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NASA NTRS1989

Long range geoid control through the European GPS traverse: Final results

The European north-south Global Positioning System (GPS)-traverse proposed by IAG SSG 3.88, should control and improve the European geoid. This traverse follows first order leveling lines, included in the United European Leveling Network. From May to August 1986 and in July 1987, the central and northern part of this traverse (approx. 3000 km) was observed using up to four TI 4100 receivers, covering Austria, Federal Republic of Germany, Denmark, Sweden and Norway. Both traverse parts contain 71 stations with distances of about 50 km. In addition, 8 stations have been occupied for overlapping connections, and traverse links were established for connecting the fundamental stations Wettzell (VLBI and SLR) and Onsala (VLBI). Final results show a GPS observation precision of a few cm for loops of some 100 km circumference. After transformation of the GPS results to geoid heights using the leveled heights, comparisons with different existing gravimetric geoid determinations including geopotential models were performed. In addition, new geopotential models complete to degree and order 360 tailored to gravity data in Europe, and gravimetric geoid solutions using 6 x 10' mean gravity anomalies were investigated. The comparison with GPS and leveling yields rms discrepancies of + or - 0.1...0.2 m over 1000 km traverse sections for the best solutions, but a strong slope is existing in Sweden and southern Norway in almost all solutions, which is probably caused by systematic errors in the available gravity data for Scandinavia. This is confirmed by a new geoid computation at the Danish Geodetic Institute where the slope has disappeared. If this new solution is taken for the northern traverse section and the best solution for the central part, the rms discrepancy reduces to approximately + or - 0.2 m over 3000 km. Thus, a + or - 10 (exp 7) relative height accuracy seems to be achievable over long distances with the GPS/leveling and the gravimetric geoid calculation techniques, applied in this experiment.

Torge, W.↗
NASA NTRS1993

Geoid-to-topography ratios on Venus: A global perspective

Recently available spherical harmonic solutions for the geoid and topography of Venus are sufficiently high resolution that they can be used to address questions concerning the relationship between geoid and topography on a regional scale. We have approached this question by mapping the geoid-to-topography ratio (GTR) on a systematic global basis. For a given point on the surface, we consider the geoid and elevation values at all points on a gridded representation of those fields located within a specified distance of the reference point. From the set of paired values, we determine the correlation coefficient and the best-fitting straight line. The latter is the GTR at that position, and the former is a measure of the significance of the derived ratio. This procedure is then repeated for all points on the global grid, yielding maps of the GTR and the correlation coefficient. Unlike previous studies of the GRT on Venus, this apprach permits us to make an objective and systematic search for regions with anomalous GTR's as well as areas that do not demonstrate any strong correlation between geoid and topography. These maps can be updated regularly as new harmonic models of the Venus geoid are produced from new Magellan tracking data. This procedure permits the development of a global perspective on the relationship between GTR and venusian surface tectonics.

Simons, Mark↗
NASA NTRS1994

Preliminary estimates of Gulf Stream characteristics from TOPEX data and a precise gravimetric geoid

TOPEX sea surface height data has been used, with a gravimetric geoid, to calculate sea surface topography across the Gulf Stream. This topography was initially computed for nine tracks on cycles 21 to 29. Due to inaccurate geoid undulations on one track, results for eight tracks are reported. The sea surface topography estimates were used to calculate parameters that describe Gulf Stream characteristics from two models of the Gulf Stream. One model was based on a Gaussian representation of the velocity while the other was a hyperbolic representation of velocity or the sea surface topography. The parameters of the Gaussian velocity model fit were a width parameter, a maximum velocity value, and the location of the maximum velocity. The parameters of the hyperbolic sea surface topography model were the width, the height jump, position, and sea surface topography at the center of the stream. Both models were used for the eight tracks and nine cycles studied. Comparisons were made between the width parameters, the maximum velocities, and the height jumps. Some of the parameter estimates were found to be highly (0.9) correlated when the hyperbolic sea surface topography fit was carried out, but such correlations were reduced for either the Gaussian velocity fits or the hyperbolic velocity model fit. A comparison of the parameters derived from 1-year TOPEX data showed good agreement with values derived by Kelly (1991) using 2.5 years of Geosat data near 38 deg N, 66 deg W longitude. Accuracy of the geoid undulations used in the calculations was of order of +/- 16 cm with the accuracy of a geoid undulation difference equal to +/- 15 cm over a 100-km line in areas with good terrestrial data coverage. This paper demonstrates that our knowledge or geoid undulations and undulation differences, in a portion of the Gulf Stream region, is sufficiently accurate to determine characteristics of the jet when used with TOPEX altimeter data. The method used here has not been shown to be more accurate than methods that average altimeter data to form a reference surface used in analysis to obtain the Gulf Stream characteristics. However, the results show the geoid approach may be used in areas where lack of current meandering reduces the accuracy of the average surface procedure.

Rapp, Richard H.↗
NASA NTRS1997

Combination of TOPEX/POSEIDON Data with a Hydrographic Inversion for Determination of the Oceanic General Circulation and its Relation to Geoid Accuracy

A global estimate of the absolute oceanic general circulation from a geostrophic inversion of in situ hydrographic data is tested against and then combined with an estimate obtained from TOPEX/POSEIDON altimetric data and a geoid model computed using the JGM-3 gravity-field solution. Within the quantitative uncertainties of both the hydrographic inversion and the geoid estimate, the two estimates derived by very different methods are consistent. When the in situ inversion is combined with the altimetry/geoid scheme using a recursive inverse procedure, a new solution, fully consistent with both hydrography and altimetry, is found. There is, however, little reduction in the uncertainties of the calculated ocean circulation and its mass and heat fluxes because the best available geoid estimate remains noisy relative to the purely oceanographic inferences. The conclusion drawn from this is that the comparatively large errors present in the existing geoid models now limit the ability of satellite altimeter data to improve directly the general ocean circulation models derived from in situ measurements. Because improvements in the geoid could be realized through a dedicated spaceborne gravity recovery mission, the impact of hypothetical much better, future geoid estimates on the circulation uncertainty is also quantified, showing significant hypothetical reductions in the uncertainties of oceanic transport calculations. Full ocean general circulation models could better exploit both existing oceanographic data and future gravity-mission data, but their present use is severely limited by the inability to quantify their error budgets.

Ganachaud, Alexandre↗
NASA NTRS1972

A detailed gravimetric geoid of North America, Eurasia, and Australia

A detailed gravimetric geoid of North America, the North Atlantic, Eurasia, and Australia computed from a combination of satellite-derived and surface 1 x 1 gravity data, is presented. Using a consistent set of parameters, this geoid is referenced to an absolute datum. The precision of this detailed geoid is + or - 2 meters in the continents but may be in the range of 5 to 7 meters in those areas where data was sparse. Comparisons of the detailed gravimetric geoid with results of Rice for the United States, Bomford and Fischer in Eurasia, and Mather in Australia are presented. Comparisons are also presented with geoid heights from satellite solutions for geocentric station coordinates in North America, the Caribbean, Europe, and Australia.

Vincent, S.↗
NASA NTRS1974

The geoid: Definition and determination

The determination of the geoid has been one of the prime goals of geodesy. Knowledge of geoid undulations with respect to some reference surface was needed for the determination of the figure of the earth, for the precise reduction of distance measurements to a reference ellipsoid, and for the determination of the geocentric location of points on the surface of the earth. Currently and in the future, undulation information can also be used in geophysical studies related to crustal structures and in oceanographic studies related to sea surface topography. The actual determination of global geoids has been carried out by using gravimetric data, satellite‐derived information related to the gravitational field of the earth, or a combination of the two techniques. Regional geoid determinations have been made by astrogeodetic techniques. For some applications of undulation information, undulation standard deviations of the order of ±5 m would be sufficient. Such an accuracy can be obtained by using data currently available. In the past few years, renewed interest in the geoid arose when the concept of satellite altimetry was proposed to measure the distance from the satellite to some area on the ocean surface.

Richard H. Rapp↗
NASA NTRS1976

Tests and comparisons of satellite-derived geoids with Skylab altimeter data

During the Skylab 4 mission, the S-193 radar altimeter was operated nearly continuously for a revolution around the world on Jan. 31, 1974. This direct measurement to the sea surface has provided an independent basis for the evaluation of the precision of global geoids computed from satellite-derived earth gravity models. This paper presents comparisons between the Skylab data and several recent gravity models published by Goddard Space Flight Center, the Smithsonian Astrophysical Observatory, and the National Oceanic and Atmospheric Administration. The differences between the altimeter geoid and the satellite geoids were as large as 20 m, rms values ranging from 8 to 10 m. These differences also indicated a systematic long-wavelength variation (about 100 deg) not related to error in the Skylab orbits. Truncation of the models to degree and order 8 did not eliminate the long-wavelength variation, but in every case the rms agreement between the satellite geoids and the altimeter geoid was slightly improved. Orbits computed with the truncated models were found to be inferior to those computed with the complete models.

Marsh, J. G.↗
NASA NTRS1976

Generation of an ocean geoid map using satellite altimeter data

A discussion of the techniques and accuracies associated with creating a geoid from satellite altimeter data is given. A sample set of Skylab S-193 altimeter data is utilized to demonstrate the generation of a local ocean geoid contour map in the Atlantic and Caribbean ocean area. The altimeter geoid compares well with existing geoids; possible sources of errors are identified. In addition, the application of a long arc (global type) pass of Skylab data for providing a common reference system and validating localized geoids is illustrated.

Wells, W. T.↗
NASA NTRS1978

The geoid spectrum from altimetry

Satellite altimetry information from the world's major oceans was analyzed to arrive at a geoid power spectrum. Using the equivalent of about 7 revolutions of data (mostly from GEOS-3) the power spectrum of the sea surface generally follows the expected values from Kaula's rule applied to the geoid. Analysis of overlapping altimetry arcs (and oceanographic data) shows that the surface spectrum is dominated by the geoid to about 500 cycles (40 km half wavelength) but that sea state departures are significant starting at about 250 cycles (80 km). Estimates of geopotential variances from a derived (smooth) geoid spectrum show significantly less power than Kaula's rule to about 60 cycles, but somewhat more from there to about 400 cycles. At less than 40 km half wavelength, the total power in the marine geoid may be negligible.

Wagner, C. A.↗
NASA NTRS1979

Estimation of the ocean geoid near the Blake Escarpment using GEOS-3 satellite altimetry

The accuracy with which the local ocean geoid structure could be determined using satellite altimetry data was investigated. The undulation and along-track component of the vertical deflection for selected passes of GEOS-3 near the Blake Escarpment were estimated and compared with independent analogous estimates based on U. S. Navy surface gravimetric survey data. The results of these comparisons show agreement in the geoid undulation values generally to within one or two meters. The nature of the discrepancy in the undulation values was primarily that of a bias error believed to be due essentially to radial orbit uncertainties. The agreement between the vertical deflection estimates was not significantly affected by orbit uncertainties over the track lengths considered in this study (100 - 1500 km), and the comparisons show typical rms differences of between one and two arc secs. In addition, the capability of the altimeter to resolve short wavelength features of the geoid was determined. This analysis involved spectrum and cross spectrum analysis of sets of closely spaced parallel subtracks to determine statistically significant short wavelength geoid resolution capability. The results of this analysis show that resolution can be achieved down to wavelengths as short as 30 km - 80 km depending on regional geoid variations.

Brammer, R. F.↗
NASA NTRS1979

Geoid anomalies and the thickness of the lithosphere

By using accepted crustal density distributions and either error function or linear temperature distributions the difference in geoid height between stable continental areas and deep ocean basins has been determined as a function of the continental lithospheric thickness. If the continental lithosphere were greater than 200 km thick, the geoid anomaly over the continents would be systematically negative in relation to that over the ocean basins. By using the GEM 9 satellite geoid the mean geoid anomalies over ocean basins and stable continental areas have been obtained. No systematic difference between continental and oceanic geoids is observed. It is concluded that the thickness of the continental lithosphere is near 180 km. This is in good agreement with various interpretations of the surface heat flow observations.

Turcotte, D. L.↗
NASA NTRS1979

On geoid heights derived from GEOS 3 altimeter data along the Hawaiian-Emperor seamount chain

The geoid heights derived from preliminary GEOS 3 satellite radar altimeter data over the Hawaiian-Emperor seamount chain are examined. Two objectives are pursued: (1) to evaluate the contribution of the topography of the seamount chain and its compensation to the marine geoid; and (2) to determine whether geoid heights derived from GEOS 3 altimeter data can be used to provide information on isostasy at geological features such as the Hawaiian-Emperor seamount chain which formed as relatively young loads on the oceanic lithosphere. Short-wavelength geoid highs of 5-12 m over the crest of the seamount chain and geoid lows over flanking regions are observed. The geological undulations can be explained by a simple model in which the seamount-chain load is supported by a strong rigid lithospheric plate. The elastic thickness estimates agree with values based on surface ship gravity and bathymetry observations, and provide further support to the hypothesis that the elastic thickness acquired at a surface load depends on the temperature gradient of the lithosphere at the time of loading.

Watts, A. B.↗
NASA NTRS1980

Geoid height versus age for symmetric spreading ridges

Geoid height-age relations have been extracted from Geos 3 altimeter data for large areas in the North Atlantic, South Atlantic, southeast Indian, and southeast Pacific oceans. Except for the southeast Pacific area, geoid height decreases approximately linearly with the age of the ocean floor for ages less than about 80 m.y. in agreement with the prediction of an isostatically compensated thermal boundary layer model (Haxby and Turcotte, 1978). The geoid-age data for 0 to 80 m.y. are consistent with constant slopes of -0.094 + or - -0.131 + or - 0.041, and -0.149 + or - 0.028 m/m.y. for the South Atlantic, southeast Indian, and North Atlantic regions, respectively. For ages greater than 80 m.y. the geoid-age relation for the North Atlantic is nearly flat, indicating a reduction in the rate of boundary layer thickening with age. The uncertainties in the geoid slope-age estimates are positively correlated with spreading velocity.

Sandwell, D.↗
NASA NTRS1981

Hotspots, polar wander, Mesozoic convection and the geoid

The geoid bears little relation to present tectonic features of the earth other than trenches. The Mesozoic supercontinent of Pangea, however, apparently occupied a central position in the Atlantic-African geoid high. This and the equatorial Pacific geoid high contain most of the world's hotspots. The plateaus and rises in the western Pacific formed in the Pacific geoid high and this may have been the early Mesozoic position of Pacifica, the fragments of which are now the Pacific rim portions of the continents. Geoid highs which are unrelated to present subduction zones may be the former sites of continental aggregations and mantle insulation and, therefore, hotter than normal mantle. The pent-up heat causes rifts and hotspots and results in extensive uplift, magmatism, fragmentation and dispersal of the continents and the subsequent formation of plateaus, aseismic ridges and seamount chains. Convection in the uppermantle would then be due to lateral temperature gradients as well as heating from below and would be intrinsically episodic.

Anderson, D. L.↗
NASA NTRS1982

Gravity and geoid anomalies of the Philippine Sea: Evidence on the depth of compensation for the negative residual water depth anomaly

A negative free-air gravity anomaly which occurs in the central part of the Philippine Sea was examined to determine the distribution and nature of possible regional mass excesses or deficiencies. Geoid anomalies from GEOS-3 observation were positive. A negative residual geoid anomaly consistent with the area of negative free-air gravity anomalies were found. Theoretical gravity-topography and geoid-topography admittance functions indicated that high density mantle at about 60 km dept could account for the magnitudes of the gravity and residual geoid anomaly and the 1 km residual water depth anomaly in the Philippine Sea. The negative residual depth anomaly may be compensated for by excess density in the uppermost mantle, but the residual geoid and regional free-air gravity anomalies and a slow surface wave velocity structure might result from low-density warm upper mantle material lying beneath the zone of high-density uppermost mantle. From a horizontal disk approximation, the depth of the low-density warm mantle was estimated to be on the order of 200 km.

Bowin, C.↗
NASA NTRS1982

GRAVSAT error analysis by means of global spectral analyses of the marine geoid from SEASAT altimeter data

The geographical variability of short wavelength geoid power spectra (geoid roughness), was mapped for the world's oceans between latitudes 72 deg N and 72 deg S. A spectral analysis of SEASAT altimeter data, reduced to sea surface heights, was performed at 2 minute intervals for 15 consecutive days of the 3-day repeat orbit. The geoid roughness represented by these spectra for wavelengths shorter than about 220 km is separated from the total sea height variance and is displayed in the form of a global contour map. The global average geoid roughness is 32 cm RMS, varying from a high in excess of 2 m RMS near deep ocean trenches to a low of 2 cm RMS in the southeast Pacific near the East Pacific Rise. This average value agrees well with previous estimates based on gravimetry and GEOS-3 altimetry. In general, the smoothest areas in the marine geoid overlie relatively young seafloor adjacent mid-ocean spreading centers, where even short-wavelength topographic variations tend to be isostatically compensated.

Source record↗
NASA NTRS1983

Roughness of the marine geoid from Seasat altimetry

The geographical variability of short wavelength geoid power spectra (geoid roughness) has been mapped for the world's oceans between latitudes 72 deg N and 72 deg S. A spectral analysis of Seasat altimeter data, reduced to sea surface heights, has been performed at 2-min intervals for 15 consecutive days of the 3-day repeat orbit. The geoid roughness represented by these spectra for wavelengths shorter than about 220 km is separated from the total sea height variance and is displayed in the form of a global contour map. The global average geoid roughness is 32 cm RMS, varying from a high in excess of 2 m RMS near deep ocean trenches to a low of 2 cm RMS in the southeast Pacific near the east Pacific rise. This average value agrees well with previous estimates based on gravimetry and GEOS 3 altimetry. In general, the smoothest areas in the marine geoid overlie relatively young sea floor adjacent mid-ocean spreading centers, where even short wavelength topographic variations tend to be isostatically compensated.

Brown, R. D.↗
NASA NTRS1985

Properties of the lithosphere and asthenosphere deduced from geoid observations

Data from the GEOS-3 and SEASAT Satellites provided a very accurate geoid map over the oceans. Broad bathymetric features in the oceans such as oceanic swells and plateaus are fully compensated. It is shown that the geoid anomalies due to the density structures of the lithosphere are proportional to the first moment of the density distribution. The deepening of the ocean basins is attributed to thermal isostasy. The thickness of the oceanic lithosphere increases with age due to the loss of heat to the sea floor. Bathymetry and the geoid provide constraints on the extent of this heat loss. Offsets in the geoid across major fracture zones can also be used to constrain this problem. Geoid bathymetry correlations show that the Hawaiian and Bermuda swells and the Cape Verde Rise are probably due to lithospheric thinning.

Turcotte, D. L.↗