Goddard Earth Model Research Articles

In Memoriam

Frank Lerch died in January 1999, at age 75. He had been a member (Geodesy) since 1976. Lerch began his career at Goddard in 1960 when NASA itself was in its infancy, and set Goddard on its current path for determining the gravity field models. As a mathematician, he was responsible for developing many of the numerical techniques that are now in common use to process satellite tracking data, combine satellite and surface gravity data, and solve for the gravity field. His career was centered on the development of the Goddard Earth Models (GEMs), Joint Gravity Models (JGMs—with the University of Texas, CNES, and JPL as partners), and he began the work toward achieving EGM96, GSFC's latest and continuing gravity modeling effort in collaboration with NIMA and the Ohio State University

Application of the GEM‐T2 gravity field to altimetric satellite orbit computation

As part of a continuing effort to provide improved orbits for use with existing altimeter data, we have recomputed ephemerides for both the Seasat and Geosat Exact Repeat altimeter missions. The orbits were computed in a consistent fashion, using the Goddard Earth Model T2 gravity field along with available ground‐based tracking data. Such an approach allows direct comparisons of sea level between the two altimeter systems. Evaluation of the resulting ephemerides indicates that root‐mean‐square accuracies of 30–50 cm have been achieved for the radial component of the orbits for both satellites. An exception occurs for the last year of the Geosat Exact Repeat Mission, when the rms radial orbit accuracy degrades to the 1‐m level at times owing to the inability to adequately model the drag force arising from the increased solar activity.

A test of GEM T2 from GEOSAT crossovers using latitude lumped coefficients

New Latitude Lumped Coefficients (LLC) of a geopotential model are defined as representing the principal differences of the radial distance to a satellite due to the model at single-orbit crossovers in an Exact Repeat Mission. In contrast with previously defined orbital lumped coefficients, the LLC here are dependent only on the geopotential order (without degree distinction) and the latitude. We examine discrepancies in altimetrically determined sea surface heights at over 30000 crossover positions of GEOSAT during its ERM, 1986–1989, after removal of many variable media and surface effects (Cheney et al., 1991) as well as initial condition orbit error. The mean of these discrepancies along well represented latitude bands in the southern hemisphere are used to determine the LLC errors for Goddard Earth Model T2, which was the reference for the GEOSAT sea surface heights. GEM T2 was derived from satelliteonly tracking data with good representation of the GEOSAT orbit. Relating the ”measured” LLC discrepancies to projections of commission error from the GEM T2 variance-covariance matrix, we find that — except for order 3 — GEM T2's performance is as expected. This test represents the first spectral calibration of a gravity model with independent, purely radial orbit data.

A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM‐T3

An improved model of Earth's gravitational field, GEM‐T3, has been developed from a combination of satellite tracking, satellite altimeter, and surface gravimetric data. GEM‐T3 provides a significant improvement in the modeling of the gravity field at half wavelengths of 400 km and longer. This model, complete to degree and order 50, yields more accurate satellite orbits and an improved geoid representation than previous Goddard Earth Models. GEM‐T3 uses altimeter data from GEOS 3 (1975–1976), Seasat (1978) and Geosat (1986–1987). Tracking information used in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The recovery of the long‐wavelength components of the solution relies mostly on highly precise satellite laser ranging (SLR) data, but also includes TRANET Doppier, optical, and satellite‐to‐satellite tracking acquired between the ATS 6 and GEOS 3 satellites. The main advances over GEM‐T2 (beyond the inclusion of altimeter and surface gravity information which is essential for the resolution of the shorter wavelength geoid) are some improved tracking data analysis approaches and additional SLR data. Although the use of altimeter data has greatly enhanced the modeling of the ocean geoid between 65°N and 60°S latitudes in GEM‐T3, the lack of accurate detailed surface gravimetry leaves poor geoid resolution over many continental regions of great tectonic interest (e.g., Himalayas, Andes). Estimates of polar motion, tracking station coordinates, and long‐wavelength ocean tidal terms were also made (accounting for 6330 parameters). GEM‐T3 has undergone error calibration using a technique based on subset solutions to produce reliable error estimates. The calibration is based on the condition that the expected mean square deviation of a subset gravity solution from the full set values is predicted by the solutions' error covariances. Data weights are iteratively adjusted until this condition for the error calibration is satisfied. In addition, gravity field tests were performed on strong satellite data sets withheld from the solution (thereby ensuring their independence). In these tests, the performance of the subset models on the withheld observations is compared to error projections based on their calibrated error covariances. These results demonstrate that orbit accuracy projections are reliable for new satellites which were not included in GEM‐T3.

Evaluation of 14th-order harmonics in the geopotential from 18 resonant satellite orbits

The values of lumped harmonics from the analyses of 18 satellite orbits at 14th-order resonance are used to determine individual tesseral harmonics of order 14 in the Earth’s gravity field. Eight C and five S coefficients are determined for odd degree and six C , S pairs for even degree. The results are most useful in providing the only independent test of the values obtained in recent comprehensive geopotential models. The models of the 1980s are generally consistent with the resonance values, which have lower or comparable standard deviations. The new Goddard Earth Model, GEM-T3, and European model, GRIM4-C1 have much lower standard deviations and show significant differences from our values.

Spectral characteristics of time‐dependent orbit errors in altimeter height measurements

A mean reference surface and time‐dependent orbit errors are estimated simultaneously for each exact‐repeat ground track from the first two years of Geosat sea level estimates based on the Goddard Earth model (GEM)‐T2 orbits. Motivated by orbit theory and empirical analysis of Geosat data, the time‐dependent orbit errors are modeled as 1 cycle per revolution (cpr) sinusoids with slowly varying amplitude and phase. The method recovers the known “bow tie effect” introduced by the existence of force model errors within the precision orbit determination (POD) procedure used to generate the GEM‐T2 orbits. The bow tie pattern of 1‐cpr orbit errors is characterized by small amplitudes near the middle and larger amplitudes (up to 160 cm in the 2 years of data considered here) near the ends of each 5‐ to 6‐day orbit arc over which the POD force model is integrated. A detailed examination of these bow tie patterns reveals the existence of daily modulations of the amplitudes of the 1‐cpr sinusoid orbit errors with typical and maximum peak‐to‐peak ranges of about 14 cm and 30 cm, respectively. The method also identifies a daily variation in the mean orbit error with typical and maximum peak‐to‐peak ranges of about 6 cm and 30 cm, respectively, that is unrelated to the predominant 1‐cpr orbit error. It is suggested that the two daily signals arise from daily adjustments of the drag coefficient in the GEM‐T2 POD procedure. Application of the simultaneous solution method to the much less accurate Geosat height estimates based on the Naval Astronautics Group orbits concludes that the accuracy of POD is not important for collinear altimetric studies of time‐dependent mesoscale variability (wavelengths shorter than 1000 km), as long as the time‐dependent orbit errors are dominated by 1‐cpr variability and a long‐arc (several orbital periods) orbit error estimation scheme such as that presented here is used. The accuracy of POD becomes more important for studies of larger‐scale variability.

New error calibration tests for gravity models using subset solutions and independent data: Applied to GEM‐T3

Orbit error projections based on the error covariance estimates of Goddard Earth Model (GEM)‐T3 have been shown to be reliable through their projection on observation residuals within independent data sets. Special geopotential solutions were developed based upon the same data set and weighting used in the GEM‐T3 gravity model, but with a significant satellite data set eliminated from the solution. These subset gravity models are then used to compute the observation residuals within orbital solutions for the omitted satellite and the results are compared to their predicted values based on the error covariance of these models. To ensure meaningful results, the tests were designed so that the observation residuals are dominated by geopotential modeling errors. This yields a reliable test of the error estimates of the subset solutions and hence tests the data weighting used in the construction of these models (GEM‐T3 and subset solutions alike). The error estimates for GEM‐T3 are based upon an optimal data weighting method and have been obtained in a separate calibration process. The test results shown here indicate that the GEM‐T3 error estimates for the gravity parameters are calibrated and that the predicted orbit errors correspond well with actual orbit accuracies. Test results of the complete GEM‐T3 model with totally independent high precision DORIS Doppler tracking data acquired on the French SPOT‐2 satellite confirms these conclusions.

GEOID90: A high‐resolution geoid for the United States

Recently, geodesy has witnessed a renaissance in geoid computation. The advances over the past decade have taken place at all wavelengths, and have brought forth major improvements in accuracy. An example of a long‐wavelength global gravitation model is the GEM‐T2 (Goddard Earth Model) solution of Marsh et al. [1989], which is complete to degree and order 36, and incomplete to degree 50. Rapp and Pavlis [1990] have computed a pair of solutions, 0SU89A and 0SU89B (Ohio State University), which are spherical harmonic models of the Earth's geopotential complete to degree and order 360. Although termed high degree global models, these solutions provide the geoid to what we may now consider a medium length scale–about 50‐km resolution. High‐resolution geoid height modeling has shown the greatest advances in accuracy. Forsberg [1990] computed a geoid model for the Nordic area on a 5‐km grid, and obtained 3–7 cm standard deviations when compared to Global Positioning System (GPS) and leveling in local networks of 50–100 km in extent.

The gravimetric geoid of Sudan

The gravimetric geoid for the Sudanese subcontinent was computed on a grid defined by the geographical coordinates 4°N–22°N, 22°E–36°E. This geoid was referred to the geodetic reference system 1980 (GRS80) and transformed to the local datum in the Sudan (Adindan datum). The precise transformation parameters between GRS80 and Adindan datum were determined from the comparison of the gravimetric geoid and its corresponding astrogeodetic geoid. The free-air co-geoid was computed from the combination of surface gravity data using a modified Stokes's kernel and the recently published GODDARD EARTH MODEL (GEM-T1) potential coefficient set. The surface gravity data consist of 1° × 1°, 10′ × 10′ and point anomaly data. Corresponding GEM-T1 anomalies were subtracted from the gravity anomalies. The atmospheric and topographic attraction effect on the gravity anomalies as well as their by-product indirect effect on the computed co-geoid is critically examined. Also the effect of neglecting the ellipticity of the reference ellipsoid on the computed geoid is outlined.

The GEM‐T2 Gravitational Model

GEM‐T2 is the latest in a series of Goddard Earth models of the terrestrial gravitational field. It is the second in a planned sequence of gravity models designed to improve both the modeling capabilities for determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10‐cm RMS and for defining the long‐wavelength geoid to support many oceanographic and geophysical applications. GEM‐T2 includes more than 6OU coefficients above degree 36, the limit for GEM‐T1, and provides a dynamically determined model of the major tidal components which contains 90 terms. Like GEM‐T1, it was produced entirely from satellite tracking data. GEM‐T2 however, now uses nearly twice as many satellites (31 versus 17), contains 3 times the number of observations (2.4 million), and has twice the number of data arcs (1130). GEM‐T2 utilizes laser tracking from 11 satellites, Doppler data from four satellites, two‐ and three‐way range rate data from Landsat‐1, satellite‐to‐satellite tracking data between the geosynchronous ATS 6 and GEOS 3, and optical observations on 20 different orbits. This observation set effectively exhausts the inclination distribution available for gravitational field development from our historical data base. The recovery of the higher degree and order coefficients in GEM‐T2 was made possible through the application of a constrained least squares technique using the known spectrum of the Earth's gravity field as a priori information. The error calibration of the model was performed concurrently with its generation by comparing the complete model against test solutions which omit each individually identifiable data set in turn. The differences between the solutions isolate the contribution of a given data set, and the magnitudes of these differences are compared for consistency against their expected values from the respective solution covariances. The process yields near optimal data weights and assures that the model will be both self‐consistent and well calibrated. GEM‐T2 has benefitted by its application as demonstrated through comparisons using independently derived gravity anomalies from altimelry. Results for the GEM‐T2 error calibration indicate significant improvement over previous satellite‐only GEM models. The accuracy assessment of the lower degree and order coefficients of GEM‐T2 shows that their uncertainties have been reduced by 20% compared to GEM‐T1. The commission error of the geoid has been reduced from 160 cm for GEM‐T1 to 130 cm for GEM‐T2 for the 36 × 36 portion of the field. The orbital accuracies achieved using GEM‐T2 are likewise improved. This is especially true for the Starlette and GEOS 3 orbits where higher‐order resonance terms not present in GEM‐T1 (e.g., terms with m = 42,43) are now well represented in GEM‐T2. The improvement in orbital accuracy of GEM‐T2 over GEM‐T1 extends across all orbit inclinations. This confirms our conclusion that GEM‐T2 offers a significant advance in knowledge of the Earth's gravity field.

Analysis of the orbital elements of the satellite COSMOS 1603 (1984-106 A) at 14th-order resonance

The orbital parameters of Cosmos 1603 (1984-106 A) have been determined at 43 epochs from over 2900 observations, of which over 80% were supplied by the U.S. Naval Research Laboratory. Hewitt camera observations were available for 25 of the determinations. Orbital elements were determined between January and December 1987, during which time the satellite was close to 14:1 resonance. The satellite experienced the interesting property of being temporarily trapped with respect to a secondary resonance parameter due to the low air-drag in 1987. This effect gave rise to a quasi-secular increase in the eccentricity and libration of the secondary resonance variable. Analysis of the inclination and eccentricity yielded six lumped harmonic coefficients of order 14. Analysis of the mean motion yielded additional pairs of lumped harmonics of orders 14, 28 and 42, the 14th-order harmonics superseding those obtained from analysis of the inclination. The derived values were used to test the Goddard Earth Models, GEM-T1 and GEM-T2, at high order.

A summary of precise orbit computation for the Geosat exact repeat mission: Haines, B.J. et al., 1989. Johns Hopkins APL tech. Dig., 10(4):393–404. Colorado Ctr. for Astrodynam. Res., Boulder, CO, USA

Recent efforts to recompute orbits for the Geosat Exact Repeat Mission have resulted in a substantial reduction in the satellite's orbit error. The improved orbits are based on Doppler tracking and on the new earth gravity models being developed at the Goddard Space Flight Center in support of requirements for the TOPEX/Poseidon mission. The first set of orbit solutions based on the Goddard Earth Model (GEM T1) gravity model and tracking data from the U.S. Navy's Operational Network system are accurate to about 85 cm root mean square (rms) in height. Preliminary tests of orbits computed with the GEM-T2 model, along with tracking data from an augmented network consisting of the Navy's Operational Network and selected Tracking Network sites, indicate that radial accuracies of 35 cm rms can be achieved.

A new gravitational model for the Earth from satellite tracking data: GEM‐T1

A major new computation of a terrestrial gravitational field model has been performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). In the development of this new model, designated Goddard Earth Model GEM‐T1, the design decisions of the past have been reassessed in light of the present state of the art in satellite geodesy. With GEM‐T1 a level of internal consistency has been achieved which is superior to any earlier Goddard Earth Model. For the first time a simultaneous solution has been made for spherical harmonic parameters of both invariant and tidal parts of the gravitational field. The solution of this satellite model to degree 36 is a major factor accounting for its improved accuracy. The addition of more precise and previously unused laser data and the introduction of consistent models were also accomplished with GEM‐T1. Another major factor allowing the creation of this model was the redesign and vectorization of our main software tools (GEODYN II and SOLVE) for the GSFC Cyber 205 computer. In particular, the high‐speed advantage (50:1), gained with the new SOLVE program, made possible an optimization of the weighting and parameter estimation scheme used in previous GEM models resulting in significant improvement in GEM‐T1. The solution for the GEM‐T1 model made use of the latest International Association of Geodesy reference constants, including the J2000 Reference System. It provided a simultaneous solution for (1) a gravity model in spherical harmonics complete to degree and order 36; (2) a subset of 66 ocean tidal coefficients for the long‐wavelength components of 12 major tides. This adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor tides and the Wahr frequency dependent solid earth tidal model; and (3) 5‐day averaged Earth rotation and polar motion parameters for the 1980 period onward. GEM‐T1 was derived exclusively from satellite tracking data acquired on 17 different satellites whose inclinations ranged from 15° to polar. In all, almost 800,000 observations were used, half of which were from third generation (<5 cm) laser systems. A calibration of the model accuracies has been performed showing GEM‐T1 to be a significant improvement over earlier GSFC “satellite‐only” models based purely on tracking data for both orbital and geoidal modeling applications. For the longest wavelength portion of the geoid (to 8×8), GEM‐T1 is a major advancement over all GEM models, even those containing altimetry and surface gravimetry. The radial accuracy for the anticipated TOPEX/POSEIDON orbit was estimated using the covariances of the GEM‐T1 model. The radial errors were found to be at the 25‐cm rms level as compared to 65 cm found using GEM‐L2. This simulation evaluated only errors arising from geopotential sources. GEM‐L2 was the best available model for TOPEX prior to the work described herein. A major step toward reaching the accuracy of gravity modeling necessary for the TOPEX/POSEIDON mission has been achieved.

The accuracy of a Goddard TOPEX gravity model as seen by independent resonant data

A recent satellite geopotential (Goddard Earth Model T1; Marsh, 1986, EOS 67, 909) has been derived from almost 800,000 precise tracking observations (laser ranges, optical positions and doppler range rates) to 17 spacecraft. This model was designed principally to minimize radial orbit errors on the forthcoming altimeter bearing ocean TOPography Experimental satellite TOPEX. The largest geopotential component of this error (over weekly data arcs) is estimated to arise from a 13th order resonance with a period of 3 days on the 127 revs per 10 day TOPEX orbit. This orbit is not near one of the 17 in the GEM T1 solution. To assess the reliability of the resonances predicted by the new model, 240 geopotential constraints derived from independent (mostly deep) resonant orbits have been examined (orders 2 and 9 through 15). Comparisons of these data with Gem T1 are generally superior to comparisons with all previous models from satellite data only. However, the error calibration results are considerably more variable than for past Goddard models. Using a single constant to scale the covariance matrix of Gem T1, these comparisons show that the new solution has probably improved the geopotential in the higher orders by about 25% overall to degree 36 from the best previous model Gem L2 (Lerch et al., 1982, Geophys. Res. Lett. 9, 1263). If this scale is valid for the significant m daily effects of low orders as well (and there is some evidence for it using 24-h satellite accelerations), TOPEX radial errors using Gem T1 (for weekly tracking arcs) will be (at best) in the neighborhood of 43 cm (r.m.s.).

Comments on Lambeck and Coleman: 'The Earth's shape and gravity field: a report of progress from 1958 to 1982'

The accuracy and validation of global gravity models based on satellite data are discussed, responding to the statistical analysis of Lambeck and Coleman (1983) (LC). Included are an evaluation of the LC error spectra, a summary of independent-observation calibrations of the error estimates of the Goddard Earth Models (GEM) 9 and L2 (Lerch et al., 1977, 1979, 1982, 1983, and 1985), a comparison of GEM-L2 with GRIM-3B (Reigber et al., 1983), a comparison of recent models with LAGEOS laser ranging, and a summary of resonant-orbit model tests. It is concluded that the accuracy of GEMs 9, 10, and L2 is much higher than claimed by LC, that the GEMs are in good agreement with independent observations and with GRIM-3B, and that the GEM calibrations were adequate. In a reply by LC, a number of specific questions regarding the error estimates are addressed, and it is pointed out that the intermodel discrepancies of the greatest geophysical interest are those in the higher-order coefficients, not discussed in the present comment. It is argued that the differences among the geoid heights of even the most recent models are large enough to call for considerable improvements.

A gravity model for crustal dynamics (GEM‐L2)

Goddard earth model, GEM‐L2, has been derived using predominantly the precise laser ranging taken on many satellites, including LAGEOS, in support of NASA's crustal dynamics activities. Only conventional satellite tracking (ground to satellite: GEM 9's data plus LAGEOS ranging) has been employed. The solution consists of 566 gravitational harmonic coefficients (complete through degree 20) and the earth‐fixed coordinates of 173 tracking stations including about 20 used exclusively for LAGEOS. In addition, 5‐day averages of earth orientations (pole position and length of day) have been derived simultaneously from the LAGEOS data for 1979–1981. These latter results have been independently confirmed by very long baseline interferometric observations. The model improves the utility of the LAGEOS data for detecting global movements of the crust and earth orientation while also enhancing our understanding of the long‐wavelength gravity field. In addition to the LAGEOS data, the solution combined laser ranging from nine satellites and optical and electronic measurements on some 20 spacecraft for a total of 1,257,000 observations. GEM‐L2 has improved the modeling of the longest‐wavelength portion of the field by more than a factor of 2 over GEM's developed in the late 1970's. A full discussion of GEM‐L2's accuracy is found elsewhere in this issue. Use of GEM‐L2 yields smaller LAGEOS positioning errors from about 1 m with GEM 9 (1979) to a current value of about 25 cm.

On the accuracy of recent Goddard gravity models

Extensive evaluations of recent Goddard earth models against independent data generally confirm previous GEM accuracy estimates as conservative. Tests with new Seasat altimetric and surface gravimetric data as well as previous unused satellite lumped harmonics and accelerations and independent optical/laser solutions all suggest that the geoid errors in the satellite only GEM‐L2 (1982) may be as low as 20 cm (rms worldwide) through degree and order 6 and only 110 cm through degree and order 20. The GEM 10B (1981) geoid appears to be accurate to better than 150‐cm rms through degree 36. Recent independently developed European models from comprehensive surface and satellite data agree well with Goddard models at low and high degree compared to estimated GEM errors. Discrepancies at intermediate degree may be due to more extensive use of satellite orbits in Goddard fields. These conclusions (particularly on low‐degree terms) conflict markedly with those made in a recent paper by Lambeck and Coleman (1983), who used an unreliable error estimator.

Individual geopotential coefficients of order 15 and 30, from resonant satellite orbits

The analysis of variations in satellite orbits when they pass through 15th-order resonance (15 revolutions per day) yields values of lumped geopotential harmonics of order 15, and sometimes of order 30. The 15th-order lumped harmonics obtained from 24 such analyses over a wide range of orbital inclinations are used here to determine individual harmonic coefficients of order 15 and degree 15,16,…35; and the 30th-order lumped harmonics (from eight of the analyses) are used to evaluate individual coefficients of order 30 and degree 30,32,…40. The new values should be more accurate than any previously obtained. The accuracy of the 15th-order coefficients of degree 15, 16,…23 is equivalent to 1 cm in geoid height, while the 30th-order coefficients of degree 30, 32 and 34 are determined with an accuracy which is equivalent to better than 2 cm in geoid height. The results are used to assess the accuracy of the Goddard Earth Model 10B.

Geopotential harmonics of order 15 and 30, from analysis of the orbit of satellite 1971-10B

The satellite 1971-10B passed through exact 15th-order resonance on 30 March 1981 and orbital parameters have been determined at 52 epochs from some 3500 observations using the RAE orbit refinement program, PROP, between September 1980 and October 1981. The variations in inclination and eccentricity during this time have been analysed, and six lumped 15th-order harmonic coefficients and two 30th-order coefficients have been evaluated. The 15th-order coefficients are the best yet obtained for an orbital inclination near 65°; and previously there were no 30th-order coefficients available at this inclination. The lumped coefficients have been used to test the Goddard Earth Model GEM 10B: there is good agreement for seven of the eight coefficients.

On gravity from SST, geoid from Seasat, and plate age and fracture zones in the Pacific

Our earlier measurements of the high degree and order (n, m>12) gravity in the central Pacific using the method of satellite‐to‐satellite tracking (SST) have been extended with an additional 50 passes of data. The SST method utilizes line of sight Doppler tracking between the very high geosynchronous ATS 6 spacecraft and the much lower (840 km) orbiting GEOS 3 spacecraft. The observed changes in velocity with time are reduced in relation to the well‐determined low degree and order (n, m≤12) Goddard Earth Model (GEM) field model, and accelerations are found by differentiation of the range rates. Because this new map is essentially identical to the earlier results, we have produced a composite map by combining all 90 passes of SST data. The resolution of the map is at worst about 5° and is much better in most places. A comparison of this map with conventional GEM models shows very good agreement. A reduction of the Seasat altimeter data has also been carried out for an additional comparison. Although the Seasat geoid contains much more high‐frequency information, it agrees very well with both the SST and the GEM fields. The maps are dominated (especially in the east) by a pattern of roughly east‐west anomalies with a transverse wavelength of about 2000 km. A further comparison with regional bathymetric data shows a good correlation of gravity and geoid with plate age. Each anomaly band is framed by major fracture zones whose regular spacing (≃10°) seems to account for the fabric in these fields. There are other anomalies that are accounted for by hot spots, and altogether, the immediate source of at least part of these Pacific anomalies is in the lithosphere itself. It therefore seems that most of the anomalies in the east half of the Pacific could be partly caused simply by regional differences in plate age. The amplitude of these geoid or gravity anomalies caused by age differences should decrease with absolute plate age, and large anomalies (∼3 m) over old, smooth seafloor may indicate a further, deeper source within or perhaps below the lithosphere. However, because of the significant effect of plate structure on the geoid and gravity fields, especially over young (<80 Ma) seafloor, lithospheric effects must be eliminated before these anomalies can be systematically ascribed to deeper sources such as small‐scale convection.