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NASA NTRS1979

Influence of the atmospheric masses on the gravitational field of the earth

Seasonal and latitude dependent corrections to the gravity and height anomalies are developed in order to account for the neglect of the atmospheric masses outside the geoid, when using Stokes' equation. It is shown that the atmospheric correction to gravity at sea level is almost constant, equal to 0.871 mgals with a variation of 2 microgals whereas the height anomaly correction varies between -0.1 cm and -1.3 cm. Further, when the combined latitudinal/seasonal dependence is neglected in the atmospheric corrections, the maximum error introduced is on the order of 40 microgals for the gravity corrections and 0.7 cm for the height anomaly corrections.

Christodoulidis, D. C.↗

NASA NTRS1979

Ocean gravity and geoid determination

Gravity anomalies have been recovered in the North Atlantic and the Indian Ocean regions. Comparisons of 63 2 deg x 2 deg mean free air gravity anomalies recovered in the North Atlantic area and 24 5 deg x 5 deg mean free air gravity anomalies in the Indian Ocean area with surface gravimetric measurements have shown agreement to + or - 8 mGal for both solutions. Geoids derived from the altimeter solutions are consistent with altimetric sea surface height data to within the precision of the data, about + or - 2 m.

Kahn, W. D.↗

NASA NTRS1979

Accuracy of relative oceanic geoid computations

An error analysis based on a model which requires potential coefficients and gravity anomaly information for the computation of oceanic geoidal undulations is developed. The rigorous models are presented and abandoned owing to the numerical difficulties associated with them. An approximate error model is developed in the frequency domain through which an idea is obtained as to the size and behavior of the errors involved. The use of the method is demonstrated by obtaining data requirements for the realization of a 10-cm relative oceanic geoid. Various data sets could result in the desired accuracy. One such set, indicative of the strictness of the requirements, involves gravity profile spacings of approximately 3 km with observational noise not exceeding 0.5 mGal inside detailed data caps of 30 deg and potential coefficients of prescribed accuracy available to degree and order 70.

Christodoulidis, D. C.↗

NASA NTRS1980

Accuracy of the determination of mean anomalies and mean geoid undulations from a satellite gravity field mapping mission

Improved knowledge of the Earth's gravity field was obtained from new and improved satellite measurements such as satellite to satellite tracking and gradiometry. This improvement was examined by estimating the accuracy of the determination of mean anomalies and mean undulations in various size blocks based on an assumed mission. In this report the accuracy is considered through a commission error due to measurement noise propagation and a truncation error due to unobservable higher degree terms in the geopotential. To do this the spectrum of the measurement was related to the spectrum of the disturbing potential of the Earth's gravity field. Equations were derived for a low-low (radial or horizontal separation) mission and a gradiometer mission. For a low-low mission of six month's duration, at an altitude of 160 km, with a data noise of plus or minus 1 micrometers sec for a four second integration time, we would expect to determine 1 deg x 1 deg mean anomalies to an accuracy of plus or minus 2.3 mgals and 1 deg x 1 deg mean geoid undulations to plus or minus 4.3 cm. A very fast Fortran program is available to study various mission configurations and block sizes.

Jekeli, C.↗

NASA NTRS1981

Earth's gravity field mapping requirements and concept

A future sensor is considered for mapping the Earth's gravity field to meet future scientific and practical requirements for earth and oceanic dynamics. These are approximately + or - 0.1 to 10 mgal over a block size of about 50 km and over land and an ocean geoid to 1 to 2 cm over a distance of about 50 km. To achieve these values requires a gravity gradiometer with a sensitivity of approximately 10 to the -4 power EU in a circular polar orbiting spacecraft with an orbital altitude ranging 160 km to 180 km.

Vonbun, F. O.↗

NASA NTRS1981

The gravity field in the central Pacific from satellite-to-satellite tracking

Satellite-to-satellite Doppler tracking between the ATS 6 and the GEOS 3 spacecraft was used to measure the high-degree and high-order gravity field over an 80-deg region in the central Pacific Ocean. Forty passes of GEOS 3/ATS 6 Doppler data have been analyzed. The precision of these range rate data is about 0.3 mm/s, and the line-of-sight gravity anomalies recovered from these data have a precision of about 0.2 mGal at the GEOS 3 altitude of about 840 km. In general, the agreement between the SST-derived map and the conventional GEM method and an altimeter-derived geoid is good. Eight significant positive gravity anomalies were exposed in the central Pacific. Generally speaking, the anomalies form a roughly east-west pattern of alternating sign in the central region, and near the East Pacific they strike about north and south.

Marsh, J. G.↗

NASA NTRS1981

Influence of gravity field uncertainties on the results from POGO and Magsat geomagnetic surveys

Errors in the gravity models used in satellite position calculations are examined as a possible source of the 0 to 100% variance found between POGO and Magsat magnetic data and the extrapolations of aerial magnetic survey data to satellite heights. For POGO data obtained over the New York Bight region using a relatively poor gravity field (a hybrid spherical harmonic model of degree 7 and order 6 with three higher order resonance terms), the magnitude of the error in the satellite height component is found to be sufficient to account for the amplitude of the discrepancy, however the frequency of the quasi-periodic orbital error is too large to explain the localized nature of the differences. For the case of the Magsat satellite, in which a more accurate gravity model was used, it is found that a 30 mgal gravitational anomaly distributed over a 5 x 5 deg area will produce insufficiently large position errors to account for the variations. The agreement between the two sets of satellite data in the New York Bight region suggests either a consistent error in satellite measurements, or problems with the reduction and processing of the aeromagnetic data.

Taylor, P. T.↗

NASA NTRS1982

Venus - Comparison of gravity and topography in the vicinity of Beta Regio

The Doppler tracking data obtained from the Pioneer Venus Orbiter when it passed near Beta Regio yielded a peak vertical anomaly of 150 mGal when analyzed by our two stage procedure. A comparison of maps of the gravity and topography at comparable resolution shows a striking correlation. A scatter plot shows that the observed gravity anomaly is approximately 0.4 of that expected from uncompensated topography of half the mean density of Venus. However, the spectral admittance shows that the gravity anomalies can not be explained either by Airy compensation at fixed depth or by a model comprising an elastic plate atop an inviscid fluid. The gravity and topography variations may signify deep compensation or dynamic support for Beta Regio and more shallow compensation for other features.

Reasenberg, R. D.↗

NASA NTRS1982

Description of the dedicated gravitational satellite mission /Gravsat/

A description of the dedicated gravitational satellite (Gravsat) mission is presented. Scientific objectives are to substantially improve knowledge of solid earth geophysics and oceanography by determining a more accurate geopotential. The most stringent requirement is determination of mean gravity anomalies over regions 100-km square to an accuracy of 2.5 mgal (1 gal = 1 cm/s squared). Fundamental geodetic data will be satellite-to-satellite measurement of relative range rate. Orbital characteristics are discussed. An error budget is presented which indicates that the requisite measurement precision can be achieved by closed-loop RF doppler measurements. Implicit in the discussion of the error budget is a description of the spacecraft and systems components.

Pisacane, V. L.↗

NASA NTRS1982

The negative gravity field over the 85 deg E ridge

Two north-south ridges in the basement topography of the Bay of Bengal may be observed on an isopach map at 85 and at 90 deg E. Free-air gravity anomaly profiles across the region show a strong gravity low (about -60 mGal) over the 85 deg E ridge, and a gravity high over the other. Using a simple two-stage loading model, the negative gravity anomaly over the 85 deg E ridge is explained as a direct consequence of sediment loading, and the flexural rigidity of the lithosphere when the ridge was formed is estimated to have been about 180 times less than the flexural rigidity during the sediment loading. An approximate relationship between flexural rigidity and crustal age shows that the 85 deg E ridge was formed on relatively young lithosphere, 5-15 million years old, and that it was buried when the lithosphere was 40-80 million years old. The alteration of the gravity field by a thick layer of sediments may occur in other large sedimentary basins or along continental margins.

Liu, C.-S.↗

NASA NTRS1982

Identification of a precambrian rift through Missouri by digital image processing of geophysical and geological data

A newly discovered feature in the midcontinent - a gravity low that begins at a break in the midcontinent gravity high in SE Nebraska, extends across Missouri in a NW-SE direction, and intersects the Mississippi Valley graben to form the Pascola arch - is discussed. The anomaly varies from 120 to 160 km in width, extends approximately 700 km, and is best expressed in southern Missouri, where it has a Bouguer amplitude of about -34 mGal. It is noted that the magnitude of the anomaly cannot be explained on the basis of a thickened section of Paleozoic sedimentary rock. The gravity data and the sparse seismic refraction data for the region are found to be consistent with an increased crustal thickness beneath the gravity low. It is thought that the gravity anomaly is probably the present expression of a failed arm of a rifting event, perhaps one associated with the spreading that led to or preceded formation of the granite and rhyolite terrain of southern Missouri.

Guinness, E. A.↗

NASA NTRS1983

The Geopotential Research Mission - Mapping the near earth gravity and magnetic fields

The Geopotential Research Mission (GRM), NASA's low-level satellite system designed to measure the gravity and magnetic fields of the earth, and its objectives are described. The GRM will consist of two, Shuttle launched, satellite systems (300 km apart) that will operate simultaneously at a 160 km circular-polar orbit for six months. Current mission goals include mapping the global geoid to 10 cm, measuring gravity-field anomalies to 2 mgal with a spatial resolution of 100 km, detecting crustal magnetic anomalies of 100 km wavelength with 1 nT accuracy, measuring the vectors components to + or - 5 arc sec and 5 nT, and computing the main dipole or core field to 5 nT with a 2 nT/year secular variation detection. Resource analysis and exploration geology are additional applications considered.

Taylor, P. T.↗

NASA NTRS1985

Altimetry data and the elastic stress tensor of subduction zones

The stress field in the lithosphere caused by the distribution of density anomalies associated to the geoidal undulations observed by the GEOS-3 and SEASAT Earth satellites in the Tonga region was studied. Different models of the lithosphere were generated with different assumptions on the density distribution and geometry, all generating a geoid profile almost identical to the observed one. The first model is the Airy isostatic hypothesis which consists of a crust of density 2.85 laying on a lithosphere of density 3.35. The models obtained with different compensation depths give residual shortwavelength anomalies of the order of several tens of mgal and several tens of meters geoidal undulations. It indicates that there is no isostasy of the Airy type in the Tonga region because the observed geoid has very smooth undulation of about 25 m over a distance of 2000 km. The Pratt isostatic hypothesis is used in a model consisting of a crust of variable density laying on a lithosphere of higher density. This model gives smaller residual anomalies but still shows that there is no isostasy of the Pratt type in the Tonga region because the observed geoidal undulation are much smaller and smoother than the residual undulations associated to the Pratt model of isostasy.

Caputo, M.↗

NASA NTRS1985

Error analyses for a gravity gradiometer mission

This paper addresses the usefulness of an orbiting gravity gradiometer as a sensor for mapping the fine structure of the earth gravity field. The exact knowledge of this field is essential for studies of the solid earth and the dynamics of the oceans. Although the earth gravity tensor, measured by a gradiometer assembly, has nine components, only five components are independent. This latter fact is as a consequence of the symmetry and conservative nature of the earth's gravity field. The most dominant component is the radial one. The error analyses considered here are therefore based only upon a single axis gradiometer sensing this radial component. The expected global gravity and geoid errors for a 50 x 50-km (1/2 x 1/2 deg) area utilizing a spaceborne gradiometer with a precision of 0.001 EU in a 160-km circular polar orbit are about 3 mGAL and 5 cm, respectively.

Kahn, W. D.↗

NASA NTRS1985

Least squares collocation applied to local gravimetric solutions from satellite gravity gradiometry data

An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.

Robbins, J. W.↗

NASA NTRS1988

Modeling and estimation of a low degree geopotential model from terrestrial gravity data

The development of appropriate modeling and adjustment procedures for the estimation of harmonic coefficients of the geopotential, from surface gravity data was studied, in order to provide an optimum way of utilizing the terrestrial gravity information in combination solutions currently developed at NASA/Goddard Space Flight Center, for use in the TOPEX/POSEIDON mission. The mathematical modeling was based on the fundamental boundary condition of the linearized Molodensky boundary value problem. Atmospheric and ellipsoidal corrections were applied to the surface anomalies. Terrestrial gravity solutions were found to be in good agreement with the satellite ones over areas which are well surveyed (gravimetrically), such as North America or Australia. However, systematic differences between the terrestrial only models and GEMT1, over extended regions in Africa, the Soviet Union, and China were found. In Africa, gravity anomaly differences on the order of 20 mgals and undulation differences on the order of 15 meters, over regions extending 2000 km in diameter, occur. Comparisons of the GEMT1 implied undulations with 32 well distributed Doppler derived undulations gave an RMS difference of 2.6 m, while corresponding comparison with undulations implied by the terrestrial solution gave RMS difference on the order of 15 m, which implies that the terrestrial data in that region are substantially in error.

Pavlis, Nikolaos K.↗

NASA NTRS1988

Topex orbit determination and gravity recovery using GPS data from repeat orbits

A covariance analysis is presented for a differential GPS-based technique for satellite tracking and gravity recovery to be demonstrated on Topex in the early 1990's. The technique employs data from an ensemble of repeat ground tracks to recover a unique satellite epoch state for each track and a set of invariant local gravity parameters common to all tracks. For satellites above about 800 km altitude, where gravity modeling is the dominant systematic error, averaging of random error over many arcs and adjustment of the gravity model reduces the final satellite position error. The local gravity parameters can then be used to produce a refined global gravity model. The analysis indicates that errors ranging from 5 to 8 cm in Topex altitude and 0.05 to 0.2 mgal for the gravity field can be achieved, depending on the number of repeat arcs used.

Wu, Jiun-Tsong↗

NASA NTRS1988

Source of the Australasian tektite strewn field - A possible off-shore impact site

Although there is a preponderance of evidence that tektites were formed by asteroid impacts on the earth, no source crater has been found for the largest and youngest of the strewn fields - the Austalasian strewn field. A combined Seasat/Geos 3 altimeter data set of sea surface heights in the northern portion of the Australasian strewn field has been examined for negative gravity anomalies on the continental shelf and slope which might be related to the source crater for these tektites. A large negative anomaly called the Qui Nhon Slope Anomaly is a sea surface depression of approximately 1.5 meters over an area of 100 km diameter. It corresponds to a gravity anomaly of about -50 mgal. It is proposed that this anomaly may be due to the impact structure that produced the Australasian strewn field.

Schnetzler, C. C.↗