Calculating the two-dimensional magnetotelluric Jacobian in finite elements using reciprocity

To speed up the calculation of the field Jacobian for 2-D magnetoteliuric inversion using finite elements, the principle of electromagnetic reciprocity is applied. The governing relationship for the Jacobian of the field along strike is obtained by differentiating the Helmholtz equation with respect to the resistivity of each region in the finite-element mesh. The result is a similar Helmholtz equation for the Jacobian, with new sources distributed over all nodes within the parameter medium. However, according to the principle of electromagnetic reciprocity, the roles of sources and receivers are interchangeable. Utilizing reciprocity, the field values obtained from the original forward problem and for new unit sources imposed at the receivers are then utilized in the calculation of the Jacobian by simple multiplication and summation with finite-element terms at each rectangle in the mesh. For the auxiliary (across-strike) fields, the Jacobian terms are obtained by solving source vectors loaded with parabola coefficients used in the approximation to Maxwell's equations. Jacobian terms for the apparent resistivity ( p _a), the impedance phase (φ) and the vertical magnetic field ( K _zy) are then calculated utilizing the parallel- and auxiliary-field Jacobians. Comparison of Jacobian values obtained from reciprocity calculations and by differencing two forward solutions show that the reciprocity method is accurate and can be used to decrease the number of calculations required to obtain sensitivities by one to two orders of magnitude.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

The conditionality of status: Experience-based reflections on the insider/outsider issue

When a researcher undertakes research into his/her own ethnic group, issues of positionality abound. These issues relate not only to the impact of inherent insider positionality when interacting with study participants but also in the interpretation and presentation of study findings. My research with contemporary Irish immigrants not only reinforced the advantages of being an insider but also highlighted the incomplete and unstable nature of insiderness. Heterogeneity within the study group, in terms of their geo-political, regional and religious origins, meant that presumptions of insiderness and outsiderness were frequently challenged. A new awareness of the conditionality of each positionality was forged from these experiences.     

Profondeur d'extraction racinaire et signature isotopique de l'eau prélevée par les racines des couverts végétaux

We seek to identify the depth to which water is extracted by the roots in the soil. Indeed, in an isotopic steady-state condition of leaf water, transpiration introduces into the atmosphere a vapour whose isotopic signature is identical to that of root water. In the isotopic models of atmospheric general circulation, it is classically allowed that the signature of transpiration belongs to the meteoric water line. This supposes that the water taken by the roots has escaped with the evaporation of the soil and comes thus from the deep layers of the soil. At the time of experimentation carried out on maize plants (Nemours, Seine-et-Marne, France), this extraction depth was inferred from the comparison between the signature of the water measured on the level of the first internode of the stems of the plants and the isotopic profile of water in the soil. When the flow of transpiration reaches a maximum value, the plant uptakes water resulting from precipitations and which preserves its non-evaporating character after having quickly infiltrated in the deep layers of the soil. This relates to only 55% of the flux transpired by the canopy, the remainder presenting an evaporating character more or less marked according to ambient conditions. This experiment invalidates the classical hypothesis used in isotopic models of general atmospheric circulation in temperate regions. In fact, only half the amount of water vapour transpired by the canopy during the day presents a signature similar to that of the rainwater sampled in deep soil layers. To cite this article: Z. Boujamlaoui et al., C. R. Geoscience 337 (2005).     

Tetrahedral Plots of the Phase Relations for Basalts

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.