Multiple regression with correlated independent variables     

Thomas A. Jones 《Mathematical Geology》1972,4(3):203-218

Multiple linear regression analysis may be used to describe the relation of one geologic variable to a number of other (independent) variables, and also may be used to fit a trend surface to geographically distributed variables. The leastsquares estimates of the regression coefficients differ unpredictably from the true coefficients if the independent variables are correlated. The estimates can be too large in absolute value, and may have the wrong sign. Also, the least-squares solution may be unstable in that replicate samples can give widely differing values of the regression coefficients. Ridgeregression analysis is a technique for removing the effect of correlations from the regression analysis. The procedure involves addition of a small constant K to the diagonal elements of the standardized covariance matrix. The estimates obtained are biased but have smaller sums of squared deviations between the coefficients and their estimates. The ridge trace, a plot of the coefficients versus K, helps determine the value of K that stabilizes the estimates. Correlations between geologic variables are common, and regression coefficients based on these data may be suspect. In trendsurface analysis, correlations between the geographic coordinates may differ widely, and extreme correlations may be introduced if higher order terms are used in the trend. Ridgeregression analysis serves to guide the geologist to a more reliable interpretation of the results of multiple regression if the independent variables are correlated.  相似文献   

Multigroup discrimination of river, beach, and dune sands using axial-ratio sample statistics of quartz grains     

Basanta K. Sahu 《Mathematical Geology》1982,14(6):577-587

Optimal discrimination among several groups can be achieved by simultaneous diagonalization of pooled within-group, W, and among-group, A, sums of squares and cross-product matrices formed by utilizing axial-ratio sample statistics of quartz grains belonging to different sieve grades. This method maximizes the ratio of among-group cross products to within-group cross product quadratic forms (V'AV/V'WV)and simultaneously yields discriminant scores whose correlation coefficients are zero for group means as well as for within each group. This procedure enables a simple Euclidean distance measure for partitioning the discriminant space for assignment. Although W^–1 and Amatrices are symmetric, the W^–1 Amatrix needed for multigroup discrimination is asymmetric and hence the eigenstructure of W^–1 Ais obtained by simultaneous diagonalization of Wand Amatrices. The first four sample statistics (mean, standard deviation, skewness, kurtosis) of normalized axial-ratios are required for discrimination, although the mean and standard deviation are the most important discriminators.  相似文献   

REVIEWS OF GEOGRAPHIC SOFTWARE     

《The Professional geographer》1987,39(4):481-486

Reviews of geographic software in this article: GEOGRAPHY MACCHORO OPS83 Population Analysis on Microcomputers with PC or MS DOS STATPAC GOLD THUNDERSCAN  相似文献   

Inconsistency in theories of violent relaxation     

I. Arad  D. Lynden-Bell 《Monthly notices of the Royal Astronomical Society》2005,361(2):385-395

  相似文献   

Efficiency of regression techniques for ore valuation at Kolar Gold Fields, India     

B. K. Verma 《Mathematical Geology》1972,4(1):25-34

The Kolar Gold Fields are some of the best known gold deposits in India. An example of ore valuation utilizing 49 ore blocks of the Oriental lode of the West Reefs, explored and developed in the Nundydroog mines, is given. In this reef system, there are large ore reserves of sulfidebearing quartz reefs, and the gold distribution is erratic both along strike and downdip. Ore valuation at present is based on the arithmetic mean of samples taken at peripheral positions of the blocks. Samples taken from internal portions of the blocks give a totally different picture of the value. To correct this discrepancy, normal regression and lognormal regression of internal block and total block values, over peripheral block values have been used to evaluate the deposits. The valuation efficiency criterion shows the logarithmic variance for distribution of ratios of unregressed and regressed block values with the corresponding arithmetic mean of internal stope values as observed inside the blocks. The studies have shown that the logarithmic variance is minimum if the logarithmic regression is used, thereby indicating maximum efficiency. Further, the undervaluation and overvaluation of low- and high-grade blocks is less for the logarithmic example. With help of the logarithmic regression equation an effective pay limit of 177.8 in.-dwt has been found for selective mining, for peripheral block values corresponding to the official pay limit of 240 in.-dwt.NGRI contribution number 71-281.  相似文献   

Geostatistical investigations of gabbro occurrences near Savantvadi, Ratnagiri district, India     

V. C. Chavadi  N. W. Gokhale  S. R. Kulkarni 《Mathematical Geology》1972,4(2):147-153

This paper embodies petrographical and statistical investigations of three gabbro occurrences. The Mangaon and Kunkeri gabbros are similar in petrography and petrochemistry, whereas they are completely different from the Vajrat gabbro. Application of recently developed statistical tests help in classifying these gabbros by using three oxides, CaO, FeO, and K₂O.This study shows that the evolution of the Mangaon and Kunkeri gabbros probably proceeded along different lines as compared to the Vajrat gabbro.  相似文献   

基于高阶统计量的相干体算法在地震中深层构造解释中应用   总被引：3，自引：2，他引：1       下载免费PDF全文

段春节  吴汉宁  马承杰  柏冠军 《地球物理学进展》2009,24(2):640-643

利用高阶统计量所具有的可抑制高斯噪声和比常规的自相关函数包含更多信息的优点,并结合地震解释的实际问题,本文采用四阶矩函数代替互相关函数进行相干计算,对第一代相干体算法进行了改进,发展了基于高阶统计量的相干体算法.该方法不仅计算速度快,而且抑制噪声能力强.通过与传统相干算法实际应用对比,该算法有效地突出了地层的高连续性特征,有利于层位追踪和断层解释,尤其利于中深层构造解释.  相似文献   

蒙城地震台地磁核旋观测数据b值初步分析     

曹志磊  周琼  张有林  成业明  汪继林  薛志明  郎孝龄 《地震地磁观测与研究》2009,30(1):64-69

利用蒙城地震台地磁核旋观测资料,进行b值统计分析,得出了其短期、长期以及周期性变化基本规律。与华东地区中强震做震例对应分析,结果表明,该台b值异常可能具有孕震效应,对中强震具有一定的预测意义。  相似文献   

NDVI spatial pattern and its differentiation on the Mongolian Plateau     

ZHANG Xue-Yan  HU Yun-Feng  PENG Da-Fang  JI Yong-Qing  MA Xin 《地理学报》2009,30(4):403-415

GIMMS NDVI database and geo-statistics were used to depict the spatial distribution and temporal stability of NDVI on the Mongolian Plateau.The results demonstrated that:(1) Regions of interest with high NDVI indices were distributed primarily in forested mountainous regions of the east and the north,areas with low NDVI indices were primarily distributed in the Gobi desert regions of the west and the southwest,and areas with moderate NDVI values were mainly distributed in a middle steppe strap from northwest to southeast.(2) The maximum NDVI values maintained for the past 22 years showed little variation.The average NDVI variance coefficient for the 22-year period was 15.2%.(3) NDVI distribution and vegetation cover showed spatial autocorrelations on a global scale.NDVI patterns from the vegetation cover also demonstrated anisotropy;a higher positive spatial correlation was indicated in a NW-SE direction,which suggested that vegetation cover in a NW-SE direction maintained increased integrity,and vegetation assemblage was mainly distributed in the same specific direction.(4) The NDVI spatial distribution was mainly controlled by structural factors,88.7% of the total spatial variation was influenced by structural and 11.3% by random factors.And the global autocorrelation distance was 1178 km,and the average vegetation patch length(NW-SE) to width(NE-SW) ratio was approximately 2.4:1.0.  相似文献   

蒙古高原NDVI的空间格局及分异   总被引：5，自引：2，他引：3  

张雪艳  胡云锋  庄大方  齐永清  马欣 《地理学报(英文版)》2009,19(4):403-415

GIMMS NDVI database and geo-statistics were used to depict the spatial distribu-tion and temporal stability of NDVI on the Mongolian Plateau. The results demonstrated that: (1) Regions of interest with high NDVI indices were distributed primarily in forested moun-tainous regions of the east and the north, areas with low NDVI indices were primarily distrib-uted in the Gobi desert regions of the west and the southwest, and areas with moderate NDVI values were mainly distributed in a middle steppe strap from northwest to southeast. (2) The maximum NDVI values maintained for the past 22 years showed little variation. The average NDVI variance coefficient for the 22-year period was 15.2%. (3) NDVI distribution and vege-tation cover showed spatial autocorrelations on a global scale. NDVI patterns from the vegetation cover also demonstrated anisotropy; a higher positive spatial correlation was in-dicated in a NW-SE direction, which suggested that vegetation cover in a NW-SE direction maintained increased integrity, and vegetation assemblage was mainly distributed in the same specific direction. (4) The NDVl spatial distribution was mainly controlled by structural factors, 88.7% of the total spatial variation was influenced by structural and 11.3% by random factors. And the global autocorrelation distance was 1178 km, and the average vegetation patch length (NW-SE) to width (NE-SW) ratio was approximately 2.4:1.0.  相似文献