Multi-Scale Texture Modeling

Patterns of crystallographic preferred orientation are referred to as texture. The specific subject of texture analysis is the experimental determination and interpretation of the statistical distribution of orientations of crystals within a specimen of polycrystalline material, which could be metals or rocks. The objective is to relate an observed pattern of preferred orientation to its generating processes and vice versa. In geosciences, texture of minerals in rocks is used to infer constraints on their tectono-metamorphic history. Since most physical properties of crystals, such as elastic moduli, the coefficients of thermal expansion, or chemical resistance to etching depends on crystal symmetry and orientation, the presence of texture imparts directional properties to the polycrystalline material. A major issue of mathematical texture analysis is the resolution of the inverse problem to determine a reasonable orientation density function on SO(3) from measured pole intensities on , which relates to the inverse of the totally geodesic Radon transform. This communication introduces a wavelet approach into mathematical texture analysis. Wavelets on the two-dimensional sphere and on the rotational group SO(3) are discussed, and an algorithms for a wavelet decomposition on both domains following the ideas of Ta-Hsin Li is given. The relationship of these wavelets on both domains with respect to the totally geodesic Radon transform is investigated. In particular, it is shown that the Radon transform of these wavelets on SO(3) are again wavelets on . A novel algorithm for the inversion of experimental pole intensities to an orientation density function based on this relationship is developed.     

Dynamics of the mid-ocean ridge plate boundary: Recent observations and theory

The global mid-ocean ridge system is one of the most active plate boundaries on the earth and understanding the dynamic processes at this plate boundary is one of the most important problems in geodynamics. In this paper I present recent results of several aspects of mid-ocean ridge studies concerning the dynamics of oceanic lithosphere at these diverging plate boundaries. I show that the observed rift valley to no-rift valley transition (globally due to the increase of spreading rate or locally due to the crustal thickness variations and/or thermal anomalies) can be explained by the strong temperature dependence of the power law rheology of the oceanic lithosphere, and most importantly, by the difference in the rheological behavior of the oceanic crust from the underlying mantle. The effect of this weaker lower crust on ridge dynamics is mainly influenced by spreading rate and crustal thickness variations. The accumulated strain pattern from a recently developed lens model, based on recent seismic observations, was proposed as an appealing mechanism for the observed gabbro layering sequence in the Oman Ophiolite. It is now known that the mid-ocean ridges at all spreading rates are offset into individual spreading segments by both transform and nontransform discontinuities. The tectonics of ridge segmentation are also spreading-rate dependent: the slow-spreading Mid-Atlantic Ridge is characterized by distinct bulls-eye shaped gravity lows, suggesting large along-axis variations in melt production and crustal thickness, whereas the fast-spreading East-Pacific Rise is associated with much smaller along-axis variations. These spreading-rate dependent changes have been attributed to a fundamental differences in ridge segmentation mechanisms and mantle upwelling at mid-ocean ridges: the mantle upwelling may be intrinsically plume-like (3-D) beneath a slow-spreading ridge but more sheet-like (2-D) beneath a fast-spreading ridge.     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.     

极性转换期间地球磁场形态学研究

本文对采自中国黄土高原西峰（35.7°N,107.6°E）和段家坡（34.2°N,109.2°E）两个剖面中黄土层L8和古土壤层S8的1281块定向古地磁样品做了详细的岩石磁学和古地磁学研究.证实了Matuyama-Brunhes（M-B）极性转换带位于L8的中下部.提出了下列观点:1.M-B极性转换过程与地球磁场方向变化相联系的持续时间为3600-4500a,而与地球磁场强度变化相联系的持续时间则为8000-9000a,即强度变化存在“超前和滞后” 效应;2.M-B转换场的形态是由三次快速倒转和一次不成功的倒转构成,或者说,转换场具有快速变换极性的振荡特征;3.M-B转换过程中地球磁场并不是以轴对称的非偶极子场为主,而是偶极子场至少与非偶极子场相当;4.中国黄土-古土壤沉积物所含磁性矿物的主要成分是磁铁矿,它是研究极性转换期间地球磁场详细结构的良好物质.     

碳中和目标下关键矿产在清洁能源转型中的作用、供需分析及其建议

在"碳中和"目标的驱动下，全球能源系统向清洁化、低碳化甚至无碳化发展已是大势所趋。针对向清洁能源转型的需求，采用了统计对比、分类汇总、综合分析等方法，分析研究了关键矿产在电池、电网、低碳发电和氢能等行业中的作用和需求。结合当前关键矿产产量的地理集中度高、项目开发周期长、资源质量下降等矿产供应和投资计划不能满足清洁能源转型的需求等问题，提出确保关键矿产多样性供应，推动价值链各环节的技术创新，扩大回收利用，增强供应链弹性和市场透明度，将更高的环境、社会和治理标准纳入主流程及加强生产者和消费者之间的国际合作等建议。     

使用价值分析优化方法在功能—技术矩阵求解中的应用

功能—技术矩阵,经众多工作者的努力研究,已渐趋成熟与实用。但如何利用功能—技术矩阵构造在广义现代设计领域中适用的科学模式,解决多学科设计方案的组成与评价问题,还存在薄弱环节。本文利用“使用价值分析优化”的概念,从设计方案技术先进性和经济合理性的协调统一的角度出发,较好地实现了功能—技术矩阵可行优化组合链的组成与评价,弥补了以往的缺陷。     

Comparative Seismic Risk Studies for German Earthquake Regions on the Basis of the European Macroseismic Scale EMS-98

Within the framework of recent research projects, basic tools for GIS-based seismic risk assessment technologies were developed and applied to the building stock and regional particularities of German earthquake regions. Two study areas are investigated, being comparable by the level of seismic hazard and the hazard-consistent scenario events (related to mean return periods of 475, 2475 and 10000 years). Significant differences exist with respect to the number of inhabitants, the grade and extent of urbanisation, the quality and quantity of building inventory: the case study of Schmölln in Eastern Thuringia seems to be representative for the majority of smaller towns in Germany, the case study of Cologne (Köln) stands for larger cities. Due to the similarities of hazard and scenario intensities, the considerable differences do not only require proper decisions concerning the appropriate methods and acceptable efforts, they enable conclusions about future research strategies and needs for disaster reduction management. Not least important, results can sharpen the focus of public interest. Seismic risk maps are prepared for different scenario intensities recognising the scatter and uncertainties of site-dependent ground motion and also of the applied vulnerability functions. The paper illustrates the impact of model assumptions and the step-wise refinements of input variables like site conditions, building stock or vulnerability functions on the distribution of expected building damage within the study areas. Furthermore, and in contrast to common research strategies, results support the conclusion that in the case of stronger earthquakes the damage will be of higher concentration within smaller cities like Schmölln due to the site-amplification potential and/or the increased vulnerability of the building stock. The extent of damage will be pronounced by the large number of masonry buildings for which lower vulnerability classes have to be assigned. Due to the effect of deep sedimentary layers and the composition of building types, the urban centre of Cologne will be less affected by an earthquake of comparable intensity.     

The First Appearance of Cattle in Denmark Occurred 6000 Years Ago: An Effect of Cultural or Climate and Environmental Changes

Stable carbon and nitrogen isotope ratios from bones of contemporaneous Late Atlantic aurochs and early cattle in eastern Denmark are significantly different and provide information on the origin and feeding strategies of the earliest domestic cattle. The data show that the early cattle were feeding on grass right from the beginning 4000 cal. yr BC. In contrast, the youngest aurochs population primarily browsed and grazed from the dense forest floor resulting in rather negative δ¹³C values measured on bone collagen. The oldest aurochs have similar isotope values to the earlier cattle, whereas the youngest aurochs have similar values to Late Atlantic red deer from the same locality. As eastern Denmark was largely covered by forest, speculations on the origin of the grazing areas are many. The grass may have grown in openings in the forest, at the forest fringe, or more likely on the newly reclaimed coastal land areas exposed by the decreasing rate of eustatic sea‐level rise contemporaneously with isostatic uplift, during the Littorina transgressions. The stable isotope values do not indicate that leaf foddering of the early cattle was of importance.