Marine Geophysical Research

, Volume 36, Issue 2–3, pp 139–147 | Cite as

Study of the permeability in melting zone of South China Sea based on percolation theory

  • Ju-ying Wan
  • He-hua Xu
  • Yan-zhen Li
  • Wei-bing Shu
Original Research Paper


Oceanic crust is formed at mid-ocean ridges. The melting zone extends up to several hundreds of km laterally, the upwelling area at the spreading axis is confined to a narrow belt of only 2–3 km width. Whereas the parameter of permeability that magma ascending from the mantle beneath mid-ocean ridges is still poorly understood, despite the important role of the process for the formation of crust. Based on continuum percolation, we build the random fracture network as magma migration channels of South China Sea; with momentum equation, we deduced the dynamic pressure distribution with passive corner flow. After which, the permeability of melting zone is calculated with finite element method. Numerical simulation results indicate that there exists a power law relationship between the permeability and magma migration channels. The simulated result is consistent with that calculated by fractal method. The discovery of the ruler provides sound theoretical basis for the formation and evolution of oceanic crust, and may help us better understanding the formation and evolution of South China Sea.


Magma migration Oceanic crust Rising divergent mantle flow Percolation method Permeability 



The national natural science foundation of China (41376061) and National major oil and gas Projects (2011ZX05008-004-44).


  1. Balberg I, Anderson CH, Alexander S et al (1984) Excluded volume and its relation to the onset of percolation. Phys. Rev. B 30:3933CrossRefGoogle Scholar
  2. Barton CC (1995) Fractal analysis of the scaling and spatialclustering of fractures in rock. In: Barton CC, La Pointe PR (eds) Fractal in the Earth Sciences. Plenum Press, New YorkCrossRefGoogle Scholar
  3. Batanova VG, Savelieva GN (2009) Melt migration in the mantle beneath spreading zones and formation of replacivedunites: a review. Russ Geol Geophys 50:763–778CrossRefGoogle Scholar
  4. Batchelor GK (1967) An introduction to fluid dynamic. Cambridge University Press, CambridgeGoogle Scholar
  5. Bear J (1972) Dynamics of fluids in porous media. Elsevier, New YorkGoogle Scholar
  6. Braun MG, Kelemen PB (2002) Dunite distribution in the Oman ophiolite: implications for melt flux through porous dunite conduits. Geochem Geophys Geosyst 3(11):1–21 Google Scholar
  7. Broadbent SR, Hammersly JM (1957) Percolation processes. Proc Camb Philos 53:629–641CrossRefGoogle Scholar
  8. Carman PZ (1956) Flow of gases through porous media. Butter-Worths, LondonGoogle Scholar
  9. Dahm T (2000) Numerical simulations of the propagation path and the arrest of fluid-filled fractures in the earth. Geophys J Int 141:623–638CrossRefGoogle Scholar
  10. Gudmundsson A (1990) Dyke emplacement at divergent plate boundaries. In: Parker AJ, Rickwood PC, Tucker DH (eds) Mafic dykes and emplacement mechanisms. Balkema, Rotterdam. Proceedings of the second international dyke conference, Adelaide, South Australia, 12–16 September 1990, pp 47–62Google Scholar
  11. Huppert HE, Worster MG (1991) Vigorous motions in magma chambers and lava lakes. In: Yuen DA (ed) Chaotic processes in the geological sciences, vol. 41. Institute of Mathematics and its Applications Series, pp 160–173Google Scholar
  12. Hersum T, Hilpert M, Marsh B (2005) Permeability and melt flow in simulated and natural partially molten basaltic magma. Earth Planet Sci Lett 237:798–814CrossRefGoogle Scholar
  13. Kelemen PB, Shimizu N, Salters VJM (1995) Extraction of mid-ocean-ridge basalt from the upwelling mantle by focused flow of melt in dunite channels. Nature 395:747–753CrossRefGoogle Scholar
  14. Kelemen PB, Hirth G, Shimizu N, Spiegelman M, Dick HJB (1997) A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges. Philos Trans: Math Phys Eng Sci 355:283–318CrossRefGoogle Scholar
  15. Kelemen PB, Braun M, Hirth G (2000) Spatial distribution of melt conduits in the mantle beneath oceanic spreading ridges: observations from the Ingalls and Oman ophiolites. Geochem Geophys Geosyst. doi: 10.1029/1999GC000012 Google Scholar
  16. Khamforoush K, Shams K, Thovert JF, Adler PM (2008) Permeability and percolation of anisotropic three-dimensional fracture networks. Phys Rev E 77(5):6307. doi: 10.1103/PhysRevE.77.056307 CrossRefGoogle Scholar
  17. King PR (1989) The use of renormalization for effective permeability. Transp Porous Media 4:37–58Google Scholar
  18. King PR (1990) The connectivity and conductivity of overlapping sand bodies. In: 2nd International conference of north sea oil and gas reservoir. Graham and Trotman, London, pp 353–358Google Scholar
  19. Kuhn D, Dahm T (2004) Simulation of magma ascent by dykes in the mantle beneath mid-ocean ridges. J Geodyn 38:147–159CrossRefGoogle Scholar
  20. Kusznir NJ, Karner GD (2007) Continental lithospheric thinning and breakup in response to upwelling divergent mantle flow: application to the Woodlark, Newfoundland and Iberia margins. In: Karner GD, Manatschal G, Pinheiro LM (eds) Imaging, mapping and modelling continental lithosphere extension and breakup. Geological Society, London, Special Publication, 282:389–419Google Scholar
  21. Mckenzie D (1984) The generation and compaction of partially molten rock. J Petrol 25(3):713–765Google Scholar
  22. Li JB, Jin XL, Gao JY (2002) Morpho-tectonic study in late-stage spreading of the Eastern Subbasin of South China Sea. Sci China Ser D 32(3):239–248Google Scholar
  23. Petford N, Koenders MAC (1998) Self-organisation and fracture connectivity in rapidly heated continental. J Struct Geol 20(9):1425–1434CrossRefGoogle Scholar
  24. Phipps Morgan J (1987) Melt migration beneath mid-ocean spreading centers. Geophys Res Lett 14(12):1238–1241CrossRefGoogle Scholar
  25. Shi X, Yan Q (2011) Geochemistry of cenozoic magmatism in the South Chian Sea and its tectonic implications. Mar Geolog Quat Geolog 31(2):59–72 (in Chinese)Google Scholar
  26. Shi X, Xu H, Qiu X et al (2008) Numerical modeling on the relationship between thermal uplift and subsequent rapid subsidence: discussions on the evolution of the Tainan Basin. Tectonics. doi: 10.1029/2007TC002163 Google Scholar
  27. Spiegelman M, McKenzie DP (1987) Simple 2-D models for melt extraction at mid-ocean ridges and island arcs. Earth Planet Sci Lett 83:137–152CrossRefGoogle Scholar
  28. Stanley R, Hart R (1993) Equilibration during mantle melting: a fractal tree model. Geology 90:11914–11918Google Scholar
  29. Stauffer D, Aharony A (1992) Introduction to percolation theory. Taylor and Francis, LondonGoogle Scholar
  30. Taylor B, Hayes DE (1983) Origin and history of the South China Sea basin. American Geophysical Union, WashingtonCrossRefGoogle Scholar
  31. Vaentini L, Perugini D, Poli G (2007) The small-world topology of rock fracture networks. Phys A 377:323–328CrossRefGoogle Scholar
  32. Valentini L, Perugini D, Poli G (2007) The ‘small-world’ nature of fracture/conduit networks: possible implications for disequilibrium transport of magmas beneath mid-ocean ridges. J Volcanol Geotherm Res 159(2007):355–365CrossRefGoogle Scholar
  33. Walsh SDC, Saar MO (2008) Magma yield stress and permeability: insights from multiphase percolation theory. J Volcanol Geotherm Res 177:1011–1019Google Scholar
  34. Xu HH, Ma H, Song HB et al (2011) Numerical simulation of Eastern South China Sea basin expansion. Chin J Geophys 54(12):3070–3078 (in Chinese)Google Scholar
  35. Xu X, Wang J, Zhang B (2006) Transport dynamics of magma and its advances. Adv Earth Sci 21(4):361–371 (in Chinese)Google Scholar
  36. Yazdi A, Hamzehpour H, Sahimi M (2011) Permeability, porosity, and percolation properties of two-dimensional disordered fracture networks. Phys Rev E 84(4):1–10CrossRefGoogle Scholar
  37. Zhang J, Song HB, Li JB (2005) Thermal modeling of the tectonic evolution of the south west sub-basin in the South China Sea. Chin J Geophys 48(6):1357–1365 (in Chinese)Google Scholar
  38. Zhang GL, Zeng Z, Beier C, Yin X, Turner S (2010) Generation and evolution of magma beneath the East Pacific Rise: constraints from U-series disequilibrium and plagioclase-hosted melt inclusions. J Volcanol Geotherm Res 193:1–17CrossRefGoogle Scholar
  39. Zhang GL, Zong CL, Yin X, Li H (2012) Geochemical constraints on a mixed pyroxenite–peridotite source for East Pacific Rise basalts. J Chem Geol 330–331:176–187CrossRefGoogle Scholar
  40. Zhu W, Hirth G (2003) A network model for permeability in partially molten rocks. Earth Planet Sci Lett 212:407–416CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Ju-ying Wan
    • 1
    • 2
  • He-hua Xu
    • 1
  • Yan-zhen Li
    • 1
    • 2
  • Wei-bing Shu
    • 1
    • 2
  1. 1.Key Laboratory of Marginal Sea Geology of Chinese Academy of Sciences, South China Sea Institute of OceanologyUniversity of Chinese Academy of SciencesGuangzhouChina
  2. 2.University of Chinese Academy of SciencesBeijingChina

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