黏弹各向异性介质中波的反射与透射问题分析

黏弹各向异性介质中传播不均匀波，其反射、透射模式不仅与介质分界面两侧速度对比有关，还与品质因子Q的对比有关. 用伪谱技术模拟黏弹各向异性介质分界面上波的反射、透射，并与弹性各向异性介质、黏弹各向同性介质和弹性各向同性介质的模拟结果做比较. 计算平面波的反射、透射系数，分析介质的黏弹性和各向异性对反射、透射系数的影响. 数值模拟了一个三层介质模型中的波场，分析两个分界面上产生的反射波的特征. 黏弹各向异性介质中，qS波比qP波衰减程度大.     

基于分数阶时间导数的黏弹性衰减VTI介质中平面波传播

目前在地震勘探频带范围内通常假设品质因子Q与频率无关,且呈衰减各向同性.事实上,相比较速度各向异性,介质的衰减各向异性同样不可忽视.本文将衰减各向异性和速度各向异性二者与常Q模型相结合,建立了黏弹性衰减VTI介质模型,并基于分数阶时间导数理论,给出了对应的本构关系和波动方程.利用均匀平面波分析和Poynting定理,推导出准压缩波qP、准剪切波qSV和纯剪切波SH的复速度、相速度、能量速度以及品质因子的解析表达式.对模型的正确性进行了数值验证,并分析了qP,qSV和SH波在介质中的传播特性.数值试验结果表明:本模型能够实现理想的恒定Q行为,表现了品质因子和速度的各向异性特征,显示出黏弹性增强将导致能量速度和相速度的频散曲线变化剧烈;速度和衰减各向异性参数与传播角度之间的耦合效应对qP,qSV和SH波的速度和能量影响明显;qP,qSV和SH波的频散曲线和波前面随着衰减各向异性强度的改变发生显著变化,其中耦合在一起的qP和qSV波变化趋势相同,而SH波与它们呈现相反的变化规律.本研究为从常Q模型角度分析地震波在衰减各向异性黏弹性介质中的传播特征奠定了理论基础.     

正交各向异性介质中qP波入射的二阶近似反射系数与透射系数

地震波在各向异性介质中以一个准P波(qP)和两个准S波(qS1和qS2)的形式传播.研究三种波的相速度、群速度以及偏振方向等传播性质能够为各向异性介质中的正反演问题提供有效支撑.具有比横向各向同性(TI)介质更一般对称性的正交各向异性介质通常需要9个独立参数对其进行描述,这使得对传播特征的计算更为复杂.当两个准S波速度相近时具有耦合性,从而令慢度的计算产生奇异性.因此,奇异点(慢度面的鞍点和交叉点)附近的反射与透射(R/T)系数的求解不稳定,会导致波场振幅不准确.本文首次通过结合耦合S波射线理论和基于迭代的各向异性相速度与偏振矢量的高阶近似解,得到了适用于正交各向异性介质以qP波入射所产生的二阶R/T系数的计算方法.与基于一阶近似的结果相比,基于二阶近似的方法提高了qP波R/T系数的精度,能得到一阶耦合近似无法表达的准确的qP-qS转换波的R/T系数解,且方法适用于较强的各向异性介质.     

任意倾斜各向异性介质中弹性波波场交错网格高阶有限差分法模拟

给出了任意倾斜各向异性介质中二维三分量一阶应力速度弹性波方程交错网格任意偶数阶精度有限差分格式及其稳定性条件,并推导出了二维任意倾斜各向异性介质完全匹配吸收层法边界条件公式和相应的交错网格任意偶数阶精度差分格式. 数值模拟结果表明,该方法模拟精度高,计算效率高,边界吸收效果好. 各向异性介质中弹性波波前面形态复杂, 且qP波波速不总是比qS波波速快. qS波波前面和同相轴的三分叉现象普遍, 且其同相轴一般不是双曲线型. 当TI介质倾斜时,3个分量上均能够观测到横波分裂现象, 而且各波形的同相轴变得不对称.      

方位各向异性粘弹性介质波场数值模拟

当地震信号通过复杂地球介质时，地层除了表现为各向异性，还表现为内在的粘弹性特征.因此，为准确描述地震波在地球介质中的传播特征，理想的地球介质模型应该能够模拟岩石的各向异性特征和衰减特征.本文给出了各向异性粘弹性介质模型的波动方程及其差分格式，并利用有限差分法实现了地震波波场数值模拟.结果表明了该介质模型中地震波场特征与各向异性主轴方位和介质的粘滞性参数之间的关系.     

基于LS-RSGFD方法优化的横向各向同性(TI)介质一阶qP波高精度数值模拟

为克服各向异性介质弹性波数值模拟中存在着计算量大和波场分离困难等局限,研究了声学近似的VTI介质和TTI介质一阶qP波数值模拟方法.首先对VTI介质弹性波方程进行声学近似,推导了VTI介质一阶qP波方程;然后基于精确的TTI介质频散关系,引入一个包含各向异性控制参数σ的新辅助波场,推导了稳定的TTI介质二阶耦合qP波波动方程,并通过引入波场的伪速度分量,推导了等价的一阶应力-速度形式.结合旋转交错网格有限差分(RSGFD)和基于最小二乘优化的有限差分(LS-FD)两种各具优势的方法,研究了最小二乘旋转交错网格有限差分(LS-RSGFD)方法,并用其数值求解VTI和TTI介质一阶qP波方程,然后通过构造其LS-RSGFD格式,实现了高精度的各向异性介质qP波波场数值模拟.数值模拟结果表明:TI介质一阶qP波方程能够准确地模拟各向异性介质中qP波的运动学特征,引入控制参数σ能够有效地减弱不稳定性问题,保证非均匀TTI介质中qP波场的稳定传播;利用优化的LS-RSGFD方法可以得到高精度的合成地震记录,同时还可以相对地提高计算效率.     

TTI介质弹性波近似解耦波动方程

借助Christoffel方程可求解出各向异性介质弹性波精确频散关系.利用近似方法进行处理,再通过傅里叶逆变换将频率波数域算子变换为时空域算子,可导出解耦的 qP波或 qS波波动方程.本文在 TTI介质弹性波精确频散关系的基础上,利用近似配方法推导了 qP波和 qSV波近似频散关系,通过傅里叶逆变换推导了 TTI介质 qP波和 qSV波解耦的波动方程.为了验证近似频散关系的有效性,利用两组模型参数对其进行数值计算,分析了相对误差在不同传播方向上的分布.随后使用有限差分方法分别对均匀、层状及复杂 TTI介质弹性波近似解耦波动方程进行数值模拟,结果显示 qP波和 qSV波完全解耦,并且在各向异性参数η＜0 以及介质对称轴倾角变化较大的情况下,纯 qP波和纯 qSV波近似波动方程依然可以保持稳定.     

粘弹性VTI介质地震波模拟特征分析

本文首先利用有限差分法分别对弹性和粘弹性VTI介质进行地震波传播数值模拟，并针对波场快照和波场记录特征，分析不同品质因子组合对波场能量衰减和频率吸收作用的影响.结果表明：对应于膨胀滞弹性形变的品质因子变化主要影响qP波的能量衰减；对应于剪切滞弹性形变的品质因子变化主要影响qSV波的能量衰减；对于qSH波，两个品质因子分别对应于垂直和水平方向的能量衰减；品质因子较小时，qSV波和qSH波的频率向低频方向移动，qP波频率变化不明显.     

应力诱导各向异性介质中地震波的传播

主要讨论了应力变化如何影响各向异性介质中波速度的问题。推导了一般各向异性介质在初始应力下的Christoffel方程,得到介质中3种波的相速度和初始应力的关系表达式;通过实验数据验证了单轴应力能够诱导各向异性,当施加单轴应力时,速度在沿应力的方向增加最大,在垂直应力的方向增加最小,实验结果与理论推导一致;用Christoffel方程的数值解模拟在3种对称情况下的弹性各向异性介质中初始应力对波速度的影响。数值结果表明:初始应力对各向异性介质中波传播速度的影响,随着各向异性强度的增加而增大,而且速度越慢,影响越大。     

黏弹性VTI介质中敏感度核函数：地震波复走时关于弹性模量及Q值偏导数的计算

实际地层中地震波传播普遍存在速度和衰减各向异性现象,研究黏弹各向异性介质中高频地震波传播理论有助于揭示地震波的传播特征.本文针对黏弹性VTI介质,从Christoffel矩阵的解析特征值出发推导出qP、qSV和qSH波的复相速度和复射线速度的解析表达式,并应用实射线追踪方法确定出均匀复射线速度矢量,由此计算出实射线速度和实射线衰减以及实射线品质因子.基于非均匀复相速度和均匀复射线速度的解析表达式,推导了实射线慢度和实射线衰减关于黏弹性模量(包括弹性模量和Q值)的敏感度核函数,该敏感度核函数反映各个黏弹性模量对地震波复走时的影响程度.不同岩石样本的数值计算结果显示,实走时对弹性模量更为敏感,而射线衰减(虚走时)对弹性模量和Q值的敏感程度相当.本研究可为黏弹性VTI介质中地震射线追踪和复走时层析成像提供理论基础.     

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.     

Improved First-Order Approximation of Group Velocities in Weakly Anisotropic Media

A first-order approximation of the group velocity is derived for qP and qS waves in weakly anisotropic media. The formula gives an explicit expression of the group velocity in terms of elastic parameters and wave normal and is independent of any reference isotropic media. The approximated group velocity differs from the first order phase velocity in direction and in magnitude, the difference being of the first order in direction and the second order in magnitude. The accuracy of the approximate formula is tested on two examples of TI media. The formula well approximates the qS-waves group velocity surface even in the presence of triplications.     

A staggered-grid high-order finite-difference modeling for elastic wave field in arbitrary tilt anisotropic media

Introduction The real Earth usually presents anisotropy. Therefore, it is of theoretical and practical sig- nificance for many fields as oil and gas, seismic exploration and production, earthquake prediction, detection of deep structure and so on to study on seismic wave theory, numerical simulation method and its applications in the anisotropic media (Crampin, 1981, 1984; Crampin et al, 1986; Hudson et al, 1996; Liu et al, 1997; Thomsen, 1986, 1995; TENG et al, 1992; HE and ZHANG, 1996)…     

Anisotropic attenuation of stratified viscoelastic media

An important cause of seismic anisotropic attenuation is the interbedding of thin viscoelastic layers. However, much less attention has been devoted to layer‐induced anisotropic attenuation. Here, we derive a group of unified weighted average forms for effective attenuation from a binary isotropic, transversely isotropic‐ and orthorhombic‐layered medium in the zero‐frequency limit by using the Backus averaging/upscaling method and analyse the influence of interval parameters on effective attenuation. Besides the corresponding interval attenuation and the real part of stiffness, the contrast in the real part of the complex stiffness is also a key factor influencing effective attenuation. A simple linear approximation can be obtained to calculate effective attenuation if the contrast in the real part of stiffness is very small. In a viscoelastic medium, attenuation anisotropy and velocity anisotropy may have different orientations of symmetry planes, and the symmetry class of the former is not lower than that of the latter. We define a group of more general attenuation‐anisotropy parameters to characterize not only the anisotropic attenuation with different symmetry classes from the anisotropic velocity but also the elastic case. Numerical tests reveal the influence of interval attenuation anisotropy, interval velocity anisotropy and the contrast in the real part of stiffness on effective attenuation anisotropy. Types of effective attenuation anisotropy for interval orthorhombic attenuation and interval transversely isotropic attenuation with a vertical symmetry (vertical transversely isotropic attenuation) are controlled only by the interval attenuation anisotropy. A type of effective attenuation anisotropy for interval TI attenuation with a horizontal symmetry (horizontal transversely isotropic attenuation) is controlled by the interval attenuation anisotropy and the contrast in the real part of stiffness. The type of effective attenuation anisotropy for interval isotropic attenuation is controlled by all three factors. The magnitude of effective attenuation anisotropy is positively correlated with the contrast in the real part of the stiffness. Effective attenuation even in isotropic layers with identical isotropic attenuation is anisotropic if the contrast in the real part of stiffness is non‐zero. In addition, if the contrast in the real part of stiffness is very small, a simple linear approximation also can be performed to calculate effective attenuation‐anisotropy parameters for interval anisotropic attenuation.     

裂隙参数对衰减各向异性影响的数值模拟

Propagation through stress-aligned fluid-filled cracks and other inclusions have been claimed to be the cause of azimuthal anisotropy observed in the crust and upper mantle.This paper examines the behavior of seismic waves attenuation caused by the internal structure of rock mass,and in particular,the internal geometry of the distribution of fluid-filled openings Systematic research on the effect of crack parameters,such as crack density,crack aspect ratio(the ratio of crack thickness to crack diameter),pore fluid properties(particularly pore fluid velocity),VP/VS ratio of the matrix material and seismic wave frequency on attenuation anisotropy has been conducted based on Hudson’s crack theory.The result shows that the crack density,aspect ratio,material filler,seismic wave frequency,and P-wave and shear wave velocity in the background of rock mass,and especially frequency has great effect on attenuation curves.Numerical research can help us know the effect of crack parameters and is a good supplement for laboratory modeling.However,attenuation is less well understood because of the great sensitivity of attenuation to details of the internal geometry.Some small changes in the characteristics of pore fluid viscosity,pore fluids containing gas and liquid phases and pore fluids containing clay can each alter attenuation coefficients by orders of magnitude.Some parameters controlling attenuation are therefore necessary to make reasonable estimations,and anisotropic attenuation is worth studying further.     

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.