共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
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
3.
M D Sharma 《Journal of Earth System Science》2018,127(1):7
Propagation of surface waves is discussed in a cylindrical borehole through a liquid-saturated porous solid of infinite extent. The porous medium is assumed to be a continuum consisting of a solid skeletal with connected void space occupied by a mixture of two immiscible inviscid fluids. This model also represents the partial saturation when liquid fills only a part of the pore space and gas bubbles span the remaining void space. In this isotropic medium, potential functions identify the existence of three dilatational waves coupled with a shear wave. For propagation of plane harmonic waves along the axially-symmetric borehole, these potentials decay into the porous medium. Boundary conditions are chosen to disallow the discharge of liquid into the borehole through its impervious porous walls. A dispersion equation is derived for the propagation of surface waves along the curved walls of no-liquid (all gas) borehole. A numerical example is studied to explore the existence of cylindrical waves in a particular model of the porous sandstone. True surface waves do not propagate along the walls of borehole when the supporting medium is partially saturated. Such waves propagate only beyond a certain frequency when the medium is fully-saturated porous or an elastic one. Dispersion in the velocity of pseudo surface waves is analysed through the changes in consolidation, saturation degree, capillary pressure or porosity. 相似文献
4.
M. D. Sharma 《Journal of Earth System Science》2007,116(6):537-551
The propagation of plane waves is considered in a general anisotropic elastic medium in the presence of initial stress. The
Christoffel equations are solved into a polynomial of degree six. The roots of this polynomial represent the vertical slowness
values for the six quasi-waves resulting from the presence of a discontinuity in the medium. Three of these six values are
identified with the three quasi-waves traveling in the medium but away from its boundary. Reflection at the free plane surface
is studied for partition of energy among the three reflected waves. For post-critical incidence, the reflected waves are inhomogeneous
(evanescent) waves. Numerical examples are considered to exhibit the effects of initial stress on the phase direction, attenuation
and reflection coefficients of the reflected waves. The phase velocities and energy shares of the reflected waves change significantly
with initial stress as well as anisotropic symmetry. The presence of initial stress, however, has a negligible effect on the
phase directions of reflected waves. 相似文献
5.
It is well known that an elastic homogeneous half-space does not allow torsional surface waves to propagate. The present paper attempts to find out the possibility of propagation of such waves in a viscoelastic half-space. The study reveals that although the homogeneous elastic half-space does not allow torsional surface waves to propagate, a viscoelastic half-space does so. The wave is damped due to the viscoelastic parameter. It has also been found that as the viscoelastic parameter decreases, the medium becomes elastic and the torsional surface waves ceases to propagate. 相似文献
6.
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
7.
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
8.
Shear wave splitting as a diagnostic of variable anisotropic structure of the upper mantle beneath central Fennoscandia 总被引：1，自引：0，他引：1
We analyze splitting of shear waves recorded during the SVEKALAPKO passive seismic experiment in south-central Finland to study fabrics of the mantle lithosphere of the Precambrian region and thus to bring information into a debate on existence of plate tectonics or its forms in the early stage of continent formation. Geographical variations of the splitting parameters and their distinct dependence on direction of wave propagation through the upper mantle allow us to identify six domains of the central Fennoscandian mantle lithosphere, including the Proterozoic–Archean transition, and to model their fabrics by joint inversion of body wave anisotropic parameters. Fabrics of the Archean mantle lithosphere can be approximated by a peridotite aggregate with lineation a dipping to the NE. On the other hand, anisotropy of the Proterozoic mantle lithosphere is weaker and we model its fabric by the (a, c) foliations dipping to the SE. We present a 3D self-consistent anisotropic model of the Proterozoic and Archean upper mantle along the SW-NE profile in the south-central Finland. Boundaries of inter-growing wedges of the Proterozoic and Archean mantle lithospheres explain the longitudinal and shear wave propagation and polarization, mantle xenolith ages, surface wave tomography and location of the upper mantle reflectors. We interpret the six anisotropic domains as fragments of mantle lithosphere retaining an old fossil olivine fabric which was created before these micro-continents assembled. 相似文献
9.
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
10.
M. D. Sharma 《Journal of Earth System Science》2008,117(6):951-958
Biot’s theory for wave propagation in saturated porous solid is modified to study the propagation of thermoelastic waves in
poroelastic medium. Propagation of plane harmonic waves is considered in isotropic poroelastic medium. Relations are derived
among the wave-induced temperature in the medium and the displacements of fluid and solid particles. Christoffel equations
obtained are modified with the thermal as well as thermoelastic coupling parameters. These equations explain the existence
and propagation of four waves in the medium. Three of the waves are attenuating longitudinal waves and one is a non-attenuating
transverse wave. Thermal properties of the medium have no effect on the transverse wave. The velocities and attenuation of
the longitudinal waves are computed for a numerical model of liquid-saturated sandstone. Their variations with thermal as
well as poroelastic parameters are exhibited through numerical examples. 相似文献
11.
LIU Mei GOU Jingwei YU Guangming LIN Jiandong Research Institute of Coal Geophysical Exploration Zhuozhou Hebei 《《地质学报》英文版》2000,74(2):425-428
Coal-bed methane is accumulated in micro-fissures and cracks in coal seams. The coal seam is the source terrace and reservoir bed of the coal-bed methane (Qian et al., 1996). Anisotropy of coal seams is caused by the existence of fissures. Based on the theory of S wave splitting: an S wave will be divided into two S waves with nearly orthogonal polarization directions when passing through anisotropic media, i.e. the fast S wave with its direction of propagation parallel to that of the fissure and slow S wave with the direction of propagation perpendicular to that of the fissure.This paper gives the results of laboratory research and field test on the S wave splitting caused by coal-seam fissures: The results show that it is, feasible to detect fissures in coal seams by applying the converted S wave and finally gives the development zone and development direction of these fissures. 相似文献
12.
基于Leclaire对饱和双相孔隙弹性介质Biot模型的扩展,研究含有两种不同固相组分的三相多孔弹性介质中体波的传播特性。以饱和冻土为例,分析了各相体积分数、颗粒形状,接触参数等因素对波动方程中惯性参数、黏性参数、刚度参数的影响;对该三相介质模型进行了退化,分析了孔隙中只含液态水或固态冰时体波的特性;以饱和冻土为例,通过数值计算,探讨了饱和冻土中体波的相速度和衰减系数与胶结参数、接触参数、频率、饱和度、孔隙率等参数的关系。结果表明：与一般的饱和土不同,饱和冻土中存在5种体波,即3种纵波和2种横波;5种体波均具有弥散性和衰减性,且P1波、S1波弥散性和衰减性远小于P2、P3、S2波;胶结参数、饱和度、孔隙率对5种体波的传播特性影响显著,接触参数对传播特性影响较小。 相似文献
13.
An anisotropic geomechanical model for jointed rock mass is presented. Simultaneously with deriving the orthotropic anisotropy elastic parameters along the positive axis, the equivalent compliance matrix for the deflection axis orthotropic anisotropy was derived through a three-dimensional coordinate transformation. In addition, Singh’s analysis of the stress concentration effects of intermittent joints was adopted, based on two groups of intermittent joints and a set of cross-cutting joints in the jointed rock mass. The stress concentration effects caused by intermittent joints and the coupling effect of cross-cutting joints along the deflection-axis are also considered. The proposed anisotropic mechanics parameters method is applied to determine the deformation parameters of jointed granite at the Taishan Nuclear Power Station. Combined with the deterministic mechanical parameters of rock blocks and joints, the deformation parameters and their variability in jointed rock masses are estimated quantitatively. The computed results show that jointed granite at the Taishan Nuclear Power Station exhibits typical anisotropic mechanical characteristics; the elastic moduli in the two horizontal directions were similar, but the elastic modulus in the vertical direction was much greater. Jointed rock elastic moduli in the two horizontal and vertical directions were respectively about 24% and 37% of the core of rock, showing weakly orthotropic anisotropy; the ratio of elastic moduli in the vertical and horizontal directions was 1.53, clearly indicating the transversely isotropic rock mass mechanical characteristics. The method can be popularized to solve other rock mechanics problems in nuclear power engineering. 相似文献
14.
15.
The velocity of elastic waves has been measured along the principal fabric directions in 110 Alpine rocks, and these data are analyzed in conjunction with previously measured data on density, porosity, specific heat, and thermal diffusivity for the same rocks. Particular attention is given to the anisotropy in the thermal and elastic properties which are up to three times larger in the direction of lineation than in the direction perpendicular to the foliation. The correlations among the various scalar properties and the average thermal and elastic properties are in general weak and are overshadowed by variations due to mineralogy. However, relative thermal and elastic properties show a significant positive correlation, and for gneisses, schists, ultramafic rocks and carbonate rocks it is meaningful to predict thermal anisotropy on the basis of elastic anisotropy. 相似文献
16.
Most theoretical investigations of seismic wave scattering rely on the assumption that the underlying medium is statistically isotropic. However, deep seismic soundings of the crust as well as geological observations often reveal the existence of elongated or preferentially oriented scattering structures. In this paper, we develop mean field and radiative transfer theories to describe the attenuation and multiple scattering of a scalar wavefield in an anisotropic random medium. The scattering mean free path is found to depend strongly on the propagation direction. We derive a radiative transfer equation for statistically anisotropic random media from the Bethe–Salpeter formalism and propose a Monte Carlo method to solve this equation numerically. At longer times, the energy density is shown to obey a tensorial diffusion equation. The components of the diffusion tensor are obtained in closed form and excellent agreement is found between Monte Carlo simulations and analytical solutions of the diffusion equation. The theory has important potential implications for lithospheric models where scatterers are for example flat structures preferentially aligned along the surface. In this simple geometry, analytical expressions of the Coda Q parameter can be given explicitly in the diffusive regime. Our results suggest that pulse broadening and coda decay are controlled by different parameters, related to the eigenvalues of the diffusion tensor. These eigenvalues can differ by more than one order of magnitude. This theory could be applied to probe the anisotropy of length scales in the lithosphere. 相似文献
17.
Egor V. Dontsov 《国际地质力学数值与分析法杂志》2019,43(2):519-529
This study investigates parametric space of solutions for a planar hydraulic fracture propagating in a homogeneous anisotropic rock. It is assumed that the fracture has an elliptical shape and is driven by a power-law fluid. The purpose of this study is to investigate the influence of anisotropy and power-law fluid rheology on the parametric space of solutions. Rock anisotropy is represented by having two values of fracture toughness, one in the vertical direction and another one in the horizontal direction. Similarly, the effect of elastic anisotropy is approximated by using two different effective elastic moduli in the vertical and horizontal directions. In contrast to the isotropic case, for which there are four limiting solutions, the problem for anisotropic rocks features six different limiting cases. These cases represent competition between toughness and viscosity in the vertical and horizontal directions and competition between fluid storage inside the fracture and fluid leak-off into formation. Approximate expressions for the limiting solutions are obtained using global volume balance and tip asymptotic solutions. Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated. 相似文献
18.
地球各向异性介质中地震波动理论、检测与应用研究 总被引：11，自引：0，他引：11
地下岩石的各向异性主要表现在地震波速度随传播方向发生变化,不同类型体波间相互耦合,横波发生分裂,波速度频散依赖于传播方向等。薄互层与裂隙定向分布等产生视各向异性,它在石油地震勘探、地震预测和岩石圈物理与动力学研究中有极大潜力和应用前景,并受到广泛重视。为此,文中讨论了地震各向异性研究在解决地球科学问题中的重要性与必要性;系统地介绍了中国在地震各向异性研究领域的各个方面,如波动传播、波场激发、数值模拟、偏移与反演成像,以及应用于油气资源探测、深部地球物理研究和地质灾害监测等方面所取得的新进展。结合笔者参加的第八届地震各向异性国际学术讨论会,及ＳＥＧ,ＩＡＳＰＥＩ,ＩＵＧＧ等有关学术会议情况,综述了国际上在该领域内的主要成果与发展动向,分析了国际上各国地震各向异性研究现状及存在问题,并对我国在该领域研究的进一步开展提供了主攻问题与相应建议。 相似文献
19.
基于弹性波在冻结饱和多孔介质与单相弹性介质中的传播理论,研究了平面P波在饱和冻土介质与单相弹性介质分界面上的透反射问题。利用Helmholtz矢量分解定理,根据分界面上的边界条件,获得了平面P波从单相弹性介质入射到饱和冻土介质分界面上透反射振幅比的理论表达式。通过数值计算,分析了在不同入射频率、胶结参数、孔隙率、饱和度和接触参数下,弹性波的透反射振幅比随入射角变化的关系。研究结果表明：P波从单相弹性介质垂直入射到饱和冻土介质分界面上时只有反射P波和3种透射P波产生,当掠入射时只产生反射而没有透射现象发生。入射频率、胶结参数、孔隙率、饱和度以及接触参数等参数对反射波和透射波的振幅比影响显著。 相似文献
20.
This paper presents an analytical solution for wave propagation in a square pile due to transient point load. The differential equation of dynamic equilibrium is established considering propagation of waves in both vertical and transverse directions. The soil resistance is simulated by Voigt model. The three-dimensional analytical solution is deduced by using Fourier transform and the separation of variable method. The arithmetical results of the proposed solution show that the velocity responses along the radial direction at the pile top are highly non-uniform. In addition, Young’s modulus and the pile side length exert undisputable influences on the velocity responses. 相似文献