BEMD与SVD方法在滇东Pt-Pd-Cu致矿异常信息提取中的应用
|
摘要
地球化学元素异常的提取一直是勘查地球化学家最重要的工作之一，但迄今还没找到一个完全令人满意的具有科学依据的方法。长期经来，人们主要使用经典的统计学方法：均值与两倍的标准离差之和（(?)+2S）作为异常下限对全部数据进行异常筛选和评价，该方法难以客观地描述成矿元素含量变量的空间分布规律，并不能很好的应用于处理非线性和非平稳数据。
“非线性”和“复杂性”科学能够深刻揭示自然复杂系统中固有的内在本质规律，是21世纪自然科学的重要前缘研究领域之一。本研究选用由云南地调院提供的滇东地区化探组合副样，针对地球化学元素的随机性、非线性和非平稳性特征，分别将二维经验模分解（BEMD）和奇异值分解（SVD）的理论与方法应用于滇东地区的Pt、Pd、Cu含量数据的异常信息提取中，并将两种方法的结果进行了进一步的对比研究，最终结合滇东地区的地质背景和成矿特征，得出具有一定矿产资源潜力的找矿有利地段和成矿远景区，为地球化学勘查的研究提供了新方法。研究成果如下：
1.二维经验模分解（BEMD）与奇异值分解（SVD）方法原理虽不同，但都有根据自身定义的低通、带通和高通滤波器滤波功能。通过各自定义的滤波器获得明显的Pt、Pd、Cu致矿异常信息，获取了两类刻画不同尺度的元素异常图：区域Pt、Pd、Cu异常和局部Pt、Pd、Cu异常。
2.根据异常产出的地质特征，区域Pt、Pd、Cu异常可进一步划分为2种亚类：其一是位于受SN向小江断裂和NE向寻甸—宣威深大断裂控制的二叠纪峨眉山玄武岩分布区的异常，其特征是具有明显的浓集中心，异常强度大；其二是分布于研究区中南部的黑色岩系中的异常，异常强度弱。其中前者是滇东Pt、Pd、Cu找矿的有利地段。局部Pt、Pd、Cu异常可进一步划分为：⑴分布于玄武岩区，受SN-NE向深大断裂与其次级断裂交汇域控制的异常；⑵分布于不同地质时期黑色岩系中的异常；其中，分布于玄武岩区的Pt、Pd、Cu局部异常强度高，规模大，是进一步找寻Pt、Pd、Cu资源的远景地段。
Extracting abnormal of geochemical elements has always been considered as one of the mostimportant work for exploration geochemistry, but until now there is no satisfied scientificmethod completely. The Classical statistical, adding two times standard deviation to mean((?)+2S), was used as the anomaly threshold to extract and evaluate abnormal for a long time.But it can not deal with nonlinear and non-stationary data very well. And it is difficult toobjectively describe spatial distribution of the content of ore-forming elements.
Nonlinearity and complexity are important research fields of natural science in the21stcentury, which can deeply reveal the internal essential rule in natural complex system. This studyselect geochemical samples in Eastern Yunnan province, Southwestern China provided byYunnan Geological Survey Institute and apply bi-dimensional empirical modedecomposition(BEMD) and singular-value decomposition(SVD) to analyze random, nonlinearand non-stationary Pt, Pd and Cu concentration data. Finally, the results of both methods will befurther researched. With the geological background and metallogenic characteristics of researcharea, we delimit preferable ore-finding areas and prospective ore-forming areas in eastern Yunan.It provides a new method for geochemical exploration research. The results are shown asfollows,
1. The principle of bi-dimensional empirical mode decomposition(BEMD) and singular-valuedecomposition(SVD) are different, but they have high-pass S_(HP)(x, y), band-pass S_(BP)(x, y) andlow-pass S_(LP)(x, y) filters according to their own characters. Through the filters, obvious Pt, Pdand Cu anomaly information were extracted, and two kinds of element anomalies in differentscales are obtained: the regional and local Pt、Pd and Cu anomalies.
2. The regional Pt、Pd and Cu anomalies can be subdivided into two categories based ongeological features of anomalies occurrence. One is those with obvious concentrated centers andhigh anomalous intensity which is located at Emeishan basalt areas controlled by the SN trend ofthe Xiaojiang fault and the NE trend of the Xundian-Xuanwei fault. The other is those with weakanomalous intensity which is distributed in black rock series of central and southern parts of thestudy area. The former is the favorable areas for prospecting Pt、Pd and Cu deposits. The localPt、Pd and Cu anomalies also can be subdivided into two sub-categories: one is those which arelocated at the Emeishan basalts controlled by the intersecting areas of both the SN and the NEtrend of deep-seated faults and their secondary faults; the second is those which are located inblack rock series with different geologic epoch. The first one with high strength of Pt-Pdanomalies are prospective areas for Pt、Pd and Cu deposits.
“非线性”和“复杂性”科学能够深刻揭示自然复杂系统中固有的内在本质规律，是21世纪自然科学的重要前缘研究领域之一。本研究选用由云南地调院提供的滇东地区化探组合副样，针对地球化学元素的随机性、非线性和非平稳性特征，分别将二维经验模分解（BEMD）和奇异值分解（SVD）的理论与方法应用于滇东地区的Pt、Pd、Cu含量数据的异常信息提取中，并将两种方法的结果进行了进一步的对比研究，最终结合滇东地区的地质背景和成矿特征，得出具有一定矿产资源潜力的找矿有利地段和成矿远景区，为地球化学勘查的研究提供了新方法。研究成果如下：
1.二维经验模分解（BEMD）与奇异值分解（SVD）方法原理虽不同，但都有根据自身定义的低通、带通和高通滤波器滤波功能。通过各自定义的滤波器获得明显的Pt、Pd、Cu致矿异常信息，获取了两类刻画不同尺度的元素异常图：区域Pt、Pd、Cu异常和局部Pt、Pd、Cu异常。
2.根据异常产出的地质特征，区域Pt、Pd、Cu异常可进一步划分为2种亚类：其一是位于受SN向小江断裂和NE向寻甸—宣威深大断裂控制的二叠纪峨眉山玄武岩分布区的异常，其特征是具有明显的浓集中心，异常强度大；其二是分布于研究区中南部的黑色岩系中的异常，异常强度弱。其中前者是滇东Pt、Pd、Cu找矿的有利地段。局部Pt、Pd、Cu异常可进一步划分为：⑴分布于玄武岩区，受SN-NE向深大断裂与其次级断裂交汇域控制的异常；⑵分布于不同地质时期黑色岩系中的异常；其中，分布于玄武岩区的Pt、Pd、Cu局部异常强度高，规模大，是进一步找寻Pt、Pd、Cu资源的远景地段。
Extracting abnormal of geochemical elements has always been considered as one of the mostimportant work for exploration geochemistry, but until now there is no satisfied scientificmethod completely. The Classical statistical, adding two times standard deviation to mean((?)+2S), was used as the anomaly threshold to extract and evaluate abnormal for a long time.But it can not deal with nonlinear and non-stationary data very well. And it is difficult toobjectively describe spatial distribution of the content of ore-forming elements.
Nonlinearity and complexity are important research fields of natural science in the21stcentury, which can deeply reveal the internal essential rule in natural complex system. This studyselect geochemical samples in Eastern Yunnan province, Southwestern China provided byYunnan Geological Survey Institute and apply bi-dimensional empirical modedecomposition(BEMD) and singular-value decomposition(SVD) to analyze random, nonlinearand non-stationary Pt, Pd and Cu concentration data. Finally, the results of both methods will befurther researched. With the geological background and metallogenic characteristics of researcharea, we delimit preferable ore-finding areas and prospective ore-forming areas in eastern Yunan.It provides a new method for geochemical exploration research. The results are shown asfollows,
1. The principle of bi-dimensional empirical mode decomposition(BEMD) and singular-valuedecomposition(SVD) are different, but they have high-pass S_(HP)(x, y), band-pass S_(BP)(x, y) andlow-pass S_(LP)(x, y) filters according to their own characters. Through the filters, obvious Pt, Pdand Cu anomaly information were extracted, and two kinds of element anomalies in differentscales are obtained: the regional and local Pt、Pd and Cu anomalies.
2. The regional Pt、Pd and Cu anomalies can be subdivided into two categories based ongeological features of anomalies occurrence. One is those with obvious concentrated centers andhigh anomalous intensity which is located at Emeishan basalt areas controlled by the SN trend ofthe Xiaojiang fault and the NE trend of the Xundian-Xuanwei fault. The other is those with weakanomalous intensity which is distributed in black rock series of central and southern parts of thestudy area. The former is the favorable areas for prospecting Pt、Pd and Cu deposits. The localPt、Pd and Cu anomalies also can be subdivided into two sub-categories: one is those which arelocated at the Emeishan basalts controlled by the intersecting areas of both the SN and the NEtrend of deep-seated faults and their secondary faults; the second is those which are located inblack rock series with different geologic epoch. The first one with high strength of Pt-Pdanomalies are prospective areas for Pt、Pd and Cu deposits.
引文
Autonne L. Sur les groupes lineaires, reelles et orthogonaus. Bull Soc Math, France,1902,30:121-133.
Beltrami E.Sulle function bilineari, Giomale di Mathematic-he ad Uso Student DelleUninersita.1873,11:98-106.An English translation by D Boley is available as University of theMinnesota,Department of Computer Science, Technical Report,1990,90-37
Buhmann M.D..Radial Basis Functions.Cambridge University Press.2003,1-38.
Carr J.C., Fright W.R., Beatson R.K.. Surface Interpolation with Radial Basis Functions forMedical Imaging. IEEE Trans.on Medical Image.1997,16(1):96-107.
Cheng J S, Yu D J, Yang Y. Research on the intrinsic mode function (IMF) criterion in EMDmethod. Mechanical Systems and Signal Processing,2006,20:817-824.
Cheng Q M. A new model for quantifying anisotropic scale invariance and for decomposing ofMixing Patterns. Mathematical Geology.2004.36(3)：345-360.
Cheng Q M. Mapping singularities with stream sediment geochemical data for prediction ofundiscovered mineral deposits in Gejiu, Yunnan Province,China. Ore Geology Reviews,2007,32:314–324.
Cheng Q M. No-linear theory and power-low models for Information Integration and mineralresources quantitative assessments. Math. Geosci,2008,40(5):503-532.
Cheng Q, Agterberg F P, Ballantyne S B. The separation of geochemical anomalies frombackground by fractal methods. Journal of geochemical Exploration,1994,51:109-130.
Cheng Q. M. A new model for incorporating spatial association and singularity in interpolation ofexploratory data, In: Leuangthong, O. D., Clay ton, V., eds., Geostatistics Banff2004.Quantitative geology and geostatistics2005,14(2).1017-1025(Springer).
Cheng Q. M. Multifractal distribution of eigenvalues and eigenvectors from2D multiplicativecascade multifractal fields. Mathematical Geology,2005,37(8),915-927.
Cheng Q. M. Multiplicative cascade mineralization processes and singular distribution of mineraldeposit associated geochemical anomalies. In: Cheng, Q. M., Bonham Carter, G.,eds.,Proceedings of Annual Conference of the International Association for MathematicalGeology(IMAG05), GIS and Spatial Analysis,2005,1:297-302.
Cui F., Shen B.,.Peng S.L.Texture segmentation using EMD refined quaternionic spec-trum.Journal of Computer Applications.2005,25(3):573-585.
Duchon J..Splines minimizing rotation-invariant semi-norms in Sobolev spaces. Con-structiveTheory of functions of several variables, Lecture Notes in mathematics. Springer, Berlin,1977,85-100.
Eckart C. and Young G..A principal axis transformation for nonhermitian matrices. NullAmer.Math.Soc.,1939,45:118-121.
Flandrin P，Rilling G，Goncalves P. Empirical mode decomposition as a filter bank.IEEE SignalProcessing Letters,2004,11(2):112-114.
Flandrin P. Some aspects of Huang’s empirical mode decomposition from interpretation toapplication. The Int. Conf. Computational Harmonic Analysis (Invited Talk), Nashville, TN.2004:56-62P.
Franke R., Nielson G.M..Scattered Data Interpolation and Applications: A Tutorial and Survey.Geometric Modeling: Methods and Their-Franke, Nielson.1991,131-160.
Freire, S. L. M., and T. J. Ulrych. Application of singular value decomposition to vertical seismicprofiling. Geophysics,1998,53:778-785.
Hardy R L. Multiquadratic equations of topography and other irregular surfaces. Journal ofGeophysical Research,1971,76:1905-1915.
Hawkes H E, Webb J S. Geochemistry in Mineral Exploration. New York: Harper&Row,1962.415-440.
Hong Z Q. Algebraic Feature Extraction of Image Recognition. Pattern Recognition,1991,24(3):211-219.
Huang J N, Zhao B B, Chen Y Q, et al. Bi-dimensional empirical mode decomposition (BEMD)for extraction of gravity anomalies associated with gold mineralization in the Tongshi goldfield, Western Shandong Uplifted Block, Eastern China. Computers and Geosciences,2010,36(7):987-995.
Huang N E, Shen Z, Long S R, et al. The empirical mode decomposion and the Hilbert spectrumfor nonlinear and non-stationary time series analysis. Proc. Roy. Soc. Lond. A,1998,454:904-995.
Huang N.E. et al. The empirical mode decomposition and the Hilbert spectrum for non-linear andnon stationary time series analysis. Proc Royal Soc. London A.1998,454:903-995.
Jackson G M, Mason I M and Greenhalgh S A. Principal component transforms of triaxialrecordings by singular value decomposition.Geophysics,1991,56(4):528~533.
Krige D G. A statistical analysis of some of the borehole values in the Orange Free State gold field.Journal of the Chemical and Metallurgical Society of South Africa,1952,53:47-64.
Li Q M. GIS-based multiracial/inversion methods for feature extraction and applications inanomaly identification for mineral exploration Ph.D. thesis, York University, Toronto, Canada,2005. P211.
Lin L, Hongbing J. Signal feature extraction based on an improved EMD method [J].Measurement: Journal of the International Measurement Confederation,2009,42:796-803.
Mandelbrot B B. The Fractal geometry of nature. San Francisco: W H Freeman and Company,1983.468
Matheron G. Principles of geostatistics. Economic Geology,1963,58:1250-1266.
Nunes J C, Bouaoune Y, Delechelle E, et al. Image analysis by bi-dimensional empirical modedecomposition. Image and Vision Computing,2003,21:1019-1026.
Nunes J C, Bouaoune Y, Delechelle E. Texture analysis based on the bi-dimensional empiricalmode decomposition. Mach.Vision App.2003.
Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms. Proc.IEEE EURASIP Workshop Nonlinear Signal Image Processing, Grado, Italy.2003:1-6P.
Shen B., Cui F., Peng S.L.. Bidimensional EMD for Texture Analysis and Estimation of theInstantaneous Frequencies of an Image. Journal of Computer-Aided Design and ComputerGraphics.(in Chinese)2005,17(10):2345-2352.
Song J.P., Zhang J.. The Application of Two-dimensional EMD to Separating Contents of OceanicRemote Sensing Images. High Technology letters.(in Chinese)2001,9:62-67.
turcotte D L著.陈颙，郑捷，李颖译.分形与混沌——在地质学和地球物理学中的应用.北京：地震出版社，1993.1227.
Z.X.Liu,H.J.Wang,S.L.Peng. Texture Classification through Directional Empiri-cal ModeDecomposition. Proceedings of the17th International Conference on Pattern Recognition2004.2004,4:803-806
Z.X.Liu,S.L.Peng. Directional EMD and Its Application to Texture Segmentation. Science InChina Series F.2005,35(2):113-123.
陈国达,彭省临，戴塔根，等。云南铜多金属壳体大地构造成矿学。长沙：中南大学出版社,2004.
陈永清,赵彬彬.应用奇异值分解与二维经验模型分解提取金矿化致矿重力异常.地质通报,2011,36(2):341-346.
陈永清,夏庆霖,刘红光.滇东Pt-Pd-Cu含矿建造地球化学特征及其含矿性分析.中国地质,2003,30(3):225.
成秋明,赵鹏大,陈建国,等，奇异性理论在个旧锡铜矿产资源预测中的应用:成矿弱信息提取和复合信息分解.地球科学-中国地质大学学报,2009,34(2):232-242.
成秋明.非线性矿床模型与非常规矿和资源评价.地球科学-中国地质大学学报,2003,28(4):445-454.
成秋明.矿床模型与非常规矿和资源评价.地球科学-中国地质大学学报,2003,28(4):1-10.
成秋明.成矿过程奇异性与矿产预测定量化的新理论与新方法.地学前缘,2007,14(5):42-53.
成秋明.多重分形理论与地球化学元素分布规律.地球科学,2000,25(3):311-318.
范德廉,张涛,叶杰,等.中国的黑色岩系及其有关矿床.北京:科学出版社,2004:1-449.
冯本智,卢民杰，张治中，等.1990.康滇地区前震旦纪地质与成矿.北京:地质出版社
冯本智.1989.论扬子准地台西缘前震旦纪基底及其成矿作用.地质学报，(4):338-348.
李庆谋,成秋明.分形奇异(特征)值分解方法与地球物理和地球化学异常重建.地球科学——中国地质大学学报,2004,29(1):109-118.
李庆谋，刘少华.GIS环境下地球物理信号的奇异值分解、多维分形特征与应用.地球物理学进展,2003,18(1),97-102.
陆文凯,李衍达.SVD分解提高地震资料的信噪比和分辩率.石油地球物理勘探.1998,33（S1）:145-149
彭省临,杨中宝,李朝艳,等.基于GIS确定地球化学异常下限的新方法.地球科学与球境学报,2004,26(3):28-31.
王文胜,陈伏兵,杨靖宇.一种基于奇异值分解的特征抽取方法.电子与信息学报,2005,27(2):294-297.
文占久,刘洪臣,高星.地球物理和地球化学异常的多重分形分析与分解.地球物理学进展,2007,22(3):972-978.
吴国学,李守义,吕志刚,等.团结沟金矿外围十三公里区隐伏矿体预测.吉林大学学报(地球科学版),2006,36(5):781-786.
夏庆霖,陈永清,赵鹏大.滇东铂钯地球化学勘查及异常评价.地质通报,2003,22(9):704.
徐冠雷,王孝通,徐晓刚,等.基于限领域EMD的图像增强.电子学报,2006,34(9):1635-1639.
玄兆燕,杨公训.经验模态分解法在大气时间序列预测中的应用.自动化学报,2008,34(1):97-101
张欢,高振敏,马德云,等.云南个旧锡矿床成因研究综述.地质地球化学,2003,31(3):70-75
张翼飞.云南省区域矿产总结（上册）.昆明:云南省地质矿产局.1993,5-20.
赵鹏大,等.非传统矿产资源概论.北京:地质出版社,2003:127-155.
赵鹏大,王京贵,饶明辉,等.中国地质异常.地球科学-中国地质大学学报,1995,20(2):117-127.
Beltrami E.Sulle function bilineari, Giomale di Mathematic-he ad Uso Student DelleUninersita.1873,11:98-106.An English translation by D Boley is available as University of theMinnesota,Department of Computer Science, Technical Report,1990,90-37
Buhmann M.D..Radial Basis Functions.Cambridge University Press.2003,1-38.
Carr J.C., Fright W.R., Beatson R.K.. Surface Interpolation with Radial Basis Functions forMedical Imaging. IEEE Trans.on Medical Image.1997,16(1):96-107.
Cheng J S, Yu D J, Yang Y. Research on the intrinsic mode function (IMF) criterion in EMDmethod. Mechanical Systems and Signal Processing,2006,20:817-824.
Cheng Q M. A new model for quantifying anisotropic scale invariance and for decomposing ofMixing Patterns. Mathematical Geology.2004.36(3)：345-360.
Cheng Q M. Mapping singularities with stream sediment geochemical data for prediction ofundiscovered mineral deposits in Gejiu, Yunnan Province,China. Ore Geology Reviews,2007,32:314–324.
Cheng Q M. No-linear theory and power-low models for Information Integration and mineralresources quantitative assessments. Math. Geosci,2008,40(5):503-532.
Cheng Q, Agterberg F P, Ballantyne S B. The separation of geochemical anomalies frombackground by fractal methods. Journal of geochemical Exploration,1994,51:109-130.
Cheng Q. M. A new model for incorporating spatial association and singularity in interpolation ofexploratory data, In: Leuangthong, O. D., Clay ton, V., eds., Geostatistics Banff2004.Quantitative geology and geostatistics2005,14(2).1017-1025(Springer).
Cheng Q. M. Multifractal distribution of eigenvalues and eigenvectors from2D multiplicativecascade multifractal fields. Mathematical Geology,2005,37(8),915-927.
Cheng Q. M. Multiplicative cascade mineralization processes and singular distribution of mineraldeposit associated geochemical anomalies. In: Cheng, Q. M., Bonham Carter, G.,eds.,Proceedings of Annual Conference of the International Association for MathematicalGeology(IMAG05), GIS and Spatial Analysis,2005,1:297-302.
Cui F., Shen B.,.Peng S.L.Texture segmentation using EMD refined quaternionic spec-trum.Journal of Computer Applications.2005,25(3):573-585.
Duchon J..Splines minimizing rotation-invariant semi-norms in Sobolev spaces. Con-structiveTheory of functions of several variables, Lecture Notes in mathematics. Springer, Berlin,1977,85-100.
Eckart C. and Young G..A principal axis transformation for nonhermitian matrices. NullAmer.Math.Soc.,1939,45:118-121.
Flandrin P，Rilling G，Goncalves P. Empirical mode decomposition as a filter bank.IEEE SignalProcessing Letters,2004,11(2):112-114.
Flandrin P. Some aspects of Huang’s empirical mode decomposition from interpretation toapplication. The Int. Conf. Computational Harmonic Analysis (Invited Talk), Nashville, TN.2004:56-62P.
Franke R., Nielson G.M..Scattered Data Interpolation and Applications: A Tutorial and Survey.Geometric Modeling: Methods and Their-Franke, Nielson.1991,131-160.
Freire, S. L. M., and T. J. Ulrych. Application of singular value decomposition to vertical seismicprofiling. Geophysics,1998,53:778-785.
Hardy R L. Multiquadratic equations of topography and other irregular surfaces. Journal ofGeophysical Research,1971,76:1905-1915.
Hawkes H E, Webb J S. Geochemistry in Mineral Exploration. New York: Harper&Row,1962.415-440.
Hong Z Q. Algebraic Feature Extraction of Image Recognition. Pattern Recognition,1991,24(3):211-219.
Huang J N, Zhao B B, Chen Y Q, et al. Bi-dimensional empirical mode decomposition (BEMD)for extraction of gravity anomalies associated with gold mineralization in the Tongshi goldfield, Western Shandong Uplifted Block, Eastern China. Computers and Geosciences,2010,36(7):987-995.
Huang N E, Shen Z, Long S R, et al. The empirical mode decomposion and the Hilbert spectrumfor nonlinear and non-stationary time series analysis. Proc. Roy. Soc. Lond. A,1998,454:904-995.
Huang N.E. et al. The empirical mode decomposition and the Hilbert spectrum for non-linear andnon stationary time series analysis. Proc Royal Soc. London A.1998,454:903-995.
Jackson G M, Mason I M and Greenhalgh S A. Principal component transforms of triaxialrecordings by singular value decomposition.Geophysics,1991,56(4):528~533.
Krige D G. A statistical analysis of some of the borehole values in the Orange Free State gold field.Journal of the Chemical and Metallurgical Society of South Africa,1952,53:47-64.
Li Q M. GIS-based multiracial/inversion methods for feature extraction and applications inanomaly identification for mineral exploration Ph.D. thesis, York University, Toronto, Canada,2005. P211.
Lin L, Hongbing J. Signal feature extraction based on an improved EMD method [J].Measurement: Journal of the International Measurement Confederation,2009,42:796-803.
Mandelbrot B B. The Fractal geometry of nature. San Francisco: W H Freeman and Company,1983.468
Matheron G. Principles of geostatistics. Economic Geology,1963,58:1250-1266.
Nunes J C, Bouaoune Y, Delechelle E, et al. Image analysis by bi-dimensional empirical modedecomposition. Image and Vision Computing,2003,21:1019-1026.
Nunes J C, Bouaoune Y, Delechelle E. Texture analysis based on the bi-dimensional empiricalmode decomposition. Mach.Vision App.2003.
Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms. Proc.IEEE EURASIP Workshop Nonlinear Signal Image Processing, Grado, Italy.2003:1-6P.
Shen B., Cui F., Peng S.L.. Bidimensional EMD for Texture Analysis and Estimation of theInstantaneous Frequencies of an Image. Journal of Computer-Aided Design and ComputerGraphics.(in Chinese)2005,17(10):2345-2352.
Song J.P., Zhang J.. The Application of Two-dimensional EMD to Separating Contents of OceanicRemote Sensing Images. High Technology letters.(in Chinese)2001,9:62-67.
turcotte D L著.陈颙，郑捷，李颖译.分形与混沌——在地质学和地球物理学中的应用.北京：地震出版社，1993.1227.
Z.X.Liu,H.J.Wang,S.L.Peng. Texture Classification through Directional Empiri-cal ModeDecomposition. Proceedings of the17th International Conference on Pattern Recognition2004.2004,4:803-806
Z.X.Liu,S.L.Peng. Directional EMD and Its Application to Texture Segmentation. Science InChina Series F.2005,35(2):113-123.
陈国达,彭省临，戴塔根，等。云南铜多金属壳体大地构造成矿学。长沙：中南大学出版社,2004.
陈永清,赵彬彬.应用奇异值分解与二维经验模型分解提取金矿化致矿重力异常.地质通报,2011,36(2):341-346.
陈永清,夏庆霖,刘红光.滇东Pt-Pd-Cu含矿建造地球化学特征及其含矿性分析.中国地质,2003,30(3):225.
成秋明,赵鹏大,陈建国,等，奇异性理论在个旧锡铜矿产资源预测中的应用:成矿弱信息提取和复合信息分解.地球科学-中国地质大学学报,2009,34(2):232-242.
成秋明.非线性矿床模型与非常规矿和资源评价.地球科学-中国地质大学学报,2003,28(4):445-454.
成秋明.矿床模型与非常规矿和资源评价.地球科学-中国地质大学学报,2003,28(4):1-10.
成秋明.成矿过程奇异性与矿产预测定量化的新理论与新方法.地学前缘,2007,14(5):42-53.
成秋明.多重分形理论与地球化学元素分布规律.地球科学,2000,25(3):311-318.
范德廉,张涛,叶杰,等.中国的黑色岩系及其有关矿床.北京:科学出版社,2004:1-449.
冯本智,卢民杰，张治中，等.1990.康滇地区前震旦纪地质与成矿.北京:地质出版社
冯本智.1989.论扬子准地台西缘前震旦纪基底及其成矿作用.地质学报，(4):338-348.
李庆谋,成秋明.分形奇异(特征)值分解方法与地球物理和地球化学异常重建.地球科学——中国地质大学学报,2004,29(1):109-118.
李庆谋，刘少华.GIS环境下地球物理信号的奇异值分解、多维分形特征与应用.地球物理学进展,2003,18(1),97-102.
陆文凯,李衍达.SVD分解提高地震资料的信噪比和分辩率.石油地球物理勘探.1998,33（S1）:145-149
彭省临,杨中宝,李朝艳,等.基于GIS确定地球化学异常下限的新方法.地球科学与球境学报,2004,26(3):28-31.
王文胜,陈伏兵,杨靖宇.一种基于奇异值分解的特征抽取方法.电子与信息学报,2005,27(2):294-297.
文占久,刘洪臣,高星.地球物理和地球化学异常的多重分形分析与分解.地球物理学进展,2007,22(3):972-978.
吴国学,李守义,吕志刚,等.团结沟金矿外围十三公里区隐伏矿体预测.吉林大学学报(地球科学版),2006,36(5):781-786.
夏庆霖,陈永清,赵鹏大.滇东铂钯地球化学勘查及异常评价.地质通报,2003,22(9):704.
徐冠雷,王孝通,徐晓刚,等.基于限领域EMD的图像增强.电子学报,2006,34(9):1635-1639.
玄兆燕,杨公训.经验模态分解法在大气时间序列预测中的应用.自动化学报,2008,34(1):97-101
张欢,高振敏,马德云,等.云南个旧锡矿床成因研究综述.地质地球化学,2003,31(3):70-75
张翼飞.云南省区域矿产总结（上册）.昆明:云南省地质矿产局.1993,5-20.
赵鹏大,等.非传统矿产资源概论.北京:地质出版社,2003:127-155.
赵鹏大,王京贵,饶明辉,等.中国地质异常.地球科学-中国地质大学学报,1995,20(2):117-127.