Multiple prediction using the homeomorphic-imaging technique

A new method for predicting different kinds of multiples and peg-leg reflections in unstacked seismic data is discussed. The basis for this method is the fact that kinematic properties of multiples can be represented as a combination of kinematic properties of primary reflections. The prediction is made using a two-step process. In the first step, the values for the angle of emergence and radius of curvature of the wavefront for primary reflections from ‘multiple-generating’ interfaces are obtained. These parameters are estimated directly from unstacked data for every source point using the homeomorphic-imaging technique. The second step consists of prediction of multiples from primary reflections that satisfy a so-called ‘multiple condition’. This condition is the equality of the absolute values of the angles of emergence calculated from the first step. This method is effective even in complex media and information on the subsurface geology is not required. The parameters are estimated directly from the unstacked data and do not require any computational efforts such as in wavefield extrapolation of data.     

Anisotropic reflection coefficients for a weak-contrast interface

In this article the interaction of plane waves with a weak-contrast interface between two weakly anisotropic half-spaces is investigated. The anisotropy dealt with is of a general type. The stress–displacement vectors of the plane waves are calculated by perturbation theory. By assuming that the jump in elastic parameters and density across the interface is small, one can derive a simple expression for the R _qPqP coefficient. In cases in which the wave motion is restricted to a symmetry plane of an anisotropic medium, simple expressions for the R _qSVqSV and R _SHSH coefficients are also derived.     

An extended Ideal Resonance Problem

An Extended Resonance Problem is defined by the Hamiltonian, $$F = B(y) + 2\mu ^2 A(y)[\sin x + \lambda (y)]^2 \mu<< 1,\lambda = O(\mu ).$$ It is noted here that the phase-plane trajectories exhibit adouble libration, enclosing two centers, for the initial conditions of motion satisfying the inequality $$1 - |\lambda |< |\alpha |< 1 + |\lambda |,$$ where α is the usualresonance parameter. A first order solution for the case of double libration is constructed here by a generalization of the procedure previously used in solving the Ideal Resonance Problem with λ=0. The solution furnishes a reference orbit for a Perturbed Ideal Problem if a double libration occurs as a result of perturbations.     

The ‘naked’ singularity in the scalar-tensor gravitation theory

The complete analysis of possible types of non-relativistic and ultra-relativistic motions in the field of the naked singularity of the STGT is given. The problem of the infall of a monochromatic radiation emitter on the naked singularity is studied. In spite of the absence of a freezing effect in the STGT, the naked singularity is not observable, for the brightness of the falling emitter decreases much faster than in the GTR. Atrr _g , the trajectory of particles and light are quite similar to that of the GTR, and due to this fact the naked singularity is observationally indistinguishable from a black hole.     

Theory of the Trojan asteroids Part II

In the previously published (1977a) Part I of the paper, the author has constructed a formal long-periodic solution for the case of 1:1 resonance in the restricted problem of three bodies. Here the accuracy of the solution is carried fromO(m) toO(m ^3/2), wherem is the mass parameter of the system.Asymptotic approximations for the period of the motion are obtained for the case of small oscillations about the Lagrangian pointL ₄, in agreement with the classical theory, and for the vicinity of a logarithmic singularity on themean separatrix, passing throughL ₃. The regularizing function (), which removes the singularities of the Poincaré type, is extended to all orders, and the result is used to prove the periodicity of the solution.     

Physico-chemical study of dead sea waters. III. On gypsum saturation in Dead Sea waters and their mixtures with Mediterranean Sea water

Gypsum solubility in mixtures of Dead Sea and Mediterranean Sea waters at different ratios and in their concentrates obtained by evaporation simulation have been calculated using the Pitzer model as formulated by Harvie and Weare (1980). The results obtained are compared with available experimental gypsum solubility data in different natural brines, sea water, sea water concentrates and NaCl solutions. The agreement between theoretically calculated and experimental solubility values is fairly good and is within the range of scatter of the individual solubility measurements.     

The role of the Pernicana Fault System in the spreading of Mt. Etna (Italy) during the 2002–2003 eruption

Flank instability and collapse are observed at many volcanoes. Among these, Mt. Etna is characterized by the spreading of its eastern and southern flanks. The eastern spreading area is bordered to the north by the E–W-trending Pernicana Fault System (PFS). During the 2002–2003 Etna eruption, ground fracturing along the PFS migrated eastward from the NE Rift, to as far as the 18 km distant coastline. The deformation consisted of dextral en-echelon segments, with sinistral and normal kinematics. Both of these components of displacement were one order of magnitude larger (~1 m) in the western, previously known, portion of the PFS with respect to the newly surveyed (~9 km long) eastern section (~0.1 m). This eastern section is located along a pre-existing, but previously unknown, fault, where displaced man-made structures give overall slip rates (1–1.9 cm/year), only slightly lower than those calculated for the western portion (1.4–2.3 cm/year). After an initial rapid motion during the first days of the 2002–2003 eruption, movement of the western portion of the PFS decreased dramatically, while parts of the eastern portion continued to move. These data suggest a model of spreading of the eastern flank of Etna along the PFS, characterized by eruptions along the NE Rift, instantaneous, short-lived, meter-scale displacements along the western PFS and more long-lived centimeter-scale displacements along the eastern PFS. The surface deformation then migrated southwards, reactivating, one after the other, the NNW–SSE-trending Timpe and Trecastagni faults, with displacements of ~0.1 and ~0.04 m, respectively. These structures, along with the PFS, mark the boundaries of two adjacent blocks, moving at different times and rates. The new extent of the PFS and previous activity over its full length indicate that the sliding eastern flank extends well below the Ionian Sea. The clustering of seismic activity above 4 km b.s.l. during the eruption suggests a deep décollement for the moving mass. The collected data thus suggests a significant movement (volume >1,100 km³) of the eastern flank of Etna, both on-shore and off-shore.Editorial responsibility: R. Cioni     

Experimental study of the stability of aluminate-borate complexes in hydrothermal solutions

Formation of aqueous aluminate-borate complexes was characterized at 25°C using ²⁷Al NMR spectroscopy, and at 50-200°C via measurements of gibbsite and boehmite solubility in the presence of boric acid. ²⁷Al spectra performed at pH = 9 in Al-B solution with m(B) = 0.02 show the presence of two peaks at 80.5 and 74.5 ppm which correspond to Al(OH)₄⁻ and a single Al-substituted Q¹_Al dimer, Al(OH)₃OB(OH)₂⁻, respectively. In 0.08 m and 0.2 m borate solution, a third peak appears at 68.5 ppm which can be assigned to the Q²_Al trimer Al(OH)₂O₂(B(OH)₂)₂⁻. These chemical shifts are close to those measured for Al(OH)₃OSi(OH)₃⁻ and Al(OH)₂O₂(Si(OH)₃)₂⁻ (74 and 69.5 ppm, respectively; Pokrovski et al., Min. Mag.62a (1998), 1194) which demonstrates the similar structure of Al-B and Al-Si complexes formed in alkaline solutions. Gibbsite and boehmite solubility were measured in weakly basic solutions as a function of boric acid concentration at 50°C and 78 to 200°C, respectively. Equilibrium was reached within several days at m(B) = 0.01-0.1, but more slowly at higher boron concentrations, and at 50°C and m(B) = 0.2, Al concentration increased continuously during at least 3 months as a result of the sluggish formation of Al-polyborates. The equilibrium constant of the reaction Al(OH)₄⁻ + B(OH)₃⁰_(aq) = Al(OH)₃OB(OH)₂⁻ + H₂O decreases very slowly with increasing temperature to 200°C. The log K values are 1.58 ± 0.10, 1.46 ± 0.10, 1.52 ± 0.15, and 1.25 ± 0.15 at 50, 78, 150 and 200°C, respectively, which result in the following values of the standard thermodynamic properties for this reaction: Δ_rG⁰ = −9.22 ± 3.25 kJ/mol, Δ_rH⁰ = −4.6 ± 2.5 kJ/mol, Δ_rS⁰ = 15.5 ± 6.9 J/mol K. The thermodynamic data generated in this study indicate that Al-B complexes can dominate aqueous aluminum speciation in solutions containing ≥0.7 g/L of boron at temperature to at least 400°C.     

Rôle des héritages latéritiques et du niveau des nappes dans l'évolution des modelés et des sols en zone intertropicale forestière humide

Analysis of landscapes and soil covers from the outer to the inner part of a $75\text{km}\times 60\text{km}$ watershed in the South-Cameroon rainforest zone, characterized by important remnants of inherited ferricretes and stable hydrostatic base levels, indicates that the development of present landforms has not involved significant erosion by slope retreat because of the relative preservation of downslope residual ferricrete and that soil covers have vertically decayed under in situ geochemical process. To cite this article: D. Bitom et al., C. R. Geoscience 336 (2004).