• 中国出版政府奖提名奖

    中国百强科技报刊

    湖北出版政府奖

    中国高校百佳科技期刊

    中国最美期刊

    留言板

    尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

    姓名
    邮箱
    手机号码
    标题
    留言内容
    验证码

    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

    李庆谋 成秋明

    李庆谋, 成秋明, 2004. 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, 29(1): 109-118.
    引用本文: 李庆谋, 成秋明, 2004. 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, 29(1): 109-118.
    LI Qing-mou, CHENG Qiu-ming, 2004. Fractal Singular-Value (Egin-Value) Decomposition Method for Geophysical and Geochemical Anomaly Reconstruction. Earth Science, 29(1): 109-118.
    Citation: LI Qing-mou, CHENG Qiu-ming, 2004. Fractal Singular-Value (Egin-Value) Decomposition Method for Geophysical and Geochemical Anomaly Reconstruction. Earth Science, 29(1): 109-118.

    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

    基金项目: 

    国家“863”计划课题 2002AA135090

    详细信息
      作者简介:

      李庆谋(1965-), 男, 教授, 1994年毕业于中国地质大学(北京)能源地质系, 获博士学位, 现在加拿大约克大学作博士后研究.E-mail: qingmou@yorku.ca, qingmou@yorku.ca

    • 中图分类号: P632

    Fractal Singular-Value (Egin-Value) Decomposition Method for Geophysical and Geochemical Anomaly Reconstruction

    • 摘要: 地球物理和地球化学异常是找矿的重要依据.地球物理和地球化学异常取决于地层、构造在成矿时间上的多样性与空间上排列、叠置的复杂性.地层、构造因素是构造、岩浆、沉积与成矿地球化学等多种动力学过程的综合反映.这些岩石和构造的因素以及动力过程相互渗透和影响决定了最终地质、地球物理与地球化学场.本文提出的在GIS环境下实现的分形奇异值分解(MSVD) 异常重建方法, 不仅可以提取地球物理和地球化学等异常, 而且能够进一步刻画其中的线性和环状构造、细微的局部纹理结构特征.该方法首先对地球物理和地球化学等网格数据进行二维矩阵的奇异值分解, 之后用左特征向量矩阵与右特征向量矩阵的直积构造一个正交完备基.地球物理和地球化学二维数据可以投影到该正交基上, 其投影系数是矩阵的奇异值.在该正交完备空间的某些子空间上对地球物理和地球化学等数据进行滤波.为了选择子空间, 本文定义了上述正交完备基中的能谱密度、能谱半径(或尺度) 与能量测度.在此基础上与空间域及频率域类比, 探讨了能量测度与能谱密度呈现分形(fractal和bifractal) 规律.利用分形关系的间断点, 设计分形奇异值重建算子, 实现对地球物理和地球化学异常的分解.以加拿大NovaScotia南部布格重力异常与As地球化学异常为例, 采用MSVD方法分解Au、Wu -Sn -U等已知矿有关的地球化学异常.发现重建异常能很好地用于解释已知矿点的分布规律.重建的地球化学异常显现了地球化学中的线状和环状异常; 重建的布格重力异常有效勾勒出原图中不易发现的纹理结构, 这些纹理结构可以合理地解释已知矿点在侵入岩体内及其周围的分布规律.应用实例表明, 该方法不仅可以从起因复杂的异常中区分出背景、异常场, 还可以识别代表了成矿源岩、流体、运移通道、赋存空间等异常因素引起的纹理、结构与构造特征.同时实现了GIS环境下交互可视化的MSVD处理与解释系统, 增强了地质异常定量分析的实用性与可操作性.

       

    • 图  1  奇异值分解能量测度定义(a) 以及As的分形奇异值分解图解(b)

      Fig.  1.  Definition of accumulated energy (b) and MSVD plot (a)

      图  2  布格重力异常分形奇异值分解图解

      Fig.  2.  MSVD plot of Bouguer anomaly

      图  3  研究区位置、岩性单元和矿点分布

      Fig.  3.  Location of study area, simplified lithology units and locations of the known mineral depositsore and mineral occurrences (Xu, 2001)

      图  4  布格重力异常的部分奇异值、特征向量与正交子空间(原始布格异常见图 7a)

      Fig.  4.  Some singular values, eigenvectors and orthogonal subspaces of Bouguer anomaly (Fig. 7a) for the original Bouguer anomaly

      图  5  地球化学As元素奇异值分解积分能量贡献(a) 与能量密度(b) 随奇异值的变化

      Fig.  5.  Accumulated energy (a) and energy spectrum density (b) of As versus the number of singular-value number

      图  6  As地球化学图(对数变换) (a)、As异常图(b) 以及解释(c)

      Fig.  6.  log-transformed As concentration map (a), MSVD anomaly (b) and interpretation (c)

      图  7  布格重力异常图(a)、MSVD重建结果(b) 以及解释(c)

      Fig.  7.  Bouguer anomaly (a), MSVD reconstructed map (b) and interpretation (c)

    • Alter, O., Brown, P.O., Boststein, D., 2000. Singular value decomposition for genome-side expression processing and modeling. Proc. Natl. Acad. Sci. USA, 97 : 10101-10106. doi: 10.1073/pnas.97.18.10101
      Bhatacharyya, B.K., 1966. Continuous spectrum of the total magnetic field anomaly due to a rectangle prismatic body. Geophysics, 31(1) : 97 -121. doi: 10.1190/1.1439767
      Bonham-Carter, G.F., Rencz, A.N., Harrris, J.R., et al., 1985. Spatial relationship of gold occurrence with lineament derived from LANDSAT and SEASAT imagery, Meguma Group, Nova Scotia. In: Bonham-Carter, G.F., ed., Proceedings of the fourth thematic conference of remote sensing fo rexploration geology, San Francisco. AGU, San Francisco, USA, 755 -768.
      Bonham-Carter, G.F., 1994. Geographic information systems for geoscientist : Modeling with GIS. Pergamon, Oxford, 398.
      Bonham-Carter, G.F., Agterberg, F.P., Wright, D.F., 1988. Integration of geological datasets for golden exploration in Nova Scotia. Phonogram Remote Sensing, 54 : 1585 -1592.
      Bonham-Carter, G.F., Agterberg, F.P., Wright, D.F., 1991. Mineral potential mapping with GIS. Unpublished notes for ashort course, November 11 -15, 1991, At Dept. of Geology, University of Ottawa, 109.
      Cagnoli, B., Ulrych, T.J., 2001. Singular value decomposition and wavy reflections in ground-penetrating radar images of base surge deposits. Journal of Applied Geophysics, 48: 175 -182. doi: 10.1016/S0926-9851(01)00089-1
      Chang, X., Lu, M., Liu, Y., 1999. Error analysis and appraisal of three general solution in seismic tomography. Acta Geophysica Sinica, 42(5) : 695 -701.
      Cheng, Q.M., 2001. Multifractal and geostatistic methods for characterizing local structure and singularity properties of exploration geochemical anomalies. Earth Science—Journal of China University of Geosciences, 26 (2) : 161 -166(in Chinese with English abstract).
      Cheng, Q.M., 2000, Multifractal theory and geochemical element distribution pattern. Earth Science—Journal of China University of Geosciences, 25(3) : 311 -318(in Chinese with English abstract).
      Cheng, Q.M., 1999. Spatial and scaling modeling for geochemical anomaly separation. Journal of Geochemical Exploration, 63(3) : 175 -194.
      Cheng, Q.M., Agterberg, F.P., Ballantyne, B.S., 1994. The separation of geochemical anomalies from background by fractal method. Journal of Geochemical Exploration, 43 (2) : 91-109.
      Cheng, Q.M., Agterberg, F.P., Bonham-Carter, G.F., 1996. A spatial analysis method for geochemical anomaly separation. Journal of Geochemical Exploration, 56 : 183 -195. doi: 10.1016/S0375-6742(96)00035-0
      Cheng, Q.M., 1995. The perimeter-area fractal model and its application to geology. Mathematical Geology, 27(1) : 69 - 82. doi: 10.1007/BF02083568
      Cheng, Q.M., Li, Q.M., 2002. A fractal concentration-area method for assigning color palette for image representation. Computer & Geosciences, 28: 567 -575.
      Cheng, Q.M., Xu, Y., Grunsky, E., 1999. Integrated spatial and spectrum analysis for geochemical anomaly separation. In : Lippard, J.L., Naess, A., Sinding-Lonsen, R., eds., Proc. Int. Assoc. Mathematical Geology, Trondheim, Norw ay Ⅰ, 87-92.
      Cheng, Q.M., Xu, Y., Grunsky, E., 2001. Multifractal power spectrum-area method for geochemical anomaly separation. Natural Resources Research, 9(1) : 43-51.
      De, F.R., Musacchio, G., 2001. Polarization filter with singular value decomposition. Geophysics, 66(3) : 932-938. doi: 10.1190/1.1444983
      Donald, L.T., 1997. Fractal and chaos in geology and geophysics. Second edition. Cambridge University Press, London, 398.
      Fedi, M., Quarta, T., Santis, A.D., 1997. Inherent power-law behavior of magnetic field power spectra from the spector and grant ensemble. Geophysics, 64(4) : 1143-1150.
      Freire, S.L.M., Ulrych, T.J., 1988. Application of singular value decomposition to vertical seismic profiling. Geophysics, 53(6) : 778-785. doi: 10.1190/1.1442513
      Garret, R.G., 1989. The Chi-square plot : A tool for multivariate outlier recognition. Journal of Geochemical Exploration, 32 (1-3) : 319-341. doi: 10.1016/0375-6742(89)90071-X
      Goncalves, M.A., Mateus, A., Oliveira, V., 2001. Geochemical anomaly separation by multi-fractal modeling. Journal of Geochemical Exploration, 72(2): 91-114. doi: 10.1016/S0375-6742(01)00156-X
      Govtt, G.J.S., Goodfellow, W.D., Chapman, R.P., et al., 1975. Exploration geochemistry distribution of elements and recognition of anomalies. Mathematical Geology, 7: 415 - 446. doi: 10.1007/BF02080498
      Gray, S.H., Etgen, J., Dellinger, J., et al., 2001. Seismic migration problems and solutions. Geophysics, 66(5) : 1622 - 1640. doi: 10.1190/1.1487107
      Groom, R.W., Bailey, R.C., 1991. Analytic investigations of the effects of near surface three-dimensional galvanic scatters on MT tensor decompositions. Geophysics, 56 (4) : 496 -518. doi: 10.1190/1.1443066
      Grunsky, E., 1997. Numerical techniques and strategies for interpretation of geochemical data current topics in GIS and integration of exploration datasets short course notes. Exploration 97 Workshop, Ottawa, GAC, Canada, 1 -147.
      Grunsky, E., Smee, B., 1999. Differentiation of soil types and mineralization from multi-element geochemistry using multivariate methods and digital topography. Journal of Geochemistry Exploration, 67(1-3) : 289-301.
      Harris, J.R., Wlkinson, L., Grunsky, E., et al., 1999. Techniques for analysis and visualization of litho geochemical data with application to Swayze Greenstone Belt, Ontario. Journal of Geochemical Exploration, 67(1-3) : 301 -344. doi: 10.1016/S0375-6742(99)00077-1
      Holter, N.S., Maritan, A., Cieplak, M., et al., 2001. Dynamic modeling of gene expression data. Proc. Natl. Acd. Sci. USA, 98 : 1693 -1698. doi: 10.1073/pnas.98.4.1693
      Kurzl, H., 1988. Exploratory data analysis : Recent advances for the interpretation of geochemical data. Journal of Geochemical Exploration, 30(3) : 143-163.
      Klaus, H., Hentschel, K., 2002. Mapping the spectrum : Techniques of visual representation in research and teaching. Oxford, New York, 362.
      Kovin, G., 1992. Fractal models in the earth science. Elsevier, Amsterdam, 408.
      Lebrun, D., Richard, V., Mace, D., et al., 2001. SVD for multioffset linarized inversion, resolution analysis multicomponent acquisition. Geophysics, 66(3) : 871 -882. doi: 10.1190/1.1444976
      Lewis, G.M., Lovejoy, S., Schertzer, D., et al., 1999. The scale invariant generator technique for quantifying anistropic scale invariance. Computers & Geosciences, 25(9) : 963 - 978.
      Li, Q.M., 1996. Milankovitch cycles analysis and application by logging data. Chinese Journal of Geophysics, 36(5) : 699 - 704.
      Li, Y.G., Oldenberg, W., 1998. Separation of regional and residual magnetic field data. Geophysics, 62(2) : 431-439.
      Li, Q.M., Cheng, Q.M., 2001. Fractal correction of well logging curves. Journal of China University of Geosciences, 12 (3) : 272 -275.
      Li, Q.M., Liu, S.H., 2000. Wavelet scalogram of well logging. Progress of Geophysics, 14(1) : 25 -39 (in Chinese with English abstract).
      Maintz, J., Viergever, M., 1998. A survey of medical image registration. Medical Image Analysis, 2: 1-36. doi: 10.1016/S1361-8415(98)80001-7
      Manderbrot, B.B., 1983. The fractal geometry of nature. Freeman, New York, 468.
      Maurizio, F., Tatiana, Q., Angelo, D.S., 1997. Inherent power-law behavior of magnetic field pow er spectra from a spector and Grant ensemble. Geophysics, 62(4) : 1143 -1149. doi: 10.1190/1.1444215
      Maus, S., Dimiri, V., 1996. Depth estimation from scaling spectrum of potential field. Geophysical Journal of International, 124(1) : 113-120. doi: 10.1111/j.1365-246X.1996.tb06356.x
      Mesco, C.A., 1966. Two dimensional filtering and the secondderivative method. Geophysics, 31(3) : 606 -617. doi: 10.1190/1.1439796
      Mickus, K.L., Aiken. C.L.V., Kennedy. W.D., 1991. Regional-residual gravity anomaly separation using the minimum-curvature technique. Geophysics, 56(2) : 279 -283. doi: 10.1190/1.1443041
      Michelena, R.J., 1993. Singular value decomposition for crosswell tomography. Geophysics, 58(11) : 1655 -1661. doi: 10.1190/1.1443381
      Panahi, A., Cheng, Q.M., Bonham-Carter, G.F., 2003. Modeling lake sediment geochemical distribution using principal component, indicator Kriging and multifractal powerspectrum analysis : A case study from Gowg anda, Ontario. Journal of Geochemistry : Exploration, Env ironment and Analysis (in press).
      Pawlowski, R.S., Hamsen, R.O., 1990. Gravity anomaly separation by wiener filtering. Geophysics, 55(5) : 539 -548. doi: 10.1190/1.1442865
      Pecknoald, S., Lovejoy, S., Schertzer, D., et al., 1997. Multifractals and resolution dependence of remotely sensed data: GSI to GIS. In : Quatrochi, D., G ooldchild, M.F., eds., Scale in remote sensing and GIS. Lewis Press, New York, 361 -394.
      Pilkington, M., 1995. Scaling nature of crustal susceptibility. Geophysical Research Letters, 32(7) : 779 -782.
      Ramachadra, R.A., Bhimasankaram, P., 2000. Linear algebra. Hindustan Book Agency, New Delhi, 414.
      Schwartz, E., Broome, J., 1994. Magnetic anomalies due to pyrrhotite in Paleozoic meta sediments in Nova Scotia, eastern Canada. J. of Applied Geophysics, 32: 1-10. doi: 10.1016/0926-9851(94)90005-1
      Sharma, K.K., Rao, V.K., M allick, K., 1999. Finite element gravity regional and residual anomalies and structural fabrics of northwest Ganga basin. Journal of the Geological Society of India, 54(2) : 169-178.
      Sinclair, A.J., 1991. A fundamental approach to threshold estimation in exploration geochemistry : Probability plots revisited. Journal of Geochemical Exploration, 41(1) : 1-22.
      Stanley, C.R., Sinclair, A.J., 1987. Anomaly recognition for multi-element geochemical data—A backg round characterization approach. Journal of Geochemical Exploration, 29 (3) : 333 -351.
      Thomson, D.J., 1982. Spectrum estimation and harmonic analysis. Proc. IEEE, 70 : 1055 -1096. doi: 10.1109/PROC.1982.12433
      Vasco, D.W., 1991. Bounding seismic velocities using a tomographic method. Geophysics, 56(4) : 478-482.
      Wang, B., Xu, S., Liu, B., et al., 1997. An example of aeromagnetic anomaly separation using multi-interpolation division. Oil Geophysical Prospecting, 32(3) : 431 -438.
      Weiland, W.L., 1989. Integ rated approach to gravity anomaly separation by geologic stripping. In : Society of Exploration Geophysicists, 59th annual international meeting. AGU, Houston, USA, 1: 325-328.
      William, R., Hendee, E., Russell, R., et al., 2002. Medical imaging physics. Wiley-Liss, New York, 512.
      Xu, Y.G., 2001. A fractal filtering technique for geochemical and geophysical data processing in GIS environment(Dissertation). York University, Toronto, Canada, 155.
      Xu, Y.G., Cheng, Q.M., 2001. A fractal filtering technique for processing regional geochemical map for mineral exploration. Journal of Geochemistry : Exploration, Environment and Analysis, 1: 147-156. doi: 10.1144/geochem.1.2.147
      Zhao, P.D., 2002. " Three-component" quantitative resource prediction and assessments: Theory and practice of digital mineral prospecting. Earth Science—Journal of China University of Geosciences, 27(5) : 482 -489(in Chinese with English abstract).
      Zurflueh, E.G., 1967. A pplication of two-dimensional linear wavelength filtering. Geophysics, 32(6) : 1015 -1035. doi: 10.1190/1.1439905
      成秋明, 2001. 多重分形与地质统计学方法用于勘查地球化学异常空间结构和奇异性分析. 地球科学———中国地质大学学报, 26(2) : 161-166. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200102012.htm
      成秋明, 2000. 多维分形和地球化学元素分布规律. 地球科学———中国地质大学学报, 25(3) : 311-318. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200003018.htm
      李庆谋, 刘少华, 2000. 地球物理测井曲线的小波波谱分析. 地球物理学进展, 14(1) : 25 -39.
      赵鹏大, 2002. " 三联式" 资源定量预测与评价———数字找矿理论与实践探讨. 地球科学———中国地质大学学报, 27 (5) : 482 -489. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200205001.htm
    • 加载中
    图(7)
    计量
    • 文章访问数:  3700
    • HTML全文浏览量:  668
    • PDF下载量:  20
    • 被引次数: 0
    出版历程
    • 收稿日期:  2003-07-30
    • 刊出日期:  2004-01-25

    目录

      /

      返回文章
      返回