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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1986

Dynamically supported geoid highs over hotspots: Observation and theory

Hotspots are associated with long wavelength geoid highs, an association that is even stronger when the geoid highs associated with subduction zones are removed. These associations are quantified by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree. The hotspot distribution spectrum is essentially white, with peaks at degrees 2 and 6. It is correlated positively with the slab residual geoid for degrees 2 to 6, with low seismic velocity in the lower mantle at degree 2, and with low seismic velocity in the upper mantle at degree 6. A variety of fluid mechanical models were tested for hotspots, including lithospheric delamination and hot plumes, by calculating their predicted dynamic geoid responses and comparing them to the observations. These models include the effects of temperature dependent rheology. The preferred hotspot model, based on observations of the geoid and seismic tomography, has plumes preferentially occurring in regions of large scale background temperature highs in a mantle with substantial viscosity increase with depth, although other models are possible.

Richards, M. A.↗
NASA NTRS1986

Global relationship between oceanic geoid and topography

The transfer function of geoid over topography as a function of wavelength is derived. The relationship between oceanic geoid and seafloor depth is analyzed. The correction of the geoid and topological data for thermal cooling of the oceanic lithosphere, sediment loading, and crustal thickening induced by volcanism under large ocean plateaus is discussed. The global residual depth and geoid anomalies are computed. The admittance and correlation between residual depth and geoid anomalies as a function of wavelength are examined.

Cazenave, A.↗
NASA NTRS1988

Dynamically supported geoid highs over hotspots - Observation and theory

Hotspots are associated with long wavelength geoid highs, an association that is even stronger when the geoid highs associated with subduction zones are removed. These associations are quantified by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree. The hotspot distribution spectrum is essentially white, with peaks at degrees 2 and 6. It is correlated positively with the slab residual geoid for degrees 2 to 6, with low seismic velocity in the lower mantle at degree 2, and with low seismic velocity in the upper mantle at degree 6. A variety of fluid mechanical models were tested for hotspots, including lithospheric delamination and hot plumes, by calculating their predicted dynamic geoid responses and comparing them to the observations. These models include the effects of temperature dependent rheology. The preferred hotspot model, based on observations of the geoid and seismic tomography, has plumes preferentially occurring in regions of large scale background temperature highs in a mantle with substantial viscosity increase with depth, although other models are possible.

Richards, Mark A.↗
NASA NTRS1993

Can weak crust explain the correlation of geoid and topography on Venus?

The effect on geoid and topography of low viscosity crust overlying a steady-state convecting mantle is estimated under the assumption that the shear between crust and mantle does not alter the mantle flow. The weak crustal layer can change the sign of the geoid to topography ratio (admittance). The positive long wavelength admittance for Venus is consistent with a weak crust overlying a mantle with a viscosity that increases strongly with depth. The accepted interpretation of the strong positive correlation of geoid and topography on Venus, is that the convecting mantle of Venus has a constant viscosity with depth. Topography results from vertical normal stresses caused by mantle convection and highlands occur where mantle upwells. For topography to be supported by normal stress, the time scale for crustal flow must be long compared to the time scale for changes in the pattern of mantle flow. Because the high surface temperature of Venus may cause the crust to have a low viscosity, this assumption may be false. Topography should then be dominated by shear coupling between the crust and mantle. In the absence of a crustal layer, convection in a constant viscosity layer gives rise to a geoid anomaly that correlates positively with surface topography. When the viscosity in the layer increases with depth by several orders of magnitude, the surface topography and geoid anomaly become anti-correlated.

Buck, W. Roger↗
NASA NTRS1998

Geoid Anomalies and Dynamic Topography from Time Dependent, Spherical Axisymmetric Mantle Convection

Geoid anomalies and dynamic topography are two important diagnostics of mantle convection. We present geoid and topography results for several time-dependent convection models in spherical axisymmetric geometry for Rayleigh numbers between 10(exp 6) and 10(exp 7) with depth-dependent viscosity and mixtures of bottom and internal heating. The models are strongly chaotic, with boundary layer instabilities erupting out of both thermal boundary layers. In some instances, instabilities from one boundary layer influence the development of instabilities in the other boundary layer. Such coupling between events at the top and bottom of the mantle has been suggested to play a role in a mid-Cretaceous episode of enhanced volcanism in the Pacific. These boundary layer instabilities produce large temporal variations in the geoid anomalies and dynamic nd to the topography associated with the convection. The amplitudes of these fluctuations depend on the detailed model parameter,.% it of this but fluctuations of 30-50% relative to the time-averaged geoid and topography are common. The convective planform is strongly sensitive to the specific initial conditions. Convection cells with larger aspect ratio tend to have larger fractional fluctuations in their geoid and topography amplitudes, because boundary layer instabilities have more time to develop in long cells. In some instances, we observe low-amplitude topographic highs adjacent to the topographic lows produced by cold downwellings. We discuss applications of these results to several situations, including the temporal variability of m basis. hotspots such as Hawaii, the topography of subduction zone outer rises, and the topography of coronae on Venus.

Kiefer, Walter S.↗
NASA NTRS1972

A detailed gravimetric geoid from North America to Eurasia

A detailed gravimetric geoid of the United States, North Atlantic, and Eurasia, which was computed from a combination of satellite derived and surface gravity data, is presented. The precision of this detailed geoid is + or - 2 to + or - 3 m in the continents but may be in the range of 5 to 7 m in those areas where data is sparse. Comparisons of the detailed gravimetric geoid with results of Rapp, Fischer, and Rice for the United States, Bomford in Europe, and Heiskanen and Fischer in India are presented. Comparisons are also presented with geoid heights from satellite solutions for geocentric station coordinates in North America, the Caribbean, and Europe.

Vincent, S. F.↗
NASA NTRS1974

Global detailed geoid computation and model analysis

Comparisons and analyses were carried out through the use of detailed gravimetric geoids which we have computed by combining models with a set of 26,000 1 deg x 1 deg mean free air gravity anomalies. The accuracy of the detailed gravimetric geoid computed using the most recent Goddard earth model (GEM-6) in conjunction with the set of 1 deg x 1 deg mean free air gravity anomalies is assessed at + or - 2 meters on the continents of North America, Europe, and Australia, 2 to 5 meters in the Northeast Pacific and North Atlantic areas, and 5 to 10 meters in other areas where surface gravity data are sparse. The R.M.S. differences between this detailed geoid and the detailed geoids computed using the other satellite gravity fields in conjuction with same set of surface data range from 3 to 7 meters.

Marsh, J. G.↗
NASA NTRS1975

Detailed gravimetric geoid confirmation of short wavelength features of sea surface topography detected by the Skylab S-193 altimeter in the Atlantic Ocean

A detailed gravimetric geoid was computed for the Northwest Atlantic Ocean and Caribbean Sea area in support of the calibration and evaluation of the GEOS-C altimeter. This geoid, computed on a 15 ft. x 15 ft. grid was based upon a combination of surface gravity data with the GSFC GEM-6 satellite derived gravity data. A comparison of this gravimetric geoid with 10 passes of SKYLAB altimeter data is presented. The agreement of the two data types is quite good with the differences generally less than 2 meters. Sea surface manifestations of numerous short wavelength (approximately 100 km) oceanographic features are now indicated in the gravimetric geoid and are also confirmed by the altimetry data.

Marsh, J. G.↗
NASA NTRS1975

Tests and comparisons of satellite derived geoids with Skylab altimeter data

The SKYLAB-193 radar altimeter was operated nearly continuously around the world on January 31, 1974. This direct measurement of the sea surface topography provided an independent basis for the evaluation of global geoids computed from satellite derived gravity models. The differences between the altimeter geoid and the satellite geoids were as large as 25 meters with rms values ranging from 8 to 10 meters. These differences also indicated a systematic long wavelength variation (approximately 100 deg) not related to error in the SKYLAB orbits. Truncation of the models to degree and order eight did not eliminate the long wavelength variation, but in every case the rms agreement between satellite and altimeter geoids was improved. Orbits computed with the truncated models were in contrast found to be inferior to those computed using the complete models.

Marsh, J. G.↗
NASA NTRS1974

Detailed gravimetric geoid for the GEOS-C altimeter calibration area

The GEOS-C spacecraft scheduled for launch in late 1974 will carry a radar altimeter for the purpose of measuring sea surface topography. In order to calibrate and evaluate the performance of the altimeter system, ground truth data are required. In this respect a detailed gravimetric geoid has been computed for the GEOS-C altimeter calibration area in the Atlantic Ocean off the East Coast of the U.S. This geoid is based upon a combination of mean free air surface gravity anomalies and the Goddard Space Flight Center GEM-6 satellite-derived spherical harmonic coefficients. Surface gravity anomalies have been used to provide information on the short wave length undulations of the geoid while the satellite-derived coefficients have provided information on the long wave length components. As part of these analyses, GSFC, SAO and OSU satellite-derived gravity models were used in the computations. Although geoid heights based upon the various satellite models differed by as much as 30 meters in the Southern Hemisphere, the differences in this Atlantic Ocean area were less than 4 meters.

Marsh, J. G.↗
NASA NTRS1974

Civil and scientific applications of the geoid

SEASAT-A can be used for determining the geoid to much higher accuracy on a world wide basis and in a relatively short time. Two basic objectives can be considered: (1) determination of the geoid to at least 1 meter. This accuracy will satisfy most geodetic requirements for applications purposes; and (2) determination of the geoid to better than 1-meter an oceanographic objective required for measurement of sea surface topography and sea slope, quasi-stationary departure from the geoid, ocean circulation, air and sea interaction, etc. The geodesy objective in this case will be to define a reference equipotential surface as a means by which the oceanographic requirements can be achieved.

Mourad, A. G.↗
NASA NTRS1976

Detailed gravimetric geoid computations in North America

A detailed gravimetric geoid has been computed for the Eastern United States and the Northwestern Atlantic Ocean by combining the Goddard Space Flight Center GEM-8 earth gravity model with the available 15 x 15 arcmin and 1 x 1 deg mean free air surface gravity observations. The short wavelength undulations were computed by applying Stokes' formula to the 15 x 15 arcmin and 1 x 1 deg surface data. The long wavelength undulations were provided by the GEM-8 model. The gravimetric geoid has been compared with Geoceiver derived and astrogeodetically determined geoid heights in the United States and the rms agreement is on the order of 1.5 meters. Excellent agreement in shape has been found between the detailed geoid and geoidal profiles derived from GEOS-III altimeter data in the Northwest Atlantic Ocean.

Marsh, J. G.↗
NASA NTRS1975

Methods for the computation of detailed geoids and their accuracy

Two methods for the computation of geoid undulations using potential coefficients and 1 deg x 1 deg terrestrial anomaly data are examined. It was found that both methods give the same final result but that one method allows a more simplified error analysis. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction that was not considered previously. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used) errors. It was found that an optimum cap size of 20 deg should be used. The geoid and its accuracy were computed in the Geos 3 calibration area using the GEM 6 potential coefficients and 1 deg x 1 deg terrestrial anomaly data. The accuracy of the computed geoid is on the order of plus or minus 2 m with respect to an unknown set of best earth parameter constants.

Rapp, R. H.↗
NASA NTRS1978

Oceanic Geoid and Tides Obtained from GEOS-3 Satellite Data in the Northwestern Atlantic Ocean

Two sets of GEO-3 altimeter data which fall within about a 2.5 degree width are analyzed for ocean geoid and tides. One set covers a linear path from Newfoundland to Cuba and the other from Puerto Rico to the North Carolina coast. Forty different analyses using various parameters are performed in order to investigate convergence. Profiles of the geoid and four tides, M sub 2 O sub 1, S sub 2, and K sub 1, are obtained along the two strips. The results demonstrate convergent solutions for all forty cases and show, within expectation, fair agreement with those obtained from the MODE deep-sea tide gauge. It is also shown that the oceanic geoid obtained through this analysis can potentially improve the short wavelength structure over existing geoid models.

Won, I. J.↗
NASA NTRS1979

Oceanic geoid and tides derived from GEOS 3 satellite data in the Northwestern Atlantic Ocean

Two sets of GEOS 3 altimeter data which fall within about a 2.5-deg width are analyzed for ocean geoid and tides. One set covers a path from Newfoundland to Cuba, and the other a path from Puerto Rico to the North Carolina coast. Forty different analyses using various parameters are performed in order to investigate convergence. Profiles of the geoid and four tides, M2, O1, S2, and K1, are derived along the two strips. While the analyses produced convergent solutions for all 40 cases, the uncertainty caused by the linear orbital bias error of the satellite is too large to claim that the solutions represent the true ocean tides in the area. A spot check of the result with the Mode deep-sea tide gauge data shows poor agreement. A positive conclusion of this study is that despite the uncertain orbital error the oceanic geoid obtained through this analysis can improve significantly the short-wavelength structure over existing spherical harmonic geoid models.

Won, I. J.↗
NASA NTRS1979

The geoid spectrum from altimetry

Preliminary estimates of the global spectrum of the sea surface and geoid are made using altimeter data from the GEOS 3 and Skylab spacecraft. In all, the equivalent of about seven revolutions of data has served from the 'global' estimates. It is found that 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) reveals that the surface spectrum is dominated by the geoid to about 500 cycles, but the sea state departures are significant starting at about 250 cycles. At less than 500 cycles (40 km half-wavelength) the total power in the marine geoid may be negligible (much less than 20 cm).

Wagner, C. A.↗
NASA NTRS1980

A comparison of altimeter and gravimetric geoids in the Tonga Trench and Indian Ocean areas

Geoids computed from GEOS-3 altimeter data are compared with gravimetric geoids computed by various techniques for 30 x 30 deg areas in the Tonga Trench and the Indian Ocean. The gravimetric geoids were calculated using the standard Stokes integration with the Molodenskii truncation procedure, the modified Stokes integration suggested by Ostach (1970) and Meissl (1971) with modified Molodenskii truncation functions, and three sets of potential coefficients including one complete to degree 180. It is found that the modified Stokes procedure with a cap size of 10 deg provides better results when used with a combined altimeter terrestrial anomaly field data set. Excellent agreement at the plus or minus 1 m level is obtained between the altimeter and gravimetric geoid using the combined data set, with the modified Stokes procedure having a greater accuracy. Coefficients derived from the 180 x 180 solution are found to be of an accuracy comparable to that of the modified Stokes method, however to require six times less computational effort.

Rapp, R. H.↗
NASA NTRS1985

Interpretation of the geoid

The superposition of the first satellite geoid determined by Iszak upon Ootilla's geoid was based on surface gravity determinations. Good agreement was observed except over the Pacific area of the globe. The poor agreement over the Pacific was interpreted as the result of inadequate observations there. Many geoids were determined from satellite observations, including Doppler measurements. It is found that the geoid is the result of density differences in the mantle maintained since the primeval Earth by its finite strength. Various models based on this assumption are developed.

Runcorn, S. K.↗