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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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At least 73 records · Page 4
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NASA NTRS1987

Geoid undulation computations at laser tracking stations

Geoid undulation computations were performed at 29 laser stations distributed around the world using a combination of terrestrial gravity data within a cap of radius 2 deg and a potential coefficient set up to 180 deg. The traditional methods of Stokes' and Meissl's modification together with the Molodenskii method and the modified Sjoberg method were applied. Performing numerical tests based on global error assumptions regarding the terrestrial data and the geopotential set it was concluded that the modified Sjoberg method is the most accurate and promising technique for geoid undulation computations. The numerical computations for the geoid undulations using all the four methods resulted in agreement with the ellipsoidal minus orthometric value of the undulations on the order of 60 cm or better for most of the laser stations in the eastern United States, Australia, Japan, Bermuda, and Europe. A systematic discrepancy of about 2 meters for most of the western United States stations was detected and verified by using two relatively independent data sets. For oceanic laser stations in the western Atlantic and Pacific oceans that have no terrestrial data available, the adjusted GEOS-3 and SEASAT altimeter data were used for the computation of the geoid undulation in a collocation method.

Despotakis, Vasilios K.↗
NASA NTRS1987

A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars

Global spectra are available for topography and geoid on the earth, Venus, Mars, and the moon. If the spectral energy density has a power law dependence on wave number, a fractal is defined. The topography spectrum for the earth is a well-defined fractal with D = 1.5; this corresponds to Brown noise with the amplitude proportional to the wavelength. Although there is more scatter for the other planetary bodies, the data for Mars and the moon correlate well with the data for the earth. Venus topography also exhibits a Brown noise behavior but with a smaller amplitude. The power law dependence of the earth's geoid is known as Kaula's law. It is shown that uncompensated Brown topography gives a geoid with a power law dependence that is in quite good agreement with Kaula's law. However, the required amplitude is only 8 percent of the observed topography. A similar result is found for the other bodies, with the ratio of the amplitude of topography required to explain the geoid to the observed topography increasing to 72 percent for the moon.

Turcotte, Donald L.↗
NASA NTRS1988

Geoid and topography for infinite Prandtl number convection in a spherical shell

Geoid anomalies and surface and lower-boundary topographies are calculated for numerically generated thermal convection for an infinite Prandtl number, Boussinesq, axisymmetric spherical fluid shell with constant gravity and viscosity, for heating both entirely from below and entirely from within. Convection solutions are obtained for Rayleigh numbers Ra up to 20 times the critical Ra in heating from below and 27 times critical for heating from within. Geoid parallels surface undulations, and boundary deformation generally increases with increasing cell wavelength. Dimensionless geoid and topography in heating from below are about 5 times greater than in heating from within. Values for heating from within correlate more closely with geophysical data than values from heating from below, suggesting a predominance of internal heating in the mantle. The study emphasizes that dynamically induced topography and geoid are sensitive to the mode of heating in the earth's mantle.

Bercovici, D.↗
NASA NTRS1991

Geoid undulations and gravity anomalies over the Aral Sea, the Black Sea and the Caspian Sea from a combined GEOS-3/SEASAT/GEOSAT altimeter data set

Satellite-based altimetric data taken by GOES-3, SEASAT, and GEOSAT over the Aral Sea, the Black Sea, and the Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25x0.25 deg. grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180x180 geopotential model is used as the reference surface for the collocation procedure. The result of geoid to gravity transformation is, however, sensitive to the information content of the reference geopotential model used. For example, considerable detailed surface gravity data were incorporated into the reference model over the Black Sea, resulting in a reference model with significant information content at short wavelengths. Thus, estimation of short wavelength gravity anomalies from gridded geoid heights is generally reliable over regions such as the Black Sea, using the conventional collocation technique with local empirical covariance functions. Over regions such as the Caspian Sea, where detailed surface data are generally not incorporated into the reference model, unconventional techniques are needed to obtain reliable gravity anomalies. Based on the predicted gravity anomalies over these inland seas, speculative tectonic structures are identified and geophysical processes are inferred.

Au, Andrew Y.↗
NASA NTRS1972

Use of altimetry data in a sampling-function approach to the geoid

Problems associated with using an altimetry sampling function approach to the geoid are examined. They include: (1) conventent mathematical representation of short-wavelength (eventually approximately 1 deg) features of the geoid or geopotential, (2) utilization of detailed data from only part of the globe (i.e., the oceans) (3) application of appropriate formalism to relate the sea-level equipotential below the atmospheric mass to the external potential above the atmosphere, (4) mathematical applicability of an adopted geopotential representation on the surface of the physical geoid.

Lundquist, C. A.↗
NASA NTRS1973

Global detailed gravimetric geoid

A global detailed gravimetric geoid has been computed by combining the Goddard Space Flight Center GEM-4 gravity model derived from satellite and surface gravity data and surface 1 deg-by-1 deg mean free air gravity anomaly data. The accuracy of the geoid is + or - 2 meters on continents, 5 to 7 meters in areas where surface gravity data are sparse, and 10 to 15 meters in areas where no surface gravity data are available. Comparisons have been made with the astrogeodetic data provided by Rice (United States), Bomford (Europe), and Mather (Australia). Comparisons have also been carried out with geoid heights derived from satellite solutions for geocentric station coordinates in North America, the Caribbean, Europe, and Australia.

Vincent, S.↗
NASA NTRS1974

Strategies for estimating the marine geoid from altimeter data

In processing altimeter data from a spacecraft borne altimeter to estimate the fine structure of the marine geoid, a problem is encountered. In order to describe the geoid fine structure, a large number of parameters must be employed and it is not possible to simultaneously estimate all of them. Unless the parameterization exhibits good orthogonality in the data, serious aliasing results. From simulation studies it has been found that amongst several competing parameterizations, the mean free air gravity anomaly model (i.e., Stokes' formula) exhibited promising geoid recovery characteristics. Using covariance analysis techniques, this report provides quantitative measures of the orthogonality properties associated with the above mentioned parameterization. It has been determined that a 5 deg x 5 deg area mean free air gravity anomaly can be estimated with an uncertainty of 1 mgal (40 cm undulation) provided that all free air gravity anomalies within a spherical radius of 10 arc degrees are simultaneously estimated.

Argentiero, P.↗
NASA NTRS1974

Calibration and evaluation of Skylab altimetry for geodetic determination of the geoid

The author has identified the following significant results. An analytical method for geodetic computation of the marine geoid (the geoid in the oceans) from satellite altimetry is developed and validated with data from Skylab mission SL-2. The criteria for achieving accurate scale and orientation of satellite altimetry geoid are shown to require marine geodetic control to offset systematic errors in the orbit (orientation is completely orbit dependent) and the altimeter data.

Mourad, A. G.↗
NASA NTRS1975

Sea surface determination from space: The GSFC geoid

The determination of the sea surface/geoid and its relative variation were investigated and results of the altimeter experiment on Skylab to test the geoid are discussed. The spaceborne altimeter on Skylab revealed that the sea surface of the world's oceans can be measured with an accuracy in the meter range. Surface variations are discussed as they relate to those computed from satellite orbital dynamics and ground based gravity data. The GSFC geoid was constructed from about 400,000 satellite tracking data (range, range rate, angles) and about 20,000 ground gravity observations. One of the last experiments on Skylab was to measure and/or test this geoid over almost one orbit. It was found that the computed water surface deviates between 5 to 20 m from the measured one. Further outlined are the influence of orbital errors on the sea surface, and numerical examples are given based upon real tracking data. Orbital height error estimates were computed for geodetic type satellites and are found to be in the order of 0.2 to 5 meters.

Vonbun, F. O.↗
NASA NTRS1975

The application of Skylab altimetry to marine geoid determination

The author had identified the following significant results. The major results can be divided broadly into two groups. One group is concerned with the effects of errors inherent in the various input data, such as the orbit emphemeris, a priori geoid etc. The other consists of the results of the actual analysis of the data from the Skylab EREP passes 4, 6, 7, and 9. Results from the first group were obtained from the analysis of some preliminary data from EREP pass 9 mode 5. The second group of results consists of a set of recovered bias terms for each of the submodes of observations and a set of nine altimetry geoid profiles corresponding to the various passes and modes. Along with each of these profiles, the a priori geoid, gravity anomaly, and the bathymetric data profiles are also presented for easy comparison.

Mourad, A. G.↗
NASA NTRS1974

Global detailed gravimetric geoid

A global detailed gravimetric geoid has been computed by combining the Goddard Space Flight Center GEM-4 gravity model derived from satellite and surface gravity data and surface 1 x 1-deg mean free-air gravity anomaly data. The accuracy of the geoid is plus or minus 2 meters on continents, 5 to 7 meters in areas where surface gravity data are sparse, and 10 to 15 meters in areas where no surface gravity data are available. Comparisons have been made with the astrogeodetic data provided by Rice (United States), Bomford (Europe), and Mather (Australia). Comparisons have also been carried out with geoid heights derived from satellite solutions for geocentric station coordinates in North America, the Caribbean, Europe and Australia.

Vincent, S.↗
NASA NTRS1975

Satellite altimetry applied to marine geoid determination

The pioneering satellite radar altimeter aboard Skylab has provided a wealth of information about ocean surface topography for both the oceanographic and geodetic communities. This report describes typical satellite altimetry concepts and discusses the parameters measured, geometry utilized, and techniques employed to generate ocean geoid estimates. The standard deviation of the noise on the altitude measurements is shown to range from one to three meters when the altimeter antenna is nadir aligned. The altimeter is shown to sense short wavelength ocean surface features which are not included in present conventional global geoids. An estimate of a local geoid in the Atlantic, using only altimeter data, is presented. Finally, results demonstrate that the Skylab radar altimeter system capability is less than 10 meters RMS.

Leitao, C. D.↗
NASA NTRS1976

Astrogeodetic geoid of Japan

Three kinds of astrogeodetic geoid maps for Japan are presented: one referred to the global (18, 18) geoid of the 1973 Smithsonian Standard Earth (III) (SE III), referred to the best-fitting ellipsoid of SE III, and one referred to the reference ellipsoid of the Tokyo datum. Interpolations of the deflection of the vertical are carried out by a least squares estimation method. The geoid height differences obtained are compared with solutions of satellite-derived station positions. Good agreement is found in a comparison with Doppler tracking stations.

Ganeko, Y.↗
NASA NTRS1977

The spectrum of the geoid from altimeter data

A variety of sources of detailed information has been analyzed to arrive at a geoid power spectrum from global altimeter data. Using the equivalent of only two revolutions of data (mostly from GEOS-3) from all the major oceans, the high frequency geoid power (rms) is estimated (most simply) to be 80.7 n to the minus 1.47th power meters, where n is in cycles/global revolutions. This law is valid for all frequencies above 19 cycles but includes sea state. The (simple) law has more power than predicted by Kaula's rule for the geopotential. However, the data shows significantly less power for frequencies below 100 cycles. A closer approximation to the altimetry accumulates 2.18m (rss) for all frequencies higher than 19 cycles/rev. (including sea state), somewhat less power than predicted by the rule. The data permits up to 1.25 (rms) non-gravitational departures from the high frequency marine geoid.

Wagner, C. A.↗
NASA NTRS1977

An astrogeodetic geoid of Japan

Three kinds of astrogeodetic geoid maps for Japan are presented: one referred to the global (18, 18) geoid of the 1973 Smithsonian Standard Earth (3) (SE 3), one referred to the ellipsoid of the SE 3 system, and one referred to the reference ellipsoid of the Tokyo datum. Interpolations of the deflection of the vertical are carried out by a least squares estimation method. The geoid height differences obtained are compared with solutions of satellite-derived station positions.

Ganeko, Y.↗
NASA NTRS1977

Gravimetric geoid in the Northwest Pacific Ocean

A total of 3708 1 x 1 deg free-air gravity anomaly averages have been used to construct a new 1 x 1 deg gravimetric geoid of the Northwest Pacific Ocean. The 1 x 1 deg averages are based on a compilation of 147,000 surface ship and pendulum gravity measurements. Difference geoid undulations range from a maximum of +19 m over the Hawaiian ridge to a minimum of -31 m over the junction of the Kuril and Aleutian trenches. The Hawaiian swell is associated with a geoidal high of up to +15 m with wavelengths of about 2200 km and the topographic rises seaward of deep-sea trenches are associated with geoidal highs of up to 4 m with wavelengths of about 220-900 km. The agreement between the gravimetric geoid and Skylab-4 and Geos-3 altimeter data is close for wavelengths greater than about 300 km but poor for shorter wavelengths.

Watts, A. B.↗
NASA NTRS1979

Techniques for interpretation of geoid anomalies

For purposes of geological interpretation, techniques are developed to compute directly the geoid anomaly over models of density within the earth. Ideal bodies such as line segments, vertical sheets, and rectangles are first used to calculate the geoid anomaly. Realistic bodies are modeled with formulas for two-dimensional polygons and three-dimensional polyhedra. By using Fourier transform methods the two-dimensional geoid is seen to be a filtered version of the gravity field, in which the long-wavelength components are magnified and the short-wavelength components diminished.

Chapman, M. E.↗
NASA NTRS1981

Ellipsoidal corrections for geoid undulation computations using gravity anomalies in a cap

Ellipsoidal correction terms have been derived for geoid undulation computations when the Stokes equation using gravity anomalies in a cap is combined with potential coefficient information. The correction terms are long wavelength and depend on the cap size in which its gravity anomalies are given. Using the regular Stokes equation, the maximum correction for a cap size of 20 deg is -33 cm, which reduces to -27 cm when the Stokes function is modified by subtracting the value of the Stokes function at the cap radius. Ellipsoidal correction terms were also derived for the well-known Marsh/Chang geoids. When no gravity was used, the correction could reach 101 cm, while for a cap size of 20 deg the maximum correction was -45 cm. Global correction maps are given for a number of different cases. For work requiring accurate geoid computations these correction terms should be applied.

Rapp, R. H.↗