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1.
M. R. Sarangi 《地球物理与天体物理流体动力学》2013,107(3):303-325
ABSTRACTA hydro-elastic frame has been considered to investigate the proliferation of waves over small base deformation on an infinitely extended flexible seabed. The flexible base surface is assumed as a thin elastic plate of very small thickness and it depends on the Euler–Bernoulli beam equation. For any particular frequency, there are two different modes of time-harmonic propagating wave exists rather than one mode of propagating wave along the positive horizontal direction. The waves with smaller wavenumber spread along the free-surface of the sea (say, free-surface mode) and the waves with higher wavenumber spread along the flexible base surface (say, flexural mode). A simplified perturbation approach is utilised to bring down the entire equations which govern the original boundary value problem (bvp) to a less complex bvp for the first-order velocity potential function. The first-order potential function along with the first-order reflection and transmission coefficients for both modes are calculated by a procedure based upon Fourier transform approach. A shape of sinusoidal swells flexible base surface is taken as an example to approve the scientific results. It is observed that when the train of normal incident propagating wave spreads over base distortion because of either the free-surface unsettling influence or the flexural wave movement in the sea, the reflected and transmitted energy are always feasible to be exchanged from one particular wave mode to another wave mode. Furthermore, we notice that the realistic changes in the flexural rigidity behaviour on the flexible base surface of the sea have a significant effect on the problem of water wave proliferation over small base deformation. Moreover, the energy conservation equation is derived with the help of the Green's integral theorem. The results for the values of reflection and transmission coefficients obtained for both the free-surface unsettling influence as well as flexural wave movement in the fluid are found to satisfy the energy conservation equation almost accurately. 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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Due to the presence of joints, waves are greatly attenuated when propagating across rock masses. Zhu et al. (2011) (Normally incident wave propagation across a joint set with virtual wave source method. J. Appl. Geophys.73, 283–288.) studied normally incident wave propagation across a joint set with the virtual wave source method (VWSM). The introduced VWSM has merits in some aspects, especially the capability of separating differently arriving transmitted waves. However, normal wave incidence is only the special case for wave incidence with arbitrary incident angles. Obliquely incident wave propagation across a joint set is more complicated than normally incident wave propagation due to wave transformation at the joints. As a continuation of the previous paper, this work is extended to analytically study obliquely incident wave propagation across joints with VWSM. Complete theoretical reflection and transmission coefficients across single joint described by displacement discontinuity model are derived through plane wave analysis. The superposition of P wave and S wave is for the first time mathematically expressed and studied. The VWSM is verified through comparison with the propagation matrix method. Through extensive parametric studies on wave transmission across single and multiple parallel joints, it is shown that transmitted wave energy is mainly constrained in the transmitted wave of the same type as the incident wave. And with increasing joint stiffness, the transmission coefficients across single joint increases except those whose wave type is different from the incident wave. The amplitude of superposed transmitted wave for P wave incidence increases with incident angle, which is coincident with field observations. Both joint spacing and number of joints have significant effects on transmission coefficients. We find that when joint spacing is sufficiently large, the transmission coefficient is no longer a constant as the normally incident wave propagation case (Zhu et al., 2011). And when joints are very closely spaced, wave attenuation depends little on the number of joints, which is different from the conclusions from equivalent medium method. 相似文献
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We revisit the equations governing the bending motions in thin rods and analyse the filtration of flexural waves in vertical drill strings pre‐stressed by gravity. The aim is to study transverse drill‐string vibrations at seismic frequencies for acoustic communication purposes and provide an algorithm for processing reflected and transmitted bending motions generated by downhole lateral vibrations. We obtain the dispersion equation, including attenuation due to a gravity pre‐stress gradient and frequency‐dependent reflection and transmission coefficients at the interface between subsequent tube intervals. We then develop a propagation‐matrix algorithm to simulate flexural waves in a drill string consisting in an assembly of multiple tube sections of different dimensions. The deflection vibrations are obtained at any arbitrary recording point in the drill string. The modelling is cross‐checked with a full‐wave grid algorithm. The analysis shows that the waves produced by a concentrated force are partitioned in standing and propagating modes, which are calculated by using the flexural impedance of the drill string. Moreover, the reflection coefficients weakly depend on the pre‐stress conditions and pre‐stress has important effects for far‐field signal transmission with variable weight on bit (WOB). We discuss the approximations and limits of the method with respect to realistic drilling conditions. 相似文献
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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
7.
为了突破目前声波远探测技术存在的局限性,提出了一种新的偶极横波远探测方法,即利用井中偶极子产生的井中弯曲波存在低频截止频率的现象,在声源截止频率以下激发偶极声波.通过对比分析井中偶极声源分别在截止频率上、下激发时,井孔内外产生的辐射声场,明确了截止频率以下井中偶极声源的远场辐射特征和低频截止频率激发偶极横波的优势,结合数值模拟,进一步对其反射声场进行了分析.结果表明,该方法可以避免艾里相的巨大振幅对数据量化产生的"饱和"效应,相比传统的远探测测井方式更具优势,常规源距即可满足专门的远探测测井仪器需求. 相似文献
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针对套管井反射式超声波水泥固井质量检测问题，本文利用超声反射波频谱中套管共振透射窗内的复合反射系数，提出了定量反演套管-地层环空间内介质的波阻抗的方法. 利用复合反射系数中多个频率点的相移反正切函数主值，给出了波阻抗的计算公式，并把套管-地层环空间介质中波的相移的整、实特性作为波阻抗反演收敛的判据. 针对井下实际测井环境中超声换能器性能受温度和压力等的影响而发生变化，导致的声源波形（子波）和复合反射系数不确定的困难，提出了用井下原地（in situ）实测波形定量估计声源波形和复合反射系数的方法. 通过对合成数据的处理，分别考察了已知介质的声学和几何参数存在的偏差对套管-地层环空间内介质的波阻抗反演结果的影响. 本文对多组模型井检验数据进行了目的层介质的波阻抗反演与成像，成像结果与真实情况吻合，验证了反演方法的有效性. 最后对现场实测资料进行了套管-地层环空间内介质的波阻抗定量反演与成像. 相似文献
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Rayleigh’s method of approximation is employed to find out the reflection and transmission coefficients due to an incident
plane SH wave at a corrugated interface between a laterally and vertically inhomogeneous anisotropic elastic solid half-space
and a laterally and vertically inhomogeneous isotropic visco-elastic solid half-space. The lateral and vertical inhomogeneities
are described by the exponential variations of elastic parameters. The formulae of reflection and transmission coefficients
are derived in closed form for the first-order approximation of the corrugation. The effects of the corrugation of the interface,
the inhomogeneity, the anisotropy, the visco-elasticity and the frequency of the incident wave on these coefficients are studied
analytically and numerically for a specific model containing a periodic interface. The results of earlier workers have been
reduced as particular cases from the present formulation. 相似文献
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利用全波解算法模拟哨声波束在甚低纬地区黎明前低电离层透射的三维能量分布，依据波场能量和偏振分布及其对波参量和电子浓度剖面的依赖特征，分析了哨声透射、反射及与大地－电离层波导耦合过程．结果表明，哨声模波存在于９０ｋｍ以上高度，吸收、反射、波束扩展及波模转换主要发生于电离层底部８０－９０ｋｍ区间；到达地面的透射能量密度衰减２０ｄＢ以上，透射衰减随频率变化不大，但随波入射角呈不对称变化；距透射区１５０ｋｍ以外区域的测向方位角有很大偏差；入射波能量的很少一部分（对５ｋＨｚ约为－２５ｄＢ）被反射并激发起哨声模波，反射波束能量集中于入射波束附近，并随频率下降而迅速增强．计算也表明，地面接收到的甚低纬哨声回波可能与使回波向极侧偏移的电离纬向梯度有关． 相似文献
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M. SCHOENBERG 《Geophysical Prospecting》1983,31(2):265-292
A periodically stratified elastic medium can be replaced by an equivalent homogeneous transverse isotropic medium in the long wavelength limit. The case of a homogeneous medium with equally spaced parallel interfaces along which there is imperfect bonding is a special instance of such a medium. Slowness surfaces are derived for all plane wave modes through the equivalent medium and reflection coefficients for a half-space of such a medium are found. The slowness surface for the SH mode is an ellipsoid. The exact solution for the reflection of SH-waves from a half-space with parallel slip interfaces is found following the matrix method of K. Gilbert applied to elastic waves. Explicit results are derived and in the long wavelength limit, shown to approach the results for waves in the equivalent homogeneous medium. Under certain conditions, a half-space of a medium with parallel slip interfaces has a reflection coefficient independent of the angle of incidence and thus acts like an acoustic reducing mirror. The method for the reflection of P- and SV-waves is fully outlined, and reflection coefficients are shown for a particular example. The solution requires finding the eigenvalues of a 4 × 4 transfer matrix, each eigenvalue being associated with a particular wave. At higher frequencies, unexpected eigenvalues are found corresponding to refracted waves for which shear and compressional parameters are completely coupled. The two eigenvalues corresponding to the transmitted wavefield give amplitude decay perpendicular to the stratification along with up- and downgoing phase propagation in some other direction. Much of this work was performed while the author was at the Department of Geophysics and Planetary Sciences, Tel-Aviv University, Ramat-Aviv, Israel. The author is grateful for illuminating discussions with K. Helbig and K. Gilbert. 相似文献
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本文研究了纵波垂直入射情况下两种介质分界面处的纵波反射和透射系数的频散特性,分界面上下两侧分别为层状双孔页岩介质和层状双孔砂岩介质.当纵波沿垂直于分界面的方向传播至分界面处时,会在上层双孔介质中产生三类反射纵波,在下层双孔介质中产生三类透射纵波.基于层状双孔介质的特性,给出了分界面处的六个边界条件.根据层状双孔介质的波动方程,利用平面波分析得到了纵波的反射和透射系数.结果表明：当多孔介质中存在流体时,纵波的反射和透射系数与频率相关,即存在频散现象.波致流体流动是造成纵波反射和透射系数频散的主要原因.此外,结果还表明局部流体流动引起地震频带内反射和透射系数的频散,宏观Biot流引起超声频带内反射和透射系数的频散.本文同时对岩石参数对反射和透射系数频散曲线的影响进行了研究. 相似文献
15.
Oblique wave scattering by undulating porous bottom in a two-layer fluid: Fourier transform approach
Srikumar Panda 《地球物理与天体物理流体动力学》2014,108(6):587-614
The problem involving scattering of oblique waves by small undulation on the porous ocean bed in a two-layer fluid is investigated within the framework of linearised theory of water waves where the upper layer is free to the atmosphere. In such a two-layer fluid, there exist waves with two different wave numbers (modes): wave with lower wave number propagates along the free surface whilst that with higher wave number propagates along the interface. When an oblique incident wave of a particular mode encounters the undulating bottom, it gets reflected and transmitted into waves of both modes so that some of the wave energy transferred from one mode to another mode. Perturbation analysis in conjunction with Fourier transform technique is used to derive the first-order corrections of velocity potentials, reflection and transmission coefficients at both modes due to oblique incident waves of both modes. One special type of undulating bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are shown in graphical forms to demonstrate the transformation of water wave energy between the two modes. Comparisons between the present results with those in the literature are made for particular cases and the agreements are found to be satisfactory. In addition, energy identity, an important relation in the study of water wave theory, is derived with the help of the Green’s integral theorem. 相似文献
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The scattering of first mode linear baroclinic Rossby waves by a top-hat ridge in a continuously stratified ocean, with Brunt-Väisälä frequency that decays exponentially with depth below a surface mixed layer, is the subject of this study. A numerical mode matching technique is used to calculate the transmission coefficients for the propagating modes over the ridge. It is found that the scattered field depends crucially upon the stratification. For example, when the majority of the density variation is confined to a thin thermocline, corresponding to a small e-folding scale, gamma ?1, for the Brunt-Väisälä frequency, a large amount of the incident wave energy is reflected by a small amplitude ridge. Appreciable energy conversion between the propagating barotropic and baroclinic modes takes place in this case. An asymptotic analysis for a small amplitude ridge is presented that confirms these numerical results. In the limit gamma ?1→ 0, it is demonstrated that the scattered field in the continuously stratified ocean model differs markedly from the two-layer solution. The latter does not exhibit appreciable reflection of the incident wave energy for a small amplitude ridge. In conclusion, the application of a two-layer ocean model to describe Rossby wave scattering by ridges in place of a continuously stratified model cannot be recommended. 相似文献
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用于低渗砂岩油气开发的压裂需要地层的纵横波时差参数;压裂形成的人工裂缝或砂泥岩中的自然裂缝是油气流入井中的主要通道.声波测井是测量地层的纵横波时差、探测连通裂缝的有效方法.本文给出了新设计的偶极子组合声波测井仪器在低渗砂泥岩地层所测量的波形.新仪器利用声波在井内传播的固有频率设计探头,利用探头阻抗随频率的变化曲线设计匹配电路,有效地提高了声发射功率,在井下采用16位A/D转换器提高了原始波形的采样精度.测量的波形比通常的声波测井波形所含的地层信息丰富.单极子长源距声波测井波形中除了通常的纵、横波和Stoneley波外,还发现了起始于纵波首波的反射波以及随深度改变其到达时间的后续波.通过与其它测井曲线综合对比发现:其反射波与井眼扩径有关,使测量的声波时差加大;后续波在显示地层特征的同时,与横波混叠在一起,使横波时差的提取变得困难.另外,在偶极子所测量的低频波形中也发现了明显的反映地层连通裂缝的反射波,该反射波可以用于指示低渗砂岩地层中的连通裂缝. 相似文献
18.
E. A. ROBINSON 《Geophysical Prospecting》1975,23(4):779-797
Dynamic predictive deconvolution makes use of an entire seismic trace including all primary and multiple reflections to yield an approximation to the subsurface structure. We consider plane-wave motion at normal incidence in an horizontally layered system sandwiched between the air and the basement rock. Energy degradation effects are neglected so that the layered system represents a lossless system in which energy is lost only by net transmission downward into the basement or net reflection upward into the air; there is no internal loss of energy by absorption within the layers. The layered system is frequency selective in that the energy from a surface input is divided between that energy which is accepted over time by net transmission downward into the basement and the remaining energy that is rejected over time by net reflection upward into the air. Thus the energy from a downgoing unit spike at the surface as input is divided between the wave transmitted by the layered system into the basement and the wave reflected by the layered system into the air. This reflected wave is the observed seismic trace resulting from the unit spike input. From surface measurements we can compute both the input energy spectrum, which by assumption is unity, and the reflection energy spectrum, which is the energy spectrum of the trace. But, by the conservation of energy, the input energy spectrum is equal to the sum of the reflection energy spectrum and the transmission energy spectrum. Thus we can compute the transmission energy spectrum as the difference of the input energy spectrum and the reflection energy spectrum. Furthermore, we know that the layered system acts as a pure feedback system in producing the transmitted wave, from which it follows that the transmitted wave is minimum-delay. Hence from the computed energy spectrum of the transmitted wave we can compute the prediction-error operator that contracts the transmitted wave to a spike. We also know that the layered system acts as a system with both a feedback component and a feed-forward component in producing the reflected wave, that is, the observed seismic trace. Moreover, this feedback component is identical to the pure feedback system that produces the transmitted wave. Thus, we can deconvolve the observed seismic trace by the prediction-error operator computed above; the result of the deconvolution is the wave-form due to the feedforward component alone. Now the feedforward component represents the wanted dynamic structure of the layered system whereas the feedback component represents the unwanted reverberatory effects of the layered system. Because this deconvolution process yields the wanted dynamic structure and destroys the unwanted reverberatory effects, we call the process dynamic predictive deconvolution. The resulting feedforward waveform in itself represents an approximation to the subsurface structure; a further decomposition yields the reflection coefficients of the interfaces separating the layers. In this work we do not make the assumption as is commonly done that the surface as a perfect reflector; that is, we do not assume that the surface reflection coefficient has magnitude unity. 相似文献
19.
The phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy. 相似文献
20.
为研究双轴各向异性介质多分量感应测井响应特征,本文基于三重傅里叶变换,推导任意方向偶极子源的谱域电磁场解析式;采用围线积分方法,自适应截断积分区间,结合谱域电磁场周期特性,实现三重傅里叶变换的精确快速积分;进而,针对双轴各向异性倾斜地层,模拟研究不同纵横向各向异性条件多分量感应测井响应特征.结果表明:利用谱域内电磁场在周向的周期特性简化解析式,可将计算速度提高4倍;自适应截断积分区间方法保证了计算精度,并极大地减少了积分节点数.对于倾斜双轴各向异性介质,倾角较大时,共面分量可反映地层横向各向异性,同轴分量可反映地层纵向各向异性;倾角较小时,同轴分量可反映地层横向各向异性,共面分量可反映地层纵向各向异性. 相似文献