Terrain effects in the atmospheric gravity and geoid corrections     

Lars E. Sjöberg 《Journal of Geodesy》1993,67(3):178-184

In view of the smallness of the atmospheric mass compared to the mass variations within the Earth, it is generally assumed in physical geodesy that the terrain effects are negligible. Subsequently most models assume a spherical or ellipsoidal layering of the atmosphere. The removal and restoring of the atmosphere in solving the exterior boundary value problems thus correspond to gravity and geoid corrections of the order of 0.9 mGal and -0.7 cm, respectively.We demonstrate that the gravity terrain correction for the removal of the atmosphere is of the order of 50µGal/km of elevation with a maximum close to 0.5 mGal at the top of Mount Everest. The corresponding effect on the geoid may reach several centimetres in mountainous regions. Also the total effect on geoid determination for removal and restoring the atmosphere may contribute significantly, in particular by long wavelengths. This is not the case for the quasi geoid in mountainous regions.  相似文献   

Reply to Marquart     

Tomas Nord  Lars E. Sjöberg 《Geophysical Journal International》1993,115(2):605-605

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Middle Proterozoic anorogenic magmatism in Sweden and worldwide     

Gran berg 《Lithos》1988,21(4):279-289

Compilation of geochronological data from southeastern Sweden indicates widespread anorogenic intrusive activity between 1.40 and 1.35 Ga ago. This activity was part of a major igneous event in a belt extending from Siberia and the Urals in the U.S.S.R. across southern Scandinavia, southern Greenland, and Labrador to western North America. It was characterized by high-level granites, sometimes rapakivilike, intruded under anorogenic conditions. The source granite melts were probably derived by the fusion of lower crust, i.e. older calc-alkaline Proterozoic granitoids, by mantle magma. These composite melts were mixed at the time of intrusion and gave rise to granitoids showing mixed I- and S-type features. The causes for the igneous activity were probably related to changes in the configuration of the continents with ensuing rifting and associated igneous activity. The 1.40-1.35 Ga old intrusions reset older isotope systems, especially the K---Ar one in southeastern Sweden. Between 1.25 and 1.20 Ga ago, there was a second event of smaller magnitude, characterized by the intrusion of acid and basic dykes. These dykes probably correspond to an initial stage of the Grenvillian (Sveconorwegian) orogeny soon to be followed by a 90° rotation of the Baltic shield.  相似文献   

Fundamentals of gas containment in unlined rock caverns   总被引：3，自引：0，他引：3  

D. C. Goodall  B. Åberg  T. L. Brekke 《Rock Mechanics and Rock Engineering》1988,21(4):235-258

Summary The criterion for gas entry into idealized, uniform, water-saturated fractures is examined for one-dimensional, elliptical and cylindrical cavern geometries. This limiting criterion is a necessary condition for gas escape from unlined, pressurized gas storages.Gas-entry phenomena were examined using 450-mm-square glass plates in Hele Shaw configuration with nominal apertures of 50 and 200 microns. The fundamentals of gas entry, as first enunciated by Åberg (1977), are confirmed by the experiments; the critical gas-entry pressure is a function of hydraulic flow regime, fracture-mouth capillarity and fracture-mouth profile. Finite-element simulation based on these fundamentals is substantiated by experimental observations and is therefore used for generalization.The gas-entry criterion is found to be sensitive to details of fracture geometry such as aperture, connection of the fractures to the groundwater regime, geometry of the intersection of the fractures with the gas cavern, disturbance of the rock mass as a consequence of excavation, and cavern shape. In view of the inability to predict or even measure these factors, an alternative criterion which ensures no gas migration away from the gas storage is proposed. This simple criterion insists that gas escape will not occur as long as the water pressure along all possible escape paths increases for some small distance in the direction of potential gas escape. This criterion is a generalization of Åberg's (1977) proposal that the vertical hydraulic gradient should exceed one for no gas escape.  相似文献   

Higher-degree reference field in the generalized Stokes-Helmert scheme for geoid computation     

Petr Vaníček  Mehdi Najafi  Zdeněk Martinec  Lars Harrie  Lars E. Sjöberg 《Journal of Geodesy》1995,70(3):176-182

In this paper we formulate two corrections that have to be applied to the higher-degree reference spheroid if one wants to use it in conjunction with the Stokes-Helmert scheme for geoid determination. We show that in a precise geoid determination one has to apply the correction for the residual topographical potential and the correction for the earth ellipticity. Both these corrections may reach several decimetres; we show how their magnitudes vary within Canada and we give their global ranges.  相似文献   

A refined conversion from normal height to orthometric height   总被引：1，自引：0，他引：1  

L. E. Sjöberg 《Studia Geophysica et Geodaetica》2006,50(4):595-606

The difference between orthometric and normal heights (or the height anomaly and the geoid height) is usually approximated by a term consisting of the Bouguer anomaly times elevation divided by normal gravity. We derive an improved formula, which includes a topographic roughness term (terrain correction) and a term due to the lateral variation of topographic density, for the practical application of this conversion. It is shown that for high mountainous areas with rough topography these two terms are of the same order as the Bouguer anomaly related term. Already for elevations of a few hundred metres they could reach the order of a centimetre. In addition, for the more precise computations in high mountainous areas, a term related with the downward continuation of topographic potential from the surface to sea level could be significant.  相似文献   

The Effects of Stokes’s Formula for an Ellipsoidal Layering of the Earth’s Atmosphere     

Lars E. Sjöberg 《Journal of Geodesy》2006,79(12):675-681

The application of Stokes’s formula to determine the geoid height requires that topographic and atmospheric masses be mathematically removed prior to Stokes integration. This corresponds to the applications of the direct topographic and atmospheric effects. For a proper geoid determination, the external masses must then be restored, yielding the indirect effects. Assuming an ellipsoidal layering of the atmosphere with 15% increase in its density towards the poles, the direct atmospheric effect on the geoid height is estimated to be −5.51 m plus a second-degree zonal harmonic term with an amplitude of 1.1 cm. The indirect effect is +5.50 m and the total geoid correction thus varies between −1.2 cm at the equator to 1.9 cm at the poles. Finally, the correction needed to the atmospheric effect if Stokes’s formula is used in a spherical approximation, rather than an ellipsoidal approximation, of the Earth varies between 0.3 cm and 4.0 cm at the equator and pole, respectively.  相似文献   

Regional geoid computation by least squares modified Hotine’s formula with additive corrections     

Silja Märdla  Artu Ellmann  Jonas Ågren  Lars E. Sjöberg 《Journal of Geodesy》2018,92(3):253-270

Geoid and quasigeoid modelling from gravity anomalies by the method of least squares modification of Stokes’s formula with additive corrections is adapted for the usage with gravity disturbances and Hotine’s formula. The biased, unbiased and optimum versions of least squares modification are considered. Equations are presented for the four additive corrections that account for the combined (direct plus indirect) effect of downward continuation (DWC), topographic, atmospheric and ellipsoidal corrections in geoid or quasigeoid modelling. The geoid or quasigeoid modelling scheme by the least squares modified Hotine formula is numerically verified, analysed and compared to the Stokes counterpart in a heterogeneous study area. The resulting geoid models and the additive corrections computed both for use with Stokes’s or Hotine’s formula differ most in high topography areas. Over the study area (reaching almost 2 km in altitude), the approximate geoid models (before the additive corrections) differ by 7 mm on average with a 3 mm standard deviation (SD) and a maximum of 1.3 cm. The additive corrections, out of which only the DWC correction has a numerically significant difference, improve the agreement between respective geoid or quasigeoid models to an average difference of 5 mm with a 1 mm SD and a maximum of 8 mm.  相似文献   

Two-step procedures for hybrid geoid modelling   总被引：1，自引：1，他引：0  

L. E. Sjöberg  W. E. Featherstone 《Journal of Geodesy》2004,78(1-2):66-75

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Equilibrium and structural studies of silicon(IV) and aluminium(III) in aqueous solution. II. Formation constants for the monosilicate ions SiO(OH)₃ and SiO₂(OH)₂. A precision study at 25°C in a simplified seawater medium     

Staffan Sjberg  Agneta Nordin  Nils Ingri 《Marine Chemistry》1981,10(6)

The hydrolysis of silicic acid, Si(OH)₄, was studied in a simplified seawater medium (0.6 M Na(Cl)) at 25°C. The measurements were performed as potentiometric titrations (hydrogen electrode) in which OH⁻ was generated coulometrically. The total concentration of Si(OH)₄, B, and log[H⁺] were varied within the limits 0.00075 B 0.008 M and 2.5 -log[H⁺] 11.7, respectively. Within these ranges the formation of SiO(OH)₃⁻ and SiO₂(OH)₂²⁻ with formation constants log β₋₁₁(Si(OH)₄ SiO(OH)₃⁻ + H⁺) = −9.472 ±0.002 and log β₋₂₁(Si(OH)₄ SiO₂(OH)₂²⁻ + 2H⁺) = −22.07 ± 0.01 was established. With B > 0.003 M polysilicate complexes are formed, however, with -log[H⁺] 10.7 their formation does not significantly affect the evaluated formation constants. Data were analyzed with the least squares computer program LETAGROPVRID.  相似文献