Is dark matter created in the gravitation field of galaxies?

Using the heuristic arguments of quantum physics we describe a new mechanism of the creation of short-living particles from the virtual ones in a stationary gravitation field. The mass of these particles is a function of the intensity of gravitation field. We suppose that the particles created in the gravitation field form a part of the non-baryonic dark matter. Having the intensity of gravitation field in a galaxy we can calculate the density of dark matter created in it by the vacuum quantum fluctuation. We calculate the distribution of this dark matter in a model galaxy and show that its total mass is comparable with the visible mass of the galaxy.     

Possibilities of GPS Kinematic Measurements for Geological Survey in East Slovakia

This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS-84 into the national geodetic grid datum S-UTCN(system of united trigonometric cadaster network) and Baa(the Baltic Sea after adjustment).Transformation from WGS-84 into SUTCN is performed most frequently by means of the 7-element Helmert transformation with three identical points.Geodetic network was adjusted by two ways.     

Evaluation of pre-CHAMP gravity models `GRIM5-S1' and `GRIM5-C1' with satellite crossover altimetry

 The new GFZ/GRGS gravity field models GRIM5-S1 and GRIM5-C1, currently used as initial models for the CHAMP mission, have been compared with other recent models (JGM 3, EGM 96) for radial orbit accuracy (by means of latitude lumped coefficients) in computations on altimetry satellite orbits. The bases for accuracy judgements are multi-year averages of crossover sea height differences from Geosat and ERS 1/2 missions. This radially sensitive data is fully independent of the data used to develop these gravity models. There is good agreement between the observed differences in all of the world's oceans and projections of the same errors from the scaled covariance matrix of their harmonic geopotential coefficients. It was found that the tentative scale factor of five for the formal standard deviations of the harmonic coefficients of the new GRIM fields is justified, i.e. the accuracy estimates, provided together with the GRIM geopotential coefficients, are realistic. Received: 20 February 2001 / Accepted: 24 October 2001     

Integral transformations of gradiometric data onto a GRACE type of observable

Integral transformations of gravitational gradients onto a Gravity Recovery And Climate Experiment (GRACE) type of observable are derived in this article. The gravitational gradients represent components of the gravitational tensor in the local north-oriented frame. The GRACE type of observable corresponds to a difference between two gravitational vectors as projected onto the line of sight between the two GRACE satellites. In total, three integral transformations relating vertical–vertical, vertical–horizontal and horizontal–horizontal gravitational gradients with the GRACE type of observable are provided. Spectral and closed forms of corresponding isotropic kernels are derived for each transformation. Special cases show that the integral transformations are general and relate gravitational gradients to many other quantities of the gravitational field, such as the gravitational vector, and its radial and tangential components. Correctness of the mathematical derivations is validated in a closed-loop simulation using synthetic data.     

Possibilities of GPS kinematic measurements for geological survey in East Slovakia

This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS-84 into the national geodetic grid datum S-UTCN (system of united trigonometric cadaster network) and Baa (the Baltic Sea after adjustment). Transformation from WGS-84 into SUTCN is performed most frequently by means of the 7-element Helmert transformation with three identical points. Geodetic network was adjusted by two ways.     

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.     

Changes of the profiles of spectral lines due to mass transfer in close binaries

In this paper, the model of the ring envelope round the primary component and the stream of the gaseous mass flowing from the secondary component to the primary is constructed on the basis of theoretical computations concerning the exchange of the mass between the components of the binary. The paper studies the influence of the gaseous mass on the profiles of spectral lines before and after occultation; the influence of the stream on the profile in case the secondary is near elongation, is also investigated. The line profiles obtained by numerical computations show that their changes caused by outflowing mass should be well detectable from spectrograms taken at particular phase of the binary. Changes in the lines may influence the measurement of radial velocities. The method for distinguishing the influence of the stream from the influence of the ring is described.     

Crustal structure of Iraq from receiver functions and surface wave dispersion: implications for understanding the deformation history of the Arabian–Eurasian collision

We report the crustal structure for two locations in Iraq estimated by joint inversion of P -wave receiver functions (RFs) and surface (Rayleigh) wave group velocity dispersion. RFs were computed from teleseismic recordings at two temporary broad-band seismic stations located in Mosul (MSL) in the Zagros Fold Belt and Baghdad (BHD) in the Mesopotamian Foredeep. Group velocity dispersion curves at the sites were derived from continental-scale tomography. The inversion results show that the crustal thicknesses are 39 km at MSL and 43 km at BHD. We observe a strong Ps _Moho at BHD consistent with a sharp Moho discontinuity. However, at MSL we observe a weak Ps _Moho suggesting a transitional Moho where crustal thickening is likely to be occurring in the deep crust. Both sites reveal low velocity surface layers consistent with sedimentary thickness of about 3 km at station MSL and 7 km at BHD and agreeing well with the previous reports. Ignoring the sediments, the crystalline crustal velocities and thicknesses are remarkably similar at both stations. The similarity of crustal structure suggests that the crust of the northeastern proto-Arabian Platform was uniform before subsidence and deposition of the sediments in the Cenozoic. If crystalline crustal structure is uniform across the northern Arabian Platform then crustal thickness variations in the Zagros Fold Belt and Thrust Zone should reveal the history of deformation and crustal shortening in the Arabian–Eurasian collision zone and not reflect pre-existing crustal thickness variations in the Arabian Plate.     

Numerical solution to the oblique derivative boundary value problem on non-uniform grids above the Earth topography

The paper presents a numerical solution of the oblique derivative boundary value problem on and above the Earth’s topography using the finite volume method (FVM). It introduces a novel method for constructing non-uniform hexahedron 3D grids above the Earth’s surface. It is based on an evolution of a surface, which approximates the Earth’s topography, by mean curvature. To obtain optimal shapes of non-uniform 3D grid, the proposed evolution is accompanied by a tangential redistribution of grid nodes. Afterwards, the Laplace equation is discretized using FVM developed for such a non-uniform grid. The oblique derivative boundary condition is treated as a stationary advection equation, and we derive a new upwind type discretization suitable for non-uniform 3D grids. The discretization of the Laplace equation together with the discretization of the oblique derivative boundary condition leads to a linear system of equations. The solution of this system gives the disturbing potential in the whole computational domain including the Earth’s surface. Numerical experiments aim to show properties and demonstrate efficiency of the developed FVM approach. The first experiments study an experimental order of convergence of the method. Then, a reconstruction of the harmonic function on the Earth’s topography, which is generated from the EGM2008 or EIGEN-6C4 global geopotential model, is presented. The obtained FVM solutions show that refining of the computational grid leads to more precise results. The last experiment deals with local gravity field modelling in Slovakia using terrestrial gravity data. The GNSS-levelling test shows accuracy of the obtained local quasigeoid model.