适用于大尺度速度场建模的MQ-B新模型

基于MQ-B方法的基本数学原理提出沿大地线度量距离构造核函数,得到一种适于大尺度范围速度场建模的MQ-B新模型,该速度场在参考椭球面上建立。将适于标量场的MQ-B方法推广到适于矢量场,拓宽了多面函数拟合方法的应用领域。实际算例表明,提出的基于大地线核函数的多面函数拟合模型与传统的通过经纬度坐标差构造核函数的多面函数拟合模型在中国区域内精度相当,但理论上更完善,可用于大尺度速度场建模。     

两种改进Stokes函数在中国近海大地水准面中的应用

基于移去计算恢复技术(RCR),结合中国近海区域Sandwell测高重力数据,分析了VK和FEO核函数不同阶数条件下,球冠半径大小对残余大地水准面结果的影响。结果表明,在本测试区域,当核函数阶数较大时(P=L=90和P=L=120),球冠半径的增加对残余大地水准面的影响不显著。综合低阶核函数和较高阶核函数的计算结果,球冠半径为3°是一个较优参数。利用GPS水准数据对计算结果进行检核表明,采用改进的椭球核函数比球面核函数计算精度可以提高1.5cm。     

半参数测量平差模型参数的二阶段估计

本文首先利用自然样条函数法,找到符合条件的非参数自然插值样条函数。其次利用核函数并综合最小二乘法建立了参数x和S非参数的估计量x、S,讨论了窗宽参数h的选取方法。最后,用一个模拟的平差算例从估值的稳定性、均方差等方面与最小二乘法进行了比较,结果说明,半参数测量模型能更接近于真实情况。     

末次冰盛期气候反馈特征研究

末次冰盛期(Last Glacial Maximum,简称LGM)被认为是较适合用来估算气候系统响应对辐射强迫变化的古气候区间之一.理解LGM时期气候反馈过程有助于进一步限定气候敏感度的范围.本研究利用辐射核方法和参加第三次古气候模式比较计划(Paleoclimate Modelling Intercomparison Project Phase Ⅲ,简称PMIP3)的8个耦合模式资料,对比研究了LGM时期与abrupt4xCO2(4CO2)情景下的气候反馈特征.结果表明:全球平均而言,不同情景下温度反馈、水汽反馈和反照率反馈的强度存在显著差异,然而这一关系并不存在于云反馈过程中,这可能与情景间/模式间云反馈的不确定性相联系;在不同情景下,不同反馈过程强度也存在明显空间差异.温度反馈过程的差异主要来源于LGM时期大陆冰盖强迫引起的温度变化的高度空间不均一性和海陆分布改变引起的热带对流活动的变化;水汽反馈变化可能与海陆分布变化引起的沃克环流变化以及全球降温相联系;大陆冰盖和海冰存在是导致LGM时期地表反照率反馈增加的主要原因;而云反馈的差异可能与低云云量和模式间不确定性有关.LGM时期单独强迫数值试验将有助于进一步厘清不同气候状态下气候反馈过程差异的原因.     

Fabric-diagram contour precision and size of counting element related to sample size by approximation theory methods

Density estimation on the unit sphere by kernel methods may be conceived as a process of approximation by singular integrals. This concept aids in the solution of the main problems concerning the contouring of fabric diagrams. The optimal size of the counting element in Schmidt's method with respect to the mean integrated square error (MISE)of the density estimation is given. It proved that the optimal size is not only a function of the sample size but seriously depends on the smoothness of the density of directions on the sphere. In the light of approximation theory the Schmidt method of contouring is qualified as a moving average process; an example of a more refined density estimator is given.     

A History of Regression and Related Model-Fitting in the Earth Sciences (1636?-2000)

The (statistical) modeling of the behavior of a dependent variate as a function of one or more predictors provides examples of model-fitting which span the development of the earth sciences from the 17th Century to the present. The historical development of these methods and their subsequent application is reviewed. Bond's predictions (c. 1636 and 1668) of change in the magnetic declination at London may be the earliest attempt to fit such models to geophysical data. Following publication of Newton's theory of gravitation in 1726, analysis of data on the length of a 1° meridian arc, and the length of a pendulum beating seconds, as a function of sin²(latitude), was used to determine the ellipticity of the oblate spheroid defining the Figure of the Earth. The pioneering computational methods of Mayer in 1750, Boscovich in 1755, and Lambert in 1765, and the subsequent independent discoveries of the principle of least squares by Gauss in 1799, Legendre in 1805, and Adrain in 1808, and its later substantiation on the basis of probability theory by Gauss in 1809 were all applied to the analysis of such geodetic and geophysical data. Notable later applications include: the geomagnetic survey of Ireland by Lloyd, Sabine, and Ross in 1836, Gauss's model of the terrestrial magnetic field in 1838, and Airy's 1845 analysis of the residuals from a fit to pendulum lengths, from which he recognized the anomalous character of measurements of gravitational force which had been made on islands. In the early 20th Century applications to geological topics proliferated, but the computational burden effectively held back applications of multivariate analysis. Following World War II, the arrival of digital computers in universities in the 1950s facilitated computation, and fitting linear or polynomial models as a function of geographic coordinates, trend surface analysis, became popular during the 1950–60s. The inception of geostatistics in France at this time by Matheron had its roots in meeting the evident need for improved estimators in spatial interpolation. Technical advances in regression analysis during the 1970s embraced the development of regression diagnostics and consequent attention to outliers; the recognition of problems caused by correlated predictors, and the subsequent introduction of ridge regression to overcome them; and techniques for fitting errors-in-variables and mixture models. Improvements in computational power have enabled ever more computer-intensive methods to be applied. These include algorithms which are robust in the presence of outliers, for example Rousseeuw's 1984 Least Median Squares; nonparametric smoothing methods, such as kernel-functions, splines and Cleveland's 1979 LOcally WEighted Scatterplot Smoother (LOWESS); and the Classification and Regression Tree (CART) technique of Breiman and others in 1984. Despite a continuing improvement in the rate of technology-transfer from the statistical to the earth-science community, despite an abrupt drop to a time-lag of about 10 years following the introduction of digital computers, these more recent developments are only just beginning to penetrate beyond the research community of earth scientists. Examples of applications to problem-solving in the earth sciences are given.     

On the combination of gravity anomalies and gravity disturbances for geoid determination in Western Australia

The geoid gradient over the Darling Fault in Western Australia is extremely high, rising by as much as 38 cm over only 2 km. This poses problems for gravimetric-only geoid models of the area, whose frequency content is limited by the spatial distribution of the gravity data. The gravimetric-only version of AUSGeoid98, for instance, is only able to resolve 46% of the gradient across the fault. Hence, the ability of GPS surveys to obtain accurate orthometric heights is reduced. It is described how further gravity data were collected over the Darling Fault, augmenting the existing gravity observations at key locations so as to obtain a more representative geoid gradient. As many of the gravity observations were collected at stations with a well-known GRS80 ellipsoidal height, the opportunity arose to compute a geoid model via both the Stokes and the Hotine approaches. A scheme was devised to convert free-air anomaly data to gravity disturbances using existing geoid models, followed by a Hotine integration to geoid heights. Interestingly, these results depended very weakly upon the choice of input geoid model. The extra gravity data did indeed improve the fit of the computed geoid to local GPS/Australian Height Datum (AHD) observations by 58% over the gravimetric-only AUSGeoid98. While the conventional Stokesian approach to geoid determination proved to be slightly better than the Hotine method, the latter still improved upon the gravimetric-only AUSGeoid98 solution, supporting the viability of conducting gravity surveys with GPS control for the purposes of geoid determination. AcknowledgementsThe author would like to thank Will Featherstone, Ron Gower, Ron Hackney, Linda Morgan, Geoscience Australia, Scripps Oceanographic Institute and the three anonymous reviewers of this paper. This research was funded by the Australian Research Council.     

BLU Estimators and Compositional Data

One of the principal objections to the logratio approach for the statistical analysis of compositional data has been the absence of unbiasedness and minimum variance properties of some estimators: they seem not to be BLU estimator. Using a geometric approach, we introduce the concept of metric variance and of a compositional unbiased estimator, and we show that the closed geometric mean is a c-BLU estimator (compositional best linear unbiased estimator with respect to the geometry of the simplex) of the center of the distribution of a random composition. Thus, it satisfies analogous properties to the arithmetic mean as a BLU estimator of the expected value in real space. The geometric approach used gives real meaning to the concepts of measure of central tendency and measure of dispersion and opens up a new way of understanding the statistical analysis of compositional data.     

On Visualization for Assessing Kriging Outcomes

Extant opinion about kriging is that all weights should be positive. Visualizations rendered by converting kriged grids to digital images are presented to show that negative weights may be beneficial to some spatial problems. In particular, variogram models with zero-valued nuggets, already well known to minimize smoothing through kriging, result in a visual resolution substantially superior to that from kriging with a variogram model having a nonzero nugget value in application to satellite acquired data. Negative weights are more likely when using variogram models with zero-valued nuggets, but resultant visualizations often show a smoother transition between extreme data values. This is true even when a variogram model having a nugget value of zero is not optimum with respect to mean square error, as is demonstrated using a nitrate data set. An analogy to digital image processing is used to suggest that the influence of negative weights in kriging is similar to a high-boost kernel.     

无网格数值方法在结构物水动力研究中的应用

运用一种移动粒子半隐式法建立无网格水流数值模型,探讨该模型在结构物水动力特性研究中的可能性。在无网格条件下,粒子间的相互作用通过核子函数来表示,并通过建立物理量光滑模型、梯度模型和二阶导数模型来离散控制方程。流体的不可压缩性是通过引入粒子数密度概念实现的。该方法不受流体变形程度和固边界形状的限制,因而具有特定的适应性。运用该模型模拟了水柱倒塌后有无透空块体两种情况下右端直墙上的压力过程。计算结果表明透空块体可使直墙压力减小42%。