Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models

The GEM-T2 gravitational model

The GEM-T2 is the latest in a series of Goddard Earth Models of the terrestrial field. It was designed to bring modeling capabilities one step closer towards ultimately determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10-cm RMS (root mean square). It also improves models of the long wavelength geoid to support many oceanographic and geophysical applications. The GEM-T2 extends the spherical harmonic field to include more than 600 coefficients above degree 36 (which was the limit for its predecessor, GEM-T1). Like GEM-T1, it was produced entirely from satellite tracking data, but it now uses nearly twice as many satellites (31 vs. 17), contains four times the number of observations (2.4 million), has twice the number of data arcs (1132), and utilizes precise laser tracking from 11 satellites. The estimation technique for the solution has been augmented to include an optimum data weighting procedure with automatic error calibration for the gravitational parameters. Results for the GEM-T2 error calibration indicate significant improvement over previous satellite-only models. The error of commission in determining the geoid has been reduced from 155 cm in GEM-T1 to 105 cm for GEM-T2 for the 36 x 36 portion of the field, and 141 cm for the entire model. The orbital accuracies achieved using GEM-T2 are likewise improved. Also, the projected radial error on the TOPEX satellite orbit indicates 9.4 cm RMS for GEM-T2, compared to 24.1 cm for GEM-T1

An improved model of the Earth's gravitational field: GEM-T1

Goddard Earth Model T1 (GEM-T1), which was developed from an analysis of direct satellite tracking observations, is the first in a new series of such models. GEM-T1 is complete to degree and order 36. It was developed using consistent reference parameters and extensive earth and ocean tidal models. It was simultaneously solved for gravitational and tidal terms, earth orientation parameters, and the orbital parameters of 580 individual satellite arcs. The solution used only satellite tracking data acquired on 17 different satellites and is predominantly based upon the precise laser data taken by third generation systems. In all, 800,000 observations were used. A major improvement in field accuracy was obtained. For marine geodetic applications, long wavelength geoidal modeling is twice as good as in earlier satellite-only GEM models. Orbit determination accuracy has also been substantially advanced over a wide range of satellites that have been tested

Gravitational model improvement at the Goddard Space Flight Center

Major new computations of terrestrial gravitational field models were performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). This development has incorporated the present state of the art results in satellite geodesy and have relied upon a more consistent set of reference constants than was heretofore utilized in GSFC's GEM models. The solutions are complete in spherical harmonic coefficients out to degree 50 for the gravity field parameters. These models include adjustment for a subset of 66 ocean tidal coefficients for the long wavelength components of 12 major ocean tides. This tidal adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor ocean tides and the Wahr frequency dependent solid earth tidal model. In addition 5-day averaged values for Earth rotation and polar motion were derived for the time period of 1980 onward. Two types of models were computed. These are satellite only models relying exclusively on tracking data and combination models which have incorporated satellite altimetry and surface gravity data. The satellite observational data base consists of over 1100 orbital arcs of data on 31 satellites. A large percentage of these observations were provided by third generation laser stations (less than 5 cm). A calibration of the model accuracy of the GEM-T2 satellite only solution indicated that it was a significant improvement over previous models based solely upon tracking data. The rms geoid error for this field is 110 cm to degree and order 36. This is a major advancement over GEM-T1 whose errors were estimated to be 160 cm. An error propagation using the covariances of the GEM-T2 model for the TOPEX radial orbit component indicates that the rms radial errors are expected to be 12 cm. The combination solution, PGS-3337, is a preliminary effort leading to the development of GEM-T3. PGS-3337 has incorporated global sets of surface gravity data and the Seasat altimetry to produce a model complete to (50,50). A solution for the dynamic ocean topography to degree and order 10 was included as part of this adjustment

Analysis of hydrogen-rich magnetic white dwarfs detected in the Sloan Digital Sky Survey

We model the structure of the surface magnetic fields of the hydrogen-rich white dwarfs in the SDSS. We have calculated a grid of state-of-the-art theoretical optical spectra of hydrogen-rich magnetic white dwarfs with magnetic field strengths between 1 MG and 1200 MG for different angles, and for effective temperatures between 7000 K and 50000 K. We used a least-squares minimization scheme with an evolutionary algorithm in order to find the magnetic field geometry best fitting the observed data. We used simple centered dipoles or dipoles which were shifted along the dipole axis to model the coadded SDSS fiber spectrum of each object. We have analysed the spectra of all known magnetic DAs from the SDSS (97 previously published plus 44 newly discovered) and also investigated the statistical properties of magnetic field geometries of this sample. The total number of known magnetic white dwarfs already more than tripled by the SDSS and more objects are expected from a more systematic search. The magnetic fields span a range between ~1 and 900 MG. Our results further support the claim that Ap/Bp population is insufficient in generating the numbers and field strength distributions of the observed MWDs, and either another source of progenitor types or binary evolution is needed. Moreover clear indications for non-centered dipoles exist in about ~50% of the objects which is consistent with the magnetic field distribution observed in Ap/Bp stars.Comment: 15 pages, accepted for publication in A&A. For online version with full appendix figures, see http://www.ari.uni-heidelberg.de/mitarbeiter/bkulebi/papers/12570_online.pd

Analysis of the Hydrogen-rich Magnetic White Dwarfs in the SDSS

We have calculated optical spectra of hydrogen-rich (DA) white dwarfs with magnetic field strengths between 1 MG and 1000 MG for temperatures between 7000 K and 50000 K. Through a least-squares minimization scheme with an evolutionary algorithm, we have analyzed the spectra of 114 magnetic DAs from the SDSS (95 previously published plus 14 newly discovered within SDSS, and five discovered by SEGUE). Since we were limited to a single spectrum for each object we used only centered magnetic dipoles or dipoles which were shifted along the magnetic dipole axis. We also statistically investigated the distribution of magnetic-field strengths and geometries of our sample.Comment: to appear in the proceedings of the 16th European Workshop on White Dwarfs, Barcelona, 200

Identification of a protein encoded in the EB-viral open reading frame BMRF2

Using monospecific rabbit sera against a peptide derived from a potential antigenic region of the Epstein-Barr viral amino acid sequence encoded in the open reading frame BMRF2 we could identify a protein-complex of 53/55 kDa in chemically induced B95-8, P3HR1 and Raji cell lines. This protein could be shown to be membrane-associated, as predicted by previous computer analysis of the secondary structure and hydrophilicity pattern, and may be a member of EBV-induced membrane proteins in lytically infected cells

Geopotential models of the Earth from satellite tracking, altimeter and surface gravity observations: GEM-T3 and GEM-T3S

Improved models of the Earth's gravitational field have been developed from conventional tracking data and from a combination of satellite tracking, satellite altimeter and surface gravimetric data. This combination model represents a significant improvement in the modeling of the gravity field at half-wavelengths of 300 km and longer. Both models are complete to degree and order 50. The Goddard Earth Model-T3 (GEM-T3) provides more accurate computation of satellite orbital effects as well as giving superior geoidal representation from that achieved in any previous GEM. A description of the models, their development and an assessment of their accuracy is presented. The GEM-T3 model used altimeter data from previous satellite missions in estimating the orbits, geoid, and dynamic height fields. Other satellite tracking data are largely the same as was used to develop GEM-T2, but contain certain important improvements in data treatment and expanded laser tracking coverage. Over 1300 arcs of tracking data from 31 different satellites have been used in the solution. Reliable estimates of the model uncertainties via error calibration and optimal data weighting techniques are discussed