斜长石、辉石混合模型的电导率有限元数值计算研究
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摘要
以岩石实验中矿物的几何形态及空间分布为建模依据,以实验条件及单矿物电导率的测量结果为约束条件,用有限元数值方法模拟了不同微观结构的斜长石、辉石混合物在施加电压后电势及电流的分布情况,并计算了混合模型在不同温度条件下的电导率.研究结果显示,数值模型网格数及矿物颗粒数的选取对电导率计算结果的精度有较大影响,在体导电情况下,模型电导率因矿物比例含量和排列结构而异.当斜长石及辉石随机分布时,随着辉石含量的增加,混合模型电导率在不同温度下均有所增加,且温度越高,增加幅度越大,电导率的有限元模拟计算结果接近于有效介质渗透理论模型,且位于并、串联模型之间以及HS模型的上、下边界范围内;在斜长石及辉石含量一定的情况下,各矿物的排列分布对电导率计算结果也有一定的影响,当矿物颗粒大小接近且分布均匀时,模型中电势沿电流传导方向变化较为均匀,模拟计算得出的电导率相对较高,当矿物颗粒大小差别较大及分布不均匀时,电势分布受到一定的扰动,电导率计算结果也较低.将混合模型电导率有限元计算结果与辉长岩、辉绿岩及玄武岩实验测量结果进行比较,显示这3种岩石样品电导率与温度变化关系的斜率均与混合模型计算结果的斜率相接近,表明这些岩石在所选温度段导电机制与斜长石、辉石混合模型相似,用斜长石、辉石混合模型的电导率研究玄武岩、辉长岩及辉绿岩的导电性具有适用性.将混合模型有限元计算结果与玄武岩、辉长岩、辉绿岩覆盖区地壳大地电磁实测结果对比,发现大地电磁电导率结果位于混合模型计算结果范围内,用斜长石、辉石混合模型模拟玄武岩、辉长岩等岩石地壳具有一定的可行性.
The finite element numerical simulation method was used to investigate the electricalconductivity and potential distribution of plagioclase-pyroxene mixed models.The two-dimensional mineral mixed models were constrained by the experimental measurement conditions,the experimental results of electrical conductivities for single minerals,and the geometrical shapes and spatial distribution of the minerals.The results show that the amount of model mesh and that of the mineral particles strongly influenced the accuracy of the calculation results.The electrical conductivities of the mixed models varied with the composition ratio and mineral arrangement structure and increased with increasing pyroxene content at same temperatures;the increase was sharper at high temperatures.The results of the finite element numerical simulation closely corresponded to those of the effective medium percolation theory model,which lies within the range of the electrical conductivity of the parallel structure model and series structure model,and lies within that of the HS+model and HS-model,either.At certain concentrations of plagioclase and pyroxene,the electrical conductivities of mixed models were relatively higher when the models had uniform distribution of mineral particles,and the electric potentials decreased smoothly from the top to the bottom of the model.However,the electrical conductivities were smaller with uneven distribution of mineral particles,and the distribution of electrical potentials was disturbed.By comparing the electrical conductivity between the experimental results of gabbro,diabase,basalt,and finite element calculation results,we found that the slope of the logarithm(electrical conductivity)versus reciprocal temperature closely corresponded to that of the mineral mixed model.This indicated that the conductive mechanisms of the abovementioned three rocks were similar to those of the plagioclase-pyroxene mixed models in the selected temperature range,and the finite element numerical calculation for basalt,gabbro,and diabase were applied to the mixed models.When applied to the crust containing gabbro,diabase,and basalt,the result of geophysical conductivity profiles lay within the range of the mineral mixed model.This correlation of the simulation results and field conductivities indicates that simulating the rock crust with the mineral mixed models in certain proportions was feasible to a certain extent.
The finite element numerical simulation method was used to investigate the electricalconductivity and potential distribution of plagioclase-pyroxene mixed models.The two-dimensional mineral mixed models were constrained by the experimental measurement conditions,the experimental results of electrical conductivities for single minerals,and the geometrical shapes and spatial distribution of the minerals.The results show that the amount of model mesh and that of the mineral particles strongly influenced the accuracy of the calculation results.The electrical conductivities of the mixed models varied with the composition ratio and mineral arrangement structure and increased with increasing pyroxene content at same temperatures;the increase was sharper at high temperatures.The results of the finite element numerical simulation closely corresponded to those of the effective medium percolation theory model,which lies within the range of the electrical conductivity of the parallel structure model and series structure model,and lies within that of the HS+model and HS-model,either.At certain concentrations of plagioclase and pyroxene,the electrical conductivities of mixed models were relatively higher when the models had uniform distribution of mineral particles,and the electric potentials decreased smoothly from the top to the bottom of the model.However,the electrical conductivities were smaller with uneven distribution of mineral particles,and the distribution of electrical potentials was disturbed.By comparing the electrical conductivity between the experimental results of gabbro,diabase,basalt,and finite element calculation results,we found that the slope of the logarithm(electrical conductivity)versus reciprocal temperature closely corresponded to that of the mineral mixed model.This indicated that the conductive mechanisms of the abovementioned three rocks were similar to those of the plagioclase-pyroxene mixed models in the selected temperature range,and the finite element numerical calculation for basalt,gabbro,and diabase were applied to the mixed models.When applied to the crust containing gabbro,diabase,and basalt,the result of geophysical conductivity profiles lay within the range of the mineral mixed model.This correlation of the simulation results and field conductivities indicates that simulating the rock crust with the mineral mixed models in certain proportions was feasible to a certain extent.
引文
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Dai L D,Karato S I.2009.Electrical conductivity of pyrope-rich garnet at high temperature and high pressure.Physics of the Earth&Planetary Interiors,176(1-2):83-88.
Dai L D,Li H P,Hu H Y,et al.2012.The effect of chemical composition and oxygen fugacity on the electrical conductivity of dry and hydrous garnet at high temperatures and pressures.Contributions to Mineralogy and Petrology,163(4):689-700.
Dai L D,Jiang J J,Li H P,et al.2015.Electrical conductivity of hydrous natural basalts at high temperatures and pressures.Journal of Applied Geophysics,112:290-297.
Du Frane W L,Roberts J J,Toffelmier D A,et al.2005.Anisotropy of electrical conductivity in dry olivine.Geophysical Research Letters,32(L24315),doi:10.1029/2005GL023879.
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Guo X Z,Yoshino T,Katayama I.2011.Electrical conductivity anisotropy of deformed talc rocks and serpentinites at 3 GPa.Physics of the Earth,and Planetary Interiors,188(1-2):69-81.
Guo Y X,Wang D J,Li D Y,et al.2013.The electrical conductivity of ophiolite in Southern Tibet.Chinese Journal of Geophysics(in Chinese),56(10):3434-3444,doi:10.6038/cjg20131019.
Guo Y X,Wang D J,Shi Y L,et al.2014.The electrical conductivity of eclogite in Tibet and its geophysical implications.Science China Earth Sciences,57(9):2071-2078.
Guo Y X,Wang D J,Zhou Y S,et al.2017.Electrical conductivities of two granite samples in southern Tibet and their geophysical implications.Science China Earth Sciences,60(8):1522-1532,doi:10.1007/s11430-016-9046-7.
Guseinov A A,Gargatsev I O.2002.Electrical conductivity of alkaline feldspars at high temperatures.Izvestiya Physics of the Solid Earth,38(6):520-523.
Hashin Z,Shtrikman S.1962.A variational approach to the theory of effective magnetic permeability of multiphase materials.Journal of Applied Physics,33,3125-3131.
Hu H Y,Li H P,Dai L D,et al.2013.Electrical conductivity of alkali feldspar solid solutions at high temperatures and high pressures.Physics and Chemistry of Minerals,40(1):51-62.
Huang X G,Bai W M,Lan C X.2005.Review of model calculations of electrical conductivity for partially molten rocks.Progress in Geophysics(in Chinese),20(3):635-639.
Huang X G,Xu Y S,Karato S I.2005.Water content in the transition zone from electrical conductivity of wadsleyite and ringwoodite.Nature,434(7034):746-749.
Krajew A P.1957.Grundlagen der Geoelektrik.VEB Verlag Technik,Berlin,358.
Kurtz R D,Ostrowski J A,Niblett E R.1986.A Magnetotelluric survey over the east bull lake gabbro-anorthosite complex.Journal of Geophysical Research:Atmospheres,91(B7):7403-7416.
Lacam A.1983.Pressure and composition dependence of the electrical conductivity of iron-rich synthetic olivines to 200kbar.Physics and Chemistry of Minerals,9(3-4):127-132.
Liu P H,Liu F L,Wang F,et al.2013.Petrological and geochronological preliminary study of the Xiliu~2.1Ga meta-gabbro from the Jiaobei terrane,the southern segment of the Jiao-Liao-Ji Belt in the North China Craton.Acta Petrologica Sinica(in Chinese),29(7):2371-2390.
Long LL,Wang Y W,Tang P Z,et al.2012.A debate on the special circumstance of rock forming and ore-forming of Haladala pluton,a mafic-ultramafic complex related to CuNi-VTiFe composite mineralization,in western Tianshan.Acta Petrologica Sinica(in Chinese),28(7):2015-2028.
Maumus J,Bagdassarov N,Schmeling H.2005.Electrical conductivity and partial melting of mafic rocks under pressure.Geochimica Et Cosmochimica Acta,69(19):4703-4718,doi:10.1016/j.gca.2005.05.010.
Parkhomenko E I,Bondarenko A T.1986.Electrical conductivity of rocks at high pressures and temperatures.American Mineralogist,96(11-12):1821-1827.
Poe B T,Romano C,Nestola F,et al.2010.Electrical conductivity anisotropy of dry and hydrous olivine at 8GPa.Physics of the Earth and Planetary Interiors,181(3-4):103-111.
Ryan M P,Ingerov A,Daniels D L,et al.2004.Deep crustal magma conduits,diabase internal structure,and coupled hydrothermal processes in Mesozoic basins of eastern North America.∥AGU Spring Meeting.USA:AGU Spring Meeting Abstracts.
Shan S M,Li H P,Dai L D,et al.2009.Influence of ionic impurities on the electrical conductivity of synthetic quartz crystals at high temperature and high pressure.Acta Mineralogica Sinica(in Chinese),29(1),109-112.
Tyburczy J A,Fisler D K.2013.Electrical properties of minerals and melts.∥Ahrens T J ed.Mineral Physics&Crystallography:AHandbook of Physical Constants.Washington DC:American Geophysical Union,185-208.
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