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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Comparison of undulation difference accuracies using gravity anomalies and gravity disturbances

Errors in the outer zone contribution to oceanic undulation differences computed from a finite set of potential coefficients based on satellite measurements of gravity anomalies and gravity disturbances are analyzed. Equations are derived for the truncation errors resulting from the lack of high-degree coefficients and the commission errors arising from errors in the available lower-degree coefficients, and it is assumed that the inner zone (spherical cap) is sufficiently covered by surface gravity measurements in conjunction with altimetry or by gravity anomaly data. Numerical computations of error for various observational conditions reveal undulation difference errors ranging from 13 to 15 cm and from 6 to 36 cm in the cases of gravity anomaly and gravity disturbance data, respectively for a cap radius of 10 deg and mean anomalies accurate to 10 mgal, with a reduction of errors in both cases to less than 10 cm as mean anomaly accuracy is increased to 1 mgal. In the absence of a spherical cap, both cases yield error estimates of 68 cm for an accuracy of 1 mgal and between 93 and 160 cm for the lesser accuracy, which can be reduced to about 110 cm by the introduction of a perfect 30-deg reference field.

Jekeli, C.↗
NASA NTRS1980

Accuracy of the determination of mean anomalies and mean geoid undulations from a satellite gravity field mapping mission

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.

Jekeli, C.↗
NASA NTRS1981

Ellipsoidal corrections for geoid undulation computations

The computation of accurate geoid undulations is usually done combining potential coefficient information and terrestrial gravity data in a cap surrounding the computation point. In doing this a spherical approximation is made that can cause the errors that were investigated. The equations dealing with ellipsoidal corrections developed by Lelgemann and by Moritz were used to develop a computational procedure considering the ellipsoid as a reference surface. Terms in the resulting expression for the geoid undulation are identified as ellipsoidal correction terms. These equations were developed for the case where the Stokes function is used, and for the case where the modified Stokes function is used. For a cap of 20 deg the correction can reach -33 cm.

Rapp, R. H.↗
NASA NTRS1991

Geoid undulations and gravity anomalies over the Aral Sea, the Black Sea and the Caspian Sea from a combined GEOS-3/SEASAT/GEOSAT altimeter data set

Satellite-based altimetric data taken by GOES-3, SEASAT, and GEOSAT over the Aral Sea, the Black Sea, and the Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25x0.25 deg. grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180x180 geopotential model is used as the reference surface for the collocation procedure. The result of geoid to gravity transformation is, however, sensitive to the information content of the reference geopotential model used. For example, considerable detailed surface gravity data were incorporated into the reference model over the Black Sea, resulting in a reference model with significant information content at short wavelengths. Thus, estimation of short wavelength gravity anomalies from gridded geoid heights is generally reliable over regions such as the Black Sea, using the conventional collocation technique with local empirical covariance functions. Over regions such as the Caspian Sea, where detailed surface data are generally not incorporated into the reference model, unconventional techniques are needed to obtain reliable gravity anomalies. Based on the predicted gravity anomalies over these inland seas, speculative tectonic structures are identified and geophysical processes are inferred.

Au, Andrew Y.↗
NASA NTRS1978

The prediction and mapping of geoidal undulations from GEOS-3 altimetry

From the adjusted altimeter data an approximation to the geoid height in ocean areas is obtained. Methods are developed to produce geoid maps in these areas. Geoid heights are obtained for grid points in the region to be mapped, and two of the parameters critical to the production of an accurate map are investigated. These are the spacing of the grid, which must be related to the half-wavelength of the altimeter signal whose amplitude is the desired accuracy of the contour; and the method adopted to predict the grid values. Least squares collocation was used to find geoid undulations on a 1 deg grid in the mapping area. Twenty maps, with their associated precisions, were produced and are included. These maps cover the Indian Ocean, Southwestern and Northeastern portions of the Pacific Ocean, and Southwest Atlantic and the U.S. Calibration Area.

Kearsley, W.↗
NASA NTRS1979

GEOS 3 data processing for the recovery of geoid undulations and gravity anomalies

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.

Rapp, R. H.↗
NASA NTRS1979

Gravity anomaly and geoid undulation results in local areas from GEOS-3 altimeter data

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.

Rapp, R. H.↗
NASA NTRS1982

Analyzing the Broken Ridge area of the Indian Ocean using magnetic and gravity anomaly maps and geoid undulation and bathymetry data

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.

Lazarewicz, A. R.↗
NASA NTRS1981

Ellipsoidal corrections for geoid undulation computations using gravity anomalies in a cap

Ellipsoidal correction terms have been derived for geoid undulation computations when the Stokes equation using gravity anomalies in a cap is combined with potential coefficient information. The correction terms are long wavelength and depend on the cap size in which its gravity anomalies are given. Using the regular Stokes equation, the maximum correction for a cap size of 20 deg is -33 cm, which reduces to -27 cm when the Stokes function is modified by subtracting the value of the Stokes function at the cap radius. Ellipsoidal correction terms were also derived for the well-known Marsh/Chang geoids. When no gravity was used, the correction could reach 101 cm, while for a cap size of 20 deg the maximum correction was -45 cm. Global correction maps are given for a number of different cases. For work requiring accurate geoid computations these correction terms should be applied.

Rapp, R. H.↗
NASA NTRS1989

Geoid undulation computations at laser tracking stations

The accuracy of numerical computations of gravimetric undulations using recently proposed modifications of the classical Stokes formula is investigated. The basic formulations of the methods are outlined, and results from trial computations are presented in tables and graphs and compared with actual gravity data and/or GEOS-3/Seasat sea-surface heights. Although all of the methods gave similar results, the method of Sjoberg (1986) is recommended because of its superior theoretical precision. The importance of including terrain-corrected free-air anomalies in the computations is indicated.

Despotakis, Vasilios K.↗
NASA NTRS2000

Undulated Nozzle for Enhanced Exit Area Mixing

A nozzle having an undulating surface for enhancing the mixing of a primary flow with a secondary flow or ambient air, without requiring an ejector. The nozzle includes a nozzle structure and design for introducing counter-rotating vorticity into the primary flow either through (i) internal surface corrugations where an axisymmetric line through each corrugation is coincident with an axisymmetric line through the center of the flow passageway or (ii) through one or more sets of alternating convexities and cavities in the internal surface of the nozzle where an axisymmetric line through each convexity and cavity is coincident with an axisymmetric line through the center of the flow passageway, and where the convexities contract from the entrance end towards the exit end. Exit area mixing is also enhanced by one or more chevrons attached to the exit edge of the nozzle. The nozzle is ideally suited for application as a jet engine nozzle. When used as a jet engine nozzle, noise suppression with simultaneous thrust augmentation/minimal thrust loss is achieved.

Seiner, John M.↗
NASA NTRS1981

Multilevel measurements of surface temperature over undulating terrain planted to barley

A ground and aircraft program was conducted to extend ground based methods for measuring soil moisture and crop water stress to aircraft and satellite altitudes. A 260ha agricultural field in California was used over the 1977-78 growing season. For cloud free days ground based temperature measurements over bare soil were related to soil moisture content. Water stress resulted from too much water, not from lack of it, as was expected. A theoretical examination of the canopy air temperature difference as affected by vapor pressure deficit and net radiation was developed. This analysis shows why surface temperatures delineate crop water stress under conditions of low humidity, but not under high humidity conditions. Multilevel temperatures acquired from the ground, low and high altitude aircraft, and the Heat Capacity Mapping Mission (HCMM) spacecraft were compared for two day and one night overpasses. The U-2 and low altitude temperatures were within 0.5 C. The HCMM data were analyzed using both the pre- and post-launch calibrations, with the former being considerably closer in agreement with the aircraft data than the latter.

Reginato, R. J.↗
NASA NTRS1988

Electromagnetic wave scattering at near-grazing incidence from a gently undulating, rough surface

Models to estimate the reflection coefficient of a statistically rough surface, for example the works of Beckmann, Smith, and Vesecky are discussed. Bistatic radar experiments carried out during the Apollo 16 mission provide a data set with which to compare theoretical models and experimental data. These bistatic S-band radar experiments provide experimental estimates of the Moon's bistatic, forward scatter, reflection coefficient for grazing angles of 2.5 to 78 deg. Theoretical expressions for the reflection coefficient are developed for comparison with these experimental data. At grazing angles below 10 deg the models of Smith and Vesecky compare favorably with the data. Beckmann's model falls significantly more rapidly with decreasing grazing angle than does the data.

Vesecky, J. F.↗