeninterpreted.

Figures 14 and 15 zoom in on an area where a detailed multibeam acousticswath survey was recently made (Goff et al 1995). In Figure 15, I have calculateda synthetic abyssal hill model following Goff & Jordan (1988) and using thevaluesλn = 10 km, λs = 30 km, rms topographic height= 300 m, andHausdorff dimension= 2.22, which are typical of the values Goff et al (1995)obtained in the area of this survey. I calculated the gravity effect of these abyssalhills at the sea surface using Equation 24, withd = 4 km andH = 6 kmin Equation 25 (Cochran 1979). Equation 25 may not correctly characterizeabyssal hill gravity anomalies if the hills indicate variations in the thicknessof crustal layers; Goff et al (1995) found some correlation between hill heightand width and residual mantle Bouguer anomaly. The point of this exerciseis merely to show that very small structures, with characteristic dimensions asshort as 10 km, can be seen in the gravity field, albeit at the limit of resolution.The fine-scale texture that looks like the skin of an orange in the gravity imagesis probably due to real fine-scale seafloor texture, such as abyssal hills.

Central Pacific Gravity RollsFigure 16 shows how the fabric in the area surrounding the East Pacific Riseis different from that of the Mid-Atlantic Ridge (Figure 11). The Pacific hasgenerally smooth areas with low rms amplitude (Figure 9), broken by a com-plex pattern of scars left from ridge jumps and plate reorganizations. Also,a lineated grain occurs on the Pacific plate that appears to be approximatelyparallel to the directions of spreading and of motion of the Pacific plate overthe hotspots. This was first recognized in SEASAT data by Haxby & Weis-sel (1986), who suggested that it was a manifestation of small-scale mantleconvection. Since then, there has been vigorous and ongoing debate about thecause of these structures. Higher-resolution gravity data have confirmed thealignment with absolute plate motion and across other structures (Wessel et al1996), and these data have suggested that amplitudes of long-wavelength com-ponents increase with age (Cazenave et al 1995), which further suggests aresponsible mechanism within the lithosphere. Tensional cracks or lithosphericboudinage have been suggested based on observations that very narrow- andhigh-amplitude topographic ridges lie in the troughs of the rolls (Winterer &Sandwell 1987, Sandwell et al 1995) and that the plate has very low strengthunder these ridges (Goodwillie & Parsons 1992). The latest work (Neumann& Zuber 1997) suggests that boudinage may not explain the observations.

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Figure 16 Area of East-Pacific Rise shows complex history of plate reorganizations and “rolls.”

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SeamountsSeamounts have long been of interest to marine geologists for their ability torecord the history of paleo–sea level, for their furnishing of samples of basalticmelts from the Earth’s interior, and for what their abundance patterns say aboutthe thermal regime of the mantle and the heat loss from the Earth. See Watts(1984) for a review. The need to chart seamounts and understand their gravityfields was probably one of the motivations that led the US Navy to launchGEOSAT. Seamounts have recently become very important in other sciences aswell. Fish that live in a particular ecological niche in deep (700–1400 m) wateron the flanks of seamounts, such as orange roughy (Hoplostethus atlanticus),now account for more than half of the fish catch in Australia and New Zealand(Koslow 1997). Seamounts are also beginning to be recognized as an importantsource of dissipation and mixing in the ocean. Dissipation on the shallowshelves has been recognized to account for only about half of the tidal energyloss in the oceans, and seamounts, particularly those that protrude into thethermocline, could account for the missing dissipation. Computer models of thegeneral ocean circulation contain crude representations of bottom topography,and this topography is not sufficient to generate the amount of mixing seen inthe real ocean unless certain fudge factors in the model are tuned. More realisticbottom conditions might solve this problem. For discussion of these issues, seeLueck & Mudge (1997).

The search for seamounts in altimeter data has a rich history that dates tothe GEOS-3 mission (Balmino et al 1979, Watts 1979). SEASAT data wereprecise enough to allow a systematic search for uncharted seamounts (Lambeck& Coleman 1982, Lazarewicz & Schwank 1982, Schwank & Lazarewicz 1982,Dixon & Parke 1983, White et al 1983, Sandwell 1984, Craig & Sandwell 1988),and some workers cautioned that the unknown elastic lithosphere thicknessHwas an important factor in designing an automated search (Dixon et al 1983,Cazenave & Dominh 1984, Watts & Ribe 1984, Craig & Sandwell 1988).However, ifH can be estimated, then a reconnaissance age can be assigned to aseamount (Watts et al 1980). Sandwell (1984) found that half of the seamountsin his altimeter gravity map of the South Pacific were uncharted.

The latest applications of altimetry to the search for seamounts have beenmade on two fronts. Many workers (see Smith & Sandwell 1994a, 1997b,for review and citations) have been interested in the possibility of predictingseamount topography from altimetry. Precise estimation of summit depths isimpossible owing to the nonlinearity in Equation 14, which must be inverted toestimate depth, and the lack of information about depth in the long-wavelengthgravity field. Smith & Sandwell’s work has applied a linear approximation (astabilized inverse of Equation 15) globally, and it has accounted for variations in

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sediment thickness but not for the nonlinear aspects, which have been tackledby other workers (Baudry et al 1987, Baudry & Calmant 1991) working insmaller areas. Wessel and his colleagues (Wessel 1997, Wessel & Kroenke1997, Wessel & Lyons 1997) have used altimeter gravity and vertical gravitygradient data to find seamounts on the Pacific plate (Figure 17) and estimatetheir approximate sizes, in order to search for geometric alignments that can beused to refine the models for the absolute motion of the Pacific plate over the

Figure 17 Large seamounts on the Pacific plate identified by Wessel & Lyons (1997) from al-timetry. After Wessel & Kroenke (1997).

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mantle hotspot frame. This work has led to the suggestion that the HollisterRidge is the location of the Louisville Hotspot (Wessel & Kroenke 1997).

CONCLUDING REMARKS

With the advent of global geodetic orbit altimeter data in 1995, a new era inthe study of tectonic fabric from satellite altimetry has begun. Experience withaltimeter data to date has demonstrated that the shortest possible length scale offabric is being resolved: Fundamental limitations (upward continuation, altime-ter engineering, sea surface variability) preclude any significant improvementin the resolving power of the technique for the foreseeable future. However,the resolution currently achieved has made possible the systematic study ofthe global distribution of tectonic phenomena and has furnished a spectacularconfirmation of the theory of plate tectonics.

Systematic global searches of altimeter data will permit the selection of ideallocalities for testing tectonic hypotheses, resulting in more efficient researchprograms and tremendous cost-savings in ship time. Such studies should leadto new understandings of a variety of processes, particularly seafloor spreadingand seamount volcanism.

While satellite altimetry has confirmed plate tectonics as a first-order theory,altimetry has also shown that the second-order details of tectonic processesare not yet fully understood. At present, it appears that much of the struc-tural variation in the tectonic fabric band is generated at mid-ocean ridgesby processes with strong temporal variability and abrupt transitions betweenmetastable states; these are the hallmarks of nonlinear processes. New theoret-ical and observational work will be required to advance and test hypotheticalmechanisms. The global distribution of phenomena, as revealed by altimetry,will be a powerful constraint that new hypotheses will have to satisfy.

Visit the Annual Reviews home pageathttp://www.AnnualReviews.org.

Literature Cited

Abbott D. 1986. A statistical correlation be-tween ridge crest offsets and spreading rate.Geophys. Res. Lett.13:157–60

Airy GB. 1855. On the computations of the ef-fect of the attraction of the mountain massesas disturbing the apparent astronomical lat-itude of stations in geodetic surveys.Phil.Trans. R. Soc. London145:101–4

Andersen OB, Woodworth PL, Flather RA.1995. Intercomparison of recent ocean tide

models.J. Geophys. Res.100:25261–82Balmino G, Brossier C, Cazenave A, Nouel F,

Dominh K, Vales N. 1979. Geoid of the Ker-guelen Islands area determined from Geos 3altimeter data.J. Geophys. Res.84:3827–32

Banks RJ, Parker RL, Huestis SP. 1977. Iso-static compensation on a continental scale:local versus regional mechanisms.Geophys.J. R. Astron. Soc.51:431–52

Barrell J. 1914–1915.The Strength of the

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u. R

ev. E

arth

Pla

net.

Sci.

1998

.26:

697-

747.

Dow

nloa

ded

from

arj

ourn

als.

annu

alre

view

s.or

gby

UN

IVE

RSI

TY

OF

AL

BE

RT

A o

n 01

/30/

08. F

or p

erso

nal u

se o

nly.



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Earth’s Crust.[A privately printed collectionof reprints of articles originally appearingin the J. Geol.22:28–48, 145–65, 209–36,289–314, 441–68, 537–55, 655–83, 729–41 (1914); and 25:27–44, 424–443, 499–515 (1915).] Silver Spring, MD: Libr. Natl.Ocean. Atmos. Admin.

Baudry N, Diament M, Albouy Y. 1987. Pre-cise location of unsurveyed seamounts in theAustral archipelago area using SEASAT data.Geophys. J. R. Astron. Soc.89:869–88

Baudry N, Calmant S. 1991. 3-D modelling ofseamount topography from satellite altime-try. Geophys. Res. Lett.18:1143–46

Bendat JS, Piersol AG. 1986.Random Data—Analysis and Measurement Procedures.NewYork: Wiley & Sons. 566 pp. 2nd ed.

Bernstein RL, ed. 1982.Seasat Special IssueI: Geophysical Evaluation.[J. Geophys. Res.87:3173–438.] Washington, DC: Am. Geo-phys. Union

Bilitza D. 1997. International reference iono-sphere—status 1995/96.Adv. Space. Res.20(9):1751–54

Born GH, Richards MA, Rosborough GW.1982. An empirical determination of the ef-fects of sea state bias on Seasat altimetry.J.Geophys. Res.87:3221–26

Bouguer P. 1749.La Figure de la Terre.Paris:Chez Charles-Antoine Jombert, Libr. R. Ar-tillerie Genie

Bracewell R. 1965.The Fourier Transform andIts Applications.New York: McGraw-Hill.381 pp.

Brown RD, Kahn WD, McAdoo DC, HimwichWE. 1983. Roughness of the marine geoidfrom SEASAT altimetry.J. Geophys. Res.88:1531–40

Brown RN, Abbott MR, Baker RN, DennerWW, Munk WH, et al. 1995.Scientific Utilityof Naval Environmental Data.McLean, VA:Mitre. 52 pp.

Bruns H. 1878.Die Figur der Erde.Berlin:Stankiewicz’ Konigl. Preuss. Geod. Inst. 49pp.

Calmant S, Cazenave A. 1987. Anomalous elas-tic thickness of the oceanic lithosphere in thesouth-central Pacific.Nature328:236–38

Cazenave A, Dominh K. 1984. Geoid heightsover the Louisville Ridge (South Pacific).J.Geophys. Res.89:11171–79

Cazenave A, Parsons B, Calcagno P. 1995.Geoid lineations of 1000 km wavelengthover the Central Pacific.Geophys. Res. Lett.22:97–100

Chelton DB, Walsh EJ, MacArthur JL. 1989.Pulse compression and adaptive height track-ing in satellite altimetry.J. Atmos. Ocean.Technol.6:407–38

Chen YJ, Morgan WJ. 1990a. Rift valley/no riftvalley transition at mid-ocean ridges.J. Geo-

phys. Res.95:17571–83Chen YJ, Morgan WJ. 1990b. A nonlinear rhe-

ology model for mid-ocean ridge axis topog-raphy.J. Geophys. Res.95:17583–604

Cheney RE, ed. 1995.TOPEX/POSEIDON:Scientific Results. J. Geophys. Res.100:24893–5382. Washington, DC: Am. Geo-phys. Union

Cheney RE, Doyle NS, Douglas BC, AgreenRW, Miller LN, et al. 1991.The CompleteGeosat Altimeter GDR Handbook, NOAAManual NOS NGS 7, Natl. Geodetic Survey.Rockville, MD: US Dep. Commer.

Cochran JR. 1979. An analysis of isostasy in theworld’s oceans, 2: mid-ocean ridge crests.J.Geophys. Res.84:4713–29

Craig CH, Sandwell DT. 1988. Global distribu-tion of seamounts from SEASAT profiles.J.Geophys. Res.93:10408–20

Devey C, Ackermand D, Binard N, DruschM, Francke B, et al. 1995.Cruise ReportSO-100: The Foundation Seamount Chain.Geol.-Palaont. Inst. Univ. Kiel Ber. Nr. 75,Kiel.

Dixon TH, Parke ME. 1983. Bathymetry esti-mates in the southern oceans from SEASATaltimetry.Nature304:407–9

Dixon TH, Mao A. 1997. A GPS estimate of rel-ative motion between North and South Amer-ica.Geophys. Res. Lett.24:535–38

Dixon TH, Naraghi M, McNutt MK, Smith SM.1983. Bathymetric prediction from SEASATaltimeter data.J. Geophys. Res.88:1563–71

Dorman LM, Lewis BTR. 1970. Experimentalisostasy, 1: theory of the determination of theearth’s isostatic response to a concentratedload.J. Geophys. Res.75:3357–65

Douglas BC, Cheney RE, eds. 1990.GEOSAT:Sea Level from Space. J. Geophys. Res.95:2833–3179; 17865–8025. Washington,DC: Am. Geophys. Union

Eanes R, Bettadpur S. 1995.The CSR 3.0 GlobalOcean Tide Model.Univ. Texas Center SpaceRes. Tech. Mem. CSR-TM-95-06. Austin,TX: Univ. Texas Press

Engelis T. 1987.Spherical harmonic expan-sion of the Levitus Sea surface topography.Dep. Geodetic Sci. Surv. Rep. 385, Ohio StateUniv., Columbus, OH

Fu L-L, Christensen EJ, Yamarone CA Jr,Lefebvre M, Menard Y, et al, eds. 1994.TOPEX/POSEIDON: Geophysical Evalua-tion. J. Geophys. Res.99:24369–5062. Wash-ington, DC: Am. Geophys. Union

Gahagan LM, Scotese CR, Royer JY, SandwellDT, Winn JK, et al. 1988. Tectonic fabric mapof the ocean basins from satellite altimetrydata.Tectonophysics155:1–26

Gaspar P, Ogor F, Le Traon PY, ZanifeOZ. 1994. Estimating the sea state biasof the TOPEX and POSEIDON altimeters

Ann

u. R

ev. E

arth

Pla

net.

Sci.

1998

.26:

697-

747.

Dow

nloa

ded

from

arj

ourn

als.

annu

alre

view

s.or

gby

UN

IVE

RSI

TY

OF

AL

BE

RT

A o

n 01

/30/

08. F

or p

erso

nal u

se o

nly.




from crossover differences.J. Geophys. Res.99:24981–94

GEBCO Guiding Committee. 1982.The Gen-eral Bathymetric Charts of the Oceans(GEBCO). A Series of 18 Charts at 1:10 Mil-lion Scale.Ottawa: Can. Hydrographic Serv.

Geli L, Bougault H, and the Pacantarctic Scien-tific Party. 1996.La Campagne Pacantarcticde N/O L’Atalante.Brest, France: IFREMER

Goff JA, Jordan TH. 1988. Stochastic model-ing of seafloor morphology: inversion of SeaBeam data for second-order statistics.J. Geo-phys. Res.93:13589–608

Goff JA, Tucholke BE, Lin J, Jaroslaw GE,Kleinrock MC. 1995. Quantitative analysisof abyssal hills in the Atlantic Ocean: a cor-relation between inferred crustal thicknessand extensional faulting.J. Geophys. Res.100:22509–22

Goodwillie AM. 1995. Short-wavelength grav-ity lineations and unusual flexure results atthe Puka Puka Volcanic Ridge System.EarthPlanet. Sci. Lett.136:297–314

Goodwillie AM, Parsons B. 1992. Placingbounds on lithospheric deformation in thecentral Pacific Ocean.Earth Planet. Sci. Lett.111:123–39

Gunn R. 1943. A quantitative study of isobaricequilibrium and gravity anomalies in theHawaiian Islands.Franklin Inst. J.236:373–90

Hamming RW. 1977.Digital Filters. Engle-wood Cliffs, NJ: Prentice Hall. 226 pp.

Haxby W. 1987.Gravity field of the world’soceans, a portrayal of gridded geophysi-cal data derived from Seasat radar altimetermeasurements of the shape of the ocean sur-face(map). Palisades, NY: Lamont-DohertyGeol. Obs. Columbia Univ. (Rep. MGG-3and Data Announcement 87-MGG-04 USNatl. Geophys. Data Center, Boulder, CO)

Haxby WF, Karner GD, LaBrecque JL, Weis-sel JK. 1983. Digital images of combinedoceanic and continental data sets and theiruse in tectonic studies.Eos Trans. Am. Geo-phys. Union64:995–1004

Haxby WF, Turcotte DL. On isostatic geoidanomalies.J. Geophys. Res.83:5473–78

Haxby WF, Weissel JK. 1986. Evidence forsmall-scale mantle convection from Seasataltimeter data.J. Geophys. Res.91:3507–20

Heiskanen WA, Moritz H. 1967.PhysicalGeodesy.San Francisco: Freeman. 364 pp.

Heiskanen WA, Vening Meinesz FA. 1958.The Earth and Its Gravity Field.New York:McGraw-Hill. 470 pp.

Jones ME, Tabor AR, Weatherall P. 1997.GEBCO 97: The GEBCO Digital Atlas 1997Supplement (CD-ROM and supporting vol.).Birkenhead, UK: Br. Ocean. Data Cent.

Kaldeich B. 1993.Proc. First ERS-1 Symp., Eur.Space Agency Publ. SP-359, 2 Vols. Noord-wijk, The Netherlands: Eur. Space Agency

Kaldeich B. 1994.Proc. Second ERS-1 Symp.,Eur. Space Agency Publ. SP-361, 2 Vols.Noordwijk, The Netherlands: Eur. SpaceAgency

Kalnay E, Kanamitsu M, Kistler R, Collins W,Deaven D, et al. 1996. The NCEP/NCAR 40-year reanalysis project.Bull. Am. Meteorol.Soc.77:437–71

Kaula WM. 1959. Statistical and harmonic anal-ysis of gravity.J. Geophys. Res.64:2401–21[See also corrigendum inJ. Geophys. Res.65:1082]

Kaula WM. 1966.Theory of Satellite Geodesy.Waltham, MA: Blaisdell. 124 pp.

Kaula WM, Lundquist CA, Sykes LR, von ArxWS, Weiffenbach GC. 1970. The terrestrialenvironment: solid earth and ocean physics.NASA Contract. Rep. CR-1599

Kirwan AD, Ahrens TJ, Born GH, eds. 1983.Seasat Special Issue II: Scientific Results.[J. Geophys. Res.88:1529–952.] Washing-ton, DC: Am. Geophys. Union

Koslow JA. 1997. Seamounts and the ecologyof deep-sea fisheries.Am. Sci.85:168–76

Lambeck K, Coleman R. 1982. A search forseamounts in the southern Cook and Australregion.Geophys. Res. Lett.9:389–92

Lame DB, Born GH. 1982. Seasat measurementsystem evaluation: achievements and limita-tions.J. Geophys. Res.87:3175–78

Laxon S, McAdoo D. 1994. Arctic Ocean grav-ity field derived from ERS 1 satellite altime-try. Science265:621–24

Lazarewicz AR, Schwank DC. 1982. Detec-tion of uncharted seamounts using satellitealtimetry.Geophys. Res. Lett.9:385–88

Leitao CD, McGoogan JT. 1975. Skylab radaraltimeter: short wavelength perturbationsdetected in ocean surface profiles.Science186:1208–9

Levitus S. 1982.Climatological Atlas of theWorld Ocean.NOAA Prof. Pap. 13. Wash-ington, DC: US Dep. Commer.

Liu C-S, Sandwell DT, Curray JR. 1982. Thenegative gravity field over the 85◦E ridge.J.Geophys. Res.87:7673–86

Livermore R, McAdoo D, Marks K. 1994. Sco-tia Sea tectonics from high-resolution satel-lite gravity.Earth Planet. Sci. Lett.123:255–68

Lonsdale P. 1988. Geography and history of theLouisville hotspot chain in the Southwest Pa-cific. J. Geophys. Res.93:3078–104

Lonsdale P. 1994. Geomorphology and struc-tural segmentation of the crest of the south-ern (Pacific-Antarctic) East Pacific Rise.J.Geophys. Res.99:4683–702

Lueck RG, Mudge TM. 1997. Topographically

Ann

u. R

ev. E

arth

Pla

net.

Sci.

1998

.26:

697-

747.

Dow

nloa

ded

from

arj

ourn

als.

annu

alre

view

s.or

gby

UN

IVE

RSI

TY

OF

AL

BE

RT

A o

n 01

/30/

08. F

or p

erso

nal u

se o

nly.



744 SMITH

induced mixing around a shallow seamount.Science276:1831–33

Macario A, Haxby WF, Goff JA, Ryan WBF,Cande SC, Raymond CA. 1994. Flow linevariations in abyssal hill morphology for thePacific-Antarctic Ridge at 65◦S.J. Geophys.Res.99:17921–34

Macdonald KC. 1986. The crest of the Mid-Atlantic Ridge: models for crustal genera-tion processes and tectonics. InThe Geologyof North America, vol. M, The Western NorthAtlantic Region, ed. PR Vogt, BE Tucholke.Boulder, CO: Geol. Soc. Am.

Malinverno A. 1991. Inverse square-root depen-dence of mid-ocean ridge flank roughness onspreading rate.Nature352:58–60

Marks KM. 1996. Resolution of the Scripps/NOAA marine gravity field from satellite al-timetry.Geophys. Res. Lett.23:2069–72

Marks KM, McAdoo DC. 1992.Gravity Atlasof the Southern Ocean. World Data Center AMarine Geol. Geophys. Rep. MGG-07.Boul-der, CO: Natl. Geophys. Data Center

Marks KM, McAdoo DC, Smith WHF. 1993.Marine Gravity Derived from Geosat.Boul-der, CO: Natl. Geophys. Data Center

Marks KM, Sailor RV. 1986. Comparison ofGEOS3 and SEASAT altimeter resolution ca-pabilities.Geophys. Res. Lett.7:697–700

Marks KM, Stock JM. 1994. Variations in ridgemorphology and depth-age relationships onthe Pacific-Antarctic Ridge.J. Geophys. Res.99:531–41

Marks KM, Stock JM. 1995. Asymmetricseafloor spreading and short ridge jumps inthe Australian-Antarctic Discordance.Ma-rine Geophys. Res.17:361–73

Marsh JG, Williamson RG. 1982. Seasat altime-ter timing bias estimation.J. Geophys. Res.87:3232–38

Marsh J, Douglas B, Vincent S, Walls D.1975.Test and comparisons of satellite de-rived geoids with Skylab altimeter data.God-dard Space Flight Cent. Doc. X-921-75-176.Greenbelt, MD: Natl. Aeronaut. Space Ad-min.

McAdoo D, Laxon S. 1997. Antarctic tectonics:constraints from an ERS 1 satellite marinegravity field.Science276:556–60

McAdoo DC, Sandwell DT. 1988. Marine grav-ity: Geosat’s exact repeat mission.Eos Trans.Am. Geophys. Union69:1568–69

McGoogan JT, Leitao CD, Wells WT. 1975.Summary of Skylab S-193 Altimeter AltitudeResults.Natl. Aeronaut. Space Admin. Tech.Mem. X-69355. Wallops Island, VA: Natl.Aeronaut. Space Admin. Wallops Flight Cen-ter. 324 pp.

McKenzie DP, Bowin C. 1976. The relation-ship between bathymetry and gravity in theAtlantic Ocean.J. Geophys. Res.81:1903–15

McNutt M. 1979. Compensation of oceanic to-pography: an application of the responsefunction technique to the Surveyor area.J.Geophys. Res.84:7589–98

McNutt M. 1984. Lithospheric flexure and ther-mal anomalies.J. Geophys. Res.89:11180–94

McNutt M, Menard HW. 1982. Constraints onyield strength in the oceanic lithosphere de-rived from observations of flexure.Geophys.J. R. Astron. Soc.71:363–83

Menard HW. 1967. Seafloor spreading, topo-graphy, and the second layer.Science157:923–24

Menke W, Abbott D. 1990.Geophysical The-ory. New York: Columbia Univ. Press. 458pp.

Moritz H. 1980. Geodetic Reference System1980.Bull. Geod.54:395–405

Muller RD, Roest WR, Royer J-Y, GahaganLM, Sclater JG. 1997. Digital isochrons ofthe world’s ocean floor.J. Geophys. Res.102:3211–14

Muller RD, Smith WHF. 1993. Deformation ofthe oceanic crust between the North Ameri-can and South American plates.J. Geophys.Res.98:8275–91

National Geophysical Data Center. 1988.ETOPO-5 bathymetry/topography data.DataAnnounc. 88-MGG-02. Boulder, CO: Natl.Ocean. Atmos. Admin., US Dep. Commer.

Nerem RS, Jekeli C, Kaula WM. 1995. Gravityfield determination and characteristics: ret-rospective and prospective.J. Geophys. Res.100:15053–74

Nerem RS, Koblinsky CJ. 1994. The geoid andocean circulation. InGeoid and Its Geophysi-cal Interpretations, ed. P Vanicek, NT Chris-tou, pp. 95–110. Boca Raton, FL: CRC Press

Neumann GA, Forsyth DW, Sandwell DT. 1993.Comparison of marine gravity from ship-board and high-density satellite altimetryalong the Mid-Atlantic Ridge, 30.5◦–35.5◦S.Geophys. Res. Lett.20:1639–42

Neumann GA, Zuber MT. 1997. Diffuse exten-sion doesn’t cause gravity rolls in the Pacific!EOS Trans. Am. Geophys. Union Fall Meet.Suppl.78:F706 (Abstr.)

Ockendon JR, Turcotte DL. 1978. On the gravi-ational potential and field anomalies due tothin mass layers.Geophys. J. R. Astron. Soc.48:479–92

Olgiati A, Balmino G, Sarrailh M, Green CM.1995. Gravity anomalies from satellite al-timetry: comparison between computationvia geoid heights and via deflections of thevertical.Bull. Geod.69:252–60

Parke ME, Stewart RH, Farless DL, CartwrightDE. 1987. On the choice of orbits for an alti-metric satellite to study ocean circulation andtides.J. Geophys. Res.92:11693–707

Ann

u. R

ev. E

arth

Pla

net.

Sci.

1998

.26:

697-

747.

Dow

nloa

ded

from

arj

ourn

als.

annu

alre

view

s.or

gby

UN

IVE

RSI

TY

OF

AL

BE

RT

A o

n 01

/30/

08. F

or p

erso

nal u

se o

nly.




Parker RL. 1973. The rapid calculation of po-tential anomalies.Geophys. J. R. Astron. Soc.31:445–55

Parsons B, Sclater JG. 1977. An analysis of thevariation of ocean floor bathymetry and heatflow with age.J. Geophys. Res.82:803–27

Phipps Morgan J, Chen YJ. 1992. Dependenceof ridge-axis morphology on magma supplyand spreading rate.Nature357:706–8

Phipps Morgan J, Chen YJ. 1993. The genesis ofoceanic crust: magma injection, hydrother-mal circulation, and crustal flow.J. Geophys.Res.98:6283–98

Phipps Morgan J, Parmentier EM. 1995. Crenu-lated seafloor: evidence for spreading-ratedependent structure of mantle upwelling andmelting beneath a mid-ocean spreading cen-ter.Earth Planet. Sci. Lett.129:73–84

Phipps Morgan J, Sandwell DT. 1994. Sys-tematics of ridge propagation south of 30◦S.Earth Planet. Sci. Lett.121:245–58

Randel DL, Vonder Harr TH, Ringerud MA,Stephens GL, Greenwald TJ, Combs CL.1996. A new global water vapor dataset.Bull.Am. Meteorol. Soc.77:1233–46

Rapley C. 1992. Satellite radar altimetry. InSpace Oceanography, ed. AP Cracknell, pp.355–73. River Edge, NJ: World Sci.

Rapp RH. 1979. Geos 3 data processing forthe recovery of geoid undulations and gravityanomalies.J. Geophys. Res.84:3784–92

Rapp RH. 1983. The determination of geoid un-dulations and gravity anomalies from Seasataltimeter data.J. Geophys. Res.88:1552–62

Rapp RH. 1986. Gravity anomalies and sea sur-face heights derived from a combined Geos3/Seasat altimeter data set.J. Geophys. Res.91:4867–76

Ribe NM, Watts AB. 1982. The distributionof intraplate volcanism in the Pacific Oceanbasin: a spectral approach.Geophys. J. R.Astron. Soc.71:333–62

Sahabi M, Géli L, Olivet J-L, Gilg-Capar L,Roult G, et al. 1996. Morphological reorga-nization within the Pacific-Antarctic Discor-dance.Earth Planet. Sci. Lett.137:157–73

Sandwell DT. 1982. Thermal isostasy: responseof a moving lithosphere to a distributed heatsource.J. Geophys. Res.87:1001–14

Sandwell DT. 1984. A detailed view of theSouth Pacific geoid from satellite altimetry.J. Geophys. Res.89:1089–104

Sandwell DT. 1991. Geophysical applicationsof satellite altimetry.Rev. Geophys. Suppl.(US Rep. Int. Union Geod. Geophys. 1987–1990) 29:132–37

Sandwell DT. 1992. Antarctic marine gravityfield from high-density satellite altimetry.Geophys. J. Int.109:437–48

Sandwell DT, McAdoo DC. 1988. Marine grav-

ity of the Southern Ocean and Antarcticmargin from GEOSAT.J. Geophys. Res.93:10389–96

Sandwell DT, McAdoo DC. 1990. High-accuracy, high-resolution gravity profilesfrom two years of the Geosat exact repeatmission.J. Geophys. Res.95:3049–60

Sandwell DT, Smith WHF. 1992. Global ma-rine gravity from ERS 1, Geosat, and Seasatreveals new tectonic fabric.Eos Trans. Am.Geophys. Union73:133

Sandwell DT, Smith WHF. 1995.Marinegravity anomaly from satellite altimetry(34× 53" map). La Jolla, CA: Geol. DataCenter, Scripps Inst. Ocean.

Sandwell D, Smith WHF. 1997. Marine gravityanomaly from GEOSAT and ERS-1 satellitealtimetry.J. Geophys. Res.102:10039–54

Sandwell DT, Winterer EL, Mammerickx J,Duncan RT, Lynch MA, et al. 1995. Evidencefor the diffuse extension of the Pacific platefrom Pukapuka ridges and cross-grain gravitylineations.J. Geophys. Res.100:15087–99

Sandwell D, Zhang B. 1989. Global mesoscalevariability from the GEOSAT exact repeatmission: correlation with ocean depth.J.Geophys. Res.94:17971–84

Schutz BE, Tapley BD, Shum C-K. 1982. Eval-uation of the Seasat altimeter time tag bias.J. Geophys. Res.87:3239–46

Schwank DC, Lazarewicz AR. 1982. Estima-tion of seamount compensation using satel-lite altimetry.Geophys. Res. Lett.9:907–10

Schwartz KP, Sideris MG, Forsberg R. 1990.The use of FFT techniques in physicalgeodesy.Geophys. J. Int.100:485–514

Sleep NH. 1969. Sensitivity of heat flow andgravity to the mechanism of seafloor spread-ing. J. Geophys. Res.74:542–49

Small C. 1995. Observations of ridge-hotspotinteractions in the Southern Ocean.J. Geo-phys. Res.100:17931–46

Small C, Sandwell DT. 1989. An abrupt changein ridge axis gravity with spreading rate.J.Geophys. Res.94:17383–92

Small C, Sandwell DT. 1992. An analysis ofridge axis gravity roughness and spreadingrate.J. Geophys. Res.97:3225–45

Small C, Sandwell DT. 1994. Imaging mid-ocean ridge transitions with satellite gravity.Geology22:123–26

Smith WHF. 1993. On the accuracy of digitalbathymetric data.J. Geophys. Res.98:9591–603

Smith WHF, Sandwell DT. 1994a. Bathymet-ric prediction from dense satellite altimetryand sparse shipboard bathymetry.J. Geophys.Res.99:21803–24

Smith WHF, Sandwell DT. 1994b.Sea Floor To-pography Predicted from Satellite Altimetryand Ship Depth Measurements, World Data

Ann

u. R

ev. E

arth

Pla

net.

Sci.

1998

.26:

697-

747.

Dow

nloa

ded

from

arj

ourn

als.

annu

alre

view

s.or

gby

UN

IVE

RSI

TY

OF

AL

BE

RT

A o

n 01

/30/

08. F

or p

erso

nal u

se o

nly.



746 SMITH

Center Mar. Geol.Geophys. Rep. MGG-09.Boulder, CO: Natl. Geophys. Data Center,US Dep. Commer.

Smith WHF, Sandwell DT. 1995a. Marine grav-ity field from declassified Geosat and ERS-1 altimetry.Eos Trans. Am. Geophys. Union(1995 Fall Meet. Suppl.)76:F156

Smith WHF, Sandwell DT. 1995b. Oceano-graphic “pseudogravity” in marine gravityfields derived from declassified Geosat andERS-1 altimetry.Eos Trans. Am. Geophys.Union (1995 Fall Meet. Suppl.)76:F151

Smith WHF, Sandwell DT. 1995c. Global com-parison of gravity anomalies measured byships and derived from dense satellite altime-try. Eos Trans. Am. Geophys. Union (1995Spring Meet. Suppl.)76:S89

Smith WHF, Sandwell DT. 1997a. Globalseafloor topography from satellite altime-try and ship depth soundings: evidence forstochastic reheating of the oceanic litho-sphere.Science277:1956–62. [See alsoSci-ence277:1921]

Smith WHF, Sandwell DT. 1997b.Measuredand Estimated Sea Floor Topography, WorldData Center Mar. Geol. Geophys. Rep. RP-01.Boulder, CO: Natl. Geophys. Data Center,US Dep. Commer.

Smith WHF, Staudigel H, Watts AB, PringleMS. 1989. The Magellan Seamounts: EarlyCretaceous record of the South Pacific iso-topic and thermal anomaly.J. Geophys. Res.94:10501–23

Smith WHF, Sandwell DT, Marks KM,McAdoo DC. 1993. On the accuracy of ma-rine gravity fields calculated from satellitealtimetry. Eos Trans. Am. Geophys. Union74:99

Stanley HR. 1979a. The Geos 3 project.J. Geo-phys. Res.84:3779–83

Stanley HR, ed. 1979b.The Geos-3 Project. J.Geophys. Res.84:3779–4079. Washington,DC: Am. Geophys. Union

Stewart RH. 1985. Methods of SatelliteOceanography.Los Angeles: Univ. Calif.Press. 360 pp.

Tai C-K, Kuhn J. 1995. Orbit and tide errorreduction for the first two years of Topex/Poseidon.J. Geophys. Res.100:25353–63

Talandier J, Okal EA. 1996. Monochromatic=waves from underwater volcanoes in the Pa-cific ocean: ringing witnesses to geyser pro-cesses?Bull. Seismol. Soc. Am.86:1529–44

Tapley BD, Born GH, Parke ME. 1982. TheSeasat altimeter data and its accuracy assess-ment.J. Geophys. Res.87:3179–88

Tapley BD, Watkins MM, Ries JC, Davis GW,Eanes RJ, et al. 1996. The joint gravity model3. J. Geophys. Res.101:28029–49

Tapponier P, Francheteau J. 1978. Necking of

the lithosphere and the mechanics of slowlyaccreting plate boundaries.J. Geophys. Res.83:3955–70

Turcotte DL, Schubert G. 1982.Geodynamics.New York: Wiley & Sons. 450 pp.

Vening Meinesz FA. 1941. Gravity over theHawaiian Archipelago and over the Madieraarea: conclusions about the Earth’s crust.Proc. Kon. Ned. Akad. Wetensia.44 pp.

Wagner CA. 1979. The geoid spectrum fromaltimetry.J. Geophys. Res.84:3861–71

Walcott RI. 1970. Flexure of the lithosphere atHawaii.Tectonophysics9:435–46

Walcott RI. 1976. Lithospheric flexure, analysisof gravity anomalies, and the propagation ofseamount chains. InThe Geophysics of thePacific Ocean Basin and Its Margins, ed. GHSutton, MH Manghnani, R Moberly,Geo-phys. Monogr. Ser.19:431–38. Washington,DC: Am. Geophys. Union

Watts AB. 1978. An analysis of isostasy inthe world’s oceans 1. Hawaiian-EmperorSeamount chain.J. Geophys. Res.83:5989–6004

Watts AB. 1979. On geoid heights derived fromGeos 3 altimeter data along the Hawaiian-Emperor Seamount chain.J. Geophys. Res.84:3817–26

Watts AB. 1983. The strength of the Earth’scrust.Marine Technol. Soc. J.17:5–17

Watts AB. 1984. Introduction to seamount spe-cial session.J. Geophys. Res.89:11066–68

Watts AB, Cochran JR. 1974. Gravity anoma-lies and flexure of the lithosphere alongthe Hawaiian-Emperor seamount chain.Geo-phys. J. R. Astron. Soc.38:119–41

Watts AB, Ribe NM. 1984. On geoid heightsand flexure of the lithosphere at seamounts.J. Geophys. Res.89:11152–70

Watts AB, Bodine JH, Ribe NM. 1980. Observa-tions of flexure and the geological evolutionof the Pacific Ocean basin.Nature283:532–37

Watts AB, Weissel JK, Duncan RA, Larson RL.1988. Origin of the Louisville Ridge and itsrelationship to the Eltanin Fracture Zone sys-tem.J. Geophys. Res.93:3051–77

Wessel P. 1992. Thermal stresses and the bi-modal distribution of elastic thickness esti-mates of the oceanic lithosphere.J. Geophys.Res.97:14177–93

Wessel P. 1997. Sizes and ages of seamountsusing remote sensing: implications for in-traplate volcanism.Science277:802–5

Wessel P, Kroenke L. 1997. A geometric tech-nique for relocating hotspots and refining ab-solute plate motions.Nature387:365–69

Wessel P, Kroenke LW, Bercovici D. 1996. Pa-cific plate motion and undulations in geoidand bathymetry.Earth Planet. Sci. Lett.140:53–66

Ann

u. R

ev. E

arth

Pla

net.

Sci.

1998

.26:

697-

747.

Dow

nloa

ded

from

arj

ourn

als.

annu

alre

view

s.or

gby

UN

IVE

RSI

TY

OF

AL

BE

RT

A o

n 01

/30/

08. F

or p

erso

nal u

se o

nly.




Wessel P, Lyons S. 1997. Distribution of largePacific seamounts from Geosat/ERS 1: im-plications for the history of intraplate volcan-ism.J. Geophys. Res.102:22459–75

Wessel P, Watts AB. 1988. On the accuracy ofmarine gravity measurements.J. Geophys.Res.93:393–413

West B, Sempére J-C, Pyle D, Phipps-MorganJ, Christie D. 1994. Evidence for variable up-per mantle temperature and crustal thicknessin and near the Australian-Antarctic Discor-dance.Earth Planet. Sci. Lett.128:135–53

White JV, Sailor RV, Lazarewicz AR, LeSchackAR. 1983. Detection of seamount signaturesin SEASAT altimeter data using matched fil-ters.J. Geophys. Res.88:1541–51

Wiener N. 1933.The Fourier Integral and Cer-tain of Its Applications.Cambridge: Cam-bridge Univ. Press. 201 pp.

Williamson RG, Nerem RS. 1994. Improvedorbit computations for the Geosat mission:benefits for oceanographic and geodynamic

studies.EOS Trans. Am. Geophys. Union(1994 Spring Meet. Suppl.) 75:S155

Winterer EL, Sandwell DT. 1987. Evidencefrom en-echelon cross-grain ridges for ten-sional cracks in the Pacific plate.Nature329:534–37

Witter DL, Chelton DB. 1991. An apparentwave height dependence in the sea-state biasin Geosat altimeter range measurements.J.Geophys. Res.96:8861–67

Yale MM, Sandwell DT, Smith WHF. 1995.Comparison of along-track resolution ofstacked Geosat, ERS 1, and TOPEX satellitealtimeters.J. Geophys. Res.100:15117–27

Zlotnicki V. 1994. The geoid from satellite al-timetry. InGeoid and Its Geophysical Inter-pretations, ed. P Vanicek, NT Christou, pp.95–110. Boca Raton, FL: CRC Press

Zlotnicki V, Fu L-L, Patzert W. 1989. Seasonalvariability in global sea level observed withGeosat altimetry.J. Geophys. Res.94:17959–69

Ann

u. R

ev. E

arth

Pla

net.

Sci.

1998

.26:

697-

747.

Dow

nloa

ded

from

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Annual Review of Earth and Planetary Science Volume 26, 1998

CONTENTSContemplation of Things Past, George W. Wetherill 1

Volcanism and Tectonics on Venus, F. Nimmo, D. McKenzie 23

TEMPERATURES IN PROTOPLANETARY DISKS, Alan P. Boss 53

THE IMPORTANCE OF PAHOEHOE, S. Self, L. Keszthelyi, Th. Thordarson 81

CHINESE LOESS AND THE PALEOMONSOON, Tungsheng Liu, Zhongli Ding 111

STELLAR NUCLEOSYNTHESIS AND THE ISOTOPIC COMPOSITION OF PRESOLAR GRAINS FROM PRIMITIVE METEORITES, Ernst Zinner

147

NOBLE GASES IN THE EARTH'S MANTLE, K. A. Farley, E. Neroda 189

SATELLITE ALTIMETRY, THE MARINE GEOID, AND THE OCEANIC GENERAL CIRCULATION, Carl Wunsch, Detlef Stammer 219

CHEMICALLY REACTIVE FLUID FLOW DURING METAMORPHISM, John M. Ferry, Martha L. Gerdes 255

CHANNEL NETWORKS, Andrea Rinaldo, Ignacio Rodriguez-Iturbe, Riccardo Rigon 289

EARLY HISTORY OF ARTHROPOD AND VASCULAR PLANT ASSOCIATIONS, Conrad C. Labandeira 329

Ecological Aspects of the Cretaceous Flowering Plant Radiation, Scott L. Wing, Lisa D. Boucher 379

The Re-Os Isotope System in Cosmochemistry and High-Temperature Geochemistry, Steven B. Shirey, Richard J. Walker 423

DYNAMICS OF ANGULAR MOMENTUM IN THE EARTH'S CORE, Jeremy Bloxham 501

FISSION TRACK ANALYSIS AND ITS APPLICATIONS TO GEOLOGICAL PROBLEMS, Kerry Gallagher, Roderick Brown, Christopher Johnson

519

Isotopic Reconstruction of the Past Continental Environments, Paul L. Koch 573

The Plate Tectonic Approximation: Plate Nonrigidity, Diffuse Plate Boundaries, and Global Plate Reconstructions, Richard G. Gordon 615

LABORATORY-DERIVED FRICTION LAWS AND THEIR APPLICATION TO SEISMIC FAULTING, Chris Marone 643

Seafloor Tectonic Fabric by Satellite Altimetry, Walter H. F. Smith 697

Ann

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Sci.

1998

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697-

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SEAFLOOR TECTONIC FABRIC FROM SATELLITE ALTIMETRY 1

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