Free networks: minimum norm solution as obtained by the inner adjustment constraint method

The main goal of this paper is to show that the solution obtained by adjusting a free network via the inner adjustment constraint method is the minimum norm solution. The latter is a special case of the class of “minimum trace” solutions, where the trace of the variance-covariance matrix for the adjusted parameters is a minimum. The derivations are carried out in terms of pseudo-inverses, the various other forms of generalized inverses having been left out of consideration.     

Le Trias comme période salifère

1. In the Earth history not a system probably comprises so many evaporites than Triassic. They are not restricted to such or such protoocean but cover huge epicontinental cratonic plateforms with very finely bedded deposits as well as they fill rifts located in very diversified geodynamic areas. The first condition in order that such deposits can exist is a severe aridity.
2. Triassic corresponds to an extraordinary transgression in the sense of a new onlap of the sedimentary realm, a reconquest of ancient areas by new deposits, however their facies may be. In that general setting evaporites are themselves remarkably transgressive and from two points of view a) they sometimes onlap directly — that is to say without any basal detritic intercalation — different terms of peneplaned basement, b) these evaporites often succeed Permian emersion or continental detritic deposits of lower parts of Triassic. They extract their salts from Ocean. They often underlie pure marine Jurassic facies. For all these reasons evaporites appear as the first emissaries of oceanic realm and so as the first witnesses of a marine transgression.
3. Evaporites occur in Triassic, particularly in the Middle East, North Africa, on the two present margins of North Atlantic, on Western and Northern Europe, etc. The whole constitutes a huge saline ring round the western part of Triassic Tethysian sea. In that area, on the less tectonized plateforms a grandiose facies distribution pattern appears clearly: going farther from open sea in a centrifugal way, there are salts more and more soluble, until detritic deposits from continent. The pellicular sheets of water which covered the large plateforms resulting from late permian peneplanation should be favourable to modification of chemism, very gradual and at last very total, producing a geographical distribution of salt deposits. The most probable mover of these “floods” could be a very likely multiphase rise of eustatic level, the effects of which we cannot imagine because they occured on plateforms unknown in the geography of recent world. Effects of local morphology which induced a pecular distribution of salts can modify the general plateform distribution pattern.

     

Seismotectonics of the Papua New Guinea—Solomon Islands region

Earthquakes for the period 1964–1973 are relocated by the method of Joint Hypocenter Determination in order better to resolve the configuration and the structure of the New Guinea—New Britain—Solomon Islands region. Focal mechanism solutions are integrated with the seismicity and interpreted closely with it. A zone of subduction exists beneath New Britain and the Solomon Islands, a zone of left-lateral strike-slip movement extends from New Ireland to New Guinea. The zone of seismicity in northern New Guinea has developed as a result of a continent—island-arc collision in late Oligocene—Miocene times and does not exhibit a well-developed inclined seismic zone. It is proposed that plate tectonics theory does not apply rigorously, but slip-line field theory allows the presentation of a new geodynamic model for this region.     

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.     

Composition isotopique du strontium d'eaux interstitielles extraites de sédiments récents: un argument en faveur de l'homogénéisation isotopique des minéraux argileux

The ${}^{87}\text{Sr}{}^{86}\text{Sr}$ ratio of interstitial waters squeezed from recent sediments of the Pacific Ocean increases from 0.70920 ± 0.00017 (2σ) to 0.70960 ± 0.0023 and 0.70984 ± 0.00040 at 1.50 and 1.60 m depth—reference value for sea water: 0.70910 ± 0.00035. This variation underlines the likely existence of exchanges between the clays and the interstitial environment. The isotopic homogenization of strontium between the clays and their environment, result of these changes, becomes thus a credible phenomenon. This is a new argument for the dating of clays by the $\text{Rb}\text{Sr}$ method.     

Rythme sedimentaire et mineralisations stratiformes dans l'environnement recifal

During the International Sedimentological Congress of Heidelberg (Germany), the author — in collaboration with his college J.Pel of the University of Liege (Belgium) — has emphasized the influence of the sedimentary rhythm about the location of the stratiform ore deposits in some facies of the reef environment and has proposed a first synthesis of the relations between several stratiform deposits of varying mineralogy and different ages also associated with reef complexes. In this paper, the author illustrates the sedimentological method used previously in resting principally on a comparative analysis of the ore conditions which characterize the stratiform lead zinc deposits of Reocin (Spain), Eastern Alps (Bavaria, Austria), Pine Point (Canada) and S. E. Missouri (United States).     

Un réseau fluviatile d'âge Burdigalien terminal dans le Sud-Est de la France : remplissage,extension, âge,implications

An integrated study combining facies analysis, multiple group biostratigraphy, identification of depositional sequences and mapping has been conducted on the Miocene Molasse Basin of the external Alps (southeastern France). The filling of the basin is described as resulting from a succession of fluvial incisions subsequently filled during marine transgressions. The major incision is dated as Latest Burdigalian and the major transgression as Langhian. This revised interpretation of the Miocene physiographic evolution of the Molasse Basin implies a re-examination of previous stratigraphic correlations within the basin. To cite this article: D. Besson et al., C. R. Geoscience 337 (2005).     

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.     

Non-linear soil–structure interaction analysis based on the boundary-element method in time domain with application to embedded foundation

The various boundary-element methods, well established in the frequency domain, are developed in the time domain for a foundation embedded in a layered halfspace. They are the weighted-residual technique and the indirect boundary-element method, based on a weighted-residual equation, and the direct boundary-element method based on a reciprocity equation, both equations involving time and space. In the indirect approach, formulating the weighted-residual equation over the last time step only results in the truncated indirect boundary-element formulation which requires a reduced computational effort. In all cases, convolution integrals occur. The truncated indirect boundary-element method leads to a highly reliable algorithm, as is verified when a linear analysis in the time domain is compared to the corresponding one in the frequency domain. This boundary-element formulation, which is non-local in space and time, represents a rigorous generally applicable method taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basemat and separation of the side wall is investigated.