The decay of the spectrum of the gravitational potential and the topography for the Earth     

R. H. Rapp 《Geophysical Journal International》1989,99(3):449-455

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Report of the IAU/IAG/COSPAR working group on cartographic coordinates and rotational elements of the planets and satellites: 1988     

M. E. Davies  V. K. Abalakin  M. Bursa  G. E. Hunt  J. H. Lieske  B. morando  R. H. Rapp  P. K. Seidelmann  A. T. Sinclair  Y. S. Tjuflin 《Celestial Mechanics and Dynamical Astronomy》1989,46(2):187-204

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Comment on the paper “On estimating gravity anomalies—A comparison of least squares collocation with conventional least squares techniques”     

Reiner Rummel  Richard H. Rapp 《Journal of Geodesy》1978,52(4):297-297

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The Earth's gravity field     

Richard H. Rapp 《Surveys in Geophysics》1975,2(2):193-216

The Earth's gravity field can be determined from gravity measurements made on the surface of the Earth, and through the analysis of the motion of Earth satellites. Gravity data can be used to solve the boundary value problem of gravimetric geodesy in various ways, from the classical formulation using a geoid to the concept of a reference surface interior to the masses of the Earth to a statistical method. We now have gravity information for 1⁰ data blocks over 46% of the Earth's surface and more than several million point measurements available.Satellite observations such as range, range-rate, and optical data have been analyzed to determine potential coefficients used to describe the Earth's gravitational potential field. Coefficients, in a spherical harmonic expansion to degree 12, can be determined from satellite data alone, and to at least degree 20 when the satellite data is combined with surface gravity material. Recent solutions for potential coefficients agree well to degree 4, but with increasing disagreement at higher degrees.  相似文献   

    

Richard H. Rapp 《Journal of Geodesy》1975,49(1):57-63

For proper computation of the Stokes’ constants, or the evaluation of potential coefficients from terrestrial gravity data, surface free-air anomalies should be corrected to sea level. Such a correction is composed of two parts; the first, the Molodensky correction, G₁, and a second, a term depending on the degree (n) and the expansion of (hΔg). This paper examines these terms numerically, computing for 1654 5° equal area blocks values of G₁ and the total correction based on spherical harmonic expansions to degree 20. The largest correction found was 0.37 mgals. Corrections to potential coefficients caused by the anomaly correction were computed and compared to the original coefficients. The ratio between the coefficient corrections and the full coefficients generally increased by degree having a maximum ratio of 0.21 percent at degree 14 indicating that at the present time the corrections considered are negligible up to at least degree 20.  相似文献   

Geoid information by wavelength     

Richard H. Rapp 《Journal of Geodesy》1973,47(4):405-411

Two models describing potential coefficient behavior are used to estimate the root mean square geoid undulation by wavelength. Four wavelength types were defined: long wavelengths: ℓ=2 to 10; intermediate wavelengths: ℓ=11 to 100; short wavelengths: ℓ=101 to 1000; and very short wavelengths: ℓ=1001 to ∞. By one representation of potential coefficient behavior the intermediate wavelength geoid information was ±5.64 m, short wavelength, ±0.66 m, and the very short wavelength, ±0.05 m. The procedures of this paper were applied to an actual residual undulation computation using detailed gravity material.  相似文献   

Comparison of mean gravity anomalies at elevation with corresponding ground anomalies     

R. H. Rapp 《Journal of Geodesy》1967,41(1):55-65

In support of requirements for the U.S. Air Force Cambridge Research Laboratories, gravity anomalies have been upward continued to several elevations in different areas of the United States. One area was 34⁰ to 40⁰ N in latitude and 96⁰ to 103⁰ W in longitude, generally called the Oklahoma area. The computations proceeded from 26, 032 point anomalies to the prediction of mean anomalies in 14, 704, 2.5′×2.5′ blocks and 9,284, 5′×5′ blocks. These anomalies were upward continued along 28 profiles at 5′ intervals for every 30′ in latitude and longitude. These anomalies at elevations were meaned in various patterns to form mean 30′×30″, 1⁰×1⁰, 5⁰×5⁰ blocks. Comparisons were then made to the corresponding ground values. The results of these comparisons lead to practical recommendations on the arrangement of flight profiles in airborne gravimetry.  相似文献   

Geoid undulation differences between geopotential models     

Richard H. Rapp  Yan Ming Wang 《Surveys in Geophysics》1993,14(4-5):373-380

Three geopotential models (OSU91A, GEM-T3, and GRIM4-C2), available in 1991, have been compared in several ways. The models have been differenced to find the geoid undulation difference are on the order of 1 m in land areas and 30 cm in ocean areas with extreme differences reaching 6 m. The models were also evaluated, augmented by higher degree terms, when necessary, through comparisons with undulations at Doppler and GPS positioned stations. The undulation difference at the Doppler stations was ± 1.57 m with no significant difference between models. Using 4 GPS test areas, differences were seen between the various models. A final comparison was made between geoid undulations implied by a Geosat 17 day cycle and undulations from the three models. The OSU91A model performed best having a difference standard deviation of ±34 cm.  相似文献   

Separation between reference surfaces of selected vertical datums   总被引：7，自引：1，他引：7  

Richard H. Rapp 《Journal of Geodesy》1994,69(1):26-31

This paper discusses the separation between the reference surface of several vertical datums and the geoid. The data used includes a set of Doppler positioned stations, transformation parameters to convert the Doppler positions to ITRF90, and a potential coefficient model composed of the JGM-2 (NASA model) from degree 2 to 70 plus the OSU91A model from degree 71 to 360. The basic method of analysis is the comparison of a geometric geoid undulation derived from an ellipsoidal height and an orthometric height with the undulation computed from the potential coefficient model The mean difference can imply a bias of the datum reference surface with respect to the geoid. Vertical datums in the following countries were considered: England, Germany, United States, and Australia. The following numbers represent the bias values of each datum after adopting an equatorial radius of 6378136.3m: England (-87 cm), Germany (4 cm), United States (NGVD29 (-26 cm)), NAVD88 (-72 cm), Australia AHD (mainland, -68 cm); AHD (Tasmania, -98 cm). A negative sign indicates the datum reference surface is below the geoid. The 91 cm difference between the datums in England and Germany has been independently estimated as 80 cm. The 30 cm difference between AHD (mainland) and AHD (Tasmania) has been independently estimated as 40 cm. These bias values have been estimated from data where the geometric/ gravimetric geoid undulation difference standard deviation, at one station, is typically ±100 cm, although the mean difference is determined more accurately.The results of this paper can be improved and expanded with more accurate geocentric station positions, more accurate and consistent heights with respect to the local vertical datum, and a more accurate gravity field for the Earth. The ideas developed here provide insight on the determination of a world height system.  相似文献   

Monazite solubility and dissolution kinetics: implications for the thorium and light rare earth chemistry of felsic magmas   总被引：12，自引：1，他引：12  

Robert P. Rapp  E. Bruce Watson 《Contributions to Mineralogy and Petrology》1986,94(3):304-316

A series of monazite dissolution experiments was conducted in a hydrous (1–6 wt.%) granitic melt at 8 kbar over the temperature range 1,000–1,400° C. A polished cube of monazite was immersed in a natural obsidian melt and allowed to partially dissolve. Electron microprobe traverses perpendicular to the crystal-melt interface revealed concentration gradients in the LREEs and P. Diffusivities of the LREEs and P were calculated from these profiles, yielding the following Arrhenius relations for the LREEs: D=0.23 exp(–60.1 kcal mol^–1/RT) at 6% water D=2.30×10⁷ exp(–122.1 kcal mol^–1/RT) at 1% water These results demonstrate the importance of dissolved water on REE diffusion. Phosphorus diffusivities are nearly identical to those of the rare-earths, suggesting that P diffusion charge-compensates REE diffusion. The concentration of LREEs required for monazite saturation in these melts is given by the level of dissolved LREEs at the crystal-melt interface. These values also show a dependence on dissolved water, with LREE_sat=60 ppm at 6% H₂O when extrapolated down to 700° C, and LREE_sat=30 ppm at 1% H₂O. Calculated dissolution rates based on the above parameters indicate that minute (<30 m diameter) monazite crystals will be readily digested by an enclosing anatectic magma under reasonable geologic conditions (i.e., T=700–800° C and >2% H₂O), whereas larger (> 50 m) crystals will likely be residual over the duration of an anatectic event. The low solubility of monazite in this melt suggests that the LREE depletion observed in some felsic differentiation suites may be the result of monazite crystallization. Limited experimental and geochemical/petrologic evidence indicates that compositional changes in the melt accompanying differentiation decrease the solubility of monazite drastically. Kinetic and chemical constraints may also lead to localized monazite saturation and inclusion in major phases or even other accessories. Variations in the REE composition of monazite from different parageneses probably reflects the REE pattern of the parent melt, and may be due to gradational differences in the stability of individual or subgroup REE-complexes as a function of melt composition. Particularly important in this regard seems to be the lime+alkali/alumina balance of the melt and its volatile content.  相似文献