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.     

Remote sensing detection of atmospheric pollutants by differential absorption LIDAR 510M/SODAR PA2 mobile system

Summary Air pollution problem in the Czech Republic is very complex due to large number of factors as turbulent dispersion and chemical reactions concurring in the status of the PBL. For this 3D distribution of pollutants is a key information that cannot be given by conventional monitoring stations. Combined use of DIAL lidar and sodar can give access to such information. Case studies of air pollutants transport are presented using 3D concentration fields of NO₂ and ozone measured by lidar and meteorological conditions monitored by Doppler Sodar.     

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.     

Complete Tertiary exhumation history of the Menderes massif, western Turkey: an alternative working hypothesis

The main exhumation of the Menderes massif, western Turkey, occurred along an originally N‐dipping Datça–Kale main breakaway fault that controlled depositions in the Kale and the Gökova basins during the Oligocene – Early Miocene interval. The isostatically controlled upward bending of the main breakaway fault brings the lower plate rocks to the surface. In the Early Miocene, E–W‐trending N‐ and S‐dipping graben‐bounding faults fragmented the exhumed, dome‐shaped massif. The development of half grabens by rolling master fault hinges has allowed further exhumation of the central Menderes massif. After the Pliocene, high‐angle normal faults cut all of the previous structures. This model suggests that the Menderes massif is a single large metamorphic core complex that has experienced a two‐stage exhumation process.     

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.     

Diamond in metasedimentary crustal rocks from Pohorje,Eastern Alps: a window to deep continental subduction

We report the first finding of diamond and moissanite in metasedimentary crustal rocks of Pohorje Mountains (Slovenia) in the Austroalpine ultrahigh‐pressure (UHP) metamorphic terrane of the Eastern Alps. Microscopic observations and Raman spectroscopy show that diamond occurs in situ as inclusions in garnet, being heterogeneously distributed. Under the optical microscope, diamond‐bearing inclusions are of cuboidal to rounded shape and of pinkish, yellow to brownish colour. The Raman spectra of the investigated diamond show a sharp, first order peak of sp³‐bonded carbon, in most cases centred between 1332 and 1330 cm^?1, with a full width at half maximum between 3 and 5 cm^?1. Several spectra show Raman bands typical for disordered graphitic (sp²‐bonded) carbon. Detailed observations show that diamond occurs either as a monomineralic, single‐crystal inclusion or it is associated with SiC (moissanite), CO₂ and CH₄ in polyphase inclusions_. This rare record of diamond occurring with moissanite as fluid‐inclusion daughter minerals implies the crystallization of diamond and moissanite from a supercritical fluid at reducing conditions. Thermodynamic modelling suggests that diamond‐bearing gneisses attained P–T conditions of ≥3.5 GPa and 800–850 °C, similar to eclogites and garnet peridotites. We argue that diamond formed when carbonaceous sediment underwent UHP metamorphism at mantle depth exceeding 100 km during continental subduction in the Late Cretaceous (c. 95–92 Ma). The finding of diamond confirms UHP metamorphism in the Pohorje Mountains, the most deeply subducted part of Austroalpine units.