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.     

巴基斯坦北Potwar形变区地震的震源机制研究

巴基斯坦北Potwar形变区是西北喜马拉雅褶皱逆冲带前陆区的一部分，绘制了该区的地震活动性图. 与相邻地区比较，该区地震并不活跃，没有显示出与地表地质构造相关的清晰地震活动图象. 做出了4次地震的震源机制解. 结果表明，有3次地震是左旋走滑断层活动，另一次地震是逆断层活动. 地震震源机制解的P轴方向为NW-SE和NE-SW. 现今的构造形变很可能也包括基底的形变.      

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.     

Inferring the mass fraction of floc-deposited mud: application to fine-grained turbidites

Fine sediment deposition in the ocean is complicated by the cohesive nature of muds and their tendency to flocculate. The result is disaggregated inorganic grain size (DIGS) distributions of bottom sediment that are influenced by single‐grain and floc deposition. This study outlines a parametric model that characterizes bottom sediment DIGS distributions. Modelled parameters are then used to infer depositional conditions that account for the regional variation in the grain sizes deposited by turbidity currents on the Laurentian Fan–Sohm Abyssal Plain, offshore south‐eastern Canada. Results indicate that, on the channellized Laurentian Fan, the mass fraction of floc‐deposited mud increases only slightly downslope. The small evolution in this fraction arises because sediment concentration and turbulent energy are associated in turbidity currents. On the Sohm Abyssal Plain, however, the mass fraction of floc‐deposited mud decreases, probably as a result of lower sediment concentration at this source‐distal site. Estimates of the mass fraction of mud deposited as flocs suggest that floc deposition is the dominant mode by which sediment is lost from suspension, although single‐grain deposition contributes more to the depositional flux in proximal areas where high energy breaks flocs and in distal areas where low sediment concentration limits floc formation. It is concluded that, throughout the dispersal system, changes in the fraction of flocculated mud deposited from turbidity currents reflect changes in sediment concentration and energy downslope.     

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.     

Spatially controlled Fe and Si isotope variations: an alternative view on the formation of the Torres del Paine pluton

We present new Fe and Si isotope ratio data for the Torres del Paine igneous complex in southern Chile. The multi-composition pluton consists of an approximately 1 km vertical exposure of homogenous granite overlying a contemporaneous 250-m-thick mafic gabbro suite. This first-of-its-kind spatially dependent Fe and Si isotope investigation of a convergent margin-related pluton aims to understand the nature of granite and silicic igneous rock formation. Results collected by MC-ICP-MS show a trend of increasing δ⁵⁶Fe and δ³⁰Si with increasing silica content as well as a systematic increase in δ⁵⁶Fe away from the mafic base of the pluton. The marginal Torres del Paine granites have heavier Fe isotope signatures (δ⁵⁶Fe = +0.25 ± 0.02 2se) compared to granites found in the interior pluton (δ⁵⁶Fe = +0.17 ± 0.02 2se). Cerro Toro country rock values are isotopically light in both Fe and Si isotopic systems (δ⁵⁶Fe = +0.05 ± 0.02 ‰; δ³⁰Si = ?0.38 ± 0.07 ‰). The variations in the Fe and Si isotopic data cannot be accounted for by local assimilation of the wall rocks, in situ fractional crystallization, late-stage fluid exsolution or some combination of these processes. Instead, we conclude that thermal diffusion or source magma variation is the most likely process producing Fe isotope ratio variations in the Torres del Paine pluton.     

Biogenic volatile compound emissions from a temperate forest,China: model simulation

Emissions of biogenic volatile organic compounds (BVOC) were measured using a relaxed eddy accumulation (REA) technique on an above-canopy tower in a temperate forest (Changbai Mountain, Jilin province, China) during the 2010 and 2011 summer seasons. Solar global radiation and photosynthetically active radiation (PAR) were also measured. Based on PAR energy dynamic balance, an empirical BVOC emission and PAR transfer model was developed that includes the processes of BVOC emissions and PAR transfer above the canopy level, including PAR absorption and consumption, and scattering by gases, liquids, and particles (GLPs). Simulated emissions of isoprene and monoterpenes were in agreement with observations. The averages of the relative estimator biases for the flux were 39.3 % for isoprene, and 27.1 % for monoterpenes in the 2010 and 2011 growing seasons, with NMSE (normalized mean square error) values of 0.133 and 0.101, respectively. The observed and simulated mean diurnal variations of isoprene and monoterpenes in the 2010 and 2011 growing seasons were evaluated for the validation of the empirical model. Under observed atmospheric conditions, the sensitivity analysis showed that emissions of isoprene and monoterpenes were more sensitive to changes in PAR than to water vapor content or to the magnitude of the scattering factor. The emissions of isoprene and monoterpenes in the 2010 and 2011 growing seasons (from June to September) were estimated using this empirical model along with hourly observational data, with mean hourly emissions of 1.71 and 1.55 mg m^?2 h^?1 for isoprene, and 0.48 and 0.47 mg m^?2 h^?1 for monoterpenes in 2010 and 2011, respectively. As formaldehyde (HCHO) is considered as the main oxidation product of isoprene and monoterpenes, it is necessary to investigate the link between HCHO and BVOC emissions. GOME-2 HCHO vertical column densities (VCDs) can be used to estimate BVOC emission fluxes in the Changbai Mountain temperate forest.