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The author has identified the following significant results. The collocation technique to filter the remaining EREP passes no. 4, no. 6, and no. 9 was completed. The correlation studies of altimetry geoid profiles with the gravity data and ocean bottom topography were also completed.
For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moritz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correction term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30 deg, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055 millionths at n = 2, m = 2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.
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 mgals 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 meters.
A determination of the fine scale sea surface topography in the GEOS-3 calibration area using the radar altimeter data is presented. Estimates of the north-south and east-west components of the deflections of the vertical as well as values of the geoidal heights were made. Three major stages of processing were used in obtaining the final results. The first two use pass processors; in the final stage, the processor combines all the pass results to compute the final results. The results obtained compare favorably with gravimetrically determined geoids for this calibration area.
Knowledge of the earth's gravity field continued to increase during the last four years. Altimetry data from the GEOS-3 satellite has provided the geoid over most of the ocean to an accuracy of about one meter. Increasing amounts of laser data has permitted the solution for 566 terms in the gravity field with which orbits of the GEOS-3 satellite have been computed to an accuracy of about one to two meters. The combination of satellite tracking data, altimetry and gravimetry has yielded a solution for 1360 terms in the earth's gravity field. A number of problems remain to be solved to increase the accuracy of the gravity field determination. New satellite systems would provide gravity data in unsurveyed areas and correction for topographic features of the ocean and improved computational procedures together with a more extensive laser network will considerably improve the accuracy of the results.
The paper discusses the analysis of GEOS 3 altimeter data for the determination of geoid heights and point and mean gravity anomalies. Methods are presented for determining the mean anomalies and mean undulations from the GEOS 3 altimeter data available by the end of September 1977 without having a complete set of precise orbits. The editing of the data is extensive to remove questionable data, although no filtering of the data is carried out. An adjustment process is carried out to eliminate orbit error and altimeter bias. Representative point anomaly values are computed to investigate anomaly behavior across the Bonin Trench and over the Patton seamounts.
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.
A determination of the fine-scale sea surface topography in the GEOS 3 calibration area using the radar altimeter data is presented. Estimates of the north-south and east-west components of the deflections of the vertical as well as values of the geoidal heights are made. Three major stages of processing are used in obtaining the final results. The first two use pass processors; in the final stage the processor combines all the pass results to compute the final results. Comparison with a gravimetrically determined geoid for the calibration area, provided by the National Aeronautics and Space Administration, yielded a mean and standard deviation of 0.45 and 1.5 m, respectively
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.
The adjusted GEOS-3 altimeter data, taken as averages within a data frame, have been used to construct free air anomaly and geoid undulation profiles and maps in areas of geophysical interest. Profiles were constructed across the Philippine Trench (at a latitude of 6 deg) and across the Bonin Trench (at a latitude of 28 deg). In the latter case an anomaly variation of 443 mgals in 143 km was derived from the altimeter data. These variations agreed reasonably with terrestrial estimates, considering the predicted point accuracy was about + or - 27 mgals. An area over the Patton Sea mounts was also investigated with the altimeter anomaly field agreeing well with the terrestrial data except for the point directly over the top of the sea mount. It is concluded that the GEOS-3 altimeter data is valuable not only for determining 5 deg and 1 deg x 1 deg mean anomalies, but also can be used to describe more local anomaly variations.
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.
A higher resolution anomaly map of the Broken Ridge area (2 degree dipole spacing) was produced and reduced to the pole using quiet time data for this area. The map was compared with equally scaled maps of gravity anomaly, geoid undulation, and bathymetry. The ESMAP results were compared with a NASA MAGSAT map derived by averaging data in two-degree bins. A survey simulation was developed to model the accuracy of MAGSAT anomaly maps as a function of satellite altitude, instrument noise level, external noise model, and crustal anomaly field model. A preliminary analysis of the geophysical structure of Broken Ridge is presented and unresolved questions are listed.
The radar altimeter is the only satellite remote sensor with a proven capability for synoptically measuring an integral property of the dynamic ocean on a near global, all weather basis. Because acquisition of global, in situ ocean data with space/time resolution adequate to describe dynamically important ocean features is practically impossible, any attempt to develop a global ocean monitoring and forecasting system will rely heavily on altimetric data for initialization and updating. Maximizing useful information from the altimeter while minimizing error sources and developing methods for assimilating altimeter data into dynamical models are, therefore, vital areas for research and development. The limits imposed on ocean prediction by errors in the geoid or apparent errors associated with ground track variations near strong geopotential gradients are examined.
Geoid undulations derived from Doppler satellite positioning are compared with corresponding values derived from terrestrial and satellite information using three different procedures. Doppler undulations are compared with uncorrected gravimetric undulations, and systematic differences of 1.6 m and 0.4 m are found for western and eastern U.S. stations, respectively. The systematic difference of 1.6 m was reduced to 0.1 m when terrain-related corrections were applied. Undulations computed from a spherical harmonic expansion to degree 180 yielded standard deviations only slightly poorer than the combined data. A more systematic difference in the western than in the eastern stations remained.
Potential and surface deformation Love numbers for internal loading have been calculated in order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces. These quantities depend on the depth and harmonic degree of loading, and can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Constructing a series of spherically symmetric, self-gravitating flow models for a variety of radial Newtonian viscosity variations and flow configurations, and calculating relaxation times for spherically symmetric viscous earth models, it is demonstrated that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound; this is much less time than the time scale for significant change in the convective flow pattern.
A composite map produced by combining 90 passes of SST data show good agreement with conventional GEM models. The SEASAT altimeter data were deduced and found to agree with both the SST and 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. Comparison with regional bathymetric data shows a remarkedly close correlation with plate age. Most anomalies in the east half of the Pacific could be partly caused 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 (approximately 3 m) over old, smooth sea floor may indicate a further deeper source within or perhaps below the lithosphere. The possible plume size and ascent velocity necessary to supply deep mantle material to the upper mantle without complete thermal equilibration was considered. A plume emanating from a buoyant layer 100 km thick and 10,000 times less viscous than the surrounding mantle should have a diameter of about 400 km and must ascend at about 10 cm/yr to arrive still anomalously hot in the uppermost mantle.
Unlike Earth, on Venus long wavelength geoid anomalies correlate well with topography. Venus's admittance curve between harmonic degrees 3 and 18 is inconsistent with Airy isostasy but is consistent with dynamic support from convection being the dominant mechanism of compensation on Venus. We model dynamic compensation on Venus using simple flow models which assume a spherically symmetric Newtonian mantle viscosity profile. Preliminary models parameterize the viscosity variation with depth as a 2 layer model with a boundary at 720 km depth. A model in which viscosity in the lower mantle is a factor of 10 lower than in the upper mantle can explain Venus's observed admittance curve for degrees 3 through 18. Dynamic models which include a chemical boundary between the upper and lower mantle do not successfully explain the observed admittance curve, indicating that Venus does not have a chemically layered mantle.
The accuracy of measurements of gravity over the North Atlantic is assessed. The effect of errors due mainly to aliasing, of the distribution of available data, and of the unresolved geoid power on geoidal estimates is determined. A crude estimate of circulation in the North Atlantic is obtained by using the simplest of preconceptions: a reasonable rms value of zeta prime, the component of the surface expression of seawater motion corresponding to the general circulation.