ALBERT

Description: The principles and problems relative to the determination of the geoid are outlined. Factors discussed include: gravity data requirements for a precise geoid; mean sea level; and satellite altimetry. It is indicated that geoid undulations can be determined on a global basis to plus or minus 3 m. Application of geoid information to oceanography and the determination of sea surface topography considered.

Description: A natural extension of the recent satellite derived potential coefficient models is the development of high degree (maximum 180 or 360) expansions. Such expansions are based on the combination of the satellite derived models with terrestrial gravity data and satellite altimeter data. Such models are useful for more precise geoid undulation computations, for simulation studies involving different typed of future missions (e.g., gradiometry), and as reference fields for different types of gravimetric computations. The attention is to the effect of the terrain, ellipsoidal terms, and weighting. The basic methods used for the high degree solutions are reviewed. Various correction terms are described and recent models are discussed and compared.

Description: Figures that demonstrate the state of terrestrial gravity coverage, and comparisons between satellite derived gravity field and terrestrial gravity data are presented. It is shown that only a few areas of the world have information accurate enough for geodesy and geophysics. A gravity field mapping space mission is recommended.

Description: Subduction zones are presently the dominant sites on Earth for recycling and mass transfer between the crust and mantle; they feed hydrated basaltic oceanic crust into the upper mantle, where dehydration reactions release aqueous fluids and/or hydrous melts. The loci for fluid and/or melt generation will be determined by the intersection of dehydration reaction boundaries of primary hydrous minerals within the subducted lithosphere with slab geotherms. For metabasalt of the oceanic crust, amphibole is the dominant hydrous mineral. The dehydration melting solidus, vapor-absent melting phase relationships; and amphibole-out phase boundary for a number of natural metabasalts have been determined experimentally, and the pressure-temperature conditions of each of these appear to be dependent on bulk composition. Whether or not the dehydration of amphibole is a fluid-generating or partial melting reaction depends on a number of factors specific to a given subduction zone, such as age and thickness of the subducting oceanic lithosphere, the rate of convergence, and the maturity of the subduction zone. In general, subduction of young, hot oceanic lithosphere will result in partial melting of metabasalt of the oceanic crust within the garnet stability field; these melts are characteristically high-Al2O3 trondhjemites, tonalites and dacites. The presence of residual garnet during partial melting imparts a distinctive trace element signature (e.g., high La/Yb, high Sr/Y and Cr/Y combined with low Cr and Y contents relative to demonstrably mantle-derived arc magmas). Water in eclogitized, subducted basalt of the oceanic crust is therefore strongly partitioned into melts generated below about 3.5 GPa in 'hot' subduction zones. Although phase equilibria experiments relevant to 'cold' subduction of hydrated natural basalts are underway in a number of high-pressure laboratories, little is known with respect to the stability of more exotic hydrous minerals (e.g., ellenbergite) and the potential for oceanic crust (including metasediments) to transport water deeper into the mantle.

Description: The effects of the permanent tidal effects of the Sun and Moon with specific applications to satellite altimeter data reduction are reviewed in the context of a consistent definition of geoid undulations. Three situations are applicable not only for altimeter reduction and geoid definition, but also for the second degree zonal harmonic of the geopotential and the equatorial radius. A recommendation is made that sea surface heights and geoid undulations placed on the Topex/Poseidon geophysical data record should be referred to the mean Earth case (i.e., with the permanent effects of the Sun and Moon included). Numerical constants for a number of parameters, including a flattening and geoid geopotential, are included.

Description: The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.

Description: Two potential coefficient fields that are complete to degree and order 360 have been computed. One field (OSU86E) excludes geophysically predicted anomalies while the other (OSU86F) includes such anomalies. These fields were computed using a set of 30' mean gravity anomalies derived from satellite altimetry in the ocean areas and from land measurements in North America, Europe, Australia, Japan and a few other areas. Where no 30' data existed, 1 deg x 1 deg mean anomaly estimates were used if available. No rigorous combination of satellite and terrestrial data was carried out. Instead advantage was taken of the adjusted anomalies and potential coefficients from a rigorous combination of the GEML2' potential coefficient set and 1 deg x 1 deg mean gravity anomalies. The two new fields were computed using a quadrature procedure with de-smoothing factors. The spectra of the new fields agree well with the spectra of the fields with 1 deg x 1 deg data out to degree 180. Above degree 180 the new fields have more power. The fields have been tested through comparison of Doppler station geoid undulations with undulations from various geopotential models. The agreement between the two types of undulations is approximately + or - 1.6 m. The use of a 360 field over a 180 field does not significantly improve the comparison. Instead it allows the comparison to be done at some stations where high frequency effects are important. In addition maps made in areas of high frequency information (such as trench areas) clearly reveal the signal in the new fields from degree 181 to 360.

Description: In June 1986 a 1 x 1 deg/mean free-air anomaly data file containing 48955 anomalies was completed. In August 1986 a 30 x 30 min mean free-air anomaly file was defined containing 31787 values. For the past three years data has been collected to upgrade these mean anomaly files. The primary emphasis was the collection of data to be used for the estimation of 30 min means anomalies in land areas. The emphasis on land areas was due to the anticipated use of 30 min anomalies derived from satellite altimeter data in the ocean areas. There were 10 data sources in the August 1986 file. Twenty-eight sources were added based on the collection of both point and mean anomalies from a number of individuals and organizations. A preliminary 30 min file was constructed from the 38 data sources. This file was used to calculate 1 x 1 deg mean anomalies. This 1 x 1 deg file was merged with a 1 x 1 deg file which was a merger of the June 1986 file plus a 1 x 1 deg file made available by DMA Aerospace Center. Certain bad 30 min anomalies were identified and deleted from the preliminary 30 min file leading to the final 30 min file (the July 1989 30 min file) with 66990 anomalies and their accuracy. These anomalies were used to again compute 1 x 1 deg anomalies which were merged with the previous June 86 DMAAC data file. The final 1 x 1 deg mean anomaly file (the July 89 1 x 1 deg data base) contained 50793 anomalies and their accuracy. The anomaly data files were significantly improved over the prior data sets in the following geographic regions: Africa, Scandinavia, Canada, United States, Mexico, Central and South America. Substantial land areas remain where there is little or no available data.

Description: A method is presented for the estimation of a global gravity anomaly field using the combination of satellite-derived potential coefficient models and the coefficients implied by the Airy-Heiskanen topographic/isostatic potential (Rummel et al., 1988) from topographic models with a 30-km depth of compensation. Gravity anomalies calculated with this method are compared with a terrestrial 1 x 1 degree anomaly file where the anomaly standard deviations were less than 10 mgals. Using the GEM T1 model (Marsh et al., 1988) to degree 36, the rms anomaly discrepency was + or - 19 mgals, while the rms values for the terrestrial anomalies was + or - 28 mgals.

Description: 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.