双相介质中导波问题研究
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摘要
双相界质(流体饱和多孔介质)波动理论较传统的单相介质理论更接近工程实际。因此,它在地震学、地震工程学、土动力学、地球物理勘探、声学和动力基础等方面有着广泛而重要的应用。本文主要针对饱和流体多孔介质中的导波开展了以下几方面工作：
一、首先回顾了双相介质理论的研究成果。然后介绍了波的分类和波传播特性中相速度、群速度、波速与波数、波的频谱图和频散图、波的衰减与能量密度等基本概念。
二、在建立双相介质波动方程的同时,重新计算了《高频范围内流体饱和多孔介质的波传播》的原始文献中的算例。发现了新的计算结果与文献中的计算结果存在着较大偏差,分析了出现偏差的一些原因。
三、对双相介质覆盖层中Love波进行了理论分析与计算,分析了在不同孔隙度情况下Love波的频散和衰减特性。结果表明love波的频散存在正负频散现象,而且在低频(地震波)范围内的Love波的频散和衰减对孔隙度的变化都不敏感,而在高频范围的二者对孔隙度的变化较敏感。最后还研究了覆盖层中Love波的振动强度、应力幅度、能留密度随着孔隙度以及覆盖层深度的变化规律。这些结论为实际应用提供了理论依据。
四、对圆柱流体与双相介质界面上Stoneley波做了理论分析和计算,首先给出了Stoneley波产生的边界条件,然后利用给定的边界条件导出了圆柱外双相介质中横波波解与纵波波解以及Stoneley波的复波数频散方程。在低频域内对此频散方程进行了数值求解,得到随孔隙度的变化的频散曲线和衰减曲线及偏振特性曲线。结果表明：Stoneley波不仅具有强衰减特性,而且Stoneley波在低频域内存在轻微的负频散；在不同的频率区域内Stonley波的频散与衰减曲线受孔隙度的影响不同；Stoneley波的衰减系数与频率、孔隙度之间存在敏感的增函数关系。还研究了圆柱流体区域和双相介质区域内声压随离圆柱中心的距离增加的变化规律。
Fluid-saturated porous media fluctuation theory, the more traditional single-phase medium theory is closer to engineering practice. Therefore, it seismology, earthquake engineering, soil dynamics, geophysical exploration, acoustic and power base, has a wide-ranging and important applications. In this paper, for the fluid saturated porous media in guided wave has undertaken the following several aspects:
Firstly, reviewed the theory of two-phase media research. Then introduced the classification of waves and wave propagation characteristics in the phase velocity, group velocity, wave velocity and wave number, wave dispersion spectrum diagrams and maps, wave attenuation and energy density of the underlying concepts.
Secondly, wave equation in the establishment of two-phase media at the same time, re-calculation of the "high-frequency within the framework of fluid-saturated porous media, wave propagation," the original examples in the literature. Found a new calculation results in the calculation results with the literature there are large deviations analysis of some of the reasons for deviation.
Thirdly, Overlay of the two-phase media in Love wave theoretical analysis and calculation, analysis of porosity in different situations Love wave dispersion and attenuation characteristics. The results show that there is dispersion of love waves in positive and negative dispersion phenomenon, but also in the low-frequency (seismic wave) within the scope of the Love wave dispersion and attenuation of the changes in porosity are not sensitive to, and in the high-frequency range of the two pairs of porosity more sensitive to changes. Finally study covering layer of Love wave vibration intensity, stress amplitude, can stay in the density as the porosity, as well as the changes of the depth of cover. These conclusions provide a theoretical basis for practical application.
Fourthly,the cylindrical fluid interface with the two-phase media have done a theoretical analysis of Stoneley wave and calculation, first of all given Stoneley waves generated by boundary conditions, and then use the given boundary conditions are derived outside the two-phase medium, horizontal cylindrical wave solution and P-wave and the Stoneley wave solution of the complex wave number dispersion equation. In the low-frequency domain of this numerical dispersion equation is solved with the change in porosity of the dispersion curves and attenuation curves and polarization curves. The results showed that: Stoneley-wave attenuation characteristics is not only strong, but low-frequency Stoneley waves exist within a small negative dispersion; in different frequency regions Stonley wave dispersion and attenuation curves affected differently by the porosity; Stoneley wave attenuation coefficient and frequency, porosity exists between an increasing function of the sensitive relationship. Also studied the cylindrical fluid region and two-phase medium with the acoustic pressure within the region to increase the distance from the cylinder center was studied.
一、首先回顾了双相介质理论的研究成果。然后介绍了波的分类和波传播特性中相速度、群速度、波速与波数、波的频谱图和频散图、波的衰减与能量密度等基本概念。
二、在建立双相介质波动方程的同时,重新计算了《高频范围内流体饱和多孔介质的波传播》的原始文献中的算例。发现了新的计算结果与文献中的计算结果存在着较大偏差,分析了出现偏差的一些原因。
三、对双相介质覆盖层中Love波进行了理论分析与计算,分析了在不同孔隙度情况下Love波的频散和衰减特性。结果表明love波的频散存在正负频散现象,而且在低频(地震波)范围内的Love波的频散和衰减对孔隙度的变化都不敏感,而在高频范围的二者对孔隙度的变化较敏感。最后还研究了覆盖层中Love波的振动强度、应力幅度、能留密度随着孔隙度以及覆盖层深度的变化规律。这些结论为实际应用提供了理论依据。
四、对圆柱流体与双相介质界面上Stoneley波做了理论分析和计算,首先给出了Stoneley波产生的边界条件,然后利用给定的边界条件导出了圆柱外双相介质中横波波解与纵波波解以及Stoneley波的复波数频散方程。在低频域内对此频散方程进行了数值求解,得到随孔隙度的变化的频散曲线和衰减曲线及偏振特性曲线。结果表明：Stoneley波不仅具有强衰减特性,而且Stoneley波在低频域内存在轻微的负频散；在不同的频率区域内Stonley波的频散与衰减曲线受孔隙度的影响不同；Stoneley波的衰减系数与频率、孔隙度之间存在敏感的增函数关系。还研究了圆柱流体区域和双相介质区域内声压随离圆柱中心的距离增加的变化规律。
Fluid-saturated porous media fluctuation theory, the more traditional single-phase medium theory is closer to engineering practice. Therefore, it seismology, earthquake engineering, soil dynamics, geophysical exploration, acoustic and power base, has a wide-ranging and important applications. In this paper, for the fluid saturated porous media in guided wave has undertaken the following several aspects:
Firstly, reviewed the theory of two-phase media research. Then introduced the classification of waves and wave propagation characteristics in the phase velocity, group velocity, wave velocity and wave number, wave dispersion spectrum diagrams and maps, wave attenuation and energy density of the underlying concepts.
Secondly, wave equation in the establishment of two-phase media at the same time, re-calculation of the "high-frequency within the framework of fluid-saturated porous media, wave propagation," the original examples in the literature. Found a new calculation results in the calculation results with the literature there are large deviations analysis of some of the reasons for deviation.
Thirdly, Overlay of the two-phase media in Love wave theoretical analysis and calculation, analysis of porosity in different situations Love wave dispersion and attenuation characteristics. The results show that there is dispersion of love waves in positive and negative dispersion phenomenon, but also in the low-frequency (seismic wave) within the scope of the Love wave dispersion and attenuation of the changes in porosity are not sensitive to, and in the high-frequency range of the two pairs of porosity more sensitive to changes. Finally study covering layer of Love wave vibration intensity, stress amplitude, can stay in the density as the porosity, as well as the changes of the depth of cover. These conclusions provide a theoretical basis for practical application.
Fourthly,the cylindrical fluid interface with the two-phase media have done a theoretical analysis of Stoneley wave and calculation, first of all given Stoneley waves generated by boundary conditions, and then use the given boundary conditions are derived outside the two-phase medium, horizontal cylindrical wave solution and P-wave and the Stoneley wave solution of the complex wave number dispersion equation. In the low-frequency domain of this numerical dispersion equation is solved with the change in porosity of the dispersion curves and attenuation curves and polarization curves. The results showed that: Stoneley-wave attenuation characteristics is not only strong, but low-frequency Stoneley waves exist within a small negative dispersion; in different frequency regions Stonley wave dispersion and attenuation curves affected differently by the porosity; Stoneley wave attenuation coefficient and frequency, porosity exists between an increasing function of the sensitive relationship. Also studied the cylindrical fluid region and two-phase medium with the acoustic pressure within the region to increase the distance from the cylinder center was studied.
引文
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