饱和土介质中地震波在水、气分界面上的反射与透射

基于修改的Biot模型,研究地震波在气饱和土中的传播特性以及地震波在饱和土中气、水界面上的反射和透射. 从理论上分析气饱和土与水饱和土的特性差异,根据界面连续条件推导了反射系数与透射系数的一般计算式;通过数值算例分析了气饱和土中波的传播特性,并分析了饱和土中P1波入射气、水界面时反射系数和透射系数与入射角及频率的关系. 结果表明,波在气饱和土中的传播与水饱和土中有较大差异; 频率和入射角度对反射系数与透射系数均有较大影响;并获得了波传播的某些新认识. 这对地震工程的波动勘测技术和场地反应分析具有理论及实际意义.      

ANISOTROPIC Q AND VELOCITY DISPERSION OF FINELY LAYERED MEDIA1

When a seismic signal propagates through a finely layered medium, there is anisotropy if the wavelengths are long enough compared to the layer thicknesses. It is well known that in this situation, the medium is equivalent to a transversely isotropic material. In addition to anisotropy, the layers may show intrinsic anelastic behaviour. Under these circumstances, the layered medium exhibits Q anisotropy and anisotropic velocity dispersion. The present work investigates the anelastic effect in the long-wavelength approximation. Backus's theory and the standard linear solid rheology are used as models to obtain the directional properties of anelasticity corresponding to the quasi-compressional mode qP, the quasi-shear mode qSV, and the pure shear mode SH, respectively. The medium is described by a complex and frequency-dependent stiffness matrix. The complex and phase velocities for homogeneous viscoelastic waves are calculated from the Christoffel equation, while the wave-fronts (energy velocities) and quality factor surfaces are obtained from energy considerations by invoking Poynting's theorem. We consider two-constituent stationary layered media, and study the wave characteristics for different material compositions and proportions. Analyses on sequences of sandstone-limestone and shale-limestone with different degrees of anisotropy indicate that the quality factors of the shear modes are more anisotropic than the corresponding phase velocities, cusps of the qSV mode are more pronounced for low frequencies and midrange proportions, and in general, attenuation is higher in the direction perpendicular to layering or close to it, provided that the material with lower velocity is the more dissipative. A numerical simulation experiment verifies the attenuation properties of finely layered media through comparison of elastic and anelastic snapshots.     

SEISMIC MIGRATION IN ELLIPTICALLY ANISOTROPIC MEDIA1

The study of wave propagation in media with elliptical velocity anisotropy shows that seismic energy is focused according to the horizontal component of the velocity field while the vertical component controls the time-to-depth relation. This implies that the vertical component cannot be determined from surface seismic velocity analysis but must be obtained using borehole or regional geological information. Both components of the velocity field are required to produce a correctly focused depth image. A paraxial wave equation is developed for elliptical anisotropic wave propagation which can be used for modelling or migration. This equation is then transformed by a change of variable to a second paraxial equation which only depends on one effective velocity field. A complete anisotropic depth migration using this transformed equation involves an imaging step followed by a depth stretching operation. This allows an approximate separation or splitting of the focusing and depth conversion steps of depth migration allowing a different velocity model to be used for each step. This split anisotropic depth migration produces a more accurate result than that obtained by a time migration using the horizontal velocity field followed by an image-ray depth conversion using the vertical velocity field. The results are also more accurate than isotropic depth migration and yield accurate imaging in depth as long as the lateral variations in the anisotropy are slow.     

APPROXIMATIONS TO SHEAR-WAVE VELOCITY AND MOVEOUT EQUATIONS IN ANISOTROPIC MEDIA1

Backus and Crampin derived analytical equations for estimating approximate phase-velocity variations in symmetry planes in weakly anisotropic media, where the coefficients of the equations are linear combinations of the elastic constants. We examine the application of similar equations to group-velocity variations in off-symmetry planes, where the coefficients of the equations are derived numerically. We estimate the accuracy of these equations over a range of anisotropic materials with transverse isotropy with both vertical and horizontal symmetry axes, and with combinations of transverse isotropy yielding orthorhombic symmetry. These modified equations are good approximations for up to 17% shear-wave anisotropy for propagations in symmetry planes for all waves in all symmetry systems examined, but are valid only for lower shear-wave anisotropy (up to 11%) in off-symmetry planes. We also obtain analytical moveout equations for the reflection of qP-, qSH-, and qSV- waves from a single interface for off-symmetry planes in anisotropic symmetry. The moveout equation consists of two terms: a hyperbolic moveout and a residual moveout, where the residual moveout is proportional to the degree of anisotropy and the spread length of the acquisition geometry. Numerical moveout curves are computed for a range of anisotropic materials to verify the analytical moveout equations.     

弹性介质中密度ρ与拉梅常数λ、μ的衍射层析成像方法研究

利用接收到的纵波信息，通过解纵波方程得到介质的密度和拉梅常数分布函数．首先，在频率波数域建立了描述入射纵波信号、接收纵波信号和介质三参数扰动量之间关系的积分方程．然后，建立了关于接收信号的各频率成份的方程组．经过正反傅氏变换求解此方程组即可得到介质三参数的分布函数．最后，就跨孔观测系统进行了数值模拟成像试验。结果表明方法有效．     

双相横向各向同性介质分界面上弹性波反射与透射问题研究

从双相横向各向同性介质弹性波波动方程出发 ,利用边界上的 4个连续性条件 ,计算双相横向各向同性介质分界面上弹性波反射和透射系数 .计算表明 ,快纵波在双相横向各向同性介质分界面上 ,要产生反射快纵波、反射转换 qSV波、反射转换慢纵波和透射快纵波、透射转换qSV波、透射转换慢纵波 .反射转换慢纵波振幅和透射转换慢纵波振幅均较小 .频率、耗散和各向异性大小影响着快纵波反射系数的大小 .     

饱和度对波在土层交界面的反射、透射系数的影响

把均匀流体概念引入Biot两相多孔介质动力理论中，用Biot的两相多孔介质模型模拟不完全饱和土层，给出SV波，P波从不完全饱和土层入射到弹性土层时，在土层交界面上反射，透射系数的表达式，结果表明与完全饱和相比，饱和度发生很小的变化就会对交界面上反射，透射系数产生很大的影响。今后应该重视饱和度变化对地震动力响应的影响。     

VTI介质中地震波反射波合成记录的方法研究

在向向异性介质中，由于地震波的相速度和群速度有较大差异，相角和群角不同，相速度、群速度及群角相与角之间的关系比较复杂，因此与各同性相比较，计算地震波相速度，群速度及群角就更加困难，其合成地震记录的难度也就之增大，本文根据VTI（具有垂直对称轴的横向各向同性）介质中地震波的运动学特征，应用射线追踪方法，计算了VTI介质中的地震波的旅行时，并合成了反 地震记录，这为反射地震波的旅行时及速度分析提供了基础。     

各向异性介质中地震波前面的偏微分方程

从含２１个弹性参数的各向异性介质中关于位移分量ｕｘ、ｕｙ与ｕｚ的偏微分波动方程组出发,通过假定平面波位移函数解,导出准Ｐ波、准ＳＶ波与准ＳＨ波的波前面偏微分控制方程,进而对各类特殊各向异性介质（横向各向同性介质、椭圆及立方体各向异性介质）中地震波前面偏微分方程进行了讨论．以上结果为研究各向异性介质中地震波传播规律以及进行正、反演研究奠定了理论基础．     

各向异性介质中地震波前面的偏微分方程

从含２１个弹性参数的各向异性介质中关于位移分量ｕ_ｘ、ｕ_ｙ与ｕ_ｚ的偏微分波动方程组出发，通过假定平面波位移函数解，导出准Ｐ波、准ＳＶ波与准ＳＨ波的波前面偏微分控制方程，进而对各类特殊各向异性介质（横向各向同性介质、椭圆及立方体各向异性介质）中地震波前面偏微分方程进行了讨论．以上结果为研究各向异性介质中地震波传播规律以及进行正、反演研究奠定了理论基础．     

论稳定电流场的入射、反射、透射间的关系

根据分界面上稳定电流场的边界条件，解稳定电流场Ｌａｐｌａｃｅ方程，给出椭球形分界面入射场、反射场及透射场的表达式，并导出圆柱形、球形分界面上入射角、反射角及透射角的关系式后，指出，只在少数特殊情况下三者才相等，对一般形状的大多数光滑连续分界面情况，它们是不相等的．其值取决于分界面的具体形状．     

论稳定电流场的入射、反射、透射间的关系

根据分界面上稳定电流场的边界条件,解稳定电流场Ｌａｐｌａｃｅ方程,给出椭球形分界面入射场、反射场及透射场的表达式,并导出圆柱形、球形分界面上入射角、反射角及透射角的关系式后,指出,只在少数特殊情况下三者才相等,对一般形状的大多数光滑连续分界面情况,它们是不相等的．其值取决于分界面的具体形状．     

各向异性介质中弹性波动高阶差分法及其稳定性的研究

稳定性是数值计算波动方程的最重要条件之一．本文就正交对称和六方对称各向异性介质中的弹性波动方程研究了时间和空间上差分精度可达任意阶的交错网格高阶差分法后,又导出了该方法的稳定性条件．为利用这种既精确又高效的数值方法来研究地震各向异性中的正反演问题提供了理论依据．     

各向异性介质中弹性波动高阶差分法及其稳定性的研究

稳定性是数值计算波动方程的最重要条件之一．本文就正交对称和六方对称各向异性介质中的弹性波动方程研究了时间和空间上差分精度可达任意阶的交错网格高阶差分法后，又导出了该方法的稳定性条件．为利用这种既精确又高效的数值方法来研究地震各向异性中的正反演问题提供了理论依据．     

双相各向异性介质中弹性波传播有限元方程及数值模拟

基于Biot双相各向异性介质理论和动态问题的哈密顿原理,推导出任意双相各向异性介质中弹性波传播的有限元方程,并给出双相各向异性介质中弹性波有限元方程的数值解法．最后进行有限元法的数值模拟,对双相各向异性介质中弹性波传播特征进行了模拟与分析．      

几种弱各向异性介质中qSV波速度和偏振异常

研究了在具有垂直对称轴的横向各向同性介质(TIV 介质)中qSV波群速度及偏振矢量,给出了相应的精确和近似计算公式,进一步讨论了用较简单的近似公式来代替复杂精确公式的可靠性;最后展示了地球内部几种常见各向异性岩石矿物中地震qSV波速度各向异性因子、偏振信息及其与传播方向之间的偏差.     

二维横向各向同性介质中人为边界反射的吸收——差分法弹性波场模拟

本文对有限差分法弹性波场三分量正演模拟中遇到的人为边界反射问题进行了研究,分别获得2-D横向各向同性介质中U_x,U_z,与U_y位移分量模拟时的边界吸收条件.从吸收边界上反射系数与入射角之间的关系可以说明,本文提出的边界吸收条件的吸收能力比较强.     

二维横向各向同性介质中人为边界反射的吸收——差分法弹性波场模拟

本文对有限差分法弹性波场三分量正演模拟中遇到的人为边界反射问题进行了研究,分别获得2-D横向各向同性介质中U_x,U_z,与U_y位移分量模拟时的边界吸收条件.从吸收边界上反射系数与入射角之间的关系可以说明,本文提出的边界吸收条件的吸收能力比较强.     

几种弱向异性介质中qSV波速度和偏振异常

研究了在具有生趣对称轴的横向各向同性介质（ＴＩＶ介质）中ｑＳＶ波群速度及偏振矢量,给出了相应的精确和近似公式,进一步讨论了用较简单的近似公式来代替复杂精确公式的可靠性;最后展示了地球内部几种常见各向异性岩石矿物中地震ｓＳＶ波速度各向异性因子、偏振信息及其与传播方向之间的偏差。