It is still argued whether we measure phase or group velocities using acoustic logging tools. In this paper, three kinds of models are used to investigate this problem by theoretical analyses and numerical simulations...It is still argued whether we measure phase or group velocities using acoustic logging tools. In this paper, three kinds of models are used to investigate this problem by theoretical analyses and numerical simulations. First, we use the plane-wave superposition model containing two plane waves with different velocities and able to change the values of phase velocity and group velocity. The numerical results show that whether phase velocity is higher or lower than group velocity, using the slowness-time coherence （STC） method we can only get phase velocities. Second, according to the results of the dispersion analysis and branch-cut integration, in a rigid boundary borehole model the results of dispersion curves and the waveforms of the first-order mode show that the velocities obtained by the STC method are phase velocities while group velocities obtained by arrival time picking. Finally, dipole logging in a slow formation model is investigated using dispersion analysis and real-axis integration. The results of dispersion curves and full wave trains show similar conclusions as the borehole model with rigid boundary conditions.展开更多
We report a first-principles calculation to investigate the structural instability of rutile TiO2. The high pressure structural parameters are well reproduced. The calculated phonon disper-sion curves agree with exper...We report a first-principles calculation to investigate the structural instability of rutile TiO2. The high pressure structural parameters are well reproduced. The calculated phonon disper-sion curves agree with experiments at zero pressure. Under compression, we capture a large softening around Γ point, which indicates the structural instability. From the high pressure elastic constants, we find that the rutile TiO2 is unstable when the applied pressure is larger than 17.7 GPa. Within the quasi-harmonic approximation, the thermal equation of state, thermal expansion oefficient, bulk modulus, and entropy are well reproduced. The thermal properties confirm the available experimental data and are extended to a wider pressure and temperature range.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 40774099, 10874202 and 11134011)National 863 Program of China (Grant No. 2008AA06Z205)
文摘It is still argued whether we measure phase or group velocities using acoustic logging tools. In this paper, three kinds of models are used to investigate this problem by theoretical analyses and numerical simulations. First, we use the plane-wave superposition model containing two plane waves with different velocities and able to change the values of phase velocity and group velocity. The numerical results show that whether phase velocity is higher or lower than group velocity, using the slowness-time coherence （STC） method we can only get phase velocities. Second, according to the results of the dispersion analysis and branch-cut integration, in a rigid boundary borehole model the results of dispersion curves and the waveforms of the first-order mode show that the velocities obtained by the STC method are phase velocities while group velocities obtained by arrival time picking. Finally, dipole logging in a slow formation model is investigated using dispersion analysis and real-axis integration. The results of dispersion curves and full wave trains show similar conclusions as the borehole model with rigid boundary conditions.
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.11247316, No.11247317, and No.11304408）, the Science and Technology Research Project of Chongqing Education Committee （No.K J120613 and No.K J130607）, and the Natural Science Foundation of Chongqing City （No.cstc2012jjA50019 and No.cstc2013jcyjA073a）.
文摘We report a first-principles calculation to investigate the structural instability of rutile TiO2. The high pressure structural parameters are well reproduced. The calculated phonon disper-sion curves agree with experiments at zero pressure. Under compression, we capture a large softening around Γ point, which indicates the structural instability. From the high pressure elastic constants, we find that the rutile TiO2 is unstable when the applied pressure is larger than 17.7 GPa. Within the quasi-harmonic approximation, the thermal equation of state, thermal expansion oefficient, bulk modulus, and entropy are well reproduced. The thermal properties confirm the available experimental data and are extended to a wider pressure and temperature range.
