地壳介质各向异性弹性本构关系讨论

论述了地壳介质中存在的各类向异性及其弹性本构关系,推导了应变能变换公式、ＥＤＡ薄层各向异性弹性常数及非对称面上ＥＤＡ构成的单斜对称弹性常数的计算公式;讨论了几种各向异性对称系统的本征方程并给出了弹性波的角散表达式,最后选取合理的参数对波的角散现象作了数值模拟。     

含垂直裂解隙PTL介质长波长等效正各向异性弹性常数

针对PTL介质中存在定向排列的铅垂裂隙系统的组合模型，探讨在长波长情况下其等效正交各向异性弹性常数的计算方法。根据Backus方法并结合Hudson微裂隙理论，推出了PTL与EDA组合之等效正交各向异性弹性常数的计算公式，且在裂隙呈稀疏分布的假设前提下，导出了等效弹性常数的具体计算表达式，并进而用伪谱法对含垂直裂隙PTL介质的弹性波场进行了数值模拟。本文的理论研究及数值计算结果表明：用5个长波长等效PTL弹性常数和3个无量钢的裂隙柔量，就可描述等效正交各向异性介质力个独立的弹性常数。     

二维TI介质非结构网格弹性波矢量逆时偏移

波场延拓得到的多分量波场中既包含纵波信息也包含横波信息,能否在全波场中实现纵横波的分离对各向同性和各向异性逆时偏移都有非常重要的意义.传统的散度旋度分离只适应于各向同性介质而对各向异性介质却无效.在非规则、非结构网格的弹性波数值模拟方法的基础上,发展了一种适应于各向异性介质的波场分离方法.该方法通过求解Christoffel方程,得到相角和极化角的关系,再利用群角和相角的关系,直接得到群角和极化角的关系.该方法与现存的各向异性波场分离相比,获得的计算效率改进更显著,而且存储量小.用简单各向异性模型和SEG各向异性Hess模型进行测试,都得到了较好的效果,证明了本文方法的有效性.     

含垂直裂解隙PTL介质长波长等效正交各向异性弹性常数

针对PTL介质中存在定向排列的铅垂裂隙系统的组合模型,探讨在长波长情况下其等效正交各向异性弹性常数的计算方法.根据Backus方法并结合Hudson微裂隙理论,推出了PTL与EDA组合之等效正交各向异性弹性常数的计算公式,且在裂隙呈稀疏分布的假设前提下,导出了等效弹性常数的具体计算表达式,并进而用伪谱法对含垂直裂隙PTL介质的弹性波场进行了数值模拟.本文的理论研究及数值计算结果表明:用5个长波长等效PTL弹性常数和3个无量钢的裂隙柔量,就可描述等效正交各向异性介质九个独立的弹性常数.     

三角网格有限元法声波与弹性波模拟频散分析

本文对声波与弹性波方程进行有限元法离散,构造有限元法频散关系的一般特征值问题,分析了时间离散格式为中心差分的三角网格有限元法声波与弹性波模拟的频散特性. 比较了三种质量矩阵即分布式质量矩阵、集中质量矩阵和混合质量矩阵对有限元法频散的影响;选取四种典型三角网格,分析了混合质量矩阵有限元（MFEM）频散的方向各向异性;数值频散、方向各向异性随插值阶数的增加逐渐减弱,当空间为三阶插值时,频散主要表现为随采样率的变化而几乎无明显方向各向异性, 其频散幅值也较小. 控制其他影响因素不变的情况下,研究了不同波速比介质中弹性波的数值频散. 最后给出了三角网格MFEM的数值耗散性.     

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．       

地壳介质弹性、电性各向异性理论及对地震过程的联合解释

本文共分 1 0章 :第 1章为引论 ;第 2～ 6章为基础理论 ;第 7～ 1 0章为应用研究。主要研究内容可分为 5个方面。1 )第 1章引论部分综述了地壳介质各向异性现象和分类 ,从发展沿革、理论方法及成果、存在的问题等几个方面分别论述了地壳介质弹性各向异性和电性各向异性。在此基础上提出了本文的研究思路和主题 :将地震学中的S波分裂法与电法中的大地电磁测深法联合起来解释地震过程中的各向异性动态特征与发震应力场的关系。围绕这个主题设定了 2个核心 :一是建立地壳介质电性各向异性微观模型 ;二是基于 EDA(广泛扩容各向异性 )裂隙模型…     

双相各向异性研究、问题与应用前景

地球内部流体的存在和岩石各向异性是地下介质的两大表征,考虑地下流体和介质各向异性问题的双相各向异性理论是当今地震学和地球物理学理论与应用研究的前沿和难题之一。孔隙流体的存在、固体和流体之间的相互作用会弱化或硬化岩石的力学属性,上起声波或弹性声波速度的频散的振幅的衰减,并产生第二类压缩波。裂缝或裂隙的定向分布、岩层的旋性沉积、应力场的定向排列,都会引起传播速度的各向异性、横波发生分裂等重要现象,这些     

各向异性弹性波场的有限元数值模拟

研究了各向异性弹性波有限元正演系统的精度和效率问题，提出了一种透射加衰减的组合人工边界方案（吸收边办条件），它对各向异性波具有较好的吸收效果，并且有较好的稳定性能，均匀TI介质中的模拟获得了非常清晰的波场快照，其波场特征与理论分析能够准确吻合，各向异性介质模型的地表地震记录表明，各向异性波炮集记录在波的类型、同相轴形态、能量分布和相位等方面与各向同性波都有很大差别。     

基于角弹性参数的多波地震储层预测方法

弹性参数作为反映岩石弹性性质的参数,在储层预测中具有重要作用.常规弹性参数的构建主要基于PP波地震信息.PP波与PS波地震振幅因其携带的信息不同,对岩性与流体的敏感性也不同.本文提出联合利用PP波与PS波弹性阻抗以及角度信息构建角弹性参数来预测有利储层.首先,对常规PS波弹性阻抗方程进行重新推导,使得PS波弹性阻抗取值的数量级不随角度变化且能够与PP波弹性阻抗具备形式上的匹配;其次,根据常规弹性参数构建公式,采用PP波弹性阻抗、PS波弹性阻抗替代纵波阻抗、横波阻抗,提出角弹性参数的概念及构建公式,从而将角度信息引入到弹性参数的构建中;最后,在PP波与PS波弹性阻抗反演的基础上构建得到对储层敏感性较强的角弹性参数,利用角弹性参数的取值特征预测有利储层.模型与实际资料测试均表明角弹性参数具备较高的储层敏感性.     

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.     

VTI介质中P-SV波转换点与各向异性参数关系

对于转换波地震勘探中的转换点位置这个重要问题,提出转换点位置不仅与纵横波速度比,偏移距深度比以及源检距有关,还与地下介质的各向异性的性质有关,计算了忽略地下介质的各向异性影响对转换点的确定带来的严重误差,从而影响地下地质体的精确成像.通过对层状VTI介质中的转换点近似方程的推导过程,引入该方程不同于传统方程的导出是对层状各向同性介质而言,该方程通过引入各向异性参数,使我们对转换波可以有进一步的认识,拓展了转换波处理中各向异性的应用.该方程对于偏移距深度比小于3.0的情况是比较准确的,这对于大偏移距转换波勘探具有实际意义.     

Classes of Anisotropic Media: A Tutorial

The purpose of the present article is to give a precise definition and analysis from first principals of anisotropy, as the term applies to elastic media, taking care to avoid unnecessary assumptions. Two fundamental concepts, material invariance and symmetry group of a material, are defined purely in terms of the stress-strain relation. The implications of material symmetry, or in other words, of anisotropy, for the structure of the stiffness tensor are then investigated. Using the reduced notation of Voigt, these results are presented as the well-known simplifications in the form taken by the six-by-six stiffness matrix that represents the material's stiffness tensor. A new, simple proof is given for the remarkable fact that an elastic medium cannot have rotational symmetry by an angle of less than 90° without being transversely isotropic. In addition, the mutual relation that the notions of elastic symmetry and crystal symmetry have with respect to the so-called orthogonal group is sketched. Despite the historical association between anisotropic elastic materials and the study of crystals, the given presentation shows that conceptually the notion of anisotropy in elastic media is entirely independent of that of crystal symmetry.     

非均匀各向异性弹性波场正演

推导了用于非均匀各向异性弹性波场正演的伪谱法基本公式，对特征值法边界修正方程进行了全面的理论推导，给出了二维和三维问题固体，流体的特征变量及各类边界修正方程，选用2个模型，模拟了2．5维弹性波场，对S波分裂的偏振图像和时间延迟作了较详细的分析。     

TTI介质的交错网格伪P波正演方法

研究了三维弱各向异性近似下,利用伪P波(伪纵波)模拟弹性波场P分量在倾斜对称轴的横向各向同性(TTI)介质中的传播过程,并对比了分别基于弹性Hooke定律、弹性波投影和运动学色散方程所建立的三种二阶差分伪P波方程的正演特点.目前这些伪P波方程数值计算主要采用规则网格差分,但是规则网格在TTI模拟中有低效率、低精度以及不稳定的缺点.为了提高计算的精度,本文构建出相应方程的交错网格有限差分格式.通过对比伪P波方程在三维TTI介质中不同的数值模拟的表达形式,本文认为基于色散方程所建立的伪P波方程在模拟弹性波中P波传播的过程中具有最小的噪声.本文分析不同的各向同性对称轴空间角度的频散特征,并引入适当的横波速度维持计算的稳定.二维模型算例表明,本文提出的交错网格正演算法可以得到稳定光滑的伪P波正演波场.使用本文交错网格算法对二维BP TTI模型的逆时偏移也具有较稳定的偏移结果.     

任意空间取向TI介质qP和qSV波解耦的波动方程

由于构造运动等作用,TI介质对称轴往往沿空间任意方向分布,具有任意空间取向对称轴的TI（ATI）介质更符合实际地质情况.VTI介质与ATI介质的相速度在形式上具有一致性,VTI介质中地震波的相角对应ATI介质对称轴与地震波传播方向的夹角.本文基于Tsvankin的VTI介质精确相速度公式,利用TI介质对称轴和地震波传播方向上单位向量的数量积和向量积来计算ATI介质的精确相速度.根据弱各向异性假设,导出qP波和qSV波的近似相速度,分析了近似公式的误差,讨论总结了ATI介质qP波和qSV波的相速度特征.本文中的单位向量采用观测坐标系表示,通过相角关系,可以较为方便地由ATI介质近似相速度导出频散关系,然后借助傅里叶逆变换推导出时间-波数域qP波和qSV波解耦的波动方程.数值算例表明本文的波动方程是qP波和qSV波解耦的,波场计算结果稳定,未出现明显的数值频散,验证了本文方法的有效性.     

气煤弹性各向异性系数实验测试

气煤裂隙丰富,具有弹性各向异性,确定气煤弹性各向异性类型与大小,对煤田各向异性研究具有重要意义. 本文在对气煤煤样孔隙率测试的基础上,测量了顺煤层面、垂直于煤层面、与煤层面成45°三个方向上纵波速度（V_P）和横波速度（V_SH、V_SV）,计算弹性常数. 对于具有垂向对称轴横向各向同性模型,各向异性系数平均值|ε|≤0.2、|δ|≤0.2和|γ|≤0.2,表明气煤是弱各向异性介质;对于横向对称轴横向各向异性模型,各向异性系数平均值ε(V)≈δ(V),按照Thomsen观点气煤各向异性是由椭圆裂隙引起弹性各向异性.本文还讨论了各向异性系数与孔隙率的关系,表明各向异性的大小与孔隙率之间有一定的关系. 因此当煤层厚度与其顶底板岩性不变或变化很小,可以认为气煤各向异性主要由裂隙引起的,气煤各向异性大小和方向能够反映煤的裂缝密度和方位.     

Generalized anisotropy parameters and approximations of attenuations and velocities in viscoelastic media of arbitrary anisotropy type – theoretical and experimental aspects*

Seismic anisotropy in geological media is now widely accepted. Parametrizations and explicit approximations for the velocities in such media, considered as purely elastic and moderately anisotropic, are now standards and have even been extended to arbitrary types of anisotropy. In the case of attenuating media, some authors have also recently published different parametrizations and velocity and attenuation approximations in viscoelastic anisotropic media of particular symmetry type (e.g., transversely isotropic or orthorhombic). This paper extends such work to media of arbitrary anisotropy type, that is to say to triclinic media. In the case of homogeneous waves and using the so‐called ‘correspondence principle’, it is shown that the viscoelastic equations (for the phase velocities, phase slownesses, moduli, wavenumbers, etc.) are formally identical to the corresponding purely elastic equations available in the literature provided that all the corresponding quantities are complex (except the unit vector in the propagation direction that remains real). In contrast to previous work, the new parametrization uses complex anisotropy parameters and constitutes a simple extension to viscoelastic media of previous work dealing with non‐attenuating elastic media of arbitrary anisotropy type. We make the link between these new complex anisotropy parameters and measurable parameters, as well as with previously published anisotropy parameters, demonstrating the usefulness of the new parametrization. We compute the explicit complete directional dependence of the exact and of the approximate (first and higher‐order perturbation) complex phase velocities of the three body waves (qP, qS1 and qS2). The exact equations are successfully compared with the ultrasonic phase velocities and phase attenuations of the three body waves measured in a strongly attenuating water‐saturated sample of Vosges sandstone exhibiting moderate velocity anisotropy but very strong attenuation anisotropy. The approximate formulas are checked on experimental data. Compared to the exact solutions, the errors observed on the first‐order approximate velocities are small (<1%) for qP‐waves and moderate (<10%) for qS‐waves. The corresponding errors on the quality factor Q are moderate (<6%) for qP‐waves but critically large (up to 160%) for the qS‐waves. The use of higher‐order approximations substantially improves the accuracy, for instance typical maximum relative errors do not exceed 0.06% on all the velocities and 0.6% on all the quality factors Q, for third‐order approximations. All the results obtained on other rock samples confirm the results obtained on this rock. The simplicity of the derivations and the generality of the results are striking and particularly convenient for practical applications.