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Use of standard estimation techniques to recover geopotential fine structure from gradiometer data requires the adjustment of small subsets of parameters while constraining others to their a priori values in order to minimize the computational load. Here, gravitational anomalies are selected as a parametrization of the gravity field which permits such an approach. Techniques coupled with numerical results for a spaceborne gravity gradiometer mission simulation are described which demonstrate that if a satellite is in a polar/circular orbit at an altitude of 160 km, 1 deg mean free air gravity anomalies can be recovered to an accuracy of 0.4 mgal, where 1 mgal = 0.001 cm/sq s.

This report is the Fourth Annual Summary of the Research Program of the Geodynamics Branch. The branch is located within the Laboratory for Terrestrial Physics of the Space and Earth Sciences Directorate of the Goddard Space Flight Center. The research activities of the branch staff cover a broad spectrum of geoscience disciplines including: tectonophysics, space geodesy, geopotential field modeling, and dynamic oceanography. The NASA programs which are supported by the work described in this document include the Geodynamics and Ocean Programs, the Crustal Dynamics Project and the proposed Ocean Topography Experiment (TOPEX). The reports highlight the investigations conducted by the Geodynamics Branch staff during calendar year 1985. The individual papers are grouped into chapters on Crustal Movements and Solid Earth Dynamics, Gravity Field Modeling and Sensing Techniques, and Sea Surface Topography. Further information on the activities of the branch or the particular research efforts described herein can be obtained through the branch office or from individual staff members.

This report is based upon the accumulated scientific and engineering studies pertaining to the Geopotential Research Mission (GRM). The scientific need and justification for the measurement of the Earth's gravity and magnetic fields are discussed. Emphasis is placed upon the studies and conclusions of scientific organizations and NASA advisory groups. The engineering design and investigations performed over the last 4 years are described, and a spacecraft design capable of fulfilling all scientific objectives is presented. In addition, critical features of the scientific requirements and state-of-the-art limitations of spacecraft design, mission flight performance, and data processing are discussed.

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.

The exploitation of the present tethered system and the need for repeat missions; multiple payloads placed along the tether; the extension of the present altitude limit to below 130 km; the development of free-flying tether satellites for studying both the Earth's atmosphere and ionosphere and also for studying the plantes; and a subtether were discussed. Areas of research were identified: aeronomy studies, gravity and magnetic potential mission, advanced sensors for geodynamics, and mapping and remote sensing.

The spaceborne gravity gradiometer is a potential sensor for mapping the fine structure of the Earth's gravity field. Error analyses were performed to investigate the accuracy of the determination of the Earth's gravity field from a gravity field satellite mission. The orbital height of the spacecraft is the dominating parameter as far as gravity field resolution and accuracies are concerned.

A broad spectrum of geoscience disciplines including space geodesy, geopotential field modeling, tectonophysics, and dynamic oceanography are discussed. The NASA programs, include the Geodynamics and Ocean Programs, the Crustal Dynamics Project, the proposed Ocean Topography Experiment (TOPEX), and the Geopotential Research Mission (GRM). The papers are grouped into chapters on Crustal Movements, Global Earth Dynamics, Gravity Field Model Development, Sea Surface Topography, and Advanced Studies.

NASA is proposing to launch a new geopotential fields exploration system called the Geopotential Research Mission (GRM). Two spacecraft will be placed in a circular polar orbit at 160 km altitude. Distances between these satellites will vary from 100 to 600 km. Both scalar and vector magnetic fields will be measured by magnetometers mounted on a boom positioned in the forward direction on the lead satellite. Gravity data will be computed from the measured change in distance between the two spacecraft. This quantity, called the range-rate, will be determined from the varying frequency (Doppler shift) between transmitter and receiver on each satellite. Expected accuracies (at the one-sigma level) are: gravity field, 1.0 milliGal, 5 cm geoid height; magnetics, scalar field 2 nT, vector to 20 arcsec, both resolved to less than 100 km. With these more accurate and higher resolution data, it will be possible to investigate the earth's structure from the crust (with the shorter wavelength gravity and magnetic anomalies) through the mantle (from the intermediate wavelength gravity field) and into the core (using the longer wavelength gravity and magnetic fields).

The research program of the Geodynamics Branch is summarized. The research activities cover a broad spectrum of geoscience disciplines including space geodesy, geopotential field modeling, tectonophysics, and dynamic oceanography. The NASA programs which are supported by the work described include the Geodynamics and Ocean Programs, the Crustal Dynamics Project, the proposed Ocean Topography Experiment (TOPEX) and Geopotential Research Mission. The individual papers are grouped into chapters on Crustal Movements, Global Earth Dynamics, Gravity Field Model Development, Sea Surface Topography, and Advanced Studies.

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.

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.

The airborne laser ranging system is a multibeam short pulse laser ranging system on board an aircraft. It simultaneously measures the distances between the aircraft and six laser retroreflectors (targets) deployed on the Earth's surface. The system can interrogate over 100 targets distributed over an area of 25,000 sq, kilometers in a matter of hours. Potentially, a total of 1.3 million individual range measurements can be made in a six hour flight. The precision of these range measurements is approximately + or - 1 cm. These measurements are used in procedure which is basically an extension of trilateration techniques to derive the intersite vector between the laser ground targets. By repeating the estimation of the intersite vector, strain and strain rate errors can be estimated. These quantities are essential for crustal dynamic studies which include determination and monitoring of regional strain in the vicinity of active fault zones, land subsidence, and edifice building preceding volcanic eruptions.

The signal characteristics and the geopotential parameter recovery capability of the SST Doppler sensor flown on the geopotential research mission (GRM) are discussed. Simulation studies of the velocity profiles resulting from the perturbation produced by a 1 deg/w/1 deg, 1 mgal anomaly as sensed by two GRM spacecraft orbiting altitudes of 160 km and 200 km respectively are described. It was found that the amplitude of the gravity signal drops off by a factor of 1.5 when going from an altitude of 160 km to 200 km. By extrapolation the signal amplitude is further decreased by a factor of 3 when the orbital altitude is increased to 250 km. Thus the amplitude of the measurement drops off as the altitude is increased to the point where it is insignificant at the 1 mgal level for altitudes above 200 km. Spectral analysis results show that for a GRM mission altitude of 160 km and a system precision of 1 micrometer/sec, gravity field information can be sensed up to 230 cycles per orbital revolution - beyond that frequency the gravity signal is characterized by white noise. It follows that at the GRM mission altitude of 160 km and a satellite to satellite Doppler system precision of 1 micrometer per second, 1/1 deg gravity and geoid anomalies can be determined to an accuracy of 3.4 mgals and 8.6 cm respectively.

Advances in satellite tracking data accuracy and coverage over the past 15 years have led to major improvements in global geopotential models. But the spacial resolution of the gravity field obtained solely from satellite dynamics sensed by tracking data is still of the order of 1000 km. Attention is given to an approach which will provide information regarding the fine structure of the gravity field on the basis of an application of local corrections to the global field. According to this approach, a basic satellite to satellite tracked (SST) range-rate measurement is constructed from the link between a ground station, a geosynchronous satellite (ATS 6), and a near-earth satellite (Apollo or GEOS 3). Attention is given to a mathematical model, the simulation of SST gravity anomaly estimation accuracies, a gravity anomaly estimation from GEOS 3/ATS 6 and Apollo/ATS 6 SST observations, and an evaluation of the mean gravity anomalies determined from SST.

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.

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.

The Goddard Apollo-Soyuz Geodynamics Experiment is described. It was performed to demonstrate the feasibility of tracking and recovering high frequency components of the earth's gravity field by utilizing a synchronous orbiting tracking station such as ATS-6. Gravity anomalies of 5 MGLS or larger having wavelengths of 300 to 1000 kilometers on the earth's surface are important for geologic studies of the upper layers of the earth's crust. Short wavelength Earth's gravity anomalies were detected from space. Two prime areas of data collection were selected for the experiment: (1) the center of the African continent and (2) the Indian Ocean Depression centered at 5% north latitude and 75% east longitude. Preliminary results show that the detectability objective of the experiment was met in both areas as well as at several additional anomalous areas around the globe. Gravity anomalies of the Karakoram and Himalayan mountain ranges, ocean trenches, as well as the Diamantina Depth, can be seen. Maps outlining the anomalies discovered are shown.

The Apollo Soyuz Test Project Geodynamics Experiment was performed to assess the feasibility of tracking and recovering high frequency components of the earth gravity field by utilizing a synchronous orbiting tracking station such as Applications Technology Satellite 6. Two prime areas of data collection were selected for this experiment. The first area is the center of the African continent, and the second area is the Indian Ocean depression centered at latitude 5 N and longitude 75 E. Preliminary results show that the detectability objective of the experiment has been achieved in both areas as well as in several additional anomalous areas around the globe. Gravity anomalies of the Karakoram and Himalayan mountain ranges of ocean trenches, and of the Diamantina depth are specific examples.

A technique is discussed for the accurate (i.e. to within fractions of cm/yr) detection of earth surface motions utilizing the latest space technology. It is shown that over a six day period and assuming a 50% cloud cover (as experienced over the last few years of laser operation) utilizing spaceborne precision ranging systems, intersite distances on the order of 5 to 15 km can be determined in the vertical and horizontal components with errors in the 0.5 to 1.5 cm range. These errors are almost independent of ground survey errors up to 0.25 meters and orbit errors up to 200 meters. A spaceborne laser ranging system is assumed to range simultaneously to two or more ground emplaced retroreflectors. The fundamental advantage derived from simultaneous ranging is the elimination to first order of errors due to the system. This means elimination of bias errors in the ranging system, errors due to propagation effects, and errors associated with the spacecraft's motion in its orbit.

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.

The accuracy with which the GEOS-C altitude may be estimated over long (7 day) and short (40 minute) orbital arcs is investigated. Over the long are excellent agreement was attained between a simulation of the orbit determination process and a covariance analysis. Both approaches yielded RMS altitude errors of about 1.5 meters over the Caribbean calibration area and approximately 7.5 meters overall. The geopotential was identified as the largest error source. For the short arc, the covariance analysis revealed that the propagated altitude error is linearly dependent upon station survey component errors which are also the largest source of altitude errors. An Appendix contains the mathematics of covariance analysis as applied to orbit determination.

The 'spaceborne laser ranging system' is a proposed short pulse laser on board an orbiting spacecraft. It measures the distances between the spacecraft and many laser retroreflectors (targets) deployed on the earth's surface. The precision of these range measurements was assumed to be about plus or minus 2 cm. These measurements were then used together with the orbital dynamics of the spacecraft to derive the intersite vector between the laser ground targets. The errors associated with this vector were on the order of 1 to 2 cm. The baseline distances determined range from 25 km to 1200 km. By repeating the measurements of the intersite vector, strain and strain rate errors were estimated. The realizable precision for intersite distance determination was estimated to be on the order of 0.5 cm at 300 km and about 1.5 cm at 1200 km. The corresponding inaccuracies for the intersite distances were larger, than is 1 cm and 3.5 cm respectively. The corresponding precision in the vertical direction was 1 cm and 3 cm.

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.

The primary experiment on the Geodynamics Experimental Ocean Satellite-3 (GEOS-3) is the radar altimeter. This experiment's major objective is to demonstrate the utility of measuring the geometry of the ocean surface; i.e., the geoid. Results obtained from this experiment so far indicate that the planned objectives of measuring the topography of the ocean surface with an absolute accuracy of + or - 5 m can be met and perhaps exceeded. The GEOS-3 satellite altimeter measurements have an instrument precision in the range of + or - 25 cm to + or - 50 cm when the altimeter is operating in the 'short pulse' mode. After one year's operations of the altimeter, data from over 5000 altimeter passes have been collected. With the mathematical models developed and the altimeter data presently available, mapping of local areas of ocean topography has been realized to the planned accuracy levels and better. This paper presents the basic data processing methods employed and some interesting results achieved with the early data. Plots of mean sea surface heights as inferred by the altimeter measurements are compared with a detailed 1 by 1 deg gravimetric geoid.

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 technique is discussed for the accurate (i.e., to within fractions of centimeters per year) detection of earth surface motions utilizing the latest space technology. It is shown that, over a six-day period and assuming a 50% cloud cover (i.e., as experienced over the past few years of laser operation), by using spaceborne precision ranging systems, intersite distances on the order of 5 to 15 km (dependent mostly on the beam width of the laser) can be determined in the vertical and horizontal components, with errors in the 0.5- to 1.5-cm range. These errors are almost independent of ground survey errors up to 0.25 m and orbit errors up to 200 m. A spaceborne laser ranging system is assumed to range to two or more ground-emplaced retroreflectors. This can be done either in a simultaneous or nonsimultaneous mode. Hardware is under development for the latter technique.

The primary experiment on the Geodynamics Experimental Ocean Satellite-3 (GEOS-3) is the radar altimeter. This experiment's major objective is to demonstrate the utility of measuring the geometry of the ocean surface, i.e. the geoid. Results obtained from this experiment so far indicate that the planned objectives of measuring the topography of the ocean surface with an absolute accuracy of + or - 5 meters can be met and perhaps exceeded. The GEOS-3 satellite altimeter measurements have an instrument precision in the range of + or - 25 cm to + or - 50 cm when the altimeter is operating in the short pulse mode.

Altimeter data from a spacecraft borne altimeter was processed to estimate the fine structure of the marine geoid. Simulation studies show that, among several competing parameterizations, the mean free air gravity anomaly model exhibited promising geoid recovery characteristics. Using covariance analysis techniques, quantitative measures of the orthogonality properties are investigated.

An experiment is proposed to test a first generation spacecraft-borne radar altimeter's capability to measure the topography of the sea surface. The initial radar altimeter will have an instrumental error of one meter and an overall accuracy to two to five meters. This instrument will thus improve the accuracy of the geoid from the present 10 to 20 meters to better than 5 meters. In order to detect storm surges, tidal forces, and ocean currents, an altimeter with an overall accuracy of at least ?1 meter will be required. The overall accuracy of the initial radar altimeter will thus primarily provide geodetic information and possible oceanographic information such as sea state.

Graphs of station contact times for Apollo parking orbits with variable launch azimuths

Mathematical models for effect of tracking systems on RMS errors in spacecraft position and velocity - least squares method

Noise characteristics of unified S-band tracking system high speed range rate and X-Y ANGULAR data obtained during aircraft flyby tests

Tracking error analysis study for Apollo project

Error analysis during transfer and lunar parking orbit phases of IMP satellite

Range and range rate system and data analysis for syncom i satellite

Tracking systems, mathematical models & errors

The detection of tides and/or currents through the analysis of data generated in connection with the Ocean Geoid Determination Investigation is presented. A discussion of the detailed objectives and approach are included.

This investigation was undertaken to improve the gravity model and hence the ocean geoid. A specific objective is the determination of the gravity field and geoid with a space resolution of approximately 5 deg and a height resolution of the order of five meters. The concept of the investigation is to utilize both GEOS-C altimeter and satellite-to-satellite tracking data to achieve the gravity model improvement. It is also planned to determine the geoid in selected regions with a space resolution of about a degree and a height resolution of the order of a meter or two. The short term objectives include the study of the gravity field in the GEOS-C calibration area outlined by Goddard, Bermuda, Antigua, and Cape Kennedy, and also in the eastern Pacific area which is viewed by ATS-F.

Laser and minitrack observational data from GEOS-2 collected during the period April 23, 1971 to May 1971, have been used for the purpose of assessing the influence of tracking station location on the accuracy of orbit determination. These data were processed using a unified set of coordinates for the tracking station locations. Concurrently, these data were processed using nonunified station locations referred to a variety of geodetic datums. The resultant orbits based on the two different sets of station locations were compared and relative differences in the position of the satellite were determined. Differences between the two groups of orbits fitted over four-day data spans ranged from 250 meters to 500 meters for orbits derived from laser data only. For orbits observed from Minitrack data alone the relative differences in GEOS-2 spacecraft position ranged from 50 meters to 190 meters. Utilizing the laser data alone in each arc, definitive orbits were computed using the unified and nonunified station location coordinates. The differences in the satellite position in the overlap region when using the unified laser station coordinates ranged from 25 meters to 150 meters, whereas when using the nonunified laser station coordinates the differences in position ranges from 180 to 650 meters.