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1.
A problem of reflection and transmission of elastic waves at a plane interface between a uniform elastic solid half-space and a porous elastic half-space containing two immiscible fluids is investigated. The theory developed by Lo, Sposito and Majer for porous media containing two immiscible fluids is employed to find out the reflection and transmission coefficients. The incident wave is assumed to propagate through the uniform elastic half-space and two cases are considered. In the first case, a beam of plane longitudinal wave is assumed to be incident and in the second case, a beam of transverse wave is assumed to be incident at the interface. By taking granite as impervious elastic medium and columbia fine sandy loam containing air-water mixture as porous medium, reflection and transmission coefficients are obtained. By neglecting the inertial coupling coefficients, these coefficients are reduced to those obtained by Tomar and Arora using the theory of Tuncay and Corapcioglu. It is found that the inertial coupling parameters significantly affect the phase speeds and the amplitude ratios of the transmitted waves. 相似文献
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《中国科学:地球科学(英文版)》2017,(6)
The relationship between the maximum shear stress in a substrate solid and the elastic wave reflection coefficient from the interface between the substrate solid and an overlying solid half-space is investigated. Both substrate and overlying solid media are assumed to be initially isotropic and stress-free. Then as the substrate is subjected to horizontal confined stresses it becomes anisotropic. It is shown that longitudinal and shear wave reflection coefficients are related to the degree of stress induced anisotropy in the substrate medium. From this relation the confined stress level and the maximum shear stress generated on the vertical planes of the substrate are estimated. Authors in their previous investigation computed plane wave reflection coefficient in a biaxially compressed solid substrate immersed in a fluid. This paper reports for the first time how the maximum shear stress in a biaxially compressed substrate medium can be measured from the plane wave reflection coefficients when the overlying medium is also a solid half-space. 相似文献
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Wave reflection and refraction in layered media is a topic closely related to seismology, acoustics, geophysics and earthquake engineering. Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials. The system is composed of ideal fluid, porous medium, and underlying elastic solid. By numerical examples, the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed. The results show that the existence of the porous medium, especially in the partially saturated case, may significantly affect the dynamic pressures of the overlying fluid. 相似文献
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弹性孔隙介质分界面上的反透射系数特征,在岩性划分、流体识别、储层边界判识等方面有重要的应用.本文研究上层为含两项不混合黏性流体孔隙介质、下层为含单项黏性流体孔隙介质分界面上的反透射理论.首先根据两种孔隙介质分界面上的能量守恒得到边界条件,再将波函数、位移、应力与应变关系代入边界条件,推导出完全连通孔隙情况下,第一类纵波入射到孔隙介质分界面上的反透射系数方程.通过建立砂岩孔隙介质模型,分别分析不同孔隙流体类型、不同含油饱和度及不同入射角情况下,各类波的反透射系数特征.研究表明,第二、三类纵波反透射系数数值比第一类纵波小多个数量级,且两者对入射角的变化不敏感,但对孔隙流体性质、含油饱和度的变化较敏感,而横波反透射系数特征恰好与此相反;第一类纵波反透射系数特征比较复杂,入射角、孔隙流体的性质及含油饱和度的变化都对其产生影响.不同孔隙流体弹性物性的差异、孔隙介质中含油饱和度的变化及不同入射角引起垂向和切向应力分量的变化都会影响各类波的反透射系数特征,分析这些特征可以为研究储层含油气性提供理论基础. 相似文献
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This study investigates the reflection and transmission of plane SH-waves in two semi-infinite anisotropic magnetoelastic media. The lower half-space is considered as initially stressed and inhomogeneous. The density of lower half-space is taken exponentially varying with depth. The solutions for half-spaces are obtained analytically. The expressions for reflection and transmission coefficient are obtained in the closed form subject to continuity conditions at the interfaces of anisotropic magnetoelastic half-spaces and the Snell’s law. It is found that these coefficients depend on the initial stress, inhomogeneity parameter, the magnetoelastic coupling parameter, and the angle at which wave crosses the magnetic field of the half-spaces. Numerical computations are performed for these coefficients for a specific model of two different anisotropic magnetoelastic half-spaces. The numerical results are illustrated by the graph of reflection and transmission coefficient versus the angle of incidence. In general, as the initial stress increases the reflection and transmission coefficient increases, the affect is more prominent for more than 10 GPa. Inhomogeneity in the density of the material also increases the reflection and transmission coefficient. The anisotropic magnetoelastic parameter and the angle at which the wave crosses the magnetic field for both the half-spaces have a quite significant effect on the reflection and transmission coefficient. 相似文献
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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. 相似文献
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Markov M. G. Markova I. A. Jarillo G. F. Ronquillo Pervago E. V. 《Izvestiya Physics of the Solid Earth》2020,56(3):357-363
Izvestiya, Physics of the Solid Earth - The problem of calculating the reflection and transmission coefficients of elastic P-wave incident from a porous half-space onto a fluid-filled crack is... 相似文献
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地下岩石由岩石骨架和孔隙流体组成,通常流体含黏性.地震波在地下介质中传播时受岩石骨架和黏性流体的影响会呈现出复杂的变化.本文将流、固体位移和应力连续作为边界条件,推导出含黏性流体孔隙介质分界面上反透射系数方程;通过建立上层为饱油、下层为饱盐水的砂岩孔隙介质模型,开展反透射系数特征研究,分别分析不同频率、不同黏滞系数条件下,含黏性流体孔隙介质分界面上反透射系数随入射角的变化.研究表明,孔隙介质分界面上和等效介质分界面上的反透射系数分别随入射角的变化趋势基本一致,说明方程推导和数值计算的正确性;快纵波反透射系数受频率、流体黏性的影响较小,而快横波反透射系数在一定入射角范围内受频率、流体黏性的影响比较大;由于黏性孔隙流体的作用,慢纵波和慢横波的反透射系数受入射角、频率及流体黏性的影响都很大. 相似文献
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B.O. Ruud 《Studia Geophysica et Geodaetica》2006,50(3):479-498
The calculation of reflection and transmission coefficients of plane waves at a plane interface between two homogeneous anelastic
media may become ambiguous because it is not always obvious how to determine the sign of the vertical component of the slowness
vector of the scattered waves. For elastic media, the sign is determined by applying so-called radiation condition when the
slowness vector is complex-valued, but it has long been known that this approach does not work satisfactorily for anelastic
media. Other approaches have been suggested, e.g., by requiring that the reflection and transmission coefficients should vary
continuously with increasing incident angles, or by relating the sign to the direction of the energy flux. In the present
paper, it is shown that these approaches may give different results, and that the results can be inconsistent with the elastic
case even for weak attenuation. Instead, it is demonstrated that the ambiguity in the reflection coefficient can be resolved
by expressing the seismic response of a point source over an interface as a superposition of plane waves and their reflection
coefficients, and solving the resulting integral by the saddle point approximation. Although the saddle point itself (point
of stationary phase) does not provide new insight, the ambiguity is removed by considering the steepest descent path through
the point. Ray synthetic seismograms computed by this method compare well with synthetics computed by the reflectivity method,
which does not suffer from the above-mentioned ambiguity since the integration path is taken along the real axis.
This paper concentrates on the isotropic case, but it is discussed how the result may be extended to layered transversely
isotropic media. The suggested approach, derived for a point source and plane layers, does not directly apply to 2-D or 3-D
laterally inhomogeneous media, or to media of general anisotropy. A generalization of the result found is that the sign of
the vertical slowness components should be chosen according to the energy flux direction for subcritical incidence and according
to the radiation condition for supercritical incidence, even if this creates a discontinuity in the coefficients at the critical
incidence angle. Such a discontinuity is sometimes necessary to get results which are consistent with the elastic case. It
is discussed how the generalized result can be obtained by applying certain continuity criteria for the sub-and supercritical
angle intervals, but the validity of this approach for general models remains to be proved. 相似文献
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The bottom simulating reflector （BSR） in gas hydrate-bearing sediments is a physical interface which is composed of solid, gas, and liquid and is influenced by temperature and pressure. Deep sea floor sediment is a porous, unconsolidated, fluid saturated media. Therefore, the reflection and transmission coefficients computed by the Zoeppritz equation based on elastic media do not match reality. In this paper, a two-phase media model is applied to study the reflection and transmission at the bottom simulating reflector in order to find an accurate wave propagation energy distribution and the relationship between reflection and transmission and fluid saturation on the BSR. The numerical experiments show that the type I compressional （fast） and shear waves are not sensitive to frequency variation and the velocities change slowly over the whole frequency range. However, type II compressional （slow） waves are more sensitive to frequency variation and the velocities change over a large range. We find that reflection and transmission coefficients change with the amount of hydrate and free gas. Frequency, pore fluid saturation, and incident angle have different impacts on the reflection and transmission coefficients. We can use these characteristics to estimate gas hydrate saturation or detect lithological variations in the gas hydrate-bearing sediments. 相似文献
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Reflection and refraction at an imperfectly bonded interface between poroelastic solid and cracked elastic solid 总被引：1，自引：1，他引：0
Porous solid is in contact with a cracked elastic solid at a plane interface between them. For the presence of vertically aligned microcracks, the elastic solid behaves transversely isotropic to wave propagation. The coefficients of elastic anisotropy depend on the crack density and crack porosity in the medium. A loose bonding is considered between the two solids so that a limiting case could be the welded contact. At the plane interface, the imperfection in welded bonding is represented by tangential slipping and, hence, results in the dissipation of a part of strain energy. Three types of waves propagate in an isotropic fluid-saturated porous medium, which are considered for incidence at the interface. Incidence of a wave results in three reflected waves and two refracted waves. Partition of incident energy among the reflected and refracted waves is studied for each incidence, varying from normal to grazing directions. Numerical example calculates the energy shares of reflected and refracted waves at the plane interface between water-saturated sandstone and basalt. These energy shares are computed and analyzed for different values of crack parameters as well as loose bonding parameter. 相似文献
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Using two-dimensional linear water wave theory, we consider the problem of normal water wave (internal wave) propagation over
small undulations in a channel flow consisting of a two-layer fluid in which the upper layer is bounded by a fixed wall, an
approximation to the free surface, and the lower one is bounded by a bottom surface that has small undulations. The effects
of surface tension at the surface of separation is neglected. Assuming irrotational motion, a perturbation analysis is employed
to calculate the first-order corrections to the velocity potentials in the two-layer fluid by using Green’s integral theorem
in a suitable manner and the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Two special forms of the shape function are considered for which explicit expressions
for reflection and transmission coefficients are evaluated. For the specific case of a patch of sinusoidal ripples having
the same wave number throughout, the reflection coefficient up to the first order is an oscillatory function in the quotient
of twice the interface wave number and the ripple wave number. When this quotient approaches one, the theory predicts a resonant
interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples.
High reflection of the incident wave energy occurs if this number is large. Again, when a patch of sinusoidal ripples having
two different wave numbers for two consecutive stretches is considered, the interaction between the bed and the interface
near resonance attains in the neighborhood of two (singular) points along the x-axis (when the ripple wave number of the bottom undulation become approximately twice as large as the interface wave number).
The theoretical observations are presented in graphical form. 相似文献
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It is known that the reflection and transmission coefficients used in the zeroth order approximation of asymptotic ray theory (ART) are identical to those obtained for the plane wave impinging on a plane interface separating two perfectly elastic half-spaces. We have used ART to compute reflection and transmission coefficients for two viscoelastic media separated by a plane interface. Our method is different from the plane-wave approach because the ART approach requires only a local application of the boundary conditions both for the eikonal and the ray amplitudes. Several types of viscoelastic media were studied. For a given model, the elastic case was emulated by setting all the quality factors Q equal to each other. Several anelastic cases were computed by keeping the same velocities and densities while changing the Qs. The quality factor is a relatively difficult parameter to measure exactly. Hence elastic coefficients are used in most synthetic seismogram computations, and the quality factors are chosen from experimental measurements or simply estimated. From these computations, amplitude and phase differences between elastic coefficients and coefficients for dissipative media are observed in some cases. These differences show the importance of knowing the exact values of Q. Incorrect Q values can lead to unrealistic moduli and to noticeable phase differences of these viscoelastic coefficients. 相似文献
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Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically. 相似文献
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Using Biot’s poroelasticity theory, we derive expressions for the reflection and transmission coefficients for a plane shear wave incident on an interface separating two different poroelastic solids. The coefficients are formulated as a function of the wave incidence angle, frequency and rock properties. Specific cases calculated include the boundary between water-saturated sand and water-saturated sandstone and the gas–water interface in sand. The results show a very different interface response to that of an incident P wave. Plane SV wave incidence does not significantly excite the Biot slow P wave if the frequency of the wave is below the transition frequency. Above this frequency, an incident plane SV wave can generate a mode-converted slow Biot P wave which is actually a normal propagating wave and not highly attenuating as in the usual (diffusive) case. For an incident SV wave onto a gas–water interface, even at very high frequency, there is no significant Biot second P wave produced. For small incident angles, the gas–water interface is essentially transparent. With increasing angles, there can arise an unusual "definitive angle" in the reflection/transmission coefficient curves which is related to the change of fluid viscosity on both sides of the interface and provides a possible new means for underground fluid assessment. 相似文献
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本文在小扰动条件下,从粘性可压缩流体的运动方程、状态方程以及连续性方程导出了它的波动方程,从而表明粘性可压缩流体中能够存在有耗损的纵波与横波。文中还针对自由界面、刚性界面、粘性流体内部分界面、粘性流体与弹性固体分界面等,求出了平面波的反射系数和透射系数。 相似文献
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Most amplitude versus offset (AVO) analysis and inversion techniques are based on the Zoeppritz equations for plane‐wave reflection coefficients or their approximations. Real seismic surveys use localized sources that produce spherical waves, rather than plane waves. In the far‐field, the AVO response for a spherical wave reflected from a plane interface can be well approximated by a plane‐wave response. However this approximation breaks down in the vicinity of the critical angle. Conventional AVO analysis ignores this problem and always utilizes the plane‐wave response. This approach is sufficiently accurate as long as the angles of incidence are much smaller than the critical angle. Such moderate angles are more than sufficient for the standard estimation of the AVO intercept and gradient. However, when independent estimation of the formation density is required, it may be important to use large incidence angles close to the critical angle, where spherical wave effects become important. For the amplitude of a spherical wave reflected from a plane fluid‐fluid interface, an analytical approximation is known, which provides a correction to the plane‐wave reflection coefficients for all angles. For the amplitude of a spherical wave reflected from a solid/solid interface, we propose a formula that combines this analytical approximation with the linearized plane‐wave AVO equation. The proposed approximation shows reasonable agreement with numerical simulations for a range of frequencies. Using this solution, we constructed a two‐layer three‐parameter least‐squares inversion algorithm. Application of this algorithm to synthetic data for a single plane interface shows an improvement compared to the use of plane‐wave reflection coefficients. 相似文献