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.     

Seismic horizontal pullout capacity of shallow vertical anchors in sand

The concept of the equivalent free surface has been extended to determine the seismic horizontal pullout capacity of shallow vertical strip plate anchors buried in sand. The analysis has been done rigorously by using the method of stress characteristics. The results have been expressed in the form of non-dimensional charts. The pullout resistance has been found to reduce quite extensively with increase in the magnitude of horizontal earthquake acceleration. The results were compared with the previously published data, and it was seen that the computed pullout resistance with the proposed method was found to be lowest. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mechanism of arrested charnockite formation at Nemmara, Palghat region, southern India

The formation of arrested charnockite is an excellent example of structurally controlled channellised fluid flow along specific sites accompanied by selective elemental mobility and mineralogical changes. The present paper recognises and focuses study on three types of arrested charnockite formation from Palghat region, namely, shear-controlled, foliation parallel and boudin-neck types, and address their spatio-temporal relations to regional-scale charnoenderbite. The shear-controlled and foliation parallel types post-date deformation and migmatisation. The boudin-neck type, on the contrary, is coeval with partial melting and followed the path of cooling and decreasing water activity in the gneiss. K-feldspar veining around plagioclase and quartz, symplectitic intergrowth of biotite+quartz after orthopyroxene and K-feldspar, and fluid inclusion data suggests the presence of alkalic supercritical brine and low-density CO₂-rich fluid during charnockite formation. Charnockite domains developed following the breakdown of hornblende, biotite and quartz are characterised by a more or less pronounced depletion of Fe, Ca, Mg and Ti and trace elements Y and Zr, compared to their counterpart gneiss. REE spectra indicate a subtle depletion in the HREE near the centre of the charnockite domain. Although close-pair samples of gneiss–charnockite are isochemical, on a scale of a few millimetres, bi-directional element movement, related to the formation of new mineral was noted. It is postulated that arrested charnockite formation developed in situ on local scale within the granitic domains of the hornblende-biotite gneiss, in the presence of CO₂-rich fluids and alkalic supercritical saline brine. This process post-dated the time of regional granulite (charnoenderbite) and large regional scale retrogression and migmatisation.     

Hydrography of the eastern Arabian Sea during summer monsoon 2002

Hydrographic observations in the eastern Arabian Sea (EAS) during summer monsoon 2002 (during the first phase of the Arabian Sea Monsoon Experiment (ARMEX)) include two approximately fortnight-long CTD time series. A barrier layer was observed occasionally during the two time series. These ephemeral barrier layers were caused byin situ rainfall, and by advection of low-salinity (high-salinity) waters at the surface (below the surface mixed layer). These barrier layers were advected away from the source region by the West India Coastal Current and had no discernible effect on the sea surface temperature. The three high-salinity water masses, the Arabian Sea High Salinity Water (ASHSW), Persian Gulf Water (PGW), and Red Sea Water (RSW), and the Arabian Sea Salinity Minimum also exhibited intermittency: they appeared and disappeared during the time series. The concentration of the ASHSW, PGW, and RSW decreased equatorward, and that of the RSW also decreased offshore. The observations suggest that the RSW is advected equatorward along the continental slope off the Indian west coast.     

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.