主成分趋势面方法在地质异常中的应用
摘要
地质异常理论是根据对立统一的哲学思想,在“求异”基础上运用多学科技术与方法,综合分析和提取各种地质信息,从而定量圈定不同尺度和不同类型的地质异常[17]。近年来,在赵鹏大院士组织下,中国地质大学开展了一系列有关成矿预测的定量综合研究,并且在固体矿产(金属矿产)预测研究方面取得了较大的进展和良好的应用效果。
本文以地质异常理论为指导,具体针对某地区的化探数据,来划分该地区的异常情况。根据成矿的影响因素过多,各因素的影响程度不同,结果也有所不同等特点,以及这些特点的相互关系,如何提取出主要元素影响关系,划分异常成为本文解决问题的重点。针对多种数据的影响作用不同来提取主要的影响因素,本文采取了主成分分析的方法,去除冗余因素,突出主要影响因素的作用,保持各元素之间的影响关系。根据元素分布的不均匀性和不规则性等特点,本文采用了B样条插值方法,保持元素的局部分布性态。而B样条最小二乘拟合算法,强调了关键数据点的作用,既可保证曲面的光顺性,又可控制误差在要求的范围内。对分段插值后的曲面进行趋势的预测和评价,采用趋势面分析的方法得到了元素的整体分布特征。通过趋势面分析和插值理论相结合的方法来突出元素的变化趋势和性质,实现了元素的随机性、局部性和整体性的关系的处理方法。通过适当的设定阈值,来划分各种异常(可以看作是尺度关系的一种应用),体现了异常具有灵活性和交互性。借助于matlab的绘图工具箱绘制出图形,通过图形指出主要因素的影响关系,直接划定异常情况。最后通过具体的实例验证该方法的可行性和有效性,表明本文为矿产预测提供了一种探索性的方法。
As geophysical and geochemical anomalies is well-know for people an important basis of forecasting, and the concept and meaning of "geological anomaly," of in the 1960s developed continuously. In recent years, organized by Zhao Pengda academicians, the China University of Geosciences launched a series of quantitative prediction of the mineralization comprehensive study, and minerals (metal ores) has made better progress and greater good effect. In fact, "geological anomaly" than the geophysical and geochemical anomaly with a deeper meaning, it has a more broad prospects both the area of mineralization forecasting and resolving basic. As a geological anomaly in the composition, structure, sequence and the causes of the surrounding environment and a significant difference in the geological or geological body composition, this concept has been covering the deposit as "useful component of natural crust in the concentration broken" natural attributes. Accordingly, posed a geological anomaly identified mineralization predictable basis. It is also a special type of deposit, and new types of prerequisites, is the root of geophysical and geochemical anomalies. Deposit is the product of geological anomalies, geophysical and geochemical anomaly is the product of the physical nature and the nature of the chemical form of expression.
The basic purpose of mineralization forecasting is to predict the location found no deposit and the deposit generally know that these basic type, size and grade. Depends not only on the unusual characteristics of various geological background and unusual material composition, but also on their occurrence and material composition. Their traditional practices are based on geological data and experienced statistical analysis of experts to study various types of geological data the relationship to achieve the forecast of mineral resources. With the large number of multi-sources of information and data (such as geology, remote sensing, earthquakes, MT, high-precision gravity and magnetic, IP, geophysical, geochemical, etc.) , the accumulation and mineralization forecasting the continuous development of their own disciplines (such as geological anomaly The theory of the establishment, from qualitative to quantitative prediction of the forecast changes, etc.), in the past , the ways of manual handling is unthinkable and not impossible. And because of the data is a typical multi-source spatial data, their different dimension, diversity, the traditional computer database technology for such a space of multi-source data management and analysis is also powerless. Therefore, how to adapt to changes in the situation, make full use of these wealth of information quickly and effectively to the economic forecast mineralization, geological workers are facing a major problem.
With the development of human technology and Earth exploration of the technology is not perfect, mankind has a power beyond their abilities, which is computer technology. on the platform of computer technology , human can identify renewedly the mystery of nature,and re-examine the Earth. China's mineral resources shortage has become a constraint on economic sustainable development one of the major bottlenecks, the application of statistical techniques to study the geological context of mineralization, geological survey and mineral resources prospecting and evaluation of the technology is an effective way.
During empirical research on geochemical data, in order to more fully and accurately reflect the distribution of mineral elements of the characteristics of the development law, people tend to consider its relations with a number of indicators, which in a multicultural statistics also known as variable . The result is as follows: On the one hand, in order to avoid the omission of important information people consider the possible number of instructions, on the other considering the increasing indicators will add to the complexity of the problem, and due to the indicators are refection of the same thing .It is inevitably led to the large number of overlapping and duplication of such information sometimes abliterate true characteristics and the inherent law,Based on the above issues, people want to quantitative study of the variables involved the less, and more message. The principal component analysis and study on the research that how to change a few of the original composition linear variable to explain the vast majority of the original information of a multiple statistical methods use principal component analysis to reduce the workload in a certain area to be more obvious characteristics of elements, element Distribution of more focused, so this is mainly used this method.
Complexity of the problem based on the geological, most of the geological variables are random variables, most of them belongs to the relationship between the correlation that the mathematical analysis can not be used in function to that. For example, in a porphyry copper deposit, the elements of the elements Cu Ag, Pb, Zn, and so there is a dependent relationship, but there is no certainty the function can only be a correlation relationship. If according to a number of pieces of laboratory specimens to identify the correlation between the value of the mathematical expression, and to measure the dependence of variables, the study of this deposit has great value. Mathematical statistics in the regression analysis is to study such a strong relationship between the mathematical tools. It is a number of variables of observational data as the starting point, through this data structure analysis, the search for variable-dependent relationship exists between. Can be summed up that regression analysis is to examine statistical correlation between variables among a number of statistical analysis. So this is also the first to take mathematics and geology the most widely used method - the method of fitting the trend, and on the basis of this improvement.
Using principal component method of delineation of the trend of geological anomalies problem, for observation of the data elements involved in the excessive, the phenomenon of redundancy, to take a principal component analysis of the methods of these interrelated variables to "transform", with Smaller, non-overlapping information of the new variables to reflect the original variables most of the information provided, through a smaller number of new variables to solve the problem of the purpose. In examining the relations between the variables commonly used method is the linear regression, in multivariate analysis, often using least-squares fitting multiple linear regression model. However, when the argument between the approximate linear relationship, that is, multicollinearity, the establishment of direct least squares multiple linear regression equation since some of the variable factor of instability. Also due to multiple linear regression of the significant test method can be used for trend surface analysis, so we wanted to use trend surface analysis to solve the problem. The trend of the commonly used a special function - polynomial functions, the trend is the selection of the number of the problems we face, in order to partially delineated abnormal, excessive fitting of the residual value of smaller, which may be part of meaningful The abnormal trend to return to, in such circumstances trend of the number should not be too high; polynomial the number too low, the extent of not fitting. In geological modeling, to fit the data points are often uneven, in order to more accurately describe the characteristics of observation points, we hope to have the greatest possible number of points around the adoption of the plane, so here is used in subparagraph To fit polynomial, which is kind of interpolation, has been a continuous surface, and B-spline surfaces can be given the interpolation surface is very smoothly, so once again we apply B-spline interpolation. In multivariate analysis, to be constructed in the surface and can be taken to the square of residuals and the smallest way, which is the least-squares fitting surface, these kind of fitting, can change the parameters with the smooth surface. And then calculated the new data fit with the trend of the data margin, the difference in the Matrix, find out in a given threshold, the abnormal fluctuations through the use of matlab graphics toolbox, to map out 3-D graphics, in the plane Graphics directly to determine anomalies. Finally, the actual data in a certain area to test the feasibility of the method.
本文以地质异常理论为指导,具体针对某地区的化探数据,来划分该地区的异常情况。根据成矿的影响因素过多,各因素的影响程度不同,结果也有所不同等特点,以及这些特点的相互关系,如何提取出主要元素影响关系,划分异常成为本文解决问题的重点。针对多种数据的影响作用不同来提取主要的影响因素,本文采取了主成分分析的方法,去除冗余因素,突出主要影响因素的作用,保持各元素之间的影响关系。根据元素分布的不均匀性和不规则性等特点,本文采用了B样条插值方法,保持元素的局部分布性态。而B样条最小二乘拟合算法,强调了关键数据点的作用,既可保证曲面的光顺性,又可控制误差在要求的范围内。对分段插值后的曲面进行趋势的预测和评价,采用趋势面分析的方法得到了元素的整体分布特征。通过趋势面分析和插值理论相结合的方法来突出元素的变化趋势和性质,实现了元素的随机性、局部性和整体性的关系的处理方法。通过适当的设定阈值,来划分各种异常(可以看作是尺度关系的一种应用),体现了异常具有灵活性和交互性。借助于matlab的绘图工具箱绘制出图形,通过图形指出主要因素的影响关系,直接划定异常情况。最后通过具体的实例验证该方法的可行性和有效性,表明本文为矿产预测提供了一种探索性的方法。
As geophysical and geochemical anomalies is well-know for people an important basis of forecasting, and the concept and meaning of "geological anomaly," of in the 1960s developed continuously. In recent years, organized by Zhao Pengda academicians, the China University of Geosciences launched a series of quantitative prediction of the mineralization comprehensive study, and minerals (metal ores) has made better progress and greater good effect. In fact, "geological anomaly" than the geophysical and geochemical anomaly with a deeper meaning, it has a more broad prospects both the area of mineralization forecasting and resolving basic. As a geological anomaly in the composition, structure, sequence and the causes of the surrounding environment and a significant difference in the geological or geological body composition, this concept has been covering the deposit as "useful component of natural crust in the concentration broken" natural attributes. Accordingly, posed a geological anomaly identified mineralization predictable basis. It is also a special type of deposit, and new types of prerequisites, is the root of geophysical and geochemical anomalies. Deposit is the product of geological anomalies, geophysical and geochemical anomaly is the product of the physical nature and the nature of the chemical form of expression.
The basic purpose of mineralization forecasting is to predict the location found no deposit and the deposit generally know that these basic type, size and grade. Depends not only on the unusual characteristics of various geological background and unusual material composition, but also on their occurrence and material composition. Their traditional practices are based on geological data and experienced statistical analysis of experts to study various types of geological data the relationship to achieve the forecast of mineral resources. With the large number of multi-sources of information and data (such as geology, remote sensing, earthquakes, MT, high-precision gravity and magnetic, IP, geophysical, geochemical, etc.) , the accumulation and mineralization forecasting the continuous development of their own disciplines (such as geological anomaly The theory of the establishment, from qualitative to quantitative prediction of the forecast changes, etc.), in the past , the ways of manual handling is unthinkable and not impossible. And because of the data is a typical multi-source spatial data, their different dimension, diversity, the traditional computer database technology for such a space of multi-source data management and analysis is also powerless. Therefore, how to adapt to changes in the situation, make full use of these wealth of information quickly and effectively to the economic forecast mineralization, geological workers are facing a major problem.
With the development of human technology and Earth exploration of the technology is not perfect, mankind has a power beyond their abilities, which is computer technology. on the platform of computer technology , human can identify renewedly the mystery of nature,and re-examine the Earth. China's mineral resources shortage has become a constraint on economic sustainable development one of the major bottlenecks, the application of statistical techniques to study the geological context of mineralization, geological survey and mineral resources prospecting and evaluation of the technology is an effective way.
During empirical research on geochemical data, in order to more fully and accurately reflect the distribution of mineral elements of the characteristics of the development law, people tend to consider its relations with a number of indicators, which in a multicultural statistics also known as variable . The result is as follows: On the one hand, in order to avoid the omission of important information people consider the possible number of instructions, on the other considering the increasing indicators will add to the complexity of the problem, and due to the indicators are refection of the same thing .It is inevitably led to the large number of overlapping and duplication of such information sometimes abliterate true characteristics and the inherent law,Based on the above issues, people want to quantitative study of the variables involved the less, and more message. The principal component analysis and study on the research that how to change a few of the original composition linear variable to explain the vast majority of the original information of a multiple statistical methods use principal component analysis to reduce the workload in a certain area to be more obvious characteristics of elements, element Distribution of more focused, so this is mainly used this method.
Complexity of the problem based on the geological, most of the geological variables are random variables, most of them belongs to the relationship between the correlation that the mathematical analysis can not be used in function to that. For example, in a porphyry copper deposit, the elements of the elements Cu Ag, Pb, Zn, and so there is a dependent relationship, but there is no certainty the function can only be a correlation relationship. If according to a number of pieces of laboratory specimens to identify the correlation between the value of the mathematical expression, and to measure the dependence of variables, the study of this deposit has great value. Mathematical statistics in the regression analysis is to study such a strong relationship between the mathematical tools. It is a number of variables of observational data as the starting point, through this data structure analysis, the search for variable-dependent relationship exists between. Can be summed up that regression analysis is to examine statistical correlation between variables among a number of statistical analysis. So this is also the first to take mathematics and geology the most widely used method - the method of fitting the trend, and on the basis of this improvement.
Using principal component method of delineation of the trend of geological anomalies problem, for observation of the data elements involved in the excessive, the phenomenon of redundancy, to take a principal component analysis of the methods of these interrelated variables to "transform", with Smaller, non-overlapping information of the new variables to reflect the original variables most of the information provided, through a smaller number of new variables to solve the problem of the purpose. In examining the relations between the variables commonly used method is the linear regression, in multivariate analysis, often using least-squares fitting multiple linear regression model. However, when the argument between the approximate linear relationship, that is, multicollinearity, the establishment of direct least squares multiple linear regression equation since some of the variable factor of instability. Also due to multiple linear regression of the significant test method can be used for trend surface analysis, so we wanted to use trend surface analysis to solve the problem. The trend of the commonly used a special function - polynomial functions, the trend is the selection of the number of the problems we face, in order to partially delineated abnormal, excessive fitting of the residual value of smaller, which may be part of meaningful The abnormal trend to return to, in such circumstances trend of the number should not be too high; polynomial the number too low, the extent of not fitting. In geological modeling, to fit the data points are often uneven, in order to more accurately describe the characteristics of observation points, we hope to have the greatest possible number of points around the adoption of the plane, so here is used in subparagraph To fit polynomial, which is kind of interpolation, has been a continuous surface, and B-spline surfaces can be given the interpolation surface is very smoothly, so once again we apply B-spline interpolation. In multivariate analysis, to be constructed in the surface and can be taken to the square of residuals and the smallest way, which is the least-squares fitting surface, these kind of fitting, can change the parameters with the smooth surface. And then calculated the new data fit with the trend of the data margin, the difference in the Matrix, find out in a given threshold, the abnormal fluctuations through the use of matlab graphics toolbox, to map out 3-D graphics, in the plane Graphics directly to determine anomalies. Finally, the actual data in a certain area to test the feasibility of the method.
引文
[1] 陈效弈等.地质建模中的 B 样条曲面拟合[J], 宁波大学学报(理工版) 第 20 第 2 期 2007 年 6 月.
[2] 何晓群编著. 多元统计分析[M], 中国人民大学出版社 2000 ,135-147.
[3] 何晓群, 刘文卿编著. 应用回归分析[M], 北京:中国人民大学出版社 2001, 15-17.
[4] 李水根编著. 分形[M], 高等教育出版社, 2000.
[5] 李岳生 ,齐东旭. 样条函数方法[M], 北京:科学出版社 1979, 25 – 45.
[6] 李岳生 .样条与插值[M], 上海:上海科学出版社 1983 ,82 – 105.
[7] 梅长林, 范金城编. 数据分析方法[M], 北京:高等教育出版社 2006. 2 113-125.
[8] 孙家昶 . 样条函数与计算几何[M], 北京:科学出版社 1982 ,149 – 190.
[9] 汤军,赵鹏大等. 测井油气地质异常及其属性数据地质意义的数学地质研究[J] 成都理工学院学报 第 29 卷第 4 期 2002 年 8 月.
[10] 王世称等. 矿产资源评价方法[M], 长春:吉林科技出版社, 1990.
[11] 王世称等. 综合信息矿产预测理论与方法[M], 科学出版社 , 2000 .
[12] 吴勃英主编. 数值分析原理[M], 科学出版社, 1999.
[13] 刑国才等. 地质异常理论在油气勘探中的应用[J] 中国海上油气, 第十六卷第一期, 2004 年 2 月.
[14] 袁志发, 周静芋主编. 多元统计分析[M], 北京:科学出版社 ,2002.
[15] 杨毅恒, 韩燕, 徐兵, 范继璋 ,夏立显编著. 多维地学数据处理技术与方法[M], 北京:科学出版社 ,2002,12-36,40-55.
[16] 杨国权,王春,蔡玉俊. 一种散乱数据曲面拟和算法[J] 机械设计与制造 第十期 2005 年 10 月.
[17] 赵鹏大, 陈永清 ,刘吉平等著. 地质异常成矿预测理论与实践[M], 武汉:中国地质大学出版社 1999.9
[18] 赵鹏大 .查明地质异常成矿预测的基础[J] 高校地质学报 1996 : 2 ( 4) , 327-381
[19] 赵鹏大,池顺都. 初论地质异常[J] 地球科学——中国地质大学学报 1991, 16 (3): 241- 248
[20] 赵鹏大, 孟宪国. 地质异常与矿产预测[J] 地球科学——中国地质大学学报 1993, 18 (1) : 39- 47
[21] 赵鹏大,王京贵, 饶明辉, 李浩昌. 中国地质异常[J] 地球科学——中国地质大学学报 1995,20 (2) : 117- 127.
[22] 赵鹏大. 成矿定量预测与深部找矿[J] 地学前缘(中国地质大学(北京);北京大学)第 14 卷第 5 期 ,2007 年 9 月.
[23] 赵鹏大, 池顺都 ,陈永清 . 查明地质异常成矿预测的基础[J] 高等地质学报, 第 2 卷, 第 4 期, 1996 年 12 月.
[24] 赵鹏大. 试论地质体数学特征[J] 地球科学——中国地质大学学报 1982, 7 (1) : 145- 155.
[25] 张晋开等.基于主成分分析的植被掩模与模式虑波方法在中等植被区蚀变信息提取中的应用[J] 中国图形图像学报 1996 2,1(2):108-114.
[26] 张寅飞等.散乱测量数据多层次 B 样条逼近曲面拟合算法[J] 机械设计与研究,14-16.
[27] Agterberg.F.P Combinining indicator patterns in weights of evidence modeling for resource evaluation Nonrenewable Resour 1992
[28] De V erle P. Harris and Guocheng Pan. Subdividing consistent geo- logic areas by ralative excep tionalness of additional information: Methods and case study. Economic geology, 1990, 85: 1072- 1083.
[29] Donald A. Singer. Basic concepts in three part quantitative assessments of undiscovered mineral resourus.Nonrenew able resources, 1993, 2 (2) : 69- 81.
[30] Grassberger.P and Procaccia.I Measuring the stragemess of strange attractors physica 1983
[31] Lee S ,Chwa K Y,Shin S Y and Wolberg G. Image metamo-rphosis using snakes and free2form deformations. Computer Graphics( Proc SIGGRAPH ’95) [ Z]11995:439-448.
[32] Saito.T and Oikawa.M Chaos and fractals from aforced artificial neural cell IEEE Trans on Neural Networks 1993
[33] Turcotte,D.L. Fractals and Chaos in Geology and Geophysics[M]: Cambridge University press 1997
[34] ZhaoPangda Theories,P rinciples,and methods for statistical prediction of mineral deposits.Mathematical Geology,1992,(6):589-595
[2] 何晓群编著. 多元统计分析[M], 中国人民大学出版社 2000 ,135-147.
[3] 何晓群, 刘文卿编著. 应用回归分析[M], 北京:中国人民大学出版社 2001, 15-17.
[4] 李水根编著. 分形[M], 高等教育出版社, 2000.
[5] 李岳生 ,齐东旭. 样条函数方法[M], 北京:科学出版社 1979, 25 – 45.
[6] 李岳生 .样条与插值[M], 上海:上海科学出版社 1983 ,82 – 105.
[7] 梅长林, 范金城编. 数据分析方法[M], 北京:高等教育出版社 2006. 2 113-125.
[8] 孙家昶 . 样条函数与计算几何[M], 北京:科学出版社 1982 ,149 – 190.
[9] 汤军,赵鹏大等. 测井油气地质异常及其属性数据地质意义的数学地质研究[J] 成都理工学院学报 第 29 卷第 4 期 2002 年 8 月.
[10] 王世称等. 矿产资源评价方法[M], 长春:吉林科技出版社, 1990.
[11] 王世称等. 综合信息矿产预测理论与方法[M], 科学出版社 , 2000 .
[12] 吴勃英主编. 数值分析原理[M], 科学出版社, 1999.
[13] 刑国才等. 地质异常理论在油气勘探中的应用[J] 中国海上油气, 第十六卷第一期, 2004 年 2 月.
[14] 袁志发, 周静芋主编. 多元统计分析[M], 北京:科学出版社 ,2002.
[15] 杨毅恒, 韩燕, 徐兵, 范继璋 ,夏立显编著. 多维地学数据处理技术与方法[M], 北京:科学出版社 ,2002,12-36,40-55.
[16] 杨国权,王春,蔡玉俊. 一种散乱数据曲面拟和算法[J] 机械设计与制造 第十期 2005 年 10 月.
[17] 赵鹏大, 陈永清 ,刘吉平等著. 地质异常成矿预测理论与实践[M], 武汉:中国地质大学出版社 1999.9
[18] 赵鹏大 .查明地质异常成矿预测的基础[J] 高校地质学报 1996 : 2 ( 4) , 327-381
[19] 赵鹏大,池顺都. 初论地质异常[J] 地球科学——中国地质大学学报 1991, 16 (3): 241- 248
[20] 赵鹏大, 孟宪国. 地质异常与矿产预测[J] 地球科学——中国地质大学学报 1993, 18 (1) : 39- 47
[21] 赵鹏大,王京贵, 饶明辉, 李浩昌. 中国地质异常[J] 地球科学——中国地质大学学报 1995,20 (2) : 117- 127.
[22] 赵鹏大. 成矿定量预测与深部找矿[J] 地学前缘(中国地质大学(北京);北京大学)第 14 卷第 5 期 ,2007 年 9 月.
[23] 赵鹏大, 池顺都 ,陈永清 . 查明地质异常成矿预测的基础[J] 高等地质学报, 第 2 卷, 第 4 期, 1996 年 12 月.
[24] 赵鹏大. 试论地质体数学特征[J] 地球科学——中国地质大学学报 1982, 7 (1) : 145- 155.
[25] 张晋开等.基于主成分分析的植被掩模与模式虑波方法在中等植被区蚀变信息提取中的应用[J] 中国图形图像学报 1996 2,1(2):108-114.
[26] 张寅飞等.散乱测量数据多层次 B 样条逼近曲面拟合算法[J] 机械设计与研究,14-16.
[27] Agterberg.F.P Combinining indicator patterns in weights of evidence modeling for resource evaluation Nonrenewable Resour 1992
[28] De V erle P. Harris and Guocheng Pan. Subdividing consistent geo- logic areas by ralative excep tionalness of additional information: Methods and case study. Economic geology, 1990, 85: 1072- 1083.
[29] Donald A. Singer. Basic concepts in three part quantitative assessments of undiscovered mineral resourus.Nonrenew able resources, 1993, 2 (2) : 69- 81.
[30] Grassberger.P and Procaccia.I Measuring the stragemess of strange attractors physica 1983
[31] Lee S ,Chwa K Y,Shin S Y and Wolberg G. Image metamo-rphosis using snakes and free2form deformations. Computer Graphics( Proc SIGGRAPH ’95) [ Z]11995:439-448.
[32] Saito.T and Oikawa.M Chaos and fractals from aforced artificial neural cell IEEE Trans on Neural Networks 1993
[33] Turcotte,D.L. Fractals and Chaos in Geology and Geophysics[M]: Cambridge University press 1997
[34] ZhaoPangda Theories,P rinciples,and methods for statistical prediction of mineral deposits.Mathematical Geology,1992,(6):589-595