The elasticity of minerals at high temperature and pressure （PT） is critical for constraining the composition and temperature of the Earth＇s interior and understand better the deep water cycle and the dynamic Earth...The elasticity of minerals at high temperature and pressure （PT） is critical for constraining the composition and temperature of the Earth＇s interior and understand better the deep water cycle and the dynamic Earth. First-principles calcula- tions without introducing any adjustable parameters, whose results can be comparable to experimental data, play a more and more important role in investigating the elasticity of minerals at high PT mainly because of （1） the quick increasing of computational powers and （2） advances in method. For example, the new method reduces the computation loads to one-tenth of the traditional method with the comparable precise as the traditional method. This is extraordinarily helpful because first-principles calculations of the elasticity of minerals at high PT are extremely time-consuming. So far the elasticity of most of lower mantle minerals has been investigated in detail. We have good idea on the effect of temperature, pressure, and iron concentration on elasticity of main minerals of the lower mantle and the unusual softening in bulk modulus by the spin crosso- ver of iron in ferropericlase. With these elastic data the lower mantle has been constrained to have 10-15 wt% ferropericlase, which is sufficient to generate some visible effects of spin crossover in seismic tomography. For example, the spin crossover causes that the temperature sensitivity of P wave at the depth of -1700 km is only a fraction of that at the depth of -2300 kin. The disruptions of global P wave structure and of P wave image below hotspots such as Hawaii and Iceland at similar depth are in consistence with the spin crossover effect of iron in ferropericlase. The spin crossover, which causes anomalous ther- modynamic properties of ferropericlase, has also been found to play a control role for the two features of the large low shear velocity provinces （LLSVPs）： the sharp edge and high elevation up to 1000 km above core-mantle boundary. All these results clearly suggest the spin crossover of iron in the lower mantle. The theoretical investigations for the elasticity of minerals at the upper mantle and water effect on elasticity of minerals at the mantle transition zone and subducting slab have also been con- ducted extensively. These researches are critical for understanding better the composition of the upper mantle and water dis- tribution and transport in the Earth＇s mantle. Most of these were static calculations, which did not include the vibrational （temperature） effect on elasticity, although temperature effect on elasticity is basic because of high temperature at the Earth＇s interior and huge temperature difference between the ambient mantle and the subducting slab. Including temperature effect on elasticity of minerals should be important future work. New method developed is helpful for these directions. The elasticity of iron and iron-alloy with various light elements has also been calculated extensively. However, more work is necessary in order to meet the demand for constraining the types and amount of light elements at the Earth＇s core. Keywords Mantle temperature, Mantle composition, Composition of Earth＇s core, Ab initio method展开更多
The determination of the gravitational potential of a prism plays an important role in physical geodesy and geophysics. However, there are few literatures that provide accurate approaches for determining the gravitati...The determination of the gravitational potential of a prism plays an important role in physical geodesy and geophysics. However, there are few literatures that provide accurate approaches for determining the gravitational potential of a prism. Discrete element method can be used to determine the gravitational potential of a prism, and can approximate the true gravitational potential values with sufficient accuracy (the smaller each element is, the more accurate the result is). Although Nagy's approach provided a closed expression, one does not know whether it is valid, due to the fact that this approach has not been confirmed in literatures. In this paper, a study on the comparison of Nagy's approach with discrete element method is presented. The results show that Nagy's formulas for determining the gravitational potential of a prism are valid in the domain both inside and outside the prism.展开更多
基金supported by the State Key Development Program of Basic Research of China(Grant No.2014CB845905)the National Natural Science Foundation of China(Grant Nos.41590621,41274087,41473011)the Chinese Academy of Sciences/State Administration of Foreign Experts Affairs International Partnership Program for Creative Research Teams
文摘The elasticity of minerals at high temperature and pressure （PT） is critical for constraining the composition and temperature of the Earth＇s interior and understand better the deep water cycle and the dynamic Earth. First-principles calcula- tions without introducing any adjustable parameters, whose results can be comparable to experimental data, play a more and more important role in investigating the elasticity of minerals at high PT mainly because of （1） the quick increasing of computational powers and （2） advances in method. For example, the new method reduces the computation loads to one-tenth of the traditional method with the comparable precise as the traditional method. This is extraordinarily helpful because first-principles calculations of the elasticity of minerals at high PT are extremely time-consuming. So far the elasticity of most of lower mantle minerals has been investigated in detail. We have good idea on the effect of temperature, pressure, and iron concentration on elasticity of main minerals of the lower mantle and the unusual softening in bulk modulus by the spin crosso- ver of iron in ferropericlase. With these elastic data the lower mantle has been constrained to have 10-15 wt% ferropericlase, which is sufficient to generate some visible effects of spin crossover in seismic tomography. For example, the spin crossover causes that the temperature sensitivity of P wave at the depth of -1700 km is only a fraction of that at the depth of -2300 kin. The disruptions of global P wave structure and of P wave image below hotspots such as Hawaii and Iceland at similar depth are in consistence with the spin crossover effect of iron in ferropericlase. The spin crossover, which causes anomalous ther- modynamic properties of ferropericlase, has also been found to play a control role for the two features of the large low shear velocity provinces （LLSVPs）： the sharp edge and high elevation up to 1000 km above core-mantle boundary. All these results clearly suggest the spin crossover of iron in the lower mantle. The theoretical investigations for the elasticity of minerals at the upper mantle and water effect on elasticity of minerals at the mantle transition zone and subducting slab have also been con- ducted extensively. These researches are critical for understanding better the composition of the upper mantle and water dis- tribution and transport in the Earth＇s mantle. Most of these were static calculations, which did not include the vibrational （temperature） effect on elasticity, although temperature effect on elasticity is basic because of high temperature at the Earth＇s interior and huge temperature difference between the ambient mantle and the subducting slab. Including temperature effect on elasticity of minerals should be important future work. New method developed is helpful for these directions. The elasticity of iron and iron-alloy with various light elements has also been calculated extensively. However, more work is necessary in order to meet the demand for constraining the types and amount of light elements at the Earth＇s core. Keywords Mantle temperature, Mantle composition, Composition of Earth＇s core, Ab initio method
基金Supported by the National Natural Science Foundation of China (No.40637034, 40974015)the National 863 Program of China (No.2006AA12Z211)
文摘The determination of the gravitational potential of a prism plays an important role in physical geodesy and geophysics. However, there are few literatures that provide accurate approaches for determining the gravitational potential of a prism. Discrete element method can be used to determine the gravitational potential of a prism, and can approximate the true gravitational potential values with sufficient accuracy (the smaller each element is, the more accurate the result is). Although Nagy's approach provided a closed expression, one does not know whether it is valid, due to the fact that this approach has not been confirmed in literatures. In this paper, a study on the comparison of Nagy's approach with discrete element method is presented. The results show that Nagy's formulas for determining the gravitational potential of a prism are valid in the domain both inside and outside the prism.
