A recurrence relation for the βn-function     

Lars Sjöberg 《Journal of Geodesy》1980,54(1):69-72

A recurrence relation is presented for the smoothing function, β_n, which is used in geodesy to relate spherical harmonics to their mean values over circular areas (caps). The proposed formula does not require the computation of the Legendre's polynomials. Moreover, it is numerically more stable than the formulas ofPellinen (1969) andMeissl (1971).  相似文献   

Using sea-level data to constrain a finite-element primitive-equation ocean model with a local SEIK filter     

Lars Nerger  Sergey Danilov  Wolfgang Hiller  Jens Schröter 《Ocean Dynamics》2006,56(5-6):634-649

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Development of Three-Dimensional Hydrostratigraphical Architecture of the Unsaturated Zone Based on Soft and Hard Data     

Elin Langsholt  Nils-Otto Kitterød  Lars Gottschalk 《Ground water》1998,36(1):104-111

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Comment on Special Issue on Geostatistics with Guest Editor A. G. Journel     

Kyrre Bratvedt  Erik Bølviken  Tore Gimse  Helge Holden  Lars Holden  Ragnar Knarud 《Mathematical Geology》1998,30(2):245-246

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A new integral approach to geopotential coefficient determinations from terrestrial gravity or satellite altimetry data     

Lars E. Sj?berg 《Journal of Geodesy》1988,62(2):93-101

The spherical harmonic coefficients of the Earth’s gravitational potential are conveniently determined by integration of gravity data or potential data (derived from satellite altimetry) over a sphere. The major problem of such a method is that the data, given on the non-spherical surface of the Earth, must be reduced to the sphere. A new integral formula over the surface of the Earth is derived. With this formula improved first order topographic corrections to the spherical formulas are obtained.  相似文献   

The age of Dar al Gani 476 and the differentiation history of the martian meteorites inferred from their radiogenic isotopic systematics     

Lars E. Borg  Larry E. Nyquist  Chi-Yu Shih 《Geochimica et cosmochimica acta》2003,67(18):3519-3536

Samarium-neodymium isotopic analysis of the martian meteorite Dar al Gani 476 yields a crystallization age of 474 ± 11 Ma and an initial ε_Nd¹⁴³ value of +36.6 ± 0.8. Although the Rb-Sr isotopic system has been disturbed by terrestrial weathering, and therefore yields no age information, an initial ⁸⁷Sr/⁸⁶Sr ratio of 0.701249 ± 33 has been estimated using the Rb-Sr isotopic composition of the maskelynite mineral fraction and the Sm-Nd age. The Sr and Nd isotopic systematics of Dar al Gani 476, like those of the basaltic shergottite QUE94201, are consistent with derivation from a source region that was strongly depleted in incompatible elements early in the history of the solar system. Nevertheless, Dar al Gani 476 is derived from a source region that has a slightly greater incompatible enrichment than the QUE94201 source region. This is not consistent with the fact that the parental magma of Dar al Gani 476 is significantly more mafic than the parental magma of QUE94201, and underscores a decoupling between the major element and trace element-isotopic systematics observed in the martian meteorite suite.Combining the ε_Nd¹⁴²-ε_Nd¹⁴³ isotopic systematics of the martian meteorites yields a model age for planetary differentiation of 4.513_+0.033^−0.027 Ga. Using this age, the parent/daughter ratios of martian mantle sources are calculated assuming a two-stage evolutionary history. The calculated sources have very large ranges of parent/daughter ratios (⁸⁷Rb/⁸⁶Sr = 0.037-0.374; ¹⁴⁷Sm/¹⁴⁴Nd = 0.182-0.285; ¹⁷⁶Lu/¹⁷⁷Hf = 0.028-0.048). These ranges exceed the ranges estimated for terrestrial basalt source regions, but are very similar to those estimated for the sources of lunar mare basalts. In fact, the range of parent/daughter ratios calculated for the martian meteorite sources can be produced by mixing between end-members with compositions similar to lunar mare basalt sources. Two of the sources have compositions that are similar to olivine and pyroxene-rich mafic cumulates with variable proportions of a Rb-enriched phase, such as amphibole, whereas the third source has the composition of liquid trapped in the cumulate pile (i.e. similar to KREEP) after ∼99% crystallization. Correlation between the proportion of trapped liquid in the meteorite source regions and estimates of f_O2, suggest that the KREEP-like component may be hydrous. The success of these models in reproducing the martian meteorite source compositions suggests that the variations in trace element and isotopic compositions observed in the martian meteorites primarily reflect melting of the crystallization products of an ancient magma ocean, and that assimilation of evolved crust by mantle derived magmas is not required. Furthermore, the decoupling of major element and trace element-isotopic systematics in the martian meteorite suite may reflect the fact that trace element and isotopic systematics are inherited from the magma source regions, whereas the major element abundances are limited by eutectic melting processes at the time of magma formation. Differences in major element abundances of parental magma, therefore, result primarily from fractional crystallization after leaving their source regions.  相似文献   

On Modelling Discrete Geological Structures as Markov Random Fields   总被引：1，自引：0，他引：1  

Tommy Norberg  Lars Rosén  Ágnes Baran  Sándor Baran 《Mathematical Geology》2002,34(1):63-77

The purpose of this paper is to extend the locally based prediction methodology of BayMar to a global one by modelling discrete spatial structures as Markov random fields. BayMar uses one-dimensional Markov-properties for estimating spatial correlation and Bayesian updating for locally integrating prior and additional information. The methodology of this paper introduces a new estimator of the field parameters based on the maximum likelihood technique for one-dimensional Markov chains. This makes the estimator straightforward to calculate also when there is a large amount of missing observations, which often is the case in geological applications. We make simulations (both unconditional and conditional on the observed data) and maximum a posteriori predictions (restorations) of the non-observed data using Markov chain Monte Carlo methods, in the restoration case by employing simulated annealing. The described method gives satisfactory predictions, while more work is needed in order to simulate, since it appears to have a tendency to overestimate strong spatial dependence. It provides an important development compared to the BayMar-methodology by facilitating global predictions and improved use of sparse data.  相似文献   

Limitations of the potentiometric titration technique in determining the proton active site density of goethite surfaces     

Johannes LützenkirchenJean-François Boily  Lars Lövgren  Staffan Sjöberg 《Geochimica et cosmochimica acta》2002,66(19):3389-3396

Density of proton active surface sites at mineral surfaces is a property of fundamental importance in equilibrium modeling of surface complexation reactions. In this article, methods for an experimental determination of these sites at the surface of α-FeOOH (goethite) are explored. It is shown that previously obtained saturation data of goethite with respect to protons do not yield a site density that can be considered as an intrinsic sorbent property: the results are below crystallographically expected values and values for different ionic media in terms of composition and concentration yield different numbers—for example, chloride would yield higher values than nitrate at the same concentration, and higher electrolyte concentration would favor higher apparent maxima. Although site saturation might be explained by electrostatic repulsion, which is more efficient at high electrolyte concentration or for certain ions, further independent experimental results show that no saturation occurs on goethite down to ph ≡ −log[H⁺] = 2.2 and possibly to ph = 1.0 in 0.6 M NaCl. For those very low pH values, the experimental charging curve was obtained by coulometric back titration (using the Gran plot) or titrations with tris (hydroxymethyl)-aminomethane of the supernatant of acidified goethite suspension. These experimental data are to our knowledge the first high quality data at such low pHs. However, small errors in the determination of proton concentrations (1%) are shown to strongly affect the shape of the charging curve for ph < 2. Furthermore, goethite dissolution (proton consumption and iron reduction in coulometric titrations) and liquid junction effects interfere at low ph, hampering the straightforward application of coulometric Gran titrations over the whole pH range. From these experiments, it can nonetheless be ascertained that a minimum of 2.5 protons/nm² can be adsorbed at the goethite surface from the point of zero charge (ph 9.4) to pH 0.9. Although these studies are restricted to goethite, those studies in which titrations with excess acid and base have been used for the determination of proton active site concentrations of sorbents should be reconsidered.  相似文献   

Origin of upper-mantle seismic scattering – evidence from Russian peaceful nuclear explosion data     

Lars Nielsen  Hans Thybo  Alan Levander  Leonid N. Solodilov 《Geophysical Journal International》2003,154(1):196-204

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Rapid and rhythmic ice sheet fluctuations in western Scandinavia 15-40 Kya–a review     

Lars Olsen  Harald Sveian  Klaas van der  Borg  Bjørn Bergstram  Maarten Broekmans 《Polar research》2002,21(2):235-242

The onshore record of Middle to Late Weichselian sediments and glacial history in Norway indicates a succession of four major ice advances alternating with rapid, considerable ice recessions and interstadial conditions. During all the glacial advances the ice sheet expanded from onshore/inland positions to the shelf areas. The basis for visualizing these variations in glaciation curves constructed along nine transects from inland to shelf, and for interpretation of the palaeoclimatic history, is the regional Quaternary stratigraphy, more than 300 datings, fossil content and some palaeomagnetic data. The methods applied in recent years for AMS radiocarbon dating of glacial sediments with low organic carbon content have given promising results with respect to accuracy and precision, and the results of such datings were an important tool for our reconstructions and for timing of the ice oscillations. The rapid and rhythmic ice fluctuations, as reconstructed in our new model, have been fairly synchronous in most parts of Norway. Ice advances commenced and culminated at 40, 30-28, 24-21 and 18-15 (¹⁴C) Kya. We describe three intervening interstadials from inland sites: Hattfjelldal I, Hattfjelldal II and Trofors. Our stratigraphical record also includes many indications of high, pre-Holocene, relative sea levels, suggesting a considerable glacioisostatic depression of western Scandinavia during the interstadials. In our glaciation model we suggest that, in addition to precipitation, the mountainous fjord and valley topography, glacial isostasy and relative sea level changes were probably more important for the size of the glacial fluctuations than were air temperature changes.  相似文献