Scale Effect on Principal Component Analysis for Vector Random Functions

Principal component analysis (PCA) is commonly applied without looking at the spatial support (size and shape, of the samples and the field), and the cross-covariance structure of the explored attributes. This paper shows that PCA can depend on such spatial features. If the spatial random functions for attributes correspond to largely dissimilar variograms and cross-variograms, the scale effect will increase as well. On the other hand, under conditions of proportional shape of the variograms and cross-variograms (i.e., intrinsic coregionalization), no scale effect may occur. The theoretical analysis leads to eigenvalue and eigenvector functions of the size of the domain and sample supports. We termed this analysis growing scale PCA, where spatial (or time) scale refers to the size and shape of the domain and samples. An example of silt, sand, and clay attributes for a second-order stationary vector random function shows the correlation matrix asymptotically approaches constants at two or three times the largest range of the spherical variogram used in the nested model. This is contrary to the common belief that the correlation structure between attributes become constant at the range value. Results of growing scale PCA illustrate the rotation of the orthogonal space of the eigenvectors as the size of the domain grows. PCA results are strongly controlled by the multivariate matrix variogram model. This approach is useful for exploratory data analysis of spatially autocorrelated vector random functions.     

Matrix Green's functions for array-type sources and receivers in multiwave layered media

Summary. A previous formulation (Lu, Felsen & Kamel) of source-excited wave propagation in a multiwave layer is here extended to multiple layers, each of which may propagate different multiple wave species, and to simultaneous excitation and detection at arbitrarily specified multiple levels. Field variables are arranged so as to reveal 'interesting'layers requiring access (for example, those containing a source and/or receiver) but to hide in collective form all other 'uninteresting'layers. An ordering of wave constituents into array vectors provides not only a physically appealing view of the wave phenomena pertaining to array-type source and receiver arrangements but may also furnish numerical advantages. The variety of alternative representations in Lu et al. can be brought to bear directly on the present formulation which is thereby endowed with substantial versatility, especially that embodied within the hybrid ray-mode format.     

Applications of graph theory to gross error detection for GPS geodetic control networks

1　ＧｒａｐｈｔｈｅｏｒｙａｎｄｄｅｆｉｎｉｔｉｏｎｓＡｇｒａｐｈＧｃｏｎｓｉｓｔｓｏｆｐｏｉｎｔｓ (ＮＯＤＥＳ)ａｎｄｌｉｎｅｓ (ＥＤＧＥＳ)ｃｏｎｎｅｃｔｉｎｇｔｈｅｓｅｐｏｉｎｔｓ .Ｔｈｅｐｏｉｎｔｓａｒｅｃａｌｌｅｄｎｏｄｅｓａｎｄｌｉｎｅｓａｒｅｅｄｇｅｓ .Ａｄｉｒｅｃｔｅｄｇｒａｐｈｉｓａｇｒａｐｈｉｎｗｈｉｃｈｔｈｅｅｄｇｅｓｃｏｎ ｎｅｃｔｉｎｇｔｈｅｎｏｄｅｓａｒｅｓｐｅｃｉｆｉｅｄ .Ａｔｒｅｅｉｓａｃｏｎｎｅｃｔｅｄｇｒａｐｈｗｉｔｈｏｕｔａｎｙｌｏｏｐ .Ａｌｏｏｐｉｓａｃｌｏｓ…     

青海东昆仑纳赤台群基质系统与外来系统的关系

以野外地层观察与测量的客观地质事实为依据，论述了东昆仑地区纳赤台群的岩性特征和内部岩层存在的3种主要接触关系，进而进一步证实该群存在着基质系统和外来系统两大系统，二者并非连续沉积和同期产物。     

The preservation potential of microstructures during static grain growth

Grain growth simulations using the microstructure simulation system Elle have been performed in materials with a pre‐existing grain shape foliation. As might be expected, the foliation is destroyed by the end of the experiment, and grain areas have increased by a factor of seven. The area of material swept by the migrating grain boundaries was monitored, and it was found that at every stage, virtually all of the grains which survived the grain growth process contain one and only one core of ‘unswept’ material. Remarkably these remnant unswept cores preserve a useable record of the initial grain size and the orientation of the grain shape foliation. This work suggests that, even for samples where no equivalent protolith can be found, it may be possible to see past a grain growth episode to estimate the original grain shape and grain size of the rock, and perhaps even reconstruct the grain boundary kinematics. In addition the identification of unswept cores has the potential to help unravel the evolution of grain boundary chemistry in rocks during metamorphism. As an example of a natural system showing these microstructures, we describe a peridotite from Almklovdalen, Norway. This peridotite was infiltrated by aqueous fluids at several stages during late Caledonian exhumation and retrogressive metamorphism. Grain boundary migration associated with the last of these infiltration events swept off abundant intragranular fluid inclusions in the original chlorite‐peridotite. At the grain scale, microstructural mapping of the fluid inclusion rich areas shows that, as with the numerical simulations, many of the grains retain exactly one core of unswept material. Examples of other natural systems discussed include dislocation density distributions and trace element zoning.     

Major and Trace Element Analysis of Silicate Rocks by XRF and Laser Ablation ICP-MS Using Lithium Borate Fused Glasses: Matrix Effects, Instrument Response and Results for International Reference Materials

Major and trace element compositions of fifteen silicate rock reference materials have been determined by a combined XRF and laser ablation ICP‐MS (LA‐ICP‐MS) technique on glasses prepared by fusing the sample with a lithium borate flux (sample:flux = 1:3). Advantages of this technique include the ability to measure major and trace element abundances on a single sample using a quick and simple preparation that attacks resistant phases such as zircon without the need for acid dissolution. The method is suitable for a wide variety of bulk compositions including mafic, intermediate and silicic rocks. Abundance‐normalized mass response patterns (the ratio of signal intensity to element concentration) of the LA‐ICP‐MS analyses vary systematically with major element composition, demonstrating the presence of a matrix effect that cannot be compensated by normalisation to a single internal standard element. Increasing the sampling distance between the ICP‐MS cone and the torch reduces the magnitude of this effect, suggesting that a mechanism related to residence time of ablated particles in the plasma may be at least partially responsible for the observed variations in mass response patterns. When using a matrix‐matched calibration, agreement of the LA‐ICP‐MS results with published reference values or those obtained by solution ICP‐MS is 10% relative. Analytical precision based on replicate analyses is typically 5% RSD. Procedural detection limits that include contributions from gas background and flux are 0.01‐0.1 μg g‐¹ for the heavy mass trace elements (Rb‐U). Major element analyses by XRF show excellent agreement with results obtained using a conventional heavy element absorbing flux. High quality major and trace element data for silicate rocks can be achieved by a combined XRF and LA‐ICP‐MS analysis of Li₂B₄O₇/LiBO₂ fused glasses provided an appropriate matrix‐matched calibration is adopted.     

Investigation of the Matrix Effect of Mg, Si, Ca, Sc, Fe, Y, La and Lu in Pyroxene Composition Synthetic Silicate Glasses by Ion Microprobe

The dependence of the count rate of singly charged secondary ions of the elements Mg, Si, Ca, Sc, Fe, Y, La and Lu on the bulk composition of the sample (known as the matrix effect) was systematically investigated for synthetic silicate glasses using a Cameca IMS 3f ion microprobe. Matrix elements in these samples, with the composition of a Mg-Fe-Ca pyroxene, comprised Mg, Si, Ca and Fe to which were added the minor elements Sc, Y, La and Lu (each at 0.1 atom %). The matrix dependence of all elements was determined quantitatively by ratioing their count rate response to the Ca or Fe yields of the sample. Measurements were conducted using four energy offsets: 0 eV, 40 eV, 80 eV and 120 eV (each 20 eV) with primary beam currents of between 0.5 and 3 nA. For the four minor elements investigated, a non-linear dependence of the absolute sensitivity factors on the Fe content was found at all the energy ranges studied. This matrix effect decreased with increasing secondary ion energy. For the major elements Mg, Si, Ca and Fe, linear as well as non-linear dependences of the absolute sensitivity factors on the Fe content were found, depending on the element and the energy level considered. Because of their importance in the geosciences, relative sensitivity factors of the elements under study relative to Si as reference element (in some cases also relative to Mg) were determined. For low energy ions, a Fe-dependent matrix effect also occurred. For Mg, Y, La and Lu, the matrix effect vanished for some values of the secondary ions energy range.     

广州市GPS控制网的设计特色和技术突破

通过对广州市GPS控制风的精心设计，科学实施，解决了当前应用GPS控制测量中较多且较难的技术问题，并达到了良好的效果。广州市GPS控制网的设计采用先进规范、分级布网、混连式网形等特色及基线文件的统一转换、方差协方差阵的平衡、超大网平差、多坐标系统的平差等技术突破和达到的实际效果，对大型控制网布测具有一定的指导作用。     

传递矩阵法分析层状地基中桩的扭转变形

研究了扭矩作用下单桩的扭转变形.采用积分变换和传递矩阵方法,求解了成层土在内部环形荷载作用下的基本解;利用此基本解并考虑桩土位移协调条件,提出了层状地基中单桩扭转变形分析的解析方法;并按此理论方法对匀质地基模型进行了数值计算,其结果与已有经典解答相当吻合.     

基于加窗Hilbert变换的复偏振分析方法及其应用

考虑到传统Hilbert变换所隐含的无限长序列假设的实际局限性, 本文将多窗分析法引入到短时序列Hilbert变换中, 通过构建复协方差矩阵和对该矩阵的特征值与特征向量的求解, 获得三分量地震记录的时变偏振参数;基于不同波型的偏振特性与实测偏振参数, 采用线性_余弦权重函数或高斯权重函数自适应空间滤波, 识别与分离具有特定偏振特性的不同地震响应. 针对天然地震三分量记录的处理结果表明, 该方法在识别、分离具有特定偏振特性的不同地震响应方面具有一定的潜力.