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A system was designed with the capability of determining 1-cm accuracy station positions in three dimensions using pulsed laser earth satellite tracking stations coupled with strictly geometric data reduction. With this high accuracy, several crucial geodetic applications become possible, including earthquake hazards assessment, precision surveying, plate tectonics, and orbital determination.
The work is reported on support of the GEOS-C Program, National Geodetic Satellite program, and the Earth Physics Program. The statement of work, and a description of the GEOS-C are presented along with the trip reports, and the Earth and Ocean Physics Application program.
A simple system of reference axes is defined for possible use in high precision geodetic studies over long periods of time for programs in earth physics. The proposed system is based on the gravitational and dynamic characteristics of the axis of rotation and the earth's center of mass as defined instantaneously at a given epoch. Techniques are outlined for its continuous representation over time intervals of significance for studies in earth physics. The relationship between the proposed system and the representation of extra-terrestrial objects using the celestial sphere concept is also discussed.
The problem is considered of obtaining accurate values of refraction corrections for geodetic measurements of celestial bodies. The basic principles of optics governing the phenomenon of refraction are defined, and differential equations are derived for the refraction corrections. The corrections fall into two main categories: (1) refraction effects due to change in the direction of propagation, and (2) refraction effects mainly due to change in the velocity of propagation. The various assumptions made by earlier investigators are reviewed along with the basic principles of improved models designed by investigators of the twentieth century. The accuracy problem for various quantities is discussed, and the conclusions and recommendations are summarized.
The author has identified the following significant results. The analysis was based on a time series intrinsic relationship between the satellite ephemeris, altimeter measured ranges, and the corresponding a priori values of subsatellite geoidal heights. Using sequential least squares processing with parameter weighting, the objective was to recover (1) the absolute geoidal heights of the subsatellite points, and (2) the associated altimeter calibration constant(s). Preliminary results from Skylab altimetry are given, using various combinations of orbit ephemeris and altimeter ranges as computed differently by NASA/JSC and NASA/Wallops. The influences of orbit accuracy, weighting functions, and a priori ground truth are described, based on the various combination solutions. It is shown that to deduce geoidal height by merely subtracting the height of the satellite from the altimeter range is inadmissible. The results of such direct subtraction can be very misleading if the orbit used is computed from data that included altimeter data used as height constraints. In view of the current state of knowledge, the use of geodetic ground truth samples as control benchmarks appears indispensable for the recovery of absolute geoidal heights with correct scale.
The author has identified the following significant results. The analysis was based on a time series intrinsic relationship between the satellite ephemeris, altimeter measured ranges, and the corresponding a priori values of subsatellite geoidal heights. Using, least squares processing with parameter weighting, the objective was to recover: (1) the absolute geoidal heights of the subsatellite points; and (2) the associated altimeter calibration constants. Preliminary results from Skylab mission SL-2 are given, using various combinations from two sets of orbit ephemeris and altimeter ranges. It is shown that correctly scaled geoidal heights cannot be deduced by merely subtracting the altimeter range from the geodetic height of the satellite unless the satellite ephemeris and the altimeter have no unknown significant systematic errors or biases and drifts. It is emphasized that the primary objective of the Skylab altimeter is to determine the instrument feasibility. Any additional applications of the data such as for geodesy, geophysics, and oceanography are desirable. Although accurate orbit is required for such applications, it is not a prerequisite for determining the instrument feasibility.
Activities related to the National Geodetic Satellite Program are reported and include a discussion of Ohio State University's OSU275 set of tracking station coordinates and transformation parameters, determination of network distortions, and plans for data acquisition and processing. The problems encountered in the development of the LAGEOS satellite are reported in an account of activities related to the Earth and Ocean Physics Applications Program. The LAGEOS problem involves transmission and reception of the laser pulse designed to make accurate determinations of the earth's crustal and rotational motions. Pulse motion, ephemeris, arc range measurements, and accuracy estimates are discussed in view of the problem. Personnel involved in the two programs are also listed, along with travel activities and reports published to date.
For the Skylab S-193 radar altimeter, data processing flow charts and identification of calibration requirements and problem areas for defined S-193 altimeter experiments are presented. An analysis and simulation of the relationship between one particular S-193 measurement and the parameter of interest for determining the sea surface scattering cross-section are considered. For the GEOS-C radar altimeter, results are presented for system analyses pertaining to signal-to-noise ratio, pulse compression threshold behavior, altimeter measurement variance characteristics, desirability of onboard averaging, tracker bandwidth considerations, and statistical character of the altimeter data in relation to harmonic analysis properties of the geodetic signal.
A geodetic analysis of Skylab S-193 altimeter preliminary data from mission SL/2 and EREP pass 9 is considered. The overall objective of the investigation was a demonstration of the feasibility of a use of altimeter data for the determination of the geoid in ocean areas. The geoid is the equipotential surface that would coincide with an 'undisturbed' mean sea level of the earth's gravity field. Analytical data handling formulations are discussed.
Computer program is capable of calculating orbit and geodetic parameter estimates. Program can also be used for translunar and interplanetary trajectories.
Oceanographic measurements taken by SEASAT-A are not only applicable to correct altimetry data for the desired geoid but also, as a result, they themselves are useful by-products for basic and applied research in the fields of sciences and engineering, exploratory development in sensor design and measurement techniques, and prediction products for operational fleet support. Among these measurements the important ones are current, sea state, and tides. Identified are parameters of the measurements which will be used to eliminate temporal environmental biases from geodetic measurements, and also to describe the physical processes involved.
Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.
An exact method for the nonzero altitude transformation from geocentric to geodetic coordinates is derived. The method is mathematically general and should serve as a primary standard.
Formulas for the general-altitude (height above the ellipsoid) transformation from geocentric to geodetic coordinates and vice versa are derived. The set of four formulas is expressed in each of two useful forms: series expansions in powers of the earth's flattening and series expansions in powers of the earth's eccentricity. The error incurred in these expansions is of the order of one part in 30 million.-
A very-long-baseline interferometer system was designed and built for geodetic applications. Each interferometer terminal records a 360-kHz spectral band of noise from a compact extragalactic radio source. The center frequency of the spectral band can be selected to sample sequentially bands covering a much wider frequency range to obtain subnanosecond accuracy in group-delay measurements. A tunnel-diode pulse generator is used to calibrate the delays in the receiver. The necessary sets of algorithms and computer programs have been developed to analyze the data and have allowed the system to be employed to make accurate determinations of vector baselines, radio-source positions, polar motion, and universal time.
The use of very-long-baseline interferometry (VLBI) observations for the estimation of geodetic and astrometric parameters is discussed. Analytic models for the dependence of delay and delay rate on these parameters are developed and used for parameter estimation by the method of weighted least squares. Results are presented from approximately 15,000 delay and delay-rate observations, obtained in a series of nineteen VLBI experiments involving a total of five stations on two continents. The closure of baseline triangles is investigated and found to be consistent with the scatter of the various baseline-component results. Estimates are made of the wobble of the earth's pole and of the irregularities in the earth's rotation rate. Estimates are also made of the precession constant and of the vertical Love number, for which a value of 0.55 + or - 0.05 was obtained.
The paper describes the use of dynamic methods of laser ranging of a low altitude satellite along with proposed experiments involving both dynamic and geodetic methods of laser ranging of the Lageos satellite. Particular attention is given to the testing of laser ranging techniques across the San Andreas Fault in California where it is hoped that plate motion will be observable after several years of measurements.
The work performed by individual contributors to the National Geodetic Satellite Program is presented. The purpose of the organization, the instruments used in obtaining the data, a description of the data itself, the theory used in processing the data, and evaluation of the results are detailed for the participating organizations.