Geoid, topography, and the Bouguer plate or shell

 Topography plays an important role in solving many geodetic and geophysical problems. In the evaluation of a topographical effect, a planar model, a spherical model or an even more sophisticated model can be used. In most applications, the planar model is considered appropriate: recall the evaluation of gravity reductions of the free-air, Poincaré–Prey or Bouguer kind. For some applications, such as the evaluation of topographical effects in gravimetric geoid computations, it is preferable or even necessary to use at least the spherical model of topography. In modelling the topographical effect, the bulk of the effect comes from the Bouguer plate, in the case of the planar model, or from the Bouguer shell, in the case of the spherical model. The difference between the effects of the Bouguer plate and the Bouguer shell is studied, while the effect of the rest of topography, the terrain, is discussed elsewhere. It is argued that the classical Bouguer plate gravity reduction should be considered as a mathematical construction with unclear physical meaning. It is shown that if the reduction is understood to be reducing observed gravity onto the geoid through the Bouguer plate/shell then both models give practically identical answers, as associated with Poincaré's and Prey's work. It is shown why only the spherical model should be used in the evaluation of topographical effects in the Stokes–Helmert solution of Stokes' boundary-value problem. The reason for this is that the Bouguer plate model does not allow for a physically acceptable condensation scheme for the topography. Received: 24 December 1999 / Accepted: 11 December 2000     

Shear-zone controlled basins in the Blouberg area, Northern Province, South Africa: syn- and post-tectonic sedimentation relating to ca. 2.0 Ga reactivation of the Limpopo Belt

The extent of the deposition and of the preservation of the Blouberg Formation and Waterberg Group was at least partially controlled by brittle reactivation along the Palala Shear Zone. The Palala Shear Zone in the Blouberg area (Northern Province, South Africa) is characterised by granulite-grade gneiss, and formed by sinistral transpressional collision between the Southern Marginal Zone (Kaapvaal Craton) and the Central Zone of the Limpopo Belt. The Limpopo collision is thought to have occurred either at 2.0 Ga or at 2.7 Ga with reactivation at 2.0 Ga. Deposition of the Blouberg Formation was characterised by syn-sedimentary tectonism, which is reflected by a sudden upward coarsening in sedimentary rocks, and by the presence of a strongly folded and thrusted lower member. Bedding orientations and slickenside lineation orientations suggest that vergence was towards the south, and such a tectonism can be inferred to have produced a highland area to the north, bound on the southern margin by the southern strand of the Melinda Fault. The presence of an inferred northerly upland area is supported by palaeocurrent directions and the preservational extent of the Setlaole and Makgabeng Formations of the Waterberg Group (post-Blouberg Formation). The extent and stratigraphy of the overlying Mogalakwena Formation suggests that these strata onlapped northwards over the denuding highlands. Younger Sibasa basalts of the Soutpansberg Group have been dated at ca. 1.85 Ga. Blouberg and Waterberg strata can therefore be interpreted as syn- and post-tectonic sedimentary rocks, respectively, following a ca. 2.0 reactivation event along the Palala Shear Zone. It is difficult to reconcile the succession of geological events at Blouberg with a ca. 2.0 Ga Limpopo orogeny, and thus sedimentary strata in the study area support a 2.7 Ga date for Limpopo collision, with syn-Blouberg tectonism relating to ca. 2.0 reactivation within the previously assembled Limpopo Belt.     

Temperature dependence of the 57Fe Mössbauer parameters in riebeckite

Mössbauer spectra for two riebeckite minerals were collected at temperatures in the range 4.2 to 500 K. The magnetic-ordering temperatures were found to be 33±1 and 31±1 K respectively. Fitting the paramagnetic spectra with a discrete number of doublets (three or four) did not lead to consistent results. Instead, a superposition of an Fe³⁺ (M2) doublet and one distributed ferrous component was found to produce adequate fits with reasonable parameter values. For both samples, a minor fraction of ferrous ions was observed to be present at the M4 sites and for one of the samples at the M2 sites as well. The temperature variations of the center shifts were well reproduced using the Debye model of the lattice vibrational spectrum to evaluate the second-order Doppler shift. The characteristic Mössbauer temperatures were calculated to be in the range 340–390 K for Fe²⁺, and 520 K for Fe³⁺. The temperature dependences of the various ferrous quadrupole splittings could not be explained in terms of the point-charge model and assuming a temperature-independent energy-level scheme for the ⁵D term. It is suggested that a gradual change with temperature of the orbital-level splittings takes place. All calculations yielded a positive sign for the principal component of the electric field gradient (EFG). The spectrum recorded at 4.2 K for one of the riebeckites was fitted with a superposition of an Fe³⁺ and a Fe²⁺ hyperfine-field distribution, the latter one primarily characterizing the Fe²⁺ (M1) cations. The following relevant hyperfine data were calculated: H _hf=161 kOe, ΔE _Q=3.11 mm/s, and V _zz<0, all referring to the maximum-propability values. For the second riebeckite at 4.2 K, an additional distributed ferrous component could independently be resolved. The two maximum-probability hyperfine fields were found to be 189 and 98 kOe and the corresponding ΔE _Q values 3.10 and 2.67 mm/s. Both components exhibit a negative V _zz. The subspectra were attributed to M1 and M3 sites respectively. The Fe³⁺ hyperfine fields are 548+-2 kOe for both riebeckites. The different values found for the Fe³⁺ quadrupole shift 2?_Q for the two samples is explained by a different angle between the hyperfine field and the EFG's principal axis. The magnetic spectra recorded at 15 K and higher, could not be reproduced adequately with reasonable parameter values.     

Crack propagation in sandstone: Combined experimental and numerical approach

Summary A combined experimental and numerical approach is adopted to investigate crack propagation in sandstone. Experiments on two types of sandstones show a simular behaviour as found in tests on concrete specimens. The heterogeneity of the material in combination with the stress situation, as a result of the applied load, governs the direction of crack propagation. Cracks that develop are not continuous, but overlaps exist mainly around the grain particles in the material. A simple lattice model, in which the material is schematized as a network of small beams, is adopted to simulate the experiments. Using the simulations carried out with the lattice model, the control parameter for stable displacement controlled four-point-shear tests was determined. The crack patterns obtained with the model are in good agreement with the experimental observations. However further study is needed to predict the load-displacement response correctly.     

A ten-to-twelve year variation in the stratosphere of the Northern Hemisphere

This review paper for STIB (Stratosphere-Troposphere Interaction and the Biosphere; a proposed core project for IGBP) summarizes several features of a recently discovered 10–12 year oscillation in the atmosphere on the Northern Hemisphere. The oscillation is especially strong in the stratosphere during the warmer half of the year, but it is evident in the stratosphere and troposphere also in winter if the data are grouped according to the phase of the Quasi-Biennial Oscillation of the wind in the equatorial stratosphere. During the 40 years with data available to describe the oscillation it was phase locked with the 11-year solar cycle.Affiliate Scientist, NCAR.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Les bilans énergétiques approchés en variables λ, ϕ,p ett

Résumé L'auteur montre comment il faut déduire les formes approchées des bilans énergétiques des mouvements atmosphériques en variables , ,p ett de leurs formes générales exactes. Il a tenu compte de la variabilité de la pression à la surface du globe.

---

Summary It is shown how the approximate energy equations of atmospheric motions expressed with the independent variables , ,p andt must bederived from their exact general form. The variability of surface pressure has been taken into account.

---

Zusammenfassung Es wird gezeigt, wie sich Näherungsformeln der Energiebilanzen der atmosphärischen Bewegungsvorgänge durch die unabhängigen Variablen , ,p undt von ihrer exakten Formulierung ableiten lassen; dabei wird der Veränderlichkeit des Luftdrucks an der Erdoberfläche Rechnung getragen.

     

Zur Mechanik der ostalpinen Deckenbildung

Zusammenfassung Die Mechanik der Deckenbildung ist eine aktuelle Streitfrage bei der Deutung alpiner Gebirgsbildung. Zwei Leitvorstellungen stehen zur Diskussion: 1. Tangentialdruck in der Erdkruste verursacht Faltungen und Deckenüberschiebungen in der mobilen geosynklinalen Zone; 2. Gravitationstektonik zufolge von endogen bedingten Hebungen und Senkungen verursacht die lateralen Massenverlagerungen der alpinen Orogenese.Im ersten Falle also Mobilismus (Wandertektonik), mit Einengung der Geosynklinale, begleitet von Verschluckung der Sialkruste oder crustal buckling. Im zweiten Falle Fixismus (Standtektonik), das heißt nur Durchbewegung der Tektonosphäre zufolge von Materialkreisläufen im geosynklinalen Bereiche, ohne daß notwendigerweise auch die Nebengebiete mitbeteiligt werden und sich nähern müssen.An der Hand von drei genetischen Profilen über Salzburg und die Hohen Tauern wird erläutert, daß es möglich ist, die ostalpine Orogenese mit Hilfe des zweiten Leitbildes zu erklären.Die Gravitationstektonik oder Sekundärtektogenese tritt in verschiedenen Stockwerken auf. Die Abgleitung der alpinen Sedimenthaut liefert Decken von helvetischem Typ. Wenn auch das kristalline Grundgebirge am lateralen Transport mitbeteiligt ist, entstehen Decken vom ostalpinen Typ. Die Verfließungen der tiefen, rheomorphen Teile der Kruste (Migma und z. T. palingenes Magma) liefern die Decken penninischen Charakters, welche im Tauernfenster aufgeschlossen sind.Die erste orogene Hauptphase war die tieforogene oder Gosauphase der mittleren Kreide, wobei die Proto-Austriden und Proto-Penniden in die Tauernvortiefe wanderten.Die zweite orogene Hauptphase war die hochorogene oder Molassephase des Mitteltertiärs, wobei die Tauernzone als Geantiklinale emporgewölbt wurde. In den nördlichen Kalkalpen fanden nordvergente, in den südlichen Kalkalpen südvergente Bewegungen statt.Zum Schlusse wurden die nördlichen Kalkalpen gegen die Molasse aufgeschoben, welche Bewegung im zentralen Tauernsektor wahrscheinlich mechanisch mit der Gailabschiebung in der Südflanke der Geantiklinale zusammenhängt.Die Deutung der Mechanik der ostalpinen Deckenbildung nach dem Leitbild der Schwerkrafttektonik führt also zum Ergebnis, daß Krustenverkürzung keine notwendige Begleiterscheinung alpiner Orogenese ist. Diese Schlußfolgerung steht in Übereinstimmung mit gravimetrischen und seismischen Beobachtungen.