Abstract
Because the ore-forming system in the crust of the Earth is a highly nonlinear system, geochemical anomaly classification is very important for improving the accuracy of metallogenic prediction. Further, since the distribution of the geochemical elements usually presents nonlinear characteristics due to the complexity and uncertainty of geology factors, the traditional linear data processing method has limited applications for an ore-forming system. The FastICA algorithm is applied to preprocessed geochemical data to reduce the interference information between elements. On the basis of obtaining the separated geochemical elements, the continuity of the spatial distribution of geochemical elements is considered, and combined with the application of the total variation (TV) in image processing; thus the total variation is introduced when processing geochemical data for anomaly analysis to eliminate the influence of singular geochemical data values. To measure the spatial distribution of geochemical elements, assays of the 1:10000 soil geochemical data in the area of Dachaidan in the Qinghai province of China are processed. The elemental anomaly zoning sequences are divided into three levels of anomaly: 85%, 90% and 95%. The anomaly isograms of Au and Cu processed by FastICA and the total variation algorithm predict the geological background of the study area better than the traditional cumulative frequency method. These results indicate that the application of the FastICA algorithm and the total variation algorithm to process geochemical data processing is valid and effective.
Similar content being viewed by others
References
Abergel R, Moisan L (2016) The shannon total variation. Journal of Mathematical Imaging & Vision 59(2):1–30. https://doi.org/10.1007/s10851-017-0733-5
Afzal, P. , Alghalandis, Y. F. , Khakzad, A. , Moarefvand, P. , & Omran, N. R. . (2011). Delineation of mineralization zones in porphyry cu deposits by fractal concentration–volume modeling. J Geochem Explor, 108(3), 0–232. doi: https://doi.org/10.1016/j.gexplo.2011.03.005, 220
Bin, L., Si, G., Youhua, W., & Zedong, Z. (2014). A Fast Independent Component Analysis Algorithm for Geochemical Anomaly Detection and Its Application to Soil Geochemistry Data Processing. J Appl Math 2014:1–12
Caté A, Schetselaar E, Mercier-Langevin P, Ross PS (2018) Classification of lithostratigraphic and alteration units from drillhole lithogeochemical data using machine learning: a case study from the lalor volcanogenic massive sulphide deposit, snow lake, Manitoba, Canada. J Geochem Explor, S0375674217305083:216–228. https://doi.org/10.1016/j.gexplo.2018.01.019
Chen G, Cheng Q (2017) Fractal-based wavelet filter for separating geophysical or geochemical anomalies from background. Math Geosci 50:249–272. https://doi.org/10.1007/s11004-017-9707-9
Cheng Q, Xu Y, Grunsky E (2000) Integrated spatial and spectrum method for geochemical anomaly separation. Nat Resour Res 9(1):43–52. https://doi.org/10.1023/A:1010109829861
Ekeland, I. , & Roger Témam. (1976). Convex analysis and variational problems Classics in Applied Mathematics, 1. https://doi.org/10.1137/1.9781611971088
Giusti E (1984) Minimal surfaces and functions of bounded variation ||. Minimal Surfaces and Functions of Bounded Variation. https://doi.org/10.1007/978-1-4684-9486-0
Hill EJ, Oliver NHS, Fisher L, Cleverley JS, Nugus MJ (2014) Using geochemical proxies to model nuggety gold deposits: an example from sunrise dam, Western Australia. J Geochem Explor 145:12–24. https://doi.org/10.1016/j.gexplo.2014.05.008
Hobbs, B. E. , Zhao, C. , Ord, A. , Peng, S. , H.B. Mühlhaus, & Liu, L. . (2004). Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones. Tectonophysics, 387(1–4), 0–64. doi: https://doi.org/10.1016/j.tecto.2004.06.007, 47
Hobbs BE, Zhao C, Ord A, Peng S (2010) Effects of mineral dissolution ratios on chemical-dissolution front instability in fluid-saturated porous media. Transp Porous Media 82(2):317–335. https://doi.org/10.1007/s11242-009-9427-9
Hobbs BE, Zhao C, Regenauer-Lieb K, Ord A (2011) Computational simulation for the morphological evolution of nonaqueous phase liquid dissolution fronts in two-dimensional fluid-saturated porous media. Comput Geosci 15(1):167–183. https://doi.org/10.1007/s10596-010-9206-2
Hongyi L, Zhengrong Z, Liang X, Zhihui W (2017) Poisson noise removal based on nonlocal total variation with Euler’s elastica pre-processing. Journal of Shanghai Jiaotong University (Science) 22 (5):609–614
Hornby P, Zhao C, Hobbs BE, Ord A, Peng S, Liu L (2008) Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks. Int J Numer Anal Methods Geomech 32(9):1107–1130. https://doi.org/10.1002/nag.661
Hoyer PO, Inki MO (2001) Topographic independent component analysis. MIT Press 13:1527–1558. https://doi.org/10.1162/089976601750264992
Iwai M, Kobayashi K (2017) Dimensional contraction by principal component analysis as preprocessing for independent component analysis at mcg. Biomed Eng Lett 7:221–227. https://doi.org/10.1007/s13534-017-0024-5
Jun Y, Sleighter RL, Elodie M, Georgina A et al (2012) Combining advanced nmr techniques with ultrahigh resolution mass spectrometry: a new strategy for molecular scale characterization of macromolecular components of soil and sedimentary organic matter. Org Geochem 42(8):903–916. https://doi.org/10.1016/j.orggeochem.2011.04.007
Liao, W. , Goossens, B. , Aelterman, J. , Luong, H. Q. , & Philips, W. . (2013). Hyperspectral image deblurring with PCA and total variation. 2013 5th workshop on hyperspectral image and signal processing: evolution in remote sensing (WHISPERS). IEEE. doi: https://doi.org/10.1109/WHISPERS.2013.8080664
Liu, B. L. , Wang, X. Q. , Guo, K. , & Zhao, Y. H. . (2015). Geochemical data processing based on wavelet de-noising. International Computer Conference on Wavelet Active Media Technology & Information Processing IEEE https://doi.org/10.1109/ICCWAMTIP20147073379
Madani N, Sadeghi B (2018) Capturing hidden geochemical anomalies in scarce data by fractal analysis and stochastic modeling. Nat Resour Res 28:833–847. https://doi.org/10.1007/s11053-018-9421-4
Naoto I, Tada-Nori G, Takafumi K, Hideaki M (2018) Robust data processing of noisy marine controlled-source electromagnetic data using independent component analysis. Exploration Geophysics 49(1):21. https://doi.org/10.1071/EG17139
O’Connor D, Vandenberghe L (2017) Total variation image deblurring with space-varying kernel. Comput Optim Appl 67(3):521–541. https://doi.org/10.1007/s10589-017-9901-1
Rejer I, Górski P (2013) Independent component analysis for EEG data preprocessing - algorithms comparison. IFIP international conference on computer information systems and industrial management. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40925-7_11
Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D Nonlinear Phenomena 60(1–4):259–268. https://doi.org/10.1016/0167-2789(92)90242-f
Schaubs P, Zhao C, Hobbs BE (2015) Acquisition of temporal-spatial geochemical information in ore-forming and carbon-dioxide sequestration systems: computational simulation approach. J Geochem Explor 164:18–27. https://doi.org/10.1016/j.gexplo.2015.09.005
Schaubs P, Zhao C, Hobbs BE (2016) Computational simulation of seepage instability problems in fluid-saturated porous rocks: potential dynamic mechanisms for controlling mineralisation patterns. Ore Geology Reviews, S0169136816300427 79:180–188. https://doi.org/10.1016/j.oregeorev.2016.05.002
Selesnick I (2017) Total variation denoising via the moreau envelope. IEEE Signal Processing Letters 24(2):216–220. https://doi.org/10.1109/LSP.2017.2647948
Shichao LI, Yuanyuan P, Wei J, Jingyao M, Laijun LU (2011) Development and application of geochemical data processing system based on fractal theory. Global Geology 14(4):231–235. https://doi.org/10.3969/j.issn.1673-9736.2011.04.03
Virta, J. , & Nordhausen, K. . (2017). On the optimal non-linearities for Gaussian mixtures in FastICA. International Conference on Latent Variable Analysis & Signal Separation Springer International Publishing https://doi.org/10.1007/978-3-319-53547-0_40
Virta J, Li B, Nordhausen K, Oja H (2016) Independent component analysis for tensor-valued data. Journal of Multivariate Analysis 162:162–192. https://doi.org/10.1016/j.jmva.2017.09.008
Wang W, He C (2017) A fast and effective algorithm for a poisson denoising model with total variation. IEEE Signal Processing Letters 24(3):269–273. https://doi.org/10.1109/LSP.2017.2654480
Wang W, Zhao J, Cheng Q (2011) Analysis and integration of geo-information to identify granitic intrusions as exploration targets in southeastern Yunnan district, China. Comput Geosci 37(12):1946–1957. https://doi.org/10.1016/j.cageo.2011.06.023
Wang S, Huang TZ, Zhao XL, Mei JJ, Huang J (2017) Speckle noise removal in ultrasound images by first- and second-order total variation. Numerical Algorithms 78:513–533. https://doi.org/10.1007/s11075-017-0386-x
Xie, Q. W., He, J. C., Qian, L., Mita, S., Chen, X., & Jiang, A. (2013). Image fusion based on TV-L1 function. International Conference on Wavelet Analysis & Pattern Recognition doi: https://doi.org/10.1109/ICWAPR.2013.6599312
Xiong Y, Zuo R (2015) Recognition of geochemical anomalies using a deep autoencoder network. Comput Geosci, S0098300415300728:75–82. https://doi.org/10.1016/j.cageo.2015.10.006
Yahya AA, Tan J, Hu M (2014) A blending method based on partial differential equations for image denoising. Multimedia Tools & Applications 73(3):1843–1862. https://doi.org/10.1007/s11042-013-1586-6
Yu, X., Hu, D., & Xu, J. (2014). 6. Fast independent component analysis and its application. Blind source separation: theory and applications. John Wiley & Sons, Singapore Pte. Ltd.
Zhao, C. . (2009). Dynamic and transient infinite elements. Springer Berlin. https://doi.org/10.1007/978-3-642-00846-7
Zhao CB (2015) Advances in numerical algorithms and methods in computational geosciences with modeling characteristics of multiple physical and chemical processes. Science China Technol Sci 58(5):783–795. https://doi.org/10.1007/s11431-015-5784-5
Zhao, C., Hobbs, B. E., & Ord, A. (2008a). Convective and Advective heat transfer in geological systems. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-79511-7
Zhao CB, Hobbs BE, Ord A (2008b) Investigating dynamic mechanisms of geological phenomena using methodology of computational geosciences: an example of equal-distant mineralization in a fault. Science in China 51(7):947–954. https://doi.org/10.1007/s11430-008-0070-z
Zhao, C., Hobbs, B., & Ord, A. (2009). Fundamentals of computational geoscience. Lect Notes Earth Sci, 122(3), 1–257. https://doi.org/10.1007/978-3-540-89743-9_1
Zhao C, Hobbs BE, Ord A (2010a) Theoretical analyses of nonaqueous phase liquid dissolution-induced instability in two-dimensional fluid-saturated porous media. Int J Numer Anal Methods Geomech, 34(17), 1767–1796. https://doi.org/10.1002/nag.880
Zhao C, Hobbs BE, Ord A, Hornby P, Peng S (2010b) Morphological evolution of three-dimensional chemical dissolution front in fluid-saturated porous media: a numerical simulation approach. Geofluids 8(2):113–127. https://doi.org/10.1111/j.1468-8123.2008.00210.x
Zhao C, Hobbs BE, Ord A (2013) Analytical solutions of nonaqueous-phase-liquid dissolution problems associated with radial flow in fluid-saturated porous media. J Hydrol 494:96–106. https://doi.org/10.1016/j.jhydrol.2013.04.038
Zhao C, Hobbs B, Alt-Epping P (2014) Modeling of ore-forming and geoenvironmental systems: roles of fluid flow and chemical reaction processes. J Geochem Explor 144:3–11. https://doi.org/10.1016/j.gexplo.2014.03.003
Zhao CB, Poulet T, Regenauer-Lieb K (2015) Replacement of annular domain with trapezoidal domain in computational modeling of nonaqueous-phase-liquid dissolution-front propagation problems. J Cent South Univ 22(5):1841–1846. https://doi.org/10.1007/s11771-015-2703-7
Zhao C, Hobbs BE, Ord A (2016) Chemical dissolution-front instability associated with water-rock reactions in groundwater hydrology: analyses of porosity-permeability relationship effects. J Hydrol 540:1078–1087. https://doi.org/10.1016/j.jhydrol.2016.07.022
Zhao CB, Bruce H, Alison O (2017) A new alternative approach for investigating acidization dissolution front propagation in fluid-saturated carbonate rocks. Science China(Technological Sciences)(08), 79–92. https://doi.org/10.1007/s11431-016-0666-1
Zhao CB, Hobbs BE, Ord A (2019) A unified theory for sharp dissolution front propagation in chemical dissolution of fluid-saturated porous rocks. Science China Technol Sci 62 (1):163–174.
Zhou S, Zhou K, Wang J, Yang G, Wang S (2018) Application of cluster analysis to geochemical compositional data for identifying ore-related geochemical anomalies. Frontiers of Earth Science 12(3):491–505. https://doi.org/10.1007/s11707-017-0682-8
Zuo R, Wang J (2015) Fractal/multifractal modeling of geochemical data: a review. J Geochem Explor, S0375674215000746:33–41. https://doi.org/10.1016/j.gexplo.2015.04.010
Zuo R, Xiong Y (2017) Big data analytics of identifying geochemical anomalies supported by machine learning methods. Nat Resour Res 27:5–13. https://doi.org/10.1007/s11053-017-9357-0
Zuo, R., Cheng, Q., Agterberg, F. P., & Xia, Q.(2009a). Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data, a case study from gangdese, Tibet, western China. J Geochem Explor, 101(3), 0–235. doi: https://doi.org/10.1016/j.gexplo.2008.08.003, 225
Zuo, R., Cheng, Q., Agterberg, F. P., & Xia, Q. (2009b). Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data, a case study from gangdese, Tibet, western China. J Geochem Explor, 101(3), 0–235. doi: https://doi.org/10.1016/j.gexplo.2008.08.003, 225
Zuo, R., Carranza, E. J. M., & Cheng, Q. (2012). Fractal/multifractal modelling of geochemical exploration data. Journal of Geochemical Exploration, 122(none). https://doi.org/10.1016/j.gexplo.2012.09.009
Acknowledgments
National Key R&D Program of China (2017YFC0601505), Opening Fund of Geomathematics Key Laboratory of Sichuan Province (Project No: scsxdz201601). Scientific Research Fund of Sichuan Province Education Department (Project No: 17ZB0046). Scientific Research Fund of Sichuan Province Education Department (Project No: 18ZB0062).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Additional information
Communicated by: H. Babaie
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, B., Zhou, Z., Dai, Q. et al. FastICA and total variation algorithm for geochemical anomaly extraction. Earth Sci Inform 13, 153–162 (2020). https://doi.org/10.1007/s12145-019-00412-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-019-00412-0