ArticlesNo Access

FRACTAL ANALYSIS OF AMPHIBOLE AGGREGATION GROWTH FROM A BASALTIC MELT AND RESIDUAL MELT AT HIGH PRESSURE AND HIGH TEMPERATURE

Key Laboratory for High Temperature and High Pressure Study of the Earth’s Interior Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, P. R. China

University of Chinese Academy of Sciences, Beijing 100049, P. R. China

Search for more papers by this author

BO ZHANG

Key Laboratory for High Temperature and High Pressure Study of the Earth’s Interior Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, P. R. China

University of Chinese Academy of Sciences, Beijing 100049, P. R. China

Search for more papers by this author

QIZHE TANG

Key Laboratory for High Temperature and High Pressure Study of the Earth’s Interior Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, P. R. China

University of Chinese Academy of Sciences, Beijing 100049, P. R. China

Search for more papers by this author

JINGUI XU

Key Laboratory for High Temperature and High Pressure Study of the Earth’s Interior Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, P. R. China

Search for more papers by this author

DAWEI FAN

Key Laboratory for High Temperature and High Pressure Study of the Earth’s Interior Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, P. R. China

Search for more papers by this author

, and

WENGE ZHOU

Key Laboratory for High Temperature and High Pressure Study of the Earth’s Interior Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, P. R. China

E-mail Address: zhouwenge@vip.gyig.ac.cn

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0218348X18500329Cited by:0 (Source: Crossref)

Abstract

The aim of this work is to quantitatively explore the texture evolution of amphibole aggregation and residual melt with pressure and temperature. The amphibole aggregation growth from a basaltic melt and the residual melt at high pressure (0.6–2.6GPa) and high temperature (860–970 $^{\circ}$ C) exhibit statistical self-similarity which made us consider studying such characteristic by fractal analysis. The bi-phase box counting method was applied for fractal analysis of each product to identify the fractal phase and the fractal dimension was estimated. In the experimental products, the residual melt is identified as the fractal and amphibole as the Euclidean except for one experiment. The results show that the residual melt can be quantified by the fractal dimension $(D_{B})$ within the range of 1.782–1.848. The temperature has a significant effect on the morphology of amphibole and the fractal dimension of the residual melt. The higher the crystallization temperature is, the more regular the amphibole grains are. At lower temperature (from 860 $^{\circ}$ C to 915 $^{\circ}$ C), the fractal dimension of the residual melt decreased with the increasing crystallization temperature, but at higher temperature (970 $^{\circ}$ C), the fractal phase changed to amphibole and the fractal dimension of amphibole is 1.816. The pressure may be the dominant factor that controls the morphology of the mineral aggregation and the residual melt. The fractal dimension of melt decreased linearly with the increasing pressure and if the linear relationship between the fractal dimension and pressure can be further verified in the future, it can be used as a potential geological barometer.

Keywords:

References

1. B. B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science 156(3775) (1967) 636–638. Web of Science, Google Scholar
2. D. L. Turcotte, Fractals in geology and geophysics, Pure Appl. Geophys. 131(1–2) (1989) 171–196. Web of Science, Google Scholar
3. D. L. Turcotte, Fractals and Chaos in Geology and Geophysics, 2nd edn. (Cambridge University Press, 1997). Google Scholar
4. B. M. Yu, J. C. Cai and M. Q. Zou, On the physical properties of apparent two-phase fractal porous media, Vadose Zone J. 8(1) (2009) 177–186. Web of Science, Google Scholar
5. M. K. Sachs, M. R. Yoder, D. L. Turcotte, J. B. Rundle and B. D. Malamud, Black swans, power laws, and dragon-kings: Earthquakes, volcanic eruptions, landslides, wildfires, floods, and SOC models, Eur. Phys. J.-Spec. Top. 205(1) (2012) 167–182. Web of Science, Google Scholar
6. B. L. Cox and J. S. Y. Wang, Fractal surfaces: Measurement and applications in the earth sciences, Fractals 1(1) (1993) 87–115. Link, Web of Science, Google Scholar
7. J. P. Ortiz, R. C. Aguilera, A. S. Balankin, M. P. Ortiz, J. C. T. Rodriguez, M. A. A. Mosqueda, M. A. M. Cruz and W. Yu, Seismic activity seen through evolution of the hurst exponent model in 3d, Fractals 24(4) (2016) 1650045. Link, Web of Science, Google Scholar
8. L. J. You, Q. Chen, Y. L. Kang, Y. F. Yu and J. G. He, Evaluation of formation damage using microstructure fractal in shale reservoirs, Fractals 23(1) (2015) 1540008. Link, Web of Science, Google Scholar
9. Y. L. Zhang, Q. Sun, H. He, L. W. Cao, W. Q. Zhang and B. Wang, Pore characteristics and mechanical properties of sandstone under the influence of temperature, Appl. Therm. Eng. 113 (2017) 537–543. Web of Science, Google Scholar
10. B. D. Malamud, G. Morein and D. L. Turcotte, Forest fires: An example of self-organized critical behavior, Science 281(5384) (1998) 1840–1842. Web of Science, Google Scholar
11. B. D. Malamud and D. L. Turcotte, Self-affine time series: I. Generation and analyses, Adv. Geophys. 40 (1999) 1–90. Web of Science, Google Scholar
12. C. G. Sammis, R. H. Osborne, J. L. Anderson, M. Banerdt and P. White, Self-similar cataclasis in the formation of fault gouge, Pure Appl. Geophys. 124(1–2) (1986) 53–78. Web of Science, Google Scholar
13. D. L. Turcotte and B. D. Malamud, Landslides, forest fires, and earthquakes: Examples of self-organized critical behavior, Physica A 340(4) (2004) 580–589. Web of Science, Google Scholar
14. D. L. Turcotte, Self-organized complexity in geomorphology: Observations and models, Geomorphology 91(3–4) (2007) 302–310. Web of Science, Google Scholar
15. F. P. Agterberg, Fractals and spatial statistics of point patterns, J. Earth Sci. China 24(1) (2013) 1–11. Web of Science, Google Scholar
16. E. Perfect and B. Donnelly, Bi-phase box counting: An improved method for fractal analysis of binary images, Fractals 23(1) (2015) 1540010. Link, Web of Science, Google Scholar
17. J. H. Kruhl and M. Nega, The fractal shape of sutured quartz grain boundaries: Application as a geothermometer, Geol. Rundsch. 85(1) (1996) 38–43. Google Scholar
18. S. Majumder and M. A. Mamtani, Fractal analysis of quartz grain boundary sutures in a granite (Malanjkhand, Central India) — Implications to infer regional tectonics, J. Geol. Soc. India 73(3) (2009) 309–319. Web of Science, Google Scholar
19. M. A. Mamtani, Strain-rate estimation using fractal analysis of quartz grains in naturally deformed rocks, J. Geol. Soc. India 75(1) (2010) 202–209. Web of Science, Google Scholar
20. M. A. Mamtani, Fractal analysis of magnetite grains — Implications for interpreting deformation mechanism, J. Geol. Soc. India 80(3) (2012) 308–313. Web of Science, Google Scholar
21. D. Perugini and U. Kueppers, Fractal analysis of experimentally generated pyroclasts: A tool for volcanic hazard assessment, Acta Geophys. 60(3) (2012) 682–698. Web of Science, Google Scholar
22. M. Takahashi, Fractal analysis of experimentally, dynamically recrystallized quartz grains and its possible application as a strain rate meter, J. Struct. Geol. 20(2–3) (1998) 269–275. Web of Science, Google Scholar
23. S. Volland and J. H. Kruhl, Anisotropy quantification: The application of fractal geometry methods on tectonic fracture patterns of a Hercynian fault zone in NW Sardinia, J. Struct. Geol. 26(8) (2004) 1499–1510. Web of Science, Google Scholar
24. M. Wang et al., Zircon U–Pb dating of Pubei granite and strontium isotope from sphalerite of the Xinhua Pb–Zn–(Ag) deposit, Yunkai Area of Guangxi Province, South China, Acta Geochim. 35(2) (2016) 156–171. Web of Science, Google Scholar
25. Z. N. Meng et al., The genetic relationship between Habo alkaline intrusion and its surrounding deposits, Yunnan Province, China: Geological and S–Pb isotopic evidences, Acta Geochim. 35(4) (2016) 391–407. Web of Science, Google Scholar
26. M. D. Higgins, Verification of ideal semi-logarithmic, lognormal or fractal crystal size distributions from 2D datasets, J. Volcanol. Geotherm. Res. 154 (1–2) (2006) 8–16. Web of Science, Google Scholar
27. W. G. Zhou, B. R. Zhang, Z. D. Zhao and H. S. Xie, Geochemical characteristics and the provenance of cenozoic basic volcanic rocks in western Henan province, China, J. Mineral. Petrol. 18(3) (1998) 52–58 (in Chinese with English abstract). Google Scholar
28. E. A. K. Middlemost, Naming materials in the magma igneous rock system, Earth-Sci. Rev. 37(3–4) (1994) 215–224. Web of Science, Google Scholar
29. P. M. Smith and P. D. Asimow, Adiabat_1ph: A new public front-end to the MELTS, pMELTS, and pHMELTS models, Geochem. Geophys. Geosyst. 6(2) (2005) Q02004. Web of Science, Google Scholar
30. H. F. Fu and C. M. Zhu, Testing parameters such as temperature, pressure in static super high pressure apparatus, Physics 9(3) (1980) 193–195 (in Chinese with English abstract). Google Scholar
31. S. M. Shan, R. P. Wang, J. Guo and H. P. Li, Pressure calibration for the sample cell of YJ-3000t multi-anvil press at high temperature and high pressure, Chin. J. High Pressure Phys. 21(4) (2007) 367–372 (in Chinese with English abstract). Google Scholar
32. D. L. Turcotte, Fractals in petrology, Lithos 65(3–4) (2002) 261–271. Web of Science, Google Scholar
33. R. Lopes and N. Betrouni, Fractal and multifractal analysis: A review, Med. Image Anal. 13(4) (2009) 634–649. Web of Science, Google Scholar
34. T. Hirata, Fractal dimension of fault systems in Japan — fractal structure in rock fracture geometry at various scales, Pure Appl. Geophys. 131(1–2) (1989) 157–170. Web of Science, Google Scholar
35. N. Otsu, Threshold selection method from gray-level histograms, IEEE Trans. Syst. Man. Cybern. 9 (1979) 62–66. Web of Science, Google Scholar
36. F. Faure, G. Trolliard, C. Nicollet and J. M. Montel, A developmental model of olivine morphology as a function of the cooling rate and the degree of undercooling, Contrib. Mineral Petrol. 145(2) (2003) 251–263. Web of Science, Google Scholar