共查询到20条相似文献，搜索用时 23 毫秒
1.
Modified Christoffel equations are derived for three-dimensional wave propagation in a general anisotropic medium under initial
stress. The three roots of a cubic equation define the phase velocities of three quasi-waves in the medium. Analytical expressions
are used to calculate the directional derivatives of phase velocities. These derivatives are, further, used to calculate the
group velocities and ray directions of the three quasi-waves in a pre-stressed anisotropic medium. Effect of initial stress
on wave propagation is observed through the deviations in phase velocity, group velocity and ray direction for each of the
quasi-waves. The variations of these deviations with the phase direction are plotted for a numerical model of general anisotropic
medium with triclinic/ monoclinic/orthorhombic symmetry 相似文献
2.
M. D. Sharma 《Journal of Earth System Science》2005,114(4):411-419
Wave propagation is studied in a general anisotropic poroelastic solid saturated with a viscous fluid flowing through its
pores of anisotropic permeability. The extended version of Biot’s theory is used to derive a system of modified Christoffel
equations for the propagation of plane harmonic waves in such media. The non-trivial solution of this system is ensured by
a biquadratic equation whose roots represent the complex velocities of four attenuating quasi-waves in the medium. These complex
velocities define phase velocity and attenuation of each quasi-wave propagating along a given phase direction in three-dimensional
space. The solution itself defines the polarisations of the quasi-waves along with phase shift. The variations of polarisations
of quasi-waves with their phase direction, are computed for a realistic numerical model. 相似文献
3.
M. D. Sharma 《Journal of Earth System Science》2007,116(4):357-367
Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic
approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive
macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic
(APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated
porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane
harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement
of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent
complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities
of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional
space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence
between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed,
for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches
are exhibited numerically. 相似文献
4.
Neetu Garg 《Journal of Earth System Science》2009,118(6):677-687
In a pre-stressed anisotropic elastic medium, three types of quasi-waves propagate along an arbitrary direction. In general, none of the waves is truly longitudinal. The present study finds the specific directions in a pre-stressed anisotropic elastic medium along which longitudinal waves may propagate. This paper demonstrates how the propagation of longitudinal waves is affected by various pre-stresses present in the medium. The study establishes the explicit expressions defining the existence and propagation of longitudinal waves in pre-stressed anisotropic elastic medium. These expressions involve not only the direction and elastic stiffness of the medium, but also the pre-stresses present in the medium. Changes in conditions for the existence of longitudinal waves in orthotropic, monoclinic and triclinic anisotropies are discussed in detail. The most important part of the paper is a practical aspect suggested to calculate the specific directions for the existence of longitudinal waves in pre-stressed anisotropic elastic medium. In this approach, only those parameters are used that can be observed by the receiver in a geophysical experiment of wave propagation. The existence of longitudinal waves has been shown graphically using a numerical example for three types of anisotropic symmetries in elastic medium. 相似文献
5.
Shishir Gupta Smita Snehamoy Pramanik Abhijit Pramanik 《Arabian Journal of Geosciences》2018,11(9):220
The present paper is incorporated into a mathematical model of transmission and reflection of shear waves through the initially stressed dry sandy medium sandwiched between two initially stressed distinct orthotropic half-spaces. The formulae of transmission and reflection coefficients have been deduced for the propagation of SH waves in the described model subjected to certain boundary conditions applying Snell’s law and Cramer’s method. These coefficients are observed as a function of wave number, phase velocity, initial stress, rigidity, and dry sandiness coefficients. The concepts of energy partition, phase shift, conservation of energy, critical angle, and slowness section are introduced. Graphical approach has been carried out to accomplish a relation between reflection/refraction coefficient, phase shift, and energy ratio with an angle of incidence and wave number on the propagation of shear wave. The study reveals that sandiness parameter, initial stress, and wave number have a cogent respond to the scattering of shear wave that has been illustrated graphically. 相似文献
6.
基于散粒体微观力学理论,忽略颗粒转动引起的相对位移,考虑颗粒接触的组构各向异性,根据宏微观能量守恒推导得到了散体材料各向异性微形态本构关系,进而通过单位接触方向积分的递推公式推导出了各向异性本构张量表达式;在此基础上,根据哈密顿原理得到了各向异性散体材料的运动平衡方程和边界条件,从而求得了平面波在各向异性散粒体中的传播规律和频散关系,最后对波的频散关系和频率带隙进行了详细的参数分析。研究表明：该模型预测了散体中包含3类12种位移波：3种纵波、6种横波和3种平面内横向剪切波;横观各向同性条件下,接触各向异性参数a20越大,纵波和横波的频率越大,而平面内横向剪切波的频率越小;正交各向异性条件下,随着接触各向异性参数a22的增大,与2方向运动相关的横波频率增大,而与3方向运动相关的横波频率则减小;但a22的变化对纵波频率影响很小。材料各向异性程度对横波带宽影响不大,但对纵波带宽影响较大：a20的增大使得声?光学波间的带宽减小,而光学波间的带宽增大,当a20>0.84时,声?光学波间的带隙消失;但是a22的增大则使得声?光学波间的带宽增大,而光学波间的带宽减小。退化为各向同性模型后,预测3类波的频散曲线与其他各向同性模型的结果基本一致。 相似文献
7.
Anisotropy is frequently present in geological structures, but usually neglected when source parameters are determined through waveform inversion. Due to the coupling of propagation and source effects in the seismic waveforms, such neglect of anisotropy will lead to an error in the retrieved source. The distortion of the mechanism of a double-couple point source located in an anisotropic medium is investigated when inverting waveforms using isotropic Green's functions. The anisotropic medium is considered to be transversely isotropic with six levels of anisotropy ranging from a fairly weak to rather strong anisotropy, up to about 24% in P waves and 11% in S waves. Inversions are based on either only direct P waves or both direct P and S waves. Two different algorithms are employed: the direct parametrization (DIRPAR, a nonlinear algorithm) and the indirect parametrization (INPAR, a hybrid scheme including linear and nonlinear steps) of the source. The orientation of the double-couple mechanism appears to be robustly retrieved. The inclination of the resulting nodal planes is very small, within 10° and 20° from the original solution, even for the highest degree of anisotropy. However, the neglect of anisotropy results in the presence of spurious isotropic and compensated linear-vector dipole (CLVD) components in the moment tensor (MT). This questions the reliability of non-double-couple components reported for numerous earthquakes. 相似文献
8.
Baljeet Singh 《Journal of Earth System Science》2002,111(1):29-37
In the present investigation, it is shown that there exists five basic waves in a microstretch elastic solid half-space. The
problem of reflection of plane waves from free surface of a microstretch elastic solid half-space is studied. The energy ratios
for various reflected waves are obtained for aluminiumepoxy composite as a microstretch elastic solid half-space. The variations
of the energy ratios with the angle of incidence are shown graphically. The microstretch effect is shown on various reflected
waves. 相似文献
9.
Anisotropic growth in the olivine-spinel transformation of Mg2GeO4 under nonhydrostatic stress 总被引：2，自引：0，他引：2
The olivine-spinel phase transformation in Mg2GeO4 does not occur by a martensitic mechanism. The evidence, from samples transformed in a Griggs-type solid medium deformation apparatus, are:
- 1. (1) lack of microstructural features in the olivine phase which can be specifically associated with a martensitic mechanism
- 2. (2) the orientation relationship between the two phases that is predicted by the martensitic mechanism does not occur nor is there any apparent consistency of relative orientations
- 3. (3) application of a differential stress to the transforming sample resulted in an anisotropic growth rate for the spinel phase indicating that growth was externally controlled rather than crystallographically controlled.
10.
Anup Saha Santimoy Kundu Shishir Gupta Pramod Kumar Vaishnav 《Journal of Earth System Science》2016,125(4):885-895
The present paper is concerned with the propagation of torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space. We assume the quadratic inhomogeneity in rigidity and density in the lower half-space and irregularity is taken in the form of rectangle at the interface separating the layer from the lower half-space. The dispersion equation for torsional waves has been obtained in a closed form. Velocity equation is also obtained in the absence of irregularity. The study reveals that the presence of irregularity, initial stress, porosity, inhomogeneity and anisotropy factor in the dispersion equation approves the significant effect of these parameters in the propagation of torsional waves in porous medium. It has also been observed that for a uniform media, the velocity equation reduces to the classical result of Love wave. 相似文献
11.
The propagation of plane waves in an anisotropic elastic medium possessing monoclinic symmetry is discussed. The expressions
for the phase velocity ofqP andqSV waves propagating in the plane of elastic symmetry are obtained in terms of the direction cosines of the propagation vector.
It is shown that, in general,qP waves are not longitudinal andqSV waves are not transverse. Pure longitudinal and pure transverse waves can propagate only in certain specific directions.
Closed-form expressions for the reflection coefficients ofqP andqSV waves incident at the free surface of a homogeneous monoclinic elastic half-space are obtained. These expressions are used
for studying numerically the variation of the reflection coefficients with the angle of incidence. The present analysis corrects
some fundamental errors appearing in recent papers on the subject. 相似文献
12.
Present paper aims to study the phenomenon of reflection and transmission when an inhomogeneous wave strikes some discontinuity in a composite porous medium saturated by two immiscible viscous fluids. The incident wave splits into six reflected and six transmitted waves at the interface. All reflected and transmitted waves are inhomogeneous in nature with different directions of propagation vector and attenuation vector. A dimensionless parameter \(\varsigma \in [0, 1]\) is introduced to represent the extent of connection among the pores at the interface. Expression of Umov–Poynting vector is derived to obtain energy flux vector. Continuity of energy flux vector at the interface gives the required boundary conditions for the system. Connecting parameter \(\varsigma \) is also employed in boundary conditions to model the partial connection of pores at the interstices of two media. For numerical discussion we consider a porous medium composed of sandstone and ice, saturated with oil and water. The effect of parameter \(\varsigma \) and angle of incidence is determined numerically on the amplitude and the energy ratios of reflected and transmitted waves. 相似文献
13.
层理对页岩力学性质和应变能的积聚和耗散具有重要影响,以不同层理面角度下龙马溪组页岩为研究对象,开展电镜扫描试验和单轴压缩试验,研究起裂、扩容和峰值特征点的应力-应变、弹性模量和泊松比的各向异性特征,分析其页岩变形破坏过程中输入应变能、可释放弹性应变能和耗散应变能的变化规律,揭示输入应变能与层理面角度和抗压强度的关系。结果表明：龙马溪组页岩脆性矿物含量达到72.58%,微观结构各向异性明显;随层理面角度增加,起裂、扩容和峰值特征点的应力和应变都先减少后增大,在 30°时均达到一个最低值,总体上呈现两边高、中间低的U型变化规律;随层理面角度增加,起裂、扩容和峰值特征点的输入应变能、可释放弹性应变能和耗散应变能也先减少后增大,在 30°时均达到一个最低值;各特征点的应力、应变和应变能各向异性敏感性明显,0°≤ ≤30°和30°≤ ≤60°内各向异性的敏感性大于60°≤ ≤90°;起裂应力和扩容应力均与峰值应力呈线性相关,同时峰值应变能与抗压强度存在相应的二次非线性关系,这为页岩气钻井、储层压裂改造和井壁稳定性预测预警提供了根据和参考。 相似文献
14.
This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy. This is the first theoretical solution of the undrained expansion of a cylindrical cavity under plane strain conditions for soft soils with anisotropic behaviour of plastic nature. The solution is rigorously developed in detail, introducing a new stress invariant to deal with the soil fabric. The semi-analytical solution requires numerical evaluation of a system of six first-order ordinary differential equations. The results agree with finite element analyses and show the influence of anisotropic plastic behaviour. The effective stresses at critical state are constant, and they may be analytically related to the undrained shear strength. The initial vertical cross-anisotropy caused by soil deposition changes towards a radial cross-anisotropy after cavity expansion. The analysis of the stress paths shows that proper modelling of anisotropic plastic behaviour involves modelling not only the initial fabric anisotropy but also its evolution with plastic straining. 相似文献
15.
Dynamic photoelasticity is used as a means for visualizing the complex interaction process between elastic waves and geometrical discontinuities. The photoelastic experiments are back-analysed by the dynamic finite difference program WAVE, and the code is assessed in terms of its accuracy and modelling capabilities. Three model geometries are investigated: (i) a stope situated within a homogeneous medium; (ii) a stope surrounded by softened material, the interface between the softened and bulk material being bonded and (iii) a stope situated within softened material, with a non-cohesive material interface. Prominent waves resulting from the diffraction, refraction and reflection of incident waves, as well as normalized dynamic stress intensification factors at the stope face, stope back area and along the hanging-wall skin are analysed in this study. The parting planes are found to reflect a portion of the incident energy and thus shield the stope. However, a non-cohesive parting plane traps energy within the hanging-wall beam, and any shielding benefits are negated. WAVE has been proven to model accurately the diffraction, refraction and reflection of stress waves in a homogeneous medium and the interaction with cohesive and non-cohesive interfaces separating two material types. 相似文献
16.
深层岩体松动爆破中不耦合装药效应的探讨 总被引：2，自引：0，他引：2
基于冲击波在交界面两侧压力和速度必须各自相等的连续性条件,求解爆轰产物中适用的反射波方程和介质中适用的冲击波方程,得到药包周围介质中冲击波的初始参数.通过波的传播机理,把集中药包应力波随距离的衰减公式扩展到延长药包,并计算耦合与不耦合装药爆破时距爆心相同距离处岩石中冲击波的参数.由计算结果可知:(1)耦合装药爆破时形成的冲击波压力超过岩石抗压强度极限几十倍以上,药包周围岩石形成粉碎区;(2)与耦合装药爆破相比,不耦合装药爆破可以降低孔壁处岩石中冲击波初始压力,但可以增加孔壁后岩石中的冲击波压力.合理的不耦合系数,可使岩石不形成粉碎区,大幅度减少能量耗散;(3)水一般认为是非线性弹性介质,因此水介质成为炸药爆轰产物与岩石间的弹性缓冲层,增加了能量传递,延长了冲击波作用时间,加大了爆炸的作用范围. 相似文献
17.
José M. Carcione Juan E. Santos Stefano Picotti 《Rock Mechanics and Rock Engineering》2012,45(5):929-942
The triaxial nature of the tectonic stress in the earth’s crust favors the appearance of vertical fractures. The resulting rheology is usually effective anisotropy with orthorhombic and monoclinic symmetries. In addition, the presence of fluids leads to azimuthally varying attenuation of seismic waves. A dense set of fractures embedded in a background medium enhances anisotropy and rock compliance. Fractures are modeled as boundary discontinuities in the displacement u and particle velocity v as $[{\varvec{ \kappa}}\cdot {\bf u} + {\varvec{\eta}} \cdot {\bf v} ],$ where the brackets denote discontinuities across the fracture surface, ${\varvec{\kappa}}$ is a fracture stiffness, and ${\varvec{\eta}}$ is a viscosity related to the energy loss. We consider a transversely isotropic background medium (e.g., thin horizontal plane layers), with sets of long vertical fractures. Schoenberg and Muir’s theory combines the background medium and sets of vertical fractures to provide the 13 complex stiffnesses of the long-wavelength equivalent monoclinic and viscoelastic medium. Long-wavelength equivalent means that the dominant wavelength of the signal is much longer than the fracture spacing. The symmetry plane is the horizontal plane. The equations for orthorhombic and transversely isotropic media follow as particular cases. We compute the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts), and quality factors. The effective medium ranges from monoclinic symmetry to hexagonal (transversely isotropic) symmetry from the low- to the high-frequency limits in the case of a particle–velocity discontinuity (lossy case) and the attenuation shows typical Zener relaxation peaks as a function of frequency. The attenuation of the coupled waves may show important differences when computed versus the ray or phase angles, with triplication appearing in the Q factor of the qS wave. We have performed a full-wave simulation to compute the field corresponding to the coupled qP–qS waves in the symmetry plane of an effective monoclinic medium. The simulations agree with the predictions of the plane-wave analysis. 相似文献
18.
地震波全波形反演是当今地质构造反演的潮流。在层析成像等为其提供初始模型的预处理中,地震波初至走时是一个非常重要的物理量。因而,高效高精度且稳定的走时计算方法对于各向异性建模具有重要的研究意义。为实现高效高精度且稳定的走时计算,首先利用扰动理论及泰勒公式将具有垂直对称轴的横向各向同性（VTI）介质程函方程展开,得到走时解;然后引入各向同性快速推进法（fast marching method,FMM）,运用改进后的迎风差分格式求取差分格式黏滞解获取单点走时。结合窄带推进技术,得到了一种新的基于快速匹配法的VTI介质走时计算方法。通过对均匀弱各向异性模型计算结果和解析值的对比,评估了其误差,相对误差稳定于0.5%以下。针对该方法的有效性和稳定性,对层状介质模型和盐丘模型反射波走时进行了试算,取得了较好的效果。理论分析和模型试算表明,该方法对VTI介质走时计算具有较高的精度,能够应用于各向异性层析成像和全波场偏移等研究中。 相似文献
19.
Sanjeev Anand Sahu Soniya Chaudhary Pradeep Kumar Saroj Amares Chattopadhyay 《Arabian Journal of Geosciences》2017,10(5):120
The study of surface waves (Rayleigh wave) finds their virtuous applications in a numerous geological and geophysical fields including water, oil, gas, and other subsurface geological probing and exploration. The present paper efforts to investigate the influence of initial stress, Earth magnetism, and gravity on propagation of Rayleigh waves. Considered model is consist of a liquid layer lying over a magnetoelastic orthotropic half-space under self-weight and initial stress. Method of separation of variable is used to solve the equation of motion. Solutions of governing equations are obtained in terms of displacement. Frequency relation for Rayleigh wave has been obtained and matched with classical Rayleigh wave equation. In addition to classical case, some existing results have been deduced as particular case of the present study. Obtained results have been shown through numerical illustrations. It is found that the considered parameters (initial stress, Earth magnetism, and gravity) have prominent effect on phase velocity of Rayleigh wave. Graphical representations have been made to exhibit the velocity profile of Rayleigh waves for different cases with the help of MATHEMATICA. The present study may be useful for seismologists and engineers who are concern with applications of wave propagation in magnetoelastic orthotropic medium. 相似文献
20.
In this paper, the propagation of Love waves in a fiber‐reinforced layered medium lying over an elastic orthotropic half‐space under initial stress has been investigated. We have obtained the velocity equations for Love wave in this media. It is observed that propagation of Love wave is influenced by reinforced parameters and initial stressed parameter. The velocity of Love wave has been computed for three different cases. Our computed equation of Love wave coincides with the standard equation of Love wave for the case of homogeneous layer and homogeneous half‐space (AEH Love, 1911). To study the effect of reinforced and initial stressed parameters, we have computed the numerical values for phase velocity and plotted in several figures. It is observed that the phase velocity decreases with the increases of reinforced parameters and initial stressed parameter. Using MATLAB software, GUI has been developed to generalize the effect of various parameters. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献