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.     

Land subsidence and caprock dolines caused by subsurface gypsum dissolution and the effect of subsidence on the fluvial system in the Upper Tigris Basin (between Bismil–Batman, Turkey)

Karstification-based land subsidence was found in the Upper Tigris Basin with dimensions not seen anywhere else in Turkey. The area of land subsidence, where there are secondary and tertiary subsidence developments, reaches 140 km². Subsidence depth ranges between 40 and 70 m. The subsidence was formed as a result of subsurface gypsum dissolution in Lower Miocene formation. Although there are limestones together with gypsum and Eocene limestone below them in the area, a subsidence with such a large area is indicative of karstification in the gypsum. The stratigraphical cross-sections taken from the wells and the water analyses also verify this fact. The Lower Miocene gypsum, which shows confined aquifer features, was completely dissolved by the aggressive waters injected from the top and discharged through by Zellek Fault. This resulted in the development of subsidence and formation of caprock dolines on loosely textured Upper Miocene–Pliocene cover formations. The Tigris River runs through the subsidence area between Batman and Bismil. There are four terrace levels as T1 (40 m), T2 (30 m), T3 (10 m) and T4 (4–5 m) in the Tigris River valley. It was also found that there were some movements of the levels of the terraces in the valley by subsidence. The subsidence developed gradually throughout the Quaternary; however no terrace was formed purely because of subsidence.     

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.     

Lateglacial vegetation and palaeoenvironment in W Norway,with new pollen data from the Sunnmøre region

Krüger, L. C., Paus, A., Svendsen, J. I. & Bjune, A. E. 2011: Lateglacial vegetation and palaeoenvironment in W Norway, with new pollen data from the Sunnmøre region. Boreas, 10.1111/j.1502‐3885.2011.00213.x. ISSN 0300‐9483. Two sediment sequences from Sunnmøre, northern W Norway, were pollen‐analytically studied to reconstruct the Lateglacial vegetation history and climate. The coastal Dimnamyra was deglaciated around 15.3 ka BP, whereas Løkjingsmyra, further inland, became ice‐free around 14 ka BP. The pioneer vegetation dominated by snow‐bed communities was gradually replaced by grassland and sparse heath vegetation. A pronounced peak in Poaceae around 12.9 ka BP may reflect warmer and/or drier conditions. The Younger Dryas (YD) cooling phase shows increasing snow‐bed vegetation and the local establishment of Artemisia norvegica. A subsequent vegetation closure from grassland to heath signals the Holocene warming. Birch forests were established 500–600 years after the YD–Holocene transition. This development follows the pattern of the Sunnmøre region, which is clearly different from the Empetrum dominance in the Lateglacial interstadial further south in W Norway. The Lateglacial oscillations GI‐1d (Older Dryas) and GI‐1b (Gerzensee) are hardly traceable in the north, in contrast to southern W Norway. The southern vegetation was probably closer to an ecotone and more susceptible to climate changes.