Determination of the Earth's gravitational field

In all three principal methods of measuring the earth's gravitational field—gravimetry, satellite orbit perturbations, and astrogeodetic networks—both mathematical theory and observational techniques have been developed in recent years to more than sufficient accuracy to define and determine the irregularities of the field significant on a planetary scale. The common defect of all three methods is inadequate distribution of observations. At present, the different methods agree only for major features such as the Indian Ocean minimum, and the normalized spherical harmonic coefficients of the potential are known to be of an order of magnitude of about ±1.3 × 10−6/(n - 1) with an uncertainty of about ±0.6 × 10−6 for the tesseral terms. Gradual improvement is anticipated with additional observations and the application of better statistical techniques made possible by modern computers.

[1]  I. J. Schoenberg Positive definite functions on spheres , 1942 .

[2]  Peter Musen,et al.  ON THE MOTION OF A 24-HOUR SATELLITE , 1962 .

[3]  B. Morando Orbites de Rsonance des Satellites de 24 H. , 1963 .

[4]  K. Findeisen Numerische Beispiele zur strengen Theorie der Figur der Erde , 1960 .

[5]  K. Moe ON THE OPTIMUM CHOICE OF A SMOOTHING INTERVAL FOR COMPUTING DEFINITIVE ORBITS OF ARTIFICIAL SATELLITES , 1963 .

[6]  W. M. Kaula,et al.  Analysis of Satellite Observations for Longitudinal Variations of the Gravitational Field , 1961 .

[7]  Motion of a satellite in the earth’s gravitational field , 1960, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  G. Garland Gravity and Isostasy , 1956 .

[9]  W. M. Kaula,et al.  Tesseral harmonics of the gravitational field and geodetic datum shifts derived from camera observations of satellites , 1963 .

[10]  J. D. G. Hunter The Figure of the Earth from Gravity Observations and the Precision Obtainable , 1935 .

[11]  T. Teichmann,et al.  Introduction To Astrodynamics , 1960 .

[12]  R. A. Hirvonen Gravity anomalies and deflections of the vertical above sea level , 1952 .

[13]  T. Teichmann,et al.  The Measurement of Power Spectra , 1960 .

[14]  S. Aoki A CONTRIBUTION TO THE THEORY OF CRITICAL INCLINATION OF CLOSE EARTH SATELLITES , 1962 .

[15]  Irène Fischer The present extent of the astro-geodetic geoid and the geodetic world datum derived from it , 1961 .

[16]  Irène Fischer A map of geoidal contours in North America , 1960 .

[17]  L. J. Peters The Direct Approach to Magnetic Interpretation and its Practical Application , 1949 .

[18]  W. Brown MINIMUM VARIANCE IN GRAVITY ANALYSIS PART II: TWO‐DIMENSIONAL , 1955 .

[19]  Dirk Brouwer,et al.  SOLUTION OF THE PROBLEM OF ARTIFICIAL SATELLITE THEORY WITHOUT DRAG , 1959 .

[20]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[21]  H. Orlin The three components of the external anomalous gravity field , 1959 .

[22]  W. M. Kaula IMPROVED GEODETIC RESULTS FROM CAMERA OBSERVATIONS OF SATELLITES , 1963 .

[23]  I. Izsak Differential Orbit Improvement with the Use of Rotated Residuals , 1961 .

[24]  BOUGUER GRAVITY CORRECTIONS USING A VARIABLE DENSITY , 1962 .

[25]  M. Ewing,et al.  Gravity anomalies and crustal section across the Tonga Trench , 1961 .

[26]  W. H. GUIER Determination of the Non-Zonal Harmonics of the Geopotential from Satellite Doppler Data , 1963, Nature.

[27]  Statistical and geological implications of trend mapping with nonorthogonal polynomials , 1963 .

[28]  M. I. Yurkina,et al.  Methods for study of the external gravitational field and figure of the earth , 1962 .

[29]  U. Uotila Investigations on the gravity field and shape of the earth , 1960 .

[30]  M. S. Molodensky,et al.  An evaluation of accuracy of stokes' series and of some attempts to improve his theory , 1962 .

[31]  D. A. Rice Deflections of the vertical from gravity anomalies , 1952 .

[32]  J. C. Rose,et al.  International gravity measurements , 1963 .

[33]  E. C. Bullard,et al.  The determination of the masses necessary to produce a given gravitational field , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[34]  M. S. Molodenskij Lösung der integralgeichung zur ermittlung der erdfigur , 1962 .

[35]  I. I. Mueller Introduction to Satellite Geodesy , 1965 .

[36]  H. Moritz STUDIES ON THE ACCURACY OF THE COMPUTATION OF GRAVITY IN HIGH ELEVATIONS , 1962 .

[37]  A. H. Cook,et al.  Report on absolute measurements of gravity , 1961 .

[38]  G. M. Clemence,et al.  Methods of Celestial Mechanics , 1962 .

[39]  Imre G. Izsak,et al.  A determination of the ellipticity of the earth's equator from the motion of two satellites , 1961 .

[40]  U. Uotila Existing Gravity Material , 1961 .

[41]  B. Szabo Application of the gravimetric method for a world geodetic system , 1962 .

[42]  W. M. Kaula Accuracy of gravimetrically computed deflections of the vertical , 1957 .

[43]  R. A. Hirvonen On the precision of the gravimetric determination of the geoid , 1956 .

[44]  M. F. Kane,et al.  Gravity anomalies in the central Sierra Nevada, California , 1961 .

[45]  F. Press Crustal structure in the California‐Nevada region , 1960 .

[46]  A. Bjerhammar A general method for an explicit determination of the shape of the earth from gravimetric data , 1962 .

[47]  T. Teichmann,et al.  Harmonic Analysis and the Theory of Probability , 1957, The Mathematical Gazette.

[48]  Desmond George King-Hele,et al.  The effect of the earth’s oblateness on the orbit of a near satellite , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[49]  D. Smith,et al.  Determination of the earth's gravitational potential from satellite orbits , 1961 .

[50]  K. Aki,et al.  Use of the Function sin x/x in Gravity Problems , 1955 .

[51]  T. D. Allan,et al.  Comparison of Graf‐Askania and LaCoste‐Romberg surface‐ship gravity meters , 1962 .

[52]  G. Woollard Crustal structure from gravity and seismic measurements , 1959 .

[53]  Y. Kozai NUMERICAL RESULTS FROM ORBITS , 1962 .

[54]  Desmond George King-Hele,et al.  Determination of the Even Harmonics in the Earth's Gravitational Potential , 1963 .

[55]  R. A. Hirvonen The Continental Undulations of the Geoid , 1934 .

[56]  W. Heiskanen The Columbus geoid , 1957 .

[57]  Richard H. Jones,et al.  Stochastic Processes on a Sphere , 1963 .

[58]  J. Vinti New method of solution for unretarded satellite orbits , 1959 .

[59]  J. Vinti,et al.  Theory of an accurate intermediary orbit for satellite astronomy , 1961 .

[60]  Y. Kozai On the Effects of the Sun and the Moon upon the Motion of a Close-Earth Satellite , 1959 .

[61]  G. Bomford The junction of the Indian and European triangulation systems , 1960 .

[62]  G. M. Clemence On the system of astronomical constants , 1948 .

[63]  E. Parzen An Approach to Time Series Analysis , 1961 .

[64]  D. A. Rice Symposium on the Reduction of Gravity Data , 1962 .

[65]  Satellite orbit analyses for geodetic purposes , 1963 .

[66]  Fraser S. Grant,et al.  A problem in the analysis of geophysical data , 1957 .

[67]  G. Veis Geodetic Uses of Artificial Satellites , 1960 .

[68]  Yoshihide Kozai,et al.  The motion of a close earth satellite , 1959 .

[69]  L. Kivioja DEVELOPMENT OF GRAVITY BOUGUER ANOMALIES OF STATE OF OHIO AND THE ISOSTATIC ANOMALIES IN NORTH ATLANTIC IN FOURIER SERIES , 1962 .

[70]  L. Blitzer,et al.  The perturbed motion of 24‐hour satellites due to equatorial ellipticity , 1963 .

[71]  W. Heiskanen,et al.  The Earth And Its Gravity Field , 1959 .

[72]  J. Kiefer,et al.  An Introduction to Stochastic Processes. , 1956 .

[73]  W. M. Kaula,et al.  A geoid and world geodetic system based on a combination of gravimetric, astrogeodetic, and satellite data , 1961 .

[74]  W. M. Kaula Gravity formulas utilizing correlation with elevation , 1958 .

[75]  P. Fougere Spherical harmonic analysis: 1. A new method and its verification , 1963 .

[76]  J. Graaff-Hunter The shape of the Earth's surface expressed in terms of gravity at ground level , 1960 .

[77]  K. Arnold Strenge theorie der absoluten lotabweichungen als funktionen der freiluftanomalien der schwere , 1959 .

[78]  D. Smith,et al.  A determination of the odd harmonics in the geo-potential function , 1963 .

[79]  J. O'keefe,et al.  The gravitational field of the earth , 1959 .

[80]  W. M. Kaula,et al.  Statistical and harmonic analysis of gravity , 1959 .

[81]  A. H. Cook,et al.  The External Gravity Field of a Rotating Spheroid to the order of e3 , 1959 .

[82]  A tentative world datum from geoidal heights based on the Hough ellipsoid and the Columbus geoid , 1959 .

[83]  H. Moritz INTERPOLATION AND PREDICTION OF GRAVITY AND THEIR ACCURACY , 1962 .

[84]  Harold Jeffreys The Determination of the Earth's Gravitational Field (Second Paper) , 1943 .

[85]  H. S. Hopfield,et al.  Odd Harmonics of the Earth's Gravitational Field , 1961, Nature.

[86]  Richard H. Jones,et al.  SPECTRAL ANALYSIS WITH REGULARLY MISSED OBSERVATIONS , 1962 .

[87]  Irène Fischer The hough ellipsoid or the figure of the earth from geoidal heights , 1959 .

[88]  Y. Kozai The potential of the earth derived from satellite motions , 1963 .

[89]  C. H. G. Oldham,et al.  Orthogonal polynomials; their use in estimating the regional effect , 1955 .

[90]  R. H. Merson The Motion of a Satellite in an Axi-symmetric Gravitational Field , 1937 .

[91]  W. C. Krumbein Trend surface analysis of contour-type maps with irregular control-point spacing , 1959 .

[92]  Peter Musen,et al.  Application of Hansen's theory to the motion of an artificial satellite in the gravitational field of the Earth , 1959 .

[93]  IMRE G. IZSAK Tesseral Harmonics in the Geopotential , 1963, Nature.

[94]  D. A. Rice A geoidal section in the united states , 1962 .

[95]  W. Heiskanen On the activity of the isostatic institute of the I.A.G. and of the worldwide gravity project of columbus, ohio, in physical geodesy , 1962 .

[96]  J. C. Harrison The Measurement of Gravity , 1962, Proceedings of the IRE.

[97]  Y. Kozai TESSERAL HARMONICS OF THE POTENTIAL OF THE EARTH AS DERIVED FROM SATELLITE MOTIONS , 1961 .

[98]  W. Dean FREQUENCY ANALYSIS FOR GRAVITY AND MAGNETIC INTERPRETATION , 1958 .

[99]  Duane Brown A MATRIX TREATMENT OF THE GENERAL PROBLEM OF LEAST SQUARES CONSIDERING CORRELATED OBSERVATIONS , 1955 .

[100]  A. Cook The calculation of deflexions of the vertical from gravity anomalies , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[101]  A. Cook A note on the errors involved in the calculation of elevations of the geoid , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[102]  Irene Fischer Parallax of the moon in terms of a world geodetic system , 1962 .

[103]  G. Woollard The Status of Gravimetric Control for Global Geodetic Studies , 1961 .

[104]  R. A. Hirvonen The reformation of geodesy , 1961 .

[105]  Y. Kozai Tesseral harmonics of the gravitational potential of the earth as derived from satellite motions , 1961 .

[106]  K. Ledersteger Der physikalische Zusammenhang zwischen der statischen Abplattung und dem inneren Aufbau der Erde auf der hypothetischen Grundlage einer sechsparametrigen Gleichgewichtsfigur , 1962 .

[107]  E. Tengström A simplified rudzki reduction as a convenient method of reducing gravity data for geodetical and geophysical purposes , 1962 .

[108]  Irene Fischer An astrogeodetic world datum from geoidal heights based on the flattening f = 1/298.3 , 1960 .

[109]  L. Blitzer,et al.  Effect of ellipticity of the equator on 24‐hour nearly circular satellite orbits , 1962 .

[110]  Walter Munk,et al.  The rotation of the earth , 1960 .

[111]  E. Thiel,et al.  Gravity anomalies, crustal structure, and geology in Alaska , 1960 .

[112]  A. Yaglom Second-order Homogeneous Random Fields , 1961 .

[113]  W. M. Kaula Analysis of Gravitational and Geometric Aspects of Geodetic Utilization of Satellites , 1961 .

[114]  R. H. Merson A Pegasus computer programme for the improvement of the orbital parameters of an earth-satellite , 1963 .

[115]  J. Levallois Considérations générales sur les réductions de la pesanteur , 1962 .

[116]  U. Grenander,et al.  Statistical analysis of stationary time series , 1957 .

[117]  M. Caputo Gravity in space and the dimensions and mass of the Earth , 1963 .

[118]  F. R. Helmert Die Mathematischen und physikalischen Theorieen der höheren Geodäsie , 1880 .

[119]  J. V. Isacker Generalized Harmonic Analysis , 1961 .

[120]  A. Shapiro,et al.  THE MEAN DISTANCE TO THE MOON AS DETERMINED BY RADAR. , 1965 .

[121]  R. Newton Ellipticity of the equator deduced from the motion of transit 4A , 1962 .

[122]  P. Musen On the motion of a satellite in an asymmetrical gravitational field , 1960 .

[123]  I. Izsak A THEORY OF SATELLITE MOTION ABOUR AN OBLATE PLANET. I. A SECONDORDER SOLUTION OF VINITI'S DYNAMICAL PROBLEM , 1959 .

[124]  J. Stearn,et al.  Adjustment of conditions with parameters and error analysis , 1962 .

[125]  I. Izsak On the Critical Inclination in Satellite Theory , 1962 .

[126]  L. P. Pellinen Accounting for topography in the calculation of quasigeoidal heights and plumb-line deflections from gravity anomalies , 1962 .

[127]  R. Rapp CORRELATION COEFFICIENTS AND THEIR USE IN THE PREDICTION OF MEAN ANOMALIES , 1962 .

[128]  J. L. Holloway Smoothing and Filtering of Time Series and Space Fields , 1958 .