Tensor structure applied to the least-squares method,revisited

The geometrical approach to the least-squares, based on differential geometry with tensor structure and notations, describes the adjustment theory in a simple and plausible manner. The development relies heavily on orthonormal space and surface vectors, and on the extrinsic properties of surfaces linking the two kinds of vectors. In order to relate geometry to adjustments, the geometrical concepts are extended to an n-dimensional space and u- or r-dimensional surfaces, where n is the number of observations, u is the number of parameters in the parametric method and r is the number of conditions in the condition method, with n=u+r. Connection is made to Hilbert spaces by demonstrating that the tensor approach to the least-squares is a classical case of the Hilbert-space approach.     

Modified equations for the determination of odd zonal harmonics

The development of the analytical theory of the motion of an artificial satellite (Berger, 1972–1975) points out the great importance of the second, third order and coupling terms between zonal harmonics. These terms have been added to the equations established byKing-Hele andCook (1968–1973) for the determination of odd zonal harmonics. This solution is compared with theirs. It satisfies all the equations much better and especially the equations relating to near-critical inclination satellites.     

Seismic analysis of non-linearly base-isolated soil-structure interacting reactor building by way of the hybrid frequency-time-domain procedure

The seismic analysis of a reactor building on a sliding-type base isolation is performed by way of the hybrid frequency-time-domain procedure. The frequency dependence of the foundation stiffness coefficients is duly accounted for in the analysis, although the problem is non-linear. The response results are shown to be reliable by way of comparison with the results of a time-stepping algorithm in the specialized case of constant foundation stiffness coefficients. The fact that such an analysis can be performed is an outstanding result, particularly when considering that no difficulties are encountered in the implementation and in the calculation. The flow chart used to implement the procedure is presented in the paper. The reactor building is analysed for three different sites with each site having three sets of material properties. It appears that the structural response is not strongly affected by the frequency dependence of the foundation stiffness coefficients. This also holds true as far as the response of equipment attached to the superstructure is concerned. For all practical purposes this frequency dependence may be disregarded in favour of constant spring and damping coefficients.     

A simple method of magnetic declination fluctuation correction for long single-streamer positioning in a seismic survey

In single‐streamer acquisition, the use of acoustic transducers to constrain the receiver positions is not possible, thus implying the use of compass birds to gather information on the streamer location. The compasses are, however, sensitive to the declination of the local magnetic field of the earth, and local fluctuations not accounted for can degrade the accuracy of reconstructed positions. In order to correct these small‐scale fluctuations, we propose a simple deterministic method to calculate a spatial correction to apply to the compasses that enhances the positioning accuracy. The local compass declination is calculated after a first reconstruction on the whole survey area. This method was applied with success to navigation data from a 3D survey offshore Japan, and the positioning accuracy was improved to the level of the DGPS accuracy.     

Effects of climate change on bioclimatic indices in vineyards along Lake Neuchatel,Switzerland

Theoretical and Applied Climatology - In this study, we investigated the consequences of climate change on bioclimatic indices in vineyards along the edge of Lake Neuchatel in Switzerland. Like in...     

Time-domain boundary element method in viscoelasticity with application to a spherical cavity

The weighted-residual technique, the indirect boundary element method, the truncated indirect boundary element method and the direct boundary element method can be used to analyse nonlinear soil-structure interaction in the time domain. They are illustrated and compared by using the one-dimensional dynamic problem of the spherical cavity in an infinite space. For realistic time steps, all formulations lead to accurate results, but the weighted-residual technique and the truncated indirect boundary element method are much more efficient than the direct boundary element method in the time domain. Hysteretic damping leads to noncausal behaviour, which can, however, be neglected from a practical point of view.     

A sampler-based technique for the study of near-bed sediment dynamics: application in the eastern English Channel

A simple technique for studying near-bed hydrodynamics and sediment dynamics is presented. The method combines the use of (1) a benthic tripod hosting a series of electromagnetic current meters, and (2) a newly developed near-bed multi-level water-sediment mixture sampler. The instrument package was deployed successfully at a shallow water station in the eastern English Channel. The currents at elevation 0.9 m above the bottom were asymmetrical, the flood current peak being slightly stronger than the ebb current peak. At elevation 0.3 m above the bottom, the ebb/flood current peak asymmetry vanished. The observed SSCs (suspended sediment concentrations) were tidally modulated, with a contrasting vertical distribution over the ebb and flood phases of the tidal current: the profile was uniform in the ebb phase whereas a stratification appeared in the flood phase. The depth dependence and time evolution of the SSCs are attributable to a combination of local resuspension and advection-dispersion of remotely suspended fine sediment by ebb currents. Suspended sediment fluxes were uniform during the ebb phase and increased with elevation above the bottom during the flood phase.     

Cosmogenic Be dating of a sackung and its faulted rock glaciers, in the Alps of Savoy (France)

Sackungs are the largest gravitational deformation observed in mountains. They are characterized by the long-term slowness of the movements, but their mechanism is still not well understood. Nowadays cosmic ray exposure (CRE) dating methods allow dating the morphologic structures involved in sackung and can contribute at the understanding of their origin. In the Alps, the 5.3 km long Arcs sackung initiated during the activity of rock glaciers. Three samples from these faulted rock glaciers provide their first CRE ages and show that at 2000 m elevation these block accumulations moved during the Younger Dryas and stopped in early Holocene. Six ¹⁰Be ages of fault scarps show that the Arcs sackung lasted only a few thousand years and stopped at about 8462 ± 432 ¹⁰Be yr. They also reveal that deformation migrated upslope in agreement with a mechanism of flexural toppling of vertical layers. This unique and long gravitational event, characterized by migration of the deformation, does not support earthquake shaking as triggering mechanism for individual faults. It shows that, in the upper Isère valley, slope deformation was delayed of several thousand years after glacial debuttressing, and is not anymore active despite its fresh morphology.