A wavelet thresholding technique for local geoid and deflection of the vertical determination using a planar approximation

A computational scheme using the wavelet transform is employed for local geoid determination, where wavelet multiresolution analysis (MRA) is introduced as an alternative approach to the well-established fast Fourier transform (FFT). The Stokes and Vening Meinesz integrals are approximated in finite MRA subspaces. The algorithm is built using an orthogonal wavelet base function. The characteristics of the base function and its effect on the final result are investigated. Hard and soft thresholding are tested in the compression of the kernel as well as global thresholding is compared to level-wise thresholding to optimize the compression level with an acceptable accuracy. Both global and level-wise thresholding are combined in order to achieve the maximum compression level, with acceptable geoid accuracy. The compression rate depends on the degree of singularity of the kernel. In the case of Stokes, a 94 per cent compression level is achieved with 1 cm (rms) accuracy in comparison to FFT and numerical integration approaches. Due to its stronger singularity, in the case of the Vening Meinesz kernel, 97 per cent compression rate is achieved with a 0.07 arc-second (rms) accuracy. The compression percentages achieved in this study are higher than those reported in pervious studies, which shows that this algorithm is very suitable for use in local geoid determination.     

On the performance of SCF in seismic isolation of the interior equipment of buildings

The dynamic response of equipment mounted on an isolated raised floor inside a building while the primary fixed base structure is subjected to harmonic and earthquake ground motions is numerically investigated. Sliding concave foundation (SCF) system is utilized for isolating the raised floor. The equations of motion for a MDOF shear building containing a SCF isolated raised floor with a mounted equipment are developed and the rigid link method is utilized to handle the non‐linearity of the system. The equipment, which can be modelled as a SDOF or MDOF system, may represent a critical computer unit or telecommunication processing system. SCF can be used easily to achieve the desired long period, necessary for protecting sensitive equipment. In this investigation, the ability of SCF in reducing the acceleration level experienced by the equipment inside a building is demonstrated while the lateral displacement is still within an acceptable range. The analysis considered the case of equipment housed in the upper floors of a building where the acceleration is amplified and the motion contains strong components at long periods. For this purpose, different excitations including both harmonic and real earthquake ground motions are employed and the performance of the system is evaluated. Copyright © 2007 John Wiley & Sons, Ltd.     

Magnetic,paleomagnetic and palynologic studies of Paleolithic depositions of the Akhshtyrskaya cave (Russia)

The paper presents the results of experimental rock-magnetic, paleomagnetic and palynologic study of Paleolithic sediments sampled along two profiles in the Akhshtyrskaya cave, situated in the vicinity of Black Sea shore. In the upper part of profiles, some magnetite was observed; in the middle and lower parts, strongly oxidized non-stoichiometric magnetite and hematite prevail. Thin maghemite covers on the surface of fine magnetite grains are present in the majority of specimens. Natural remanence has one characteristic component (CHRM), mostly of chemical origin, although in few specimens containing magnetite it may be sedimentary. Directions of CHRM obtained by standard paleomagnetic methods revealed anomalous pattern only in layer 3/2, which is slightly older than the overlying layer 3/1 whose age was established as (35±2)×10³ years BP by the U-Th method. This suggests that this paleomagnetic anomaly (PMA) can be correlated with Kargapolovo excursion dated on about (45−39)×10³ years BP. In the remaining overlying and underlying layers, directions of CHRM are grouped around the present geomagnetic field. Depth distributions of scalar magnetic parameters generally coincide with the lithological division of the profiles. Palynologic study revealed the presence of 22 pollen zones. Five thermomers separated with colder periods were found in the middle and lower parts of profile. The non-magnetite composition of magnetic fraction of the majority of studied sediments — oxidized nonstoichiometric magnetite and hematite — resulted in the lack of correlations between paleoclimatic and scalar magnetic characteristics.     

Anisotropic radiation transfer in dispersive media

Equations for radiation, scattered anisotropically from dispersive media are obtained for general boundary conditions. The Padé approximant technique is used to calculate the reflection coefficients for these media. Numerical results are given for diffuse reflected boundary condition.     

Diffuse reflection and transmission of radiation for Rayleigh phase function

Diffuse reflection and transmission coefficients in a plane parallel medium are calculated for a Rayleigh phase-function averaged over polarization and Rayleigh polarized phase-function. This is calculated by imbedding the finite medium into a semi-infinite scattering and absorbing medium. Numerical calculations for semi-infinite albedo are compared with Pomraning results. The albedos for finite medium are calculated via the imbedding equations which converge for large τ to the value of semi-infinite medium.     

The instability of hydromagnetic planetary-gravity waves in a zonal flow and transverse magnetic field

Hydromagnetic planetary-gravity waves propagating on a β-plane through a zonal flow and transverse magnetic field are examined for instability. Such instabilities may be related to same physical phenomena in the atmospheres of the Sun and planets and in the Earth's core. It is found that the onset of instability depends on the directions of the vertical and transverse wave-numbers and the zonal flow. It is also shown that as the magnetic field intensity is kept uniform instability can onset provided that the zonal flow strength does not exceed a certain factor, which depends on the parameters of the medium, and then the zonal wavenumbers that can become unstable are limited to a given range. If the basic Alfvén wave speed is allowed to vary whereas the zonal flow is kept uniform the zonal wavenumbers that can exhibit instability are again limited but the basic Alfvén wave speed can assume any value.     

Apport de la gravimétrie à l'étude de la structure du bassin des Triffa (Maroc nord-oriental) : implications hydrogéologiques

Various techniques (horizontal and vertical derivatives, upward continuation, Euler deconvolution) have been applied to the gravity data from the Triffa's plain and the north flank of the Beni-Snassen massif to delineate various major geological structures such as faults and basins. These results allow the production of a structural map showing the fault systems for the survey area. This map forms the basis for planning future hydrogeological research in this region. To cite this article: D. Khattach et al., C. R. Geoscience 336 (2004).     

Silver and silver-bearing minerals at the Um Samiuki volcanogenic massive sulphide deposit, Eastern Desert, Egypt

The Um Samiuki Zn–Cu–Pb–Ag mineralisation, south Eastern Desert, Egypt is hosted by felsic volcanic rocks which form part of the 712-Ma-old, east-west-trending Shadli Volcanic Belt. Two major occurrences of massive sulphides are present at the top of rhyolitic breccia in the Western and Eastern mine areas. In each occurrence, a bornite-bearing zone is overlain by a pyrite-chalcopyrite-bearing zone and underlain by a disseminated, Cu-depleted zone. In the massive sulphide ore, sphalerite, chalcopyrite, pyrite, galena, bornite and tetrahedrite–tennantite are major minerals, whereas arsenopyrite, pyrrhotite, molybdenite and magnetite are accessory phases. Covellite and digenite are common secondary minerals. Bornite, tetrahedrite–tennantite and covellite contain high amounts of silver (averages of 1.97, 1.39 and 1.82 wt% respectively). Based on mineralogical balance calculations, bornite and covellite accommodate 80% of silver in the Um Samiuki deposit. Ag was incorporated in the crystal structure of the early-crystallised copper sulphides and sulphosalts and silver minerals. The temperature, sequential precipitation of the fluids and the structure of the crystallising phases control the distribution of silver. Post-depositional deformation and metamorphic processes caused liberation, remobilisation and redeposition of silver within the massive sulphides.Editorial handling: D. Lentz     

Efremovka 101.1: a CAI with ultrarefractory REE patterns and enormous enrichments of Sc, Zr, and Y in Fassaite and Perovskite

Inclusion 101.1 from the CV3 carbonaceous chondrite Efremovka is a compact Type A Ca-Al-rich inclusion (CAI) highly enriched in ultrarefractory (UR) oxides. It is the first complete CAI with a UR rare earth element (REE) pattern found in a CV3 chondrite. The inclusion is petrographically complex and was formed in a multistage process. It consists of several lithologically unrelated units.The core contains abundant Y- and Zr-perovskite, Sc- and Zr-rich fassaite, and metallic FeNi enclosed in melilite. All mineral species (except spinel) in all lithological units exhibit the same basic UR REE pattern. Four different populations of perovskites are distinguished by different Y/Zr ratios. A few of the perovskites have Y/Zr ratios similar to those obtained from crystal/liquid fractionation experiments. Perovskites from the other three populations have either chondritic, lower than chondritic Y/Zr ratios or extremely low Zr contents. Ca isotopic ratios differ among three perovskites from different populations, demonstrating a variety of sources and formational processes. Most fassaites crystallized in situ through reaction between the CAI liquid and preexisting perovskites. This process induced redistribution of Zr, Y, Sc, and V between perovskite and fassaite, thus overprinting the original abundances in perovskite. Fassaite reaction rims around FeNi metals are also encountered. They are enriched in V, which was gained from the metal through oxidation of V in metal during fassaite crystallization. The relative abundances of Zr, Y, and Sc in perovskites are complementary to the abundances of these elements in Sc- and Zr-fassaite, indicating subsolidus partitioning of these elements between the two phases. Perovskites are enriched in Y and depleted in Sc and Zr in comparison to fassaites.The core contains two complete captured CAIs, several sinuous fragments, and fine-grained polygonal refractory fragments. An assemblage of andradite-wollastonite-hedenbergite and pure metallic iron is encountered as enclaves in the interior of some sinuous fragments. Metallic Fe and wollastonite formed by reduction of preexisting andradite and hedenbergite nebular alteration products upon inclusion in the highly reduced CAI melt. Numerous spinel clusters and framboids with varying V₂O₃ and Cr₂O₃ concentrations are enclosed in individual melilite crystals in the host CAI and captured CAIs. The rim sequence of the host consists of six layers (from the inside outward): (a) FeO-poor spinel, (b) Sc-bearing fassaite, (c) Al-diopside, (d) Al- and Ca-bearing olivine, (e) pure diopside, and (f) Ca-poor olivine. Like the constituents of the CAI core, all mineral layers of the rim sequence, except spinel, have the same UR REE pattern. However, the total REE abundances decrease systematically by 1 order of magnitude from layer 2 to layer 6. This feature strongly suggests formation of the rim sequence by successive condensation from a unique reservoir enriched in UR elements and excludes formation by flash heating. Petrography, mineral chemistry, REE, refractory lithophile element abundances, and Ca isotopic compositions demonstrate the complex multistage formation history of a CAI that on the surface looks like a regular Type A inclusion.