Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.     

Local Oceanic Vertical Deflection Determination with Gravity Data Along a Profile

Deflections of the vertical (DOVs) over oceans cannot be directly measured, which restricts their applications. A local covariance function of anomalous potential is put forward in this paper in conjunction with the least-squares collocation (LSC) method to compute the oceanic DOVs utilization of oceanic gravity data along a profile. The covariance functions of gravity field quantities have been derived directly as functions of x, y and z without the need to introduce coordinate transformations corresponding to along- or cross-profile components. In the proposed methodology, gravity data along a profile were used to calculate the residual gravity anomaly using the remove-compute-restore technique. The residual gravity anomaly was used to calculate the parameters of the proposed covariance function of the local anomalous gravity field, which was used in the LSC to compute the residual DOVs along the profile. The residual DOVs added model DOVs to recover the DOVs along the profile. The results of a simulation experiment prove that the proposed methodology is feasible and effective.     

基于经验模态分解和小波分解估算海气通量涡相关计算中的截断时间尺度

基于时长38天的海表风场实测数据,应用经验模态分解(EmpiricalModeDecomposition,EMD)和小波分解(Wavelet Decomposition, WD)这两种数据处理方法首先对涡相关法中的截断时间尺度(CutoffTimescale,CTS)进行估算,结果显示:基于EMD与WD方法估算出的CTS一般都在40秒左右(EMD的结果略小),远远小于传统涡相关法中CTS的取值(固定为10分钟),且EMD和WD的使用使得每一段数据都能够根据自身的湍流特点而获得合适的CTS; EMD方法和WD方法有效的去除了计算结果中的非湍部分,且对通量传输方向的刻画也更加合理,极大提高了通量的计算精度,所得通量与传统方法计算的通量偏差平均值高达45%;研究还对EMD和WD的优缺点进行了对比分析,结果表明EMD相比于WD有更高的自主性,而WD对信号的分离程度则更高。     

Comparison of ordinary and disjunctive kriging in an Indian iron ore deposit

This paper presents the results of disjunctive kriging applied to a supergene iron ore deposit of Bailadila Range of India. Disjunctive kriging is applied firstly to compare estimates of the blocks by ordinary kriging and secondly to estimate benchwise local recoverable reserves of the orebody. Good agreement exists between block estimates by ordinary kriging and disjunctive kriging except for peripheral blocks with less borehole information. Estimation of benchwise reserves shows that the behavior of the distribution of grades is different in various benches. The study shows that disjunctive kriging can be applied successfully for estimation of local recoverable reserves in the case of a good grade hematite iron ore deposit.     

The Fourier Integral Method: An efficient spectral method for simulation of random fields

The Fourier Integral Method (FIM) of spectral simulation, adapted to generate realizations of a random function in one, two, or three dimensions, is shown to be an efficient technique of non-conditional geostatistical simulation. The main contribution is the use of the fast Fourier transform for both numerical calculus of the density spectral function and as generator of random finite multidimensional sequences with imposed covariance. Results obtained with the FIM are compared with those obtained by other classic methods: Shinozuka and Jan Method in 1D and Turning Bands Method in 2D and 3D, the points for and against different methodologies are discussed. Moreover, with the FIM the simulation of nested structures, one of which can be a nugget effect and the simulation of both zonal and geometric anisotropy is straightforward. All steps taken to implement the FIM methodology are discussed.     

三分量地震资料中各向异性检测

各向异性研究是当令地震学研究领域中重要课题之一；三分量地震资料中各向异性的检测是各向异性理论研究成果解决地球科学实际问题的重要桥梁。本文简要描述了各向异性介质中横波分裂现象，分别介绍了现有的四种主要检测技术，即偏振图法、协方差拒阵法、质，点振动分辨率法及传输矩阵法，并对这四种技术作了一定的评述。     

统一方差分量估计公式

本文提出了一种适用于协方差阵奇异或非奇异、设计阵列满秩或降秩时的方差分量估计方法;其公式推导简单,形式统一,不需解线性方程组,同时可保证迭代计算方差分量的非负要求。作为特例还和Helmert法及MINQUE法作了比较。最后讨论了用真误差进行方差分量估计的计算公式,并给出了一个测距误差分析的实例。     

The equivalence of predictions from universal kriging and intrinsic random-function kriging

A proof is provided that the predictions obtained from kriging based on intrinsic random functions of orderk are identical to those obtained from anappropriate universal kriging model. This is a theoretical result based on known variability measures. It does not imply that people performing traditional universal kriging will get the same predictions as those using intrinsic random functions, because traditionally these methods differ in how variability is modeled. For intrinsic random functions, the same proof shows that predictions do not depend on the specific choice of the generalized covariance function. It is argued that the choice between these methods is really one of modeling and estimating the variability in the data.