Topographic and atmospheric effects on goce gradiometric data in a local north-oriented frame: A case study in Fennoscandia and Iran     

Mehdi Eshagh  Lars E. Sjöberg 《Studia Geophysica et Geodaetica》2009,53(1):61-80

Satellite gradiometry is an observation technique providing data that allow for evaluation of Stokes’ (geopotential) coefficients. This technique is capable of determining higher degrees/orders of the geopotential coefficients than can be achieved by traditional dynamic satellite geodesy. The satellite gradiometry data include topographic and atmospheric effects. By removing those effects, the satellite data becomes smoother and harmonic outside sea level and therefore more suitable for downward continuation to the Earth’s surface. For example, in this way one may determine a set of spherical harmonics of the gravity field that is harmonic in the exterior to sea level. This article deals with the above effects on the satellite gravity gradients in the local north-oriented frame. The conventional expressions of the gradients in this frame have a rather complicated form, depending on the first-and second-order derivatives of the associated Legendre functions, which contain singular factors when approaching the poles. On the contrary, we express the harmonic series of atmospheric and topographic effects as non-singular expressions. The theory is applied to the regions of Fennoscandia and Iran, where maps of such effects and their statistics are presented and discussed.  相似文献   

Temporal Gravity Variations near Shrinking Vatnajökull Ice Cap, Iceland     

Wolfgang R. Jacoby  Oliver Hartmann  Herbert Wallner  Peter L. Smilde  Stefan Bürger  Lars E. Sjöberg  Sigurdur Erlingsson  Detlef Wolf  Volker Klemann  Ingo Sasgen 《Pure and Applied Geophysics》2009,166(8-9):1283-1302

Repeated gravity measurements were carried out from 1991 until 1999 at sites SE of Vatnajökull, Iceland, to estimate the mass flow and deformation accompanying the shrinking of the ice cap. Published GPS data show an uplift of about 13 ± 5 mm/a near the ice margin. A gravity decrease of –2 ± 1 μGal/a relative to the Höfn base station, was observed for the same sites. Control measurements at the Höfn station showed a gravity decrease of –2 ± 0.5 µGal/a relative to the station RVIK 5473 at Reykjavík (about 250 km from Höfn). This is compatible, as a Bouguer effect, with a 10 ± 3 mm/a uplift rate of the IGS point at Höfn and an uplift rate of ~20 mm/a near the ice margin. Although the derived gravity change rates at individual sites have large uncertainties, the ensemble of the rates varies systematically and significantly with distance from the ice. The relationship between gravity and elevation changes and the shrinking ice mass is modelled as response to the loading history. The GPS data can be explained by 1-D modelling (i.e., an earth model with a 15-km thick elastic lithosphere and a 7·10¹⁷ Pa·s asthenosphere viscosity), but not the gravity data. Based on 2-D modelling, the gravity data favour a low-viscosity plume in the form of a cylinder of 80 km radius and 10¹⁷ to 10¹⁸ Pa·s viscosity below a 6 km-thick elastic lid, embedded in a layered PREM-type earth, although the elevation data are less well explained by this model. Strain-porosity-hydrology effects are likely to enhance the magnitude of the gravity changes, but need verification by drilling. More accurate data may resolve the discrepancies or suggest improved models.  相似文献   

On the error of analytical continuation in physical geodesy     

Lars E. Sjöberg 《Journal of Geodesy》1996,70(11):724-730

Analytical continuation of gravity anomalies and height anomalies is compared with Helmert's second condensation method. Assuming that the density of the terrain is constant and known the latter method can be regarded as correct. All solutions are limited to the second power of H/R, where H is the orthometric height of the terrain and R is mean sea-level radius. We conclude that the prediction of free-air anomalies and height anomalies by analytical continuation with Poisson's formula and Stokes's formula goes without error. Applying the same technique for geoid determination yields an error of the order of H², stemming from the failure of analytical continuation inside the masses of the Earth.  相似文献   

The IAG approach to the atmospheric geoid correction in Stokes' formula and a new strategy     

L. E. Sjöberg 《Journal of Geodesy》1999,73(7):362-366

The well-known International Association of Geodesy (IAG) approach to the atmospheric geoid correction in connection with Stokes' integral formula leads to a very significant bias, of the order of 3.2 m, if Stokes' integral is truncated to a limited region around the computation point. The derived truncation error can be used to correct old results. For future applications a new strategy is recommended, where the total atmospheric geoid correction is estimated as the sum of the direct and indirect effects. This strategy implies computational gains as it avoids the correction of direct effect for each gravity observation, and it does not suffer from the truncation bias mentioned above. It can also easily be used to add the atmospheric correction to old geoid estimates, where this correction was omitted. In contrast to the terrain correction, it is shown that the atmospheric geoid correction is mainly of order H of terrain elevation, while the term of order H ² is within a few millimetres. Received: 20 May 1998 / Accepted: 19 April 1999  相似文献   

Dating mafic–ultramafic intrusions by ion-microprobing contact-melt zircon: examples from SW Sweden     

Anders Scherstén  Hans Årebäck  David Cornell  Paul Hoskin  Anton Åberg  Richard Armstrong 《Contributions to Mineralogy and Petrology》2000,139(1):115-125

Zircons from anatectic melts of the country rocks of three Proterozoic mafic–ultramafic intrusions from the Sveconorwegian Province in SW Sweden were microanalyzed for U–Th–Pb and rare earth elements. Melting and interaction of the wall rocks with the intrusions gave rise to new magmas that crystallized zircon as new grains and overgrowths on xenocrysts. The ages of the intrusions can be determined by dating this newly crystallized zircon. The method is applied to three intrusions that present different degrees of complexity, related to age differences between intrusion and country rocks, and the effects of post-intrusive metamorphism. By careful study of cathodoluminescent images and selection of ion probe spots in zircon grains, we show that this approach is a powerful tool for obtaining accurate and precise ages. In the contact melts around the 916?±?11?Ma Hakefjorden Complex, Pb-loss occurred in some U-rich parts of xenocrystic zircon due to the heat from the intrusion. In back-veins of the 1624?±?6?Ma Olstorp intrusion we succeeded in geochemically distinguishing new magmatic from xenocrystic zircon despite small age differences. At Borås the mafic intrusion mixed with country rock granite to form a tonalite in which new zircon grew at 1674?±?8?Ma. Reworking of zircon occurred during 930+33/–34?Ma upper amphibolite facies Sveconorwegian metamorphism. Pb-loss was the result of re-equilibration with metamorphic fluids. REE-profiles show consistent differences between xenocrystic, magmatic, and metamorphic zircon in all cases. They typically differ in Lu/La_N, Ce/Ce*, and Eu/Eu*, and igneous zircon with marked positive Ce/Ce* and negative Eu/Eu* lost its anomalies during metamorphism.  相似文献   

Definition of Physical Height Systems for Telluric Planets and Moons     

Robert Tenzer  Ismael Foroughi  Lars E. Sjöberg  Mohammad Bagherbandi  Christian Hirt  Martin Pitoňák 《Surveys in Geophysics》2018,39(3):313-335

In planetary sciences, the geodetic (geometric) heights defined with respect to the reference surface (the sphere or the ellipsoid) or with respect to the center of the planet/moon are typically used for mapping topographic surface, compilation of global topographic models, detailed mapping of potential landing sites, and other space science and engineering purposes. Nevertheless, certain applications, such as studies of gravity-driven mass movements, require the physical heights to be defined with respect to the equipotential surface. Taking the analogy with terrestrial height systems, the realization of height systems for telluric planets and moons could be done by means of defining the orthometric and geoidal heights. In this case, however, the definition of the orthometric heights in principle differs. Whereas the terrestrial geoid is described as an equipotential surface that best approximates the mean sea level, such a definition for planets/moons is irrelevant in the absence of (liquid) global oceans. A more natural choice for planets and moons is to adopt the geoidal equipotential surface that closely approximates the geometric reference surface (the sphere or the ellipsoid). In this study, we address these aspects by proposing a more accurate approach for defining the orthometric heights for telluric planets and moons from available topographic and gravity models, while adopting the average crustal density in the absence of reliable crustal density models. In particular, we discuss a proper treatment of topographic masses in the context of gravimetric geoid determination. In numerical studies, we investigate differences between the geodetic and orthometric heights, represented by the geoidal heights, on Mercury, Venus, Mars, and Moon. Our results reveal that these differences are significant. The geoidal heights on Mercury vary from ? 132 to 166 m. On Venus, the geoidal heights are between ? 51 and 137 m with maxima on this planet at Atla Regio and Beta Regio. The largest geoid undulations between ? 747 and 1685 m were found on Mars, with the extreme positive geoidal heights under Olympus Mons in Tharsis region. Large variations in the geoidal geometry are also confirmed on the Moon, with the geoidal heights ranging from ? 298 to 461 m. For comparison, the terrestrial geoid undulations are mostly within ± 100 m. We also demonstrate that a commonly used method for computing the geoidal heights that disregards the differences between the gravity field outside and inside topographic masses yields relatively large errors. According to our estimates, these errors are ? 0.3/+ 3.4 m for Mercury, 0.0/+ 13.3 m for Venus, ? 1.4/+ 125.6 m for Mars, and ? 5.6/+ 45.2 m for the Moon.  相似文献   

The Modified Best Quadratic Unbiased Non-Negative Estimator (MBQUNE) of variance components   总被引：2，自引：0，他引：2  

M. Eshagh  L. E. Sjöberg 《Studia Geophysica et Geodaetica》2008,52(3):305-320

Estimated variance components may come out as negative numbers without physical meaning. One way out of this problem is to use non-negative methods. Different approaches have been presented for the solution. Sjöberg presented a method of Best Quadratic Unbiased Non-Negative Estimator (BQUNE) in the Gauss-Helmert model. This estimator does not exist in the general case. Here we present the Modified BQUNE (MBQUNE) obtained by a simple transformation from the misclosures used in the BQUE to residuals. In the Gauss-Markov adjustment model the BQUNE and MBQUNE are identical, and they differ in condition and Gauss-Helmert models only by a simple transformation. If the observations are composed of independent/disjunctive groups the MBQUNE exists in any adjustment model and it carries all the properties of the BQUNE (when it exists). The presented variance component models are tested numerically in some simple examples. It is shown that the MBQUNE works well for disjunctive groups of observations.  相似文献   

Deciphering seismic and normal-force fluctuation signatures of debris flows: An experimental assessment of effects of flow composition and dynamics     

Tjalling de Haas  Amanda S. Åberg  Fabian Walter  Zhen Zhang 《地球表面变化过程与地形》2021,46(11):2195-2210

Debris flows are gravity-driven mass movements that are common natural hazards in mountain regions worldwide. Previous work has shown that measurements of ground vibrations are capable of detecting the timing, speed, and location of debris flows. A remaining question is to what extent additional flow properties, such as grain-size distribution and flow depth can be inferred reliably from seismic data. Here, we experimentally explore the relation of seismic vibrations and normal-force fluctuations with debris-flow composition and dynamics. We use a 5.4 m long and 0.3 m wide channel inclined at 20°, equipped with a geophone plate and force plate. We show that seismic vibrations and normal-force fluctuations induced by debris flows are strongly correlated, and that both are affected by debris-flow composition. We find that the effects of the large-particle distribution on seismic vibrations and normal-force fluctuations are substantially more pronounced than the effects of water fraction, clay fraction, and flow volume, especially when normalized by flow depth. We further show that for flows with similar coarse-particle distributions seismic vibrations and normal-force fluctuations can be reasonably well related to flow depth, even if total flow volume, water fraction, and the size distribution of fines varies. Our experimental results shed light on how changes in large-particle, clay, and water fractions affect the seismic and force-fluctuation signatures of debris flows, and provide important guidelines for their interpretation.  相似文献   

Persistence and biodegradation of kerosene in high-arctic intertidal sediment     

Røberg S  Stormo SK  Landfald B 《Marine environmental research》2007,64(4):417-428

A kerosene type hydrocarbon fraction (equivalent to 7 L m(-2)) was added to enclosures in the surface layer of high-arctic intertidal beach sediment. The experimental spill was repeated in two consecutive years in the period July-September. The rate and extent of hydrocarbon removal and the accompanying bacterial response were monitored for 79 days (2002) and 78 days (2003). The bulk of added kerosene, i.e. 94-98%, was lost from the upper 5 cm layer by putatively abiotic processes within 2 days and a residual fraction in the range 0.6-1.2mg per g dry sediment was stably retained. Concomitant addition of oleophilic fertilizer led to higher initial retention, as 24% of the kerosene remained after 2 days in the presence of a modified, cold-climate adapted version of the well-known Inipol EAP 22 bioremediation agent. In these enclosures, which showed an increase in hydrocarbon-degrader counts from 6.5 x 10(3) to 4.1 x 10(7) per g dry sediment within 8 days, a 17% contribution by biodegradation to subsequent hydrocarbon removal was estimated. Stimulation in hydrocarbon-degrader counts in fertilizer-alone control enclosures was indistinguishable from the stimulation observed with both kerosene and fertilizer present, suggesting that the dynamics in numbers of hydrocarbon-degrading bacteria was primarily impacted by the bioremediation agent.  相似文献   

The effect on the geoid of lateral topographic density variations     

L. E. Sjöberg 《Journal of Geodesy》2004,78(1-2):34-39

Gravimetric geoid determination by Stokes formula requires that the effects of topographic masses be removed prior to Stokes integration. This step includes the direct topographic and the downward continuation (DWC) effects on gravity anomaly, and the computations yield the co-geoid height. By adding the effect of restoration of the topography, the indirect effect on the geoid, the geoid height is obtained. Unfortunately, the computations of all these topographic effects are hampered by the uncertainty of the density distribution of the topography. Usually the computations are limited to a constant topographic density, but recently the effects of lateral density variations have been studied for their direct and indirect effects on the geoid. It is emphasised that the DWC effect might also be significantly affected by a lateral density variation. However, instead of computing separate effects of lateral density variation for direct, DWC and indirect effects, it is shown in two independent ways that the total geoid effect due to the lateral density anomaly can be represented as a simple correction proportional to the lateral density anomaly and the elevation squared of the computation point. This simple formula stems from the fact that the significant long-wavelength contributions to the various topographic effects cancel in their sum. Assuming that the lateral density anomaly is within 20% of the standard topographic density, the derived formula implies that the total effect on the geoid is significant at the centimetre level for topographic elevations above 0.66 km. For elevations of 1000, 2000 and 5000 m the effect is within ± 2.2, ± 8.8 and ± 56.8 cm, respectively. For the elevation of Mt. Everest the effect is within ± 1.78 m.  相似文献