AR（P）参数估计协方差方法与其改进型方法的对比研究

定性分析协方差方法及其改进型在ＡＲ（Ｐ）参数估计中的应用，提供了一种估计参数的计算机上机流程图，比较了协方差方法及其改进型谱估计结果。     

协方差阵二次型容许估计的一个必要条件

研究协方差阵Σ的二次型容许估计问题。设 y1,y2 ,… ,yniid,n≥ 2 ,y1与 p维正态分布N (β,Σ )有相同的前四阶矩。其中β =(β1,β2 ,… ,βp)′∈ Rp与Σ =(σij) p× p >0均未知。记 y =△ (y1,y2 ,… ,yn)′。在二次损失 L (d ,Σ ) =tr(d -Σ) 2下给出Σ的二次型估计 a S2 + nby-y-′是容许估计的必要条件为 :(n - 1) a + b + 2 max(a,b)≤ 1。此必要条件比张立振等协方差阵的二次型容许估计中的必要条件有了明显的加强     

抗差最小二乘配置在数字化地图几何纠正中的应用讨论

抗差估计具有较好的抗拒异常观测值及粗差的能力,而最小二乘配置又能较好地处理系统误差,本文结合两者的优点,利用抗差最小二乘配置对数字化地图进行几何纠正,其中对协方差函数采用抗差拟合,得到了较好的结果。实验证明在GIS数据处理的扫描数字化地图几何纠正中,抗差最小二乘配置在抗拒异常值和处理系统误差方面优于单纯的最小二乘估计和单纯的最小二乘配置方法。     

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.     

Size Scaling of Cross Correlation Between Multiple Variables

Reservoir models have large uncertainty because of spatial variability and limited sample data. The ultimate aim is to use simultaneously all available data sources to reduce uncertainty and provide reliable reservoir models for resource assessment and flow simulation. Seismic impedance or some other attribute provides a key source of data for reservoir modeling. These seismic data are at a coarser scale than the hard well data and it not an exact measurement of facies proportions or porosity. A requirement for data integration is the cross-covariance between the well and seismic data.The size-scaling behavior of the cross correlation for different measurement scales was nvestigated. The size-scaling relationship is derived theoretically and validated by numerical studies (including an example with real data). The limit properties of the cross-correlation coefficient when the averaging volume becomes large is shown. After some averaging volume, the volume-dependent cross-correlation coefficient reaches a limit value. This plateau value is controlled mainly by the large-scale behavior of the cross and direct variograms.The cross correlation can increase or decrease with volume support depending on the relative importance of long- and short-scale covariance structures. If the direct and cross variograms are proportional, there is no change in the cross correlation as the averaging volume changes. Our study shows that the volume-dependent cross-correlation coefficient is sensitive to the shape of the cross variogram and differences between the direct variograms of the well data and seismic data.     

Monitoring volcanic hazard using eddy covariance at Solfatara volcano, Naples, Italy

An eddy covariance (EC) station was deployed at Solfatara crater, Italy, June 8–25, 2001 to assess if EC could reliably monitor CO₂ fluxes continuously at this site. Deployment at six different locations within the crater allowed areas of focused gas venting to be variably included in the measured flux. Turbulent (EC) fluxes calculated in 30-min averages varied between 950 and 4460 g CO₂ m⁻² d⁻¹; the highest measurements were made downwind of degassing pools. Comparing turbulent fluxes with chamber measurements of surface fluxes using footprint models in diffuse degassing regions yielded an average difference of 0% (±4%), indicating that EC measurements are representative of surface fluxes at this volcanic site. Similar comparisons made downwind of degassing pools yielded emission rates from 12 to 27 t CO₂ d⁻¹ for these features. Reliable EC measurements (i.e. measurements with sufficient and stationary turbulence) were obtained primarily during daytime hours (08:00 and 20:00 local time) when the wind speed exceeded 2 m s⁻¹. Daily average EC fluxes varied by ±50% and variations were likely correlated to changes in atmospheric pressure. Variations in CO₂ emissions due to volcanic processes at depth would have to be on the same order of magnitude as the measured diurnal variability in order to be useful in predicting volcanic hazard. First-order models of magma emplacement suggest that emissions could exceed this rate for reasonable assumptions of magma movement. EC therefore provides a useful method of monitoring volcanic hazard at Solfatara. Further, EC can monitor significantly larger areas than can be monitored by previous methods.     

Geostatistical inversion of coupled problems: dealing with computational burden and different types of data

Practical application of geostatistical inversion to coupled problems is hampered by a number of difficulties. In this paper, we address two of them: first, the computational cost of sensitivity (Jacobian) matrices and, second, the evaluation of the relative weights of different types of data. Regarding the first, we revise the adjoint state equations to propose a form whose cost is independent of the number of unknown parameters and only grows with the number of observation wells. Regarding the second, we derive expressions for the relative weights of different types of data. These expressions are based on minimizing the expected likelihood, rather than the likelihood itself. The efficiency of both improvements is tested on a synthetic example. The example analyzes a wide range of groundwater flow and solute transport conditions. Yet, the expected likelihood consistently yields the optimal weights. The proposed form of the adjoint state equations leads to one order of magnitude reduction in CPU time with respect to the conventional sensitivity equations.     

Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields

The basic concepts of spectral and multiscale selective reconstruction of (geophysically relevant) vector fields on the sphere from error-affected data is outlined in detail. The reconstruction mechanism is formulated under the assumption that spectral as well as multiscale approximation is well-representable in terms of only a certain number of expansion coefficients at the various resolution levels. It is shown that spectral denoising by means of orthogonal expansions in terms of vector spherical harmonics reflects global a priori information of the noise (e.g., in form of a covariance tensor field), whereas multiscale signal-to-noise thresholding can be performed under locally dependent noise information within a multiresolution analysis in terms of spherical vector wavelets. An application of the multiscale formalism to Earth's magnetic field determination is presented.     

ω循环型边界条件

通过利用预条件共轭梯度法对对称正定Toeplitz 矩阵系统进行分析，重点介绍了一种新的嵌入式预条件矩阵构造方法，证明了以前的预条件矩阵构造方法大都是这种方法的特例.提出了ω循环型边界条件，并将其与普通循环型及螺旋型边界条件作了分析、比较后得到了一种新的边界条件即混合型边界条件.