EDA介质中地震波传播特征及参数反演研究
摘要
裂隙介质是工程中最常见的介质,裂隙的发育程度、裂隙的性质及其组合状态对岩石稳定性和工程安全具有非常影响非常大,而且裂隙较发育的岩体往往含地下水丰富,岩石稳定性差,容易引起涌水、塌方等工程灾害,因此探测裂隙发育程度和裂隙的性质就显得非常重要。地震勘探是探测岩石裂隙、评价岩体质量的有效果方法之一,但是传统地震勘探,都假设地下介质完全是各向同性的,而实际上它们基本上都是各向异性的,这样的假设会导致错误的成像,从而影响勘探结果的准确性。为了提高反演精度,趋合精细化勘探的发展趋势,研究地下介质的各向异性及地震波的波动特性也显得日益紧迫,也是目前地震勘探研究的热点和难点之一。
本文首先从VTI介质出发推导了HTI介质中地震波精确相速度和群速度计算公式,讨论了HTI介质与VTI介质的相似特征,然后由HTI介质,通过Bond变换推导出EDA介质中地震波的精确相速度和群速度计算公式,并基于摄动理论,以各向同性介质为背景介质推导出HTI、EDA介质的相速度、群速度的弱各向异性近似公式。由christoffel方程出发,结合边界条件、应力应变关系,推导出EDA介质中P、SV、SH波的精确反射系数,以弹性各向同性介质为背景介质推导出EDA介质中的P波近似反射系数计算公式。
在carcion、杜启振等人研究的基础上,叙述了粘弹性EDA介质中地震波的波动方程推导过程,并进行了退化验证；利用Vavrycuk提出的粘弹性实射线追踪法,成功实现粘弹性EDA介质中地震波场数值模拟。
利用特殊分量法,由christoffel方程推导出粘弹性HTI、EDA介质中均匀、非均匀P、SV、SH波的精确相速度、群速度、慢度和偏振向量,研究了SH相速度随非均匀角的变化规律；以弹性各向异性介质为背景介质,推导出粘弹性各向异性介质中地震波的近似相速度、群速度、偏振向量计算公式。由christoffel方程出发推导出HTI、EDA介质中均匀、非均匀地震波的精确相衰减系数和群众衰减系数。
由VTI介质出发利用Bond变换和有限相似原则,推导出HTI、EDA介质的时距方程和倾斜HTI、EDA介质中动校正速度的表达式,得到动校正速度与方位角、各向异性参数、倾角的关系式。以多层倾斜EDA模型为例进行参数反演并由地震波走和射线追踪法确定地下界面的几何参数,并对反演结果进行了误差分析,然后利用反演的各向异性参数,由各向异性参数裂隙密度及柔度比的关系计算了模型的裂隙密度、预测了模型的富水程度,达到了预期效果。最后以云阳山隧道为例证明了反演的可行性及其勘探精度。
Fractured media is the most common media in engineering. The density、characteristics and distribution of fracture have important effects on stability of rocks and safety of engineering. Fractured rocks is often abundant with groundwater and it's stability is poor and often cause water gushing or collapse. Seismic exploration is the one of most effective method in fracture detection and rock quality assessment.
Traditionally,the media is assumed to be totally isotropic, but in fact they are essentially anisotropic.This assumption may lead to erroneous imaging, thus affecting the accuracy of exploration results. In order to improve the inversion accuracy and satisfy the trend of fine exploration, the research of the seismic anisotropy and the characteristics of seismic wave propagation is becoming more and more urgent and has becoming one of the hot and challenge topics of seismology.
Firstly, the exact formula of phase velocity and group velocity for the HTI media are derived from VTI media, then the similarities between HTI and VTI are discussed. This similarities are used to derive the calculation formulas of EDA media. Starting from HTI media,the exact formula for phase and group velocity are derived using Bond transfer. Based on perturbation theory, the weak anisotropy approximate formula for phase velocity, group velocity of HTI, EDA media are derived with isotropic media as the background media.
Starting from christoffel equation, the exact formula for reflection coefficients of P, SV, SH waves in EDA medium are derived considering the Boundary conditions, stress-strain relationship. The approximation formula for the reflection coefficient of P wave in EDA media are derived using perturbation method with isotropic media as the background media.
Based on the study of casion and Du qizheng the derive of the wave equation for viscoelastic EDA media is described.With the real ray tracing method proposed by Vavrycuk,the wavefield in EDA media was simulated successfully.
Using the mixed specification,the exact formula for phase velocity slowness and polarization of P、SV、SH-wave both in HTI and EDA media are derived from Christoffel equation and the characteristics of SH-wave phase velocity varying with the changing of inhomogeneity angle are studied.
The approximation formula for phase velocity, group velocity and polarization vector are derived by Perturbation method with elastic anisotropic media as the background media. The exact formula for phase and group attenuation coefficients of homogeneous and inhomogeneous seismic wave are derived from christoffel equation.
Starting from the formulas of VTI, the nonhyperbolic quation and the formula for DMO velocity in HTI、EDA media are derived and with this formula the relation between NMO velocity and azimuth、anisotropy parameters、dip angle become clear.
Multi-layer diping EDA model is used as an example for elastic parameters estimation and the geometric parameters of the interface are decided by traveltime and raytracing,the error of the inversion result are analysised, then the anisotropic parameter is used to calculate the fracture density and forecast water content.Finally,the geology exploration for yunyan shan tunnel verified that the inversion algorihm is feasible,the inversion result are reliable and accuracy.
本文首先从VTI介质出发推导了HTI介质中地震波精确相速度和群速度计算公式,讨论了HTI介质与VTI介质的相似特征,然后由HTI介质,通过Bond变换推导出EDA介质中地震波的精确相速度和群速度计算公式,并基于摄动理论,以各向同性介质为背景介质推导出HTI、EDA介质的相速度、群速度的弱各向异性近似公式。由christoffel方程出发,结合边界条件、应力应变关系,推导出EDA介质中P、SV、SH波的精确反射系数,以弹性各向同性介质为背景介质推导出EDA介质中的P波近似反射系数计算公式。
在carcion、杜启振等人研究的基础上,叙述了粘弹性EDA介质中地震波的波动方程推导过程,并进行了退化验证；利用Vavrycuk提出的粘弹性实射线追踪法,成功实现粘弹性EDA介质中地震波场数值模拟。
利用特殊分量法,由christoffel方程推导出粘弹性HTI、EDA介质中均匀、非均匀P、SV、SH波的精确相速度、群速度、慢度和偏振向量,研究了SH相速度随非均匀角的变化规律；以弹性各向异性介质为背景介质,推导出粘弹性各向异性介质中地震波的近似相速度、群速度、偏振向量计算公式。由christoffel方程出发推导出HTI、EDA介质中均匀、非均匀地震波的精确相衰减系数和群众衰减系数。
由VTI介质出发利用Bond变换和有限相似原则,推导出HTI、EDA介质的时距方程和倾斜HTI、EDA介质中动校正速度的表达式,得到动校正速度与方位角、各向异性参数、倾角的关系式。以多层倾斜EDA模型为例进行参数反演并由地震波走和射线追踪法确定地下界面的几何参数,并对反演结果进行了误差分析,然后利用反演的各向异性参数,由各向异性参数裂隙密度及柔度比的关系计算了模型的裂隙密度、预测了模型的富水程度,达到了预期效果。最后以云阳山隧道为例证明了反演的可行性及其勘探精度。
Fractured media is the most common media in engineering. The density、characteristics and distribution of fracture have important effects on stability of rocks and safety of engineering. Fractured rocks is often abundant with groundwater and it's stability is poor and often cause water gushing or collapse. Seismic exploration is the one of most effective method in fracture detection and rock quality assessment.
Traditionally,the media is assumed to be totally isotropic, but in fact they are essentially anisotropic.This assumption may lead to erroneous imaging, thus affecting the accuracy of exploration results. In order to improve the inversion accuracy and satisfy the trend of fine exploration, the research of the seismic anisotropy and the characteristics of seismic wave propagation is becoming more and more urgent and has becoming one of the hot and challenge topics of seismology.
Firstly, the exact formula of phase velocity and group velocity for the HTI media are derived from VTI media, then the similarities between HTI and VTI are discussed. This similarities are used to derive the calculation formulas of EDA media. Starting from HTI media,the exact formula for phase and group velocity are derived using Bond transfer. Based on perturbation theory, the weak anisotropy approximate formula for phase velocity, group velocity of HTI, EDA media are derived with isotropic media as the background media.
Starting from christoffel equation, the exact formula for reflection coefficients of P, SV, SH waves in EDA medium are derived considering the Boundary conditions, stress-strain relationship. The approximation formula for the reflection coefficient of P wave in EDA media are derived using perturbation method with isotropic media as the background media.
Based on the study of casion and Du qizheng the derive of the wave equation for viscoelastic EDA media is described.With the real ray tracing method proposed by Vavrycuk,the wavefield in EDA media was simulated successfully.
Using the mixed specification,the exact formula for phase velocity slowness and polarization of P、SV、SH-wave both in HTI and EDA media are derived from Christoffel equation and the characteristics of SH-wave phase velocity varying with the changing of inhomogeneity angle are studied.
The approximation formula for phase velocity, group velocity and polarization vector are derived by Perturbation method with elastic anisotropic media as the background media. The exact formula for phase and group attenuation coefficients of homogeneous and inhomogeneous seismic wave are derived from christoffel equation.
Starting from the formulas of VTI, the nonhyperbolic quation and the formula for DMO velocity in HTI、EDA media are derived and with this formula the relation between NMO velocity and azimuth、anisotropy parameters、dip angle become clear.
Multi-layer diping EDA model is used as an example for elastic parameters estimation and the geometric parameters of the interface are decided by traveltime and raytracing,the error of the inversion result are analysised, then the anisotropic parameter is used to calculate the fracture density and forecast water content.Finally,the geology exploration for yunyan shan tunnel verified that the inversion algorihm is feasible,the inversion result are reliable and accuracy.
引文
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