Sequential solution to Kepler’s equation

Seven sequential starter values for solving Kepler’s equation are proposed for fast orbit propagation. The proposed methods have constant complexity (not iterative), do not require pre-computed data, and can be implemented in just a few lines of code. The resulting sequential orbit propagation techniques can be done at different levels of accuracy and speed, depending essentially on the value of orbit eccentricity. Accuracy and algorithmic complexity are evaluated for all the proposed approaches and compared with several existing single-point techniques to solve Kepler’s equation. The new methods obtain improved accuracy at lower computational cost as compared to the best existing methods.     

S-wave splitting intensity analysis and inversion

Analysing S-wave splitting has become a routine step in processing multicomponent data. Typically, this analysis leads to determining the principal directions of a transversely isotropic medium with a horizontal symmetry axis, which is assumed to be responsible for azimuthal anisotropy, and to the time delays between the fast and slow S-waves. These parameters are commonly estimated layer-by-layer from the top. Errors in layer stripping occurring in shallow layers might propagate to deeper layers. We propose a method for S-wave splitting analysis and compensation that consists of inverting interval values of splitting intensity to obtain a model of anisotropic parameters that vary with time and/or depth. Splitting intensity is a robust attribute with respect to structural variations and is commutative, which means that it can be summed along a ray (or throughout a sensitivity kernel volume) and can be linearly related to anisotropic perturbations at depth. Therefore, it is possible to estimate anisotropic properties within a geological formation (e.g. the reservoir) by analysing the differences of splitting intensity measured at the top and at the bottom of the layer. This allows us to avoid layer stripping, in particular, for shallow layers where anisotropic parameters are difficult to estimate due to poor coverage, and it makes S-wave splitting analysis simpler to apply. We demonstrate this method on synthetic and real data. Because the splitting intensity attribute shows usefulness in S-wave splitting analysis in transversely isotropic media, we extend the splitting intensity theory to lower symmetry classes. It enables the characterization of tilted transversely isotropic and tilted orthorhombic media, opening new opportunities for anisotropic model building.     

Initial orbit determination using multiple observations

A novel approach for initial orbit determination based on multiple angles-only observations is presented. The proposed technique is iterative and uses Lagrangian coefficients, f and g. The proposed method does not show singularity for the coplanar cases. In addition, the method is capable of handling multiple observations, providing higher accuracy, whereas the level of the algorithm complexity and processor running time remain almost invariant. The technique presented is compared with the Double r-iteration and Gauss’ methods using data corrupted by noise to simulate true measurements. Results show that the proposed method is a valid alternative to the classical methods of orbit determination.     

High-temperature vesuvianite: crystal chemistry and surface considerations

A multi-methodical approach has been applied for characterizing the bulk and surface crystal chemical features of a high-temperature vesuvianite crystal from skarns of Mount Somma-Vesuvius Volcano (Naples, Italy). Vesuvianite belongs to the space group P4/nnc with unit cell parameters a = 15.633(1) Å, c = 11.834(1) Å and chemical formula (Ca_18.858 Na_0.028 Ba_0.004 K_0.006 Sr_0.005 □_0.098)_19.000 (Al_8.813 Ti_0.037 Mg_2.954 Mn_0.008 Fe_0.114²⁺ Fe_1.375³⁺ Cr_0.008 B_0.202)_13.511 Si_18.000(O_0.261 F_0.940 OH_7.799)_9.000. Structure refinement, which converges at R = 0.0328, demonstrates a strong positional disorder down the fourfold axes, indicating that the Y1 site is split into two positions (Y1A and Y1B) alternatively occupied. However, because of X4 proximity to Y1B and Y1A, X4 cannot be occupied if Y1B or Y1A are. Overall Y1 occupancy (Y1A + Y1B) reaches approximately 0.5, as common in vesuvianite and occupancy of Y1B site is extremely limited. Moreover, T1 position, limitedly occupied, accommodates the excess of cations generally related to Y position. A small quantity (0.202 apfu) of boron is sited at the T2 site that, like T1, is poorly occupied. The determination of the amount of each element on the (100) vesuvianite surface, obtained through X-ray photoelectron spectroscopy high-resolution spectra in the region of the Si_2p, Al_2p, Mg_1s, and Ca_2p core levels, evidences that a greater amount of aluminum and a smaller amount of calcium characterize the surface with respect to the bulk. Although both of these features require further investigation, we may consider the Al increase can be related to preferential orientation of Al-rich sites on the (100) plane. Furthermore, the surface structure of vesuvianite suggests that Al, Ca, and Mg cations maintain coordination features at the surface similar to the bulk. Silica, however, while presenting fourfold coordination, shows also a [1]-fold small coordinated component at binding energy 99.85 eV, due to broken Si–O bonds at the surface. The presence of eight- and nine-coordinated Ca cations is suggested by a large XPS feature resulting from the merging of Ca_2p3/2 and Ca_2p1/2 peaks at 348.45 and 352.05 eV, respectively.     

Directional response of a reconstituted fine‐grained soil—Part I: experimental investigation

This paper discusses the results of a large experimental program designed to investigate in a systematic manner the main features of the incremental response of fine‐grained soils. The results are obtained from triaxial stress probing experiments carried out on a French silty clay (Beaucaire Marl). All the tests have been performed on reconstituted specimens, normally consolidated to an initial state which is either isotropic or anisotropic. In the interpretation of the experimental results, extensive use is made of the concept of strain response envelope. The response envelopes obtained for different stress increment magnitudes are remarkably consistent with each other and indicate an inelastic and irreversible material response, i.e. a strong dependence on the stress increment direction, also at relatively small strain levels. A companion paper (Int. J. Numer. Anal. Meth. Geomech., this issue, 2006) assesses the performance of some advanced constitutive models in reproducing the behaviour of reconstituted Beaucaire Marl as observed in this experimental program. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic safety of reinforced concrete members and structures

Based on cyclic load tests of large-scale reinforced concrete elements and assemblages, a probabilistic model of member failure is developed. The model gives the probability of survival at time t as a functional of damage ratio and dissipated energy up to t. After extension to multivariate survival of several members with correlated resistance, the model is used to calculate the safety of reinforced concrete frames subjected to given input motions. Results are in terms of the probability of local failure and of no failure anywhere in the system.     

Crystal chemistry, surface morphology and X-ray photoelectron spectroscopy of Fe-rich osumilite from Mt. Arci, Sardinia (Italy)

Microprobe analysis, single crystal X-ray diffraction, X-ray photoelectron spectroscopy, atomic force microscopy, and X-ray absorption spectroscopy were applied on Fe-rich osumilite from the volcanic massif of Mt. Arci, Sardinia, Italy. Osumilite belongs to the space group P6/mcc with unit cell parameters a = 10.1550(6), c = 14.306(1) Å and chemical formula (K_0.729)_C (Na_0.029)_B (Si_10.498 Al_1.502)_T1 (Al_2.706 Fe _0.294 ²⁺ )_T2 (Mg_0.735 Mn_0.091 Fe _1.184 ²⁺ )_AO₃₀. Structure refinement converged at R = 0.0201. Unit cell parameter a is related to octahedral edge length as well as to Fe²⁺ content, unlike the c parameter which does not seem to be affected by chemical composition. The determination of the amount of each element on the mineral surface, obtained through X-ray photoelectron spectroscopy high-resolution spectra in the region of the Si_2p, Al_2p, Mg_1s and Fe_2p core levels, suggests that Fe presents Fe²⁺ oxidation state and octahedral coordination. Two peaks at 103.1 and 100.6 eV can be related to Si⁴⁺ and Si¹⁺ components, respectively, both in tetrahedral coordination. The binding energy of Al_2p, at 74.5 eV, indicates that Al is mostly present in the distorted T2 site, whereas the Mg peak at 1,305.2 eV suggests that this cation is located at the octahedral site. X-ray absorption at the Fe L_2,3-edges confirms that iron is present in the mineral structure, prevalently in the divalent state and at the A octahedral site.     

Holocene vegetation and fire dynamics in the supra‐mediterranean belt of the Nebrodi Mountains (Sicily,Italy)

High‐resolution pollen, macrofossil and charcoal data, combined with accelerator mass spectrometry ¹⁴C dating and multivariate analysis, were used to reconstruct Holocene vegetation and fire dynamics at Urio Quattrocchi, a small lake in the supra‐mediterranean belt in the Nebrodi Mountains of Sicily (Italy). The data suggest that after 10 000 cal a BP increasing moisture availability supported closed forests with deciduous (Quercus cerris, Fagus sylvatica and Fraxinus spp.) and evergreen (Quercus ilex) species. Species‐rich closed forest persisted until 6850 cal a BP, when Neolithic activities caused a forest decline and affected plant diversity. Secondary forest with abundant Ilex aquifolium recovered between 6650 and 6000 cal a BP, indicating moist conditions. From 5000 cal a BP, agriculture and pastoralism led to the currently fragmented landscape with sparse deciduous forests (Quercus cerris). The study suggests that evergreen broadleaved species were more important at elevations above 1000 m a.s.l. before ca. 5000 cal a BP than subsequently, which might reflect less human impact or warmer‐than‐today climatic conditions between 10 000 and 5000 cal a BP. Despite land use since Neolithic times, deciduous supra‐mediterranean forests were never completely displaced from the Nebrodi Mountains, because of favourable moist conditions that persisted throughout the Holocene. Reconstructed vegetation dynamics document the absence of any pronounced mid‐ or late‐Holocene ‘aridification’ trend at the site, an issue which is controversially debated in Italy and the Mediterranean region. Copyright © 2012 John Wiley & Sons, Ltd.