基于分形理论的板块形态重建

doi:10.13745/j.esf.sf.2020.4.45

摘要/Abstract

摘要：

全球板块重建的精细化和区域化是当前研究的热点领域之一。值得注意的是,针对重建板块形态分布规律的研究,尚未充分展开。在大数据背景下,本文根据已有板块重建模型,对中生代以来的重建板块的形态,进行了分形维数分析,并结合斑岩型铜矿床的频数分布规律,讨论了分形维数和斑岩型矿床频数对板块重建整体性评估的意义。研究结果表明,自250 Ma以来的地质历史时期,全球重建板块形态的分形维数具有先下降后上升的特点,在65 Ma达到最小,可能代表了由Pangea超大陆向未来超大陆Amasia的转换。此外,全球斑岩型铜矿床的频数异常与板块重建形态的分形维数异常具有良好的对应关系,表明板块运动过程中产生的快速形变与斑岩型铜矿床形成之间具有密切的联系。该结果可能将为整体性评估重建板块形态的真实性提供一个全新的方法,特别是对约束古老板块的形态方面,具有一定的科学价值;同时,也能为斑岩型铜矿床的成因,提供对照参考的数据基础。

关键词: 分形维数, 板块重建, 评估, 斑岩型铜矿床, 频数分布

Abstract:

The refinement and regionalization of global plate reconstruction is currently a hot topic in geological study. However, determination of shape distribution of reconstruction plates has not been fully carried out. Based on the existing plate reconstruction models, we analyzed the relationship between fractal dimensions of the reconstruction plates and frequency of global porphyry copper deposits since the Mesozoic. The results showed that the fractal dimensions of 250-65 Ma plates has a minimum at 65 Ma, which reflects the switching process from Pangea breakup to Amasia assembly. Moreover, the frequency anomalies of global porphyry copper deposits correspond well with the fractal dimension anomalies of reconstruction plates since 250 Ma, which suggests that the rapid change of plate morphology may affect the formation of porphyry copper deposits. Our findings provide new insights into evaluating authenticities of reconstruction plates and restricting morphology of ancient plates. Meanwhile, they can also provide reference data for the genesis of porphyry copper deposits.

Key words: fractal dimension, plate reconstruction, evaluation, porphyry copper deposit, frequency distribution

中图分类号:

朱平平, 成秋明, 周远志, 张雨维, 孙家振. 基于分形理论的板块形态重建[J]. 地学前缘, 2020, 27(4): 150-157.

ZHU Pingping, CHENG Qiuming, ZHOU Yuanzhi, ZHANG Yuwei, SUN Jiazhen. Plate reconstruction based on fractal theory[J]. Earth Science Frontiers, 2020, 27(4): 150-157.

图/表 4

图1 全球重建板块(0 Ma)边缘形态的相关关系

Fig.1 Correlation of global reconstruction plate boundaries at 0 Ma

图2 中生代以来全球重建板块形态的分形维数图中误差棒表示特定时间内重建板块分形维数DAP的标准差,间距=2.5 Ma。

Fig.2 Fractal dimensions of global reconstruction plates since 250 Ma

图3 中生代以来全球斑岩型铜矿床频数分布图斑岩型铜矿床年代数据来源美国地质调查局(USGS, https://mrdata.usgs.gov/),N=908,间距=2.5 Ma。

Fig.3 Frequency distribution of global porphyry copper deposits (PCDs) since 250 Ma

图4 中生代以来重建板块分形维数(a)与斑岩型矿床频数分布(b)的对应关系间距=2.5 Ma。

Fig.4 Correction between fractal dimension of reconstruction plates(a) and frequency distribution of porphyry deposits(b) since 250 Ma

参考文献 77

[1]	李三忠, 余珊, 赵淑娟, 等. 超大陆旋回与全球板块重建趋势[J]. 海洋地质与第四纪地质, 2015, 35(1):51-60.
[2]	李三忠, 余珊, 赵淑娟, 等. 超大陆与全球板块重建派别[J]. 海洋地质与第四纪地质, 2014, 34(6):97-117.
[3]	WEGENER A. The origins of the continents[J]. Journal of Geodynamics, 2001, 32:29-63.
[4]	SETON M, MÜLLER R D, ZAHIROVIC S, et al. Global continental and ocean basin reconstructions since 200 Ma[J]. Earth-Science Reviews, 2012, 113(3):212-270.
[5]	MCPHEE P J, VAN HINSBERGEN D J J. Tectonic reconstruction of Cyprus reveals Late Miocene continental collision of Africa and Anatolia[J]. Gondwana Research, 2019, 68:158-173.
[6]	GURNIS M, YANG T, CANNON J, et al. Global tectonic reconstructions with continuously deforming and evolving rigid plates[J]. Computers and Geosciences, 2018, 116:32-41. DOI URL
[7]	WEGENER A. The origins of the continents[J]. Geologische Rundschau, 1915, 3:276-292. DOI URL
[8]	LIU S F, GURNIS M, MA P F, et al. Reconstruction of northeast Asian deformation integrated with western Pacific plate subduction since 200Ma[J]. Earth-Science Reviews, 2017, 175:114-142.
[9]	CHENG Q M. The perimeter-area fractal model and its application to geology[J]. Mathematical Geology, 1995, 27(1):69-82. DOI URL
[10]	CHENG Q M. The gliding box method for multifractal modeling[J]. Computers and Geosciences, 1999, 25(9):1073-1079. DOI URL
[11]	WANG Z J, CHENG Q M, CAO L, et al. Fractal modelling of the microstructure property of quartz mylonite during deformation process[J]. Mathematical Geology, 2007, 39(1):53-68. DOI URL
[12]	CHENG Q M. Non-linear theory and Power-Law models for information integration and mineral resources quantitative assessments[J]. Mathematical Geosciences, 2008, 40(5):503-532. DOI URL
[13]	ZUO R G, CHENG Q M, AGTERBERG F P, et al. Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data, a case study from Gangdese, Tibet, western China[J]. Journal of Geochemical Exploration, 2009, 101(3):225-235. DOI URL
[14]	MALLARD C, COLTICE N, SETON M, et al. Subduction controls the distribution and fragmentation of Earth's tectonic plates[J]. Nature, 2016, 535(7610):140-143.
[15]	TURCOTTE D L. Fractals in petrology[J]. Lithos, 2002, 65(3/4):261-271. DOI URL
[16]	VERMEESCH P. Tectonic discrimination diagrams revisited[J]. Geochemistry, Geophysics, Geosystems, 2006, 7(6):1-55.
[17]	RICHARDS J P. Tectono-magmatic precursors for porphyry Cu-(Mo-Au) deposit formation[J]. Economic Geology, 2003, 98(8):1515-1533. DOI URL
[18]	侯增谦, 曲晓明, 杨竹森, 等. 青藏高原碰撞造山带: Ⅲ. 后碰撞伸展成矿作用[J]. 矿床地质, 2006, 25(6):629-651.
[19]	侯增谦, 杨竹森, 徐文艺, 等. 青藏高原碰撞造山带: Ⅰ. 主碰撞造山成矿作用[J]. 矿床地质, 2006, 25(4):337-358.
[20]	侯增谦, 潘桂棠, 王安建, 等. 青藏高原碰撞造山带: Ⅱ. 晚碰撞转换成矿作用[J]. 矿床地质, 2006, 25(5):521-543.
[21]	MATTHEWS K J, HALE A J, GURNIS M, et al. Dynamic subsidence of Eastern Australia during the Cretaceous[J]. Gondwana Research, 2011, 19(2):372-383. DOI URL
[22]	RICHARDS J P. Making faults run backwards: the Wilson Cycle and ore deposits[J]. Canadian Journal of Earth Sciences, 2014, 51(3):266-271. DOI URL
[23]	张洪瑞, 侯增谦. 大陆碰撞造山样式与过程: 来自特提斯碰撞造山带的实例[J]. 地质学报, 2015, 89(9):1539-1559.
[24]	RICHARDS J P. Tectonic, magmatic, and metallogenic evolution of the Tethyan orogen: from subduction to collision[J]. Ore Geology Reviews, 2015, 70:323-345.
[25]	MATTHEWS K J, MALONEY K T, ZAHIROVIC S, et al. Global plate boundary evolution and kinematics since the late Paleozoic[J]. Global and Planetary Change, 2016, 146:226-250. DOI URL
[26]	刘少峰, 王成善. 构造古地理重建与动力地形[J]. 地学前缘, 2016, 23(6):61-79.
[27]	丁林, SATYBAEV M, 蔡福龙, 等. 印度与欧亚大陆初始碰撞时限、封闭方式和过程[J]. 中国科学: 地球科学, 2017, 47(3):293-309.
[28]	李晓峰, 华仁民, 马东升, 等. 大陆岩石圈伸展与斑岩铜矿成矿作用[J]. 岩石学报, 2019, 35(1):76-88.
[29]	MANDELBROT B. How long is the coast of Britain? Statistical self-similarity and fractional dimension[J]. Science, 1967, 156(3775):636. DOI URL
[30]	MANDELBROT B B, PASSOJA D E, PAULLAY A J. Fractal character of fracture surfaces of metal[J]. Nature, 1984, 308(5961):721-722. DOI URL
[31]	BARTON C C, TEBBENS S F. Fractals in the Earth sciences[M]. New York: Spring, 1995: 1-265.
[32]	SORNETTE D, PISARENKO V. Fractal plate tectonics[J]. Geophysical Research Letters, 2003, 30(3):1105. DOI URL
[33]	申维. 中国白垩纪矿床时空分布的分形分析[J]. 地质力学学报, 2008, 14(1):57-64.
[34]	ZUO R G, CHENG Q M, XIA Q L, et al. Application of fractal models to distinguish between different mineral phases[J]. Mathematical Geosciences, 2009, 41(1):71-80.
[35]	XIE S Y, CHENG Q M, ZHANG SS, et al. Assessing microstructures of pyrrhotites in basalts by multifractal analysis[J]. Nonlinear Processes in Geophysics, 2010, 17(4):319-327. DOI URL
[36]	ALI E H M, KHAKZAD A, LOTFI M, et al. Prospecting of Ni mineralization using fractal models based on lithogeochemical data in Patang area, Eastern Iran[J]. Arabian Journal of Geosciences, 2015, 8(11):9667-9677. DOI URL
[37]	RANGUELOV B, IVANOV Y. Fractal properties of the elements of plate tectonics[J]. Journal of Mining and Geological Sciences, 2017, 60:83-89.
[38]	ZUO R G. A fractal measure of mass transfer in fluid-rock interaction[J]. Ore Geology Reviews, 2018, 95:569-574.
[39]	CHENG Q M. Singularity analysis of global zircon U-Pb age series and implication of continental crust evolution[J]. Gondwana Research, 2017, 51:51-63. DOI URL
[40]	CHEN G X, CHENG Q M. Cyclicity and persistence of Earth's evolution over time: wavelet and fractal analysis[J]. Geophysical Research Letters, 2018, 45(16):8223-8230. DOI URL
[41]	CHENG Q M. Singularity analysis of magmatic flare-ups caused by India-Asia collisions[J]. Journal of Geochemical Exploration, 2018, 189(Suppl I):25-31. DOI URL
[42]	BRINKHOFF L A, SAVIGNY C V, RANDALL C E, et al. The fractal perimeter dimension of noctilucent clouds: sensitivity analysis of the area-perimeter method and results on the seasonal and hemispheric dependence of the fractal dimension[J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2015, 127:66-72.
[43]	SILLITOE R H. Porphyry copper systems[J]. Economic Geology, 2010, 105(1):3-41. DOI URL
[44]	RICHARDS J P, MUMIN A H. Magmatic-hydrothermal processes within an evolving Earth: iron oxide-copper-gold and porphyry Cu-Mo-Au deposits[J]. Geology, 2013, 41(7):767-770. DOI URL
[45]	WANG R, WEINBERG R F, COLLINS W J, et al. Origin of postcollisional magmas and formation of porphyry Cu deposits in southern Tibet[J]. Earth-Science Reviews, 2018, 181:122-143.
[46]	RICHARDS J P, RAZAVI A M, SPELL T L, et al. Magmatic evolution and porphyry-epithermal mineralization in the Taftan volcanic complex, southeastern Iran[J]. Ore Geology Reviews, 2018, 95:258-279.
[47]	RICHARDS J P. Postsubduction porphyry Cu-Au and epithermal Au deposits: products of remelting of subduction-modified lithosphere[J]. Geology, 2009, 37(3):247-250. DOI URL
[48]	HOU Z Q, YANG Z M, LU Y J, et al. A genetic linkage between subduction- and collision-related porphyry Cu deposits in continental collision zones[J]. Geology, 2015, 43(3):643-650. DOI URL
[49]	CHIARADIA M. Copper enrichment in arc magmas controlled by over riding plate thickness[J]. Nature Geoscience, 2013, 7(1):43-46. DOI URL
[50]	芮宗瑶, 张立生, 陈振宇, 等. 斑岩铜矿的源岩或源区探讨[J]. 岩石学报, 2004(2):229-238.
[51]	HU R Z, BURNARD P G, BI X W, et al. Helium and argon isotope geochemistry of alkaline intrusion-associated gold and copper deposits along the Red River-Jinshajiang fault belt, SW China[J]. Chemical Geology, 2004, 203(3):305-317. DOI URL
[52]	胡瑞忠, 毛景文, 范蔚茗, 等. 华南陆块陆内成矿作用的一些科学问题[J]. 地学前缘, 2010, 17(2):13-26.
[53]	GOLDFARB R J, BRADLEY D, LEACH D L. Secular variation in economic geology[J]. Economic Geology, 2010, 105(3):459-465. DOI URL
[54]	GROVES D I, VIELREICHER R M, GOLDFARB R J, et al. Controls on the heterogeneous distribution of mineral deposits through time[J]. Geological Society of London, Special Publication, 2005, 248:71-101. DOI URL
[55]	李三忠, 索艳慧, 刘博, 等. 微板块构造理论: 全球洋内与陆缘微地块研究的启示[J]. 地学前缘, 2018, 25(5):324-356.
[56]	LI S, SUO Y, LI X, et al. Microplate tectonics: new insights from micro-blocks in the global oceans, continental margins and deep mantle[J]. Earth-Science Reviews, 2018, 185:1029-1064. DOI URL
[57]	REZEAU H, MORITZ R, WOTZLAW J F, et al. Temporal and genetic link between incremental pluton assembly and pulsed porphyry Cu-Mo formation in accretionary orogens[J]. Geology, 2016, 44(8):627-630. DOI URL
[58]	GRONDAHL C, ZAJACZ Z. Magmatic controls on the genesis of porphyry Cu-Mo-Au deposits: the Bingham Canyon example[J]. Earth and Planetary Science Letters, 2017, 480:53-65. DOI URL
[59]	侯增谦, 杨志明. 中国大陆环境斑岩型矿床: 基本地质特征、岩浆热液系统和成矿概念模型[J]. 地质学报, 2009, 83(12):1779-1817.
[60]	ZHENG Y C, LIU S A, WU C D, et al. Cu isotopes reveal initial Cu enrichment in sources of giant porphyry deposits in a collisional setting[J]. Geology, 2019, 47(2):135-138. DOI URL
[61]	侯增谦. 大陆碰撞成矿论[J]. 地质学报, 2010, 84(1):30-58.
[62]	WU W B, NI S D, IRVING J. Inferring Earth's discontinuous chemical layering from the 660-kilometer boundary topography[J]. Science, 2019, 363(6428):736-740. DOI URL
[63]	PARMAN S W. Helium isotopic evidence for episodic mantle melting and crustal growth[J]. Nature, 2007, 446(7138):900-903. DOI URL
[64]	PEARSON D G, PARMAN S W, NOWELL G M. A link between large mantle melting events and continent growth seen in osmium isotopes[J]. Nature, 2007, 449(7159):202. DOI URL
[65]	YUAN H Y. Secular change in Archaean crust formation recorded in Western Australia[J]. Nature Geoscience, 2015, 8(10):808-813. DOI URL
[66]	郑永飞, 陈伊翔, 戴立群, 等. 发展板块构造理论: 从洋壳俯冲带到碰撞造山带[J]. 中国科学: 地球科学, 2015, 45(6):711-735.
[67]	LOVEJOY S, SCHERTZER D. Scaling and multifractal fields in the solid earth and topography[J]. Nonlinear Processes in Geophysics, 2007, 14(4):293-315. DOI URL
[68]	NEWMAN M. Power laws, Pareto distributions and Zipf's law[J]. Contemporary Physics, 2005, 46(5):323-351. DOI URL
[69]	BURET Y, VON QUADT A, HEINRICH C, et al. From a long-lived upper-crustal magma chamber to rapid porphyry copper emplacement: reading the geochemistry of zircon crystals at Bajo de la Alumbrera (NW Argentina)[J]. Earth and Planetary Science Letters, 2016, 450:120-131. DOI URL
[70]	MARSH T M, EINAUDI M T, MCWILLIAMS M. ⁴⁰Ar/³⁹Ar geochronology of Cu-Au and Au-Ag mineralization in the Potrerillos District, Chile[J]. Economic Geology, 1997, 92:784-806. DOI URL
[71]	REYNOLDS P, RAVENHURST C, ZENTILLI M, et al. High-precision ⁴⁰Ar/³⁹Ar dating of two consecutive hydrothermal events in the Chuquicamata porphyry copper system, Chile[J]. Chemical Geology, 1998, 148(1):45-60. DOI URL
[72]	LI X F, HU R Z, RUSK B, et al. U-Pb and Ar-Ar geochronology of the Fujiawu porphyry Cu-Mo deposit, Dexing district, Southeast China: implications for magmatism, hydrothermal alteration, and mineralization[J]. Journal of Asian Earth Sciences, 2013, 74:330-342. DOI URL
[73]	BARRA F, ALCOTA H, RIVERA S, et al. Timing and formation of porphyry Cu-Mo mineralization in the Chuquicamata district, northern Chile: new constraints from the Toki cluster[J]. Mineralium Deposita, 2013, 48(5):629-651. DOI URL
[74]	JAGOUTZ O, ROYDEN L, HOLT A F, et al. Anomalously fast convergence of India and Eurasia caused by double subduction[J]. Nature Geoscience, 2015, 8(6):475-478. DOI URL
[75]	VOICE P J, KOWALEWSKI M, ERIKSSON K A. Quantifying the timing and rate of crustal evolution: global compilation of radiometrically dated detrital zircon grains[J]. The Journal of Geology, 2011, 119(2):109-126. DOI URL
[76]	BELOUSOVA E A, KOSTITSYN Y A, GRIFFIN W L, et al. The growth of the continental crust: constraints from zircon Hf-isotope data[J]. Lithos, 2010, 119(3/4):457-466. DOI URL
[77]	SPENCER C J, CAWOOD P A, HAWKESWORTH C J, et al. Proterozoic onset of crustal reworking and collisional tectonics: reappraisal of the zircon oxygen isotope record[J]. Geology, 2014, 42(5):451-454. DOI URL