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.     

Exploration Indices and Mineral Potential Map of the Kuroko Deposits in Northeast Japan

Abstract. Recent discoveries of seafloor hydrothermal mineralization in submarine volcanic centers of felsic magma in western Pacific island arcs are regarded as modern analogues of Kuroko type deposits. Studies of these deposits and their surrounding geology raised question whether the exploration activity for the Kuroko deposits on land which peaked in the 1960's was adequate or not. However, such an evaluation is not easy because the exploration data are about to be lost as a result of the closure of all the Kuroko mines in the area since 1994.
The Metal Mining Agency of Japan (MMAJ), therefore, decided to compile existing data on about 180 Kuroko deposits and related mineral occurrences in northeast Japan as a new Kuroko database.
This study extends a concept called "exploration indices" which was developed based on a case study of the thoroughly surveyed Hokuroku district to draw a potential map of the Kuroko occurrences for the entire northeast Japan quantitatively with a Geographical Information System (GIS). Effective exploration indices include: 1) distribution of dacitic-rhy-olitic submarine volcanic rocks of the Nishikurosawa and Onnagawa stages, 2) distribution of intrusive rocks of pre- and post-Kuroko horizon, 3) low aeromagnetic anomaly caused by hydrothermal alteration of magnetite, 4) low gravity anomaly which suggests depressions in the basement rocks such as a tectonic basin and/or caldera, and 5) nearby existence of vein type deposits. It is concluded that about 33 % of known Kuroko deposits fall within the high potential zone (score=4 and 5) that occupies only 4 % of the entire northeast Japan arc. The Kuroko potential map is, therefore, useful for limiting the target area for Kuroko type deposits in an island arc setting.     

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.     

Tropical synoptic-scale wave disturbances over the western Pacific simulated by a global cloud-system resolving model

Lower-tropospheric tropical synoptic-scale disturbances (TSDs) are associated with severe weather systems in the Asian Monsoon region. Therefore, exact prediction of the development and behavior of TSDs using atmospheric general circulation models is expected to improve weather forecasting for this region. Recent state-of-the art global cloud-system resolving modeling approaches using a Nonhydrostatic Icosahedral Atmospheric Model (NICAM) may improve representation of TSDs. This study evaluates TSDs over the western Pacific in output from an Atmospheric Model Intercomparison Project (AMIP)-like control experiment using NICAM. Data analysis compared the simulated and observed fields. NICAM successfully simulates the average activity, three-dimensional structures, and characteristics of the TSDs during the Northern summer. The variance statistics and spectral analysis showed that the average activity of the simulated TSDs over the western Pacific during Northern summer broadly captures that of observations. The composite analysis revealed that the structures of the simulated TSDs resemble the observed TSDs to a large degree. The simulated TSDs exhibited a typical southeast- to northwest-oriented wave-train pattern that propagates northwestward from near the equator around 150 ^° E toward the southern coast of China. However, the location of the simulated wave train and wave activity center was displaced northward by approximately a few degrees of latitude from that in the observation. This displacement can be attributed to the structure and strength of the background basic flow in the simulated fields. Better representation of the background basic states is required for more successful simulation of TSDs.     

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.