正交距离圆曲线拟合方法

在分析圆曲线拟合准则基础上,提出采用正交最小二乘法拟合圆曲线。该方法以圆曲线正交距离残差平方和极小为准则。基于间接平差原理详细推导了相关模型和算法,并以实际算例说明了该方法的效果。     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

联合多种测高数据确定中国海及其邻域1．5′×1．5′重力异常

联合多种测高资料和Geosat/GM波形重构数据,基于EIGEN_CG01C重力场模型,采用沿轨迹加权最小二乘方法和逆Vening-Meinesz公式,确定了中国海及其邻域1.5′×1.5′重力异常。将计算结果与最新船测资料进行了比较,标准差为3.37×10-5m.s-2。     

A Reconnaissance Method for Delineation of Tracts for Regional-Scale Mineral-Resource Assessment Based on Geologic-Map Data

The U.S. Geological Survey (USGS) is proposing to conduct a global mineral-resource assessment using geologic maps, significant deposits, and exploration history as minimal data requirements. Using a geologic map and locations of significant pluton-related deposits, the pluton-related-deposit tract maps from the USGS national mineral-resource assessment have been reproduced with GIS-based analysis and modeling techniques. Agreement, kappa, and Jaccard's C correlation statistics between the expert USGS and calculated tract maps of 87%, 40%, and 28%, respectively, have been achieved using a combination of weights-of-evidence and weighted logistic regression methods. Between the experts' and calculated maps, the ranking of states measured by total permissive area correlates at 84%. The disagreement between the experts and calculated results can be explained primarily by tracts defined by geophysical evidence not considered in the calculations, generalization of tracts by the experts, differences in map scales, and the experts' inclusion of large tracts that are arguably not permissive. This analysis shows that tracts for regional mineral-resource assessment approximating those delineated by USGS experts can be calculated using weights of evidence and weighted logistic regression, a geologic map, and the location of significant deposits. Weights of evidence and weighted logistic regression applied to a global geologic map could provide quickly a useful reconnaissance definition of tracts for mineral assessment that is tied to the data and is reproducible.     

PLS法与隧道围岩稳定性分类

围岩稳定性是隧道工程支护设计的基本参数,采用偏最小二乘回归法,综合考虑多因变量影响因素,对隧道围岩稳定性分类进行回归建模,并取得较好效果.     

加权最小范数平差的伪观测解法

首先证明了加权最小范数平差一般解的一个重要性质，由此提出了利用附加的观测值来求解加权最小范数平差问题的方法，并证明了该法与利用一般解法等价性的充要条件。     

A Least-squares Approach to Depth Determination from Numerical Horizontal Self-potential Gradients

We have developed a least-squares minimization approach to depth determination of a buried ore deposit from numerical horizontal gradients obtained from self-potential (SP) data using filters of successive window lengths (graticule spacings). The problem of depth determination from SP gradients has been transformed into the problem of finding a solution to a nonlinear equation of the form f(z)=0. Formulas have been derived for vertical and horizontal cylinders and spheres. Procedures are also formulated to estimate the electrical dipole moment and the polarization angle. The method is applied to synthetic data with and without random noise. Finally, the validity of the method is tested on two field examples. In both cases, the depth obtained is found to be in a very good agreement with that obtained from drilling information.     

A GIS Analysis to Evaluate Areas Suitable for Crushed Stone Aggregate Quarries in New England,USA

Aggregate is a low unit-value mineral commodity. Costs to move aggregate from the mine site to the point of use is a large fraction of the resource cost to users. Production sites for aggregate occur where suitable source materials exist and where transportation and market conditions are favorable. The increasing demand for aggregate and the difficulty of developing and permitting new sites and of renewal of permits on existing sites of aggregate production indicates that aggregate will be supplied from sources yet to be developed or delineated in many areas. Site development and permitting for aggregate production is difficult because many land management plans and zoning actions fail to anticipate prospective source areas for aggregate in a way that is consistent with both the source rock quality and the transportation and socioeconomic factors that define the economic viability of the industry. Spatial analysis provides a method to integrate both geology and economic (transportation and marketplace) parameters in a regional model. Weights of evidence (WofE) analysis has been used to measure the spatial correlation of geologic map, transportation network, and population data with current production sites for crushed stone aggregate in the New England region of the northeastern United States. Weighted logistic regression (WLR) is used with the WofE results to rank areas in terms of their relative suitability for production of crushed stone. Spatial analysis indicates that 85% of the 106 crushed stone aggregate quarries in New England are sited within 1.6 km (1 mile) of either a principal highway or rail line in the region. Seventy-eight percent of crushed stone aggregate quarries are sited in census tracts with population densities exceeding 100 people/mile². These relations illustrate the importance of proximity to both transportation corridors and developing areas where aggregate is predominately used. Only one active crushed stone quarry is located in a census tract with a population density less than 15 people/mile², reflecting the lack of sufficient market demand in many rural areas to develop an operation there. However, since 1990, almost all new quarries have been developed in census tracts with population densities less than 200 people/mile², indicating the difficulty of permitting new quarry sites in highly populated areas. Crushed stone aggregate is produced predominately from three hard rock types that are distributed widely in New England; 28% of sites use granitic rock, 25% use carbonate rocks, and 25% use mafic rock types that are categorized as trap rock by the aggregate industry. The other crushed stone aggregate sources include a variety of fine-grained metamorphic rock types. Carbonate rocks and Jurassic basalt (the primary trap rock source) are the most prevalent source rocks on an area-weighted basis. Spatial analysis can be used on a regional scale to rank areas by their relative suitabilityfor crushed stone aggregate production based on geology, transportation, and population parameters. The results of this regional analysis can identify areas for more detailed evaluation. As transportation or population features change, the model can be revised easily to reflect these changes.     

Histogram and variogram inference in the multigaussian model

Several iterative algorithms are proposed to improve the histogram and variogram inference in the framework of the multigaussian model. The starting point is the variogram obtained after a traditional normal score transform. The subsequent step consists in simulating many sets of gaussian values with this variogram at the data locations, so that the ranking of the original values is honored. The expected gaussian transformation and the expected variogram are computed by an averaging operation over the simulated datasets. The variogram model is then updated and the procedure is repeated until convergence. Such an iterative algorithm can adapt to the case of tied data and despike the histogram. Two additional issues are also examined, referred to the modeling of the empirical transformation function and to the optimal pair weighting when computing the sample variogram.     

Variational analysis of dynamics of fissured poroelastic rocks

Rocks can be modeled in a continuum framework as fissured, poroelastic materials, i.e., materials with two degrees of porosity, one due to the fissures and another one due to the pores. The governing equations of motion of fissured poroelastic rocks established by Beskos are rederived here by establishing a variational statement which also provides the boundary conditions of the problem. This is accomplished by considering strain, dissipation and kinetic energies as well as the work of external forces. The above statement is also derived here by employing the method of weighted residuals.