Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

流体-镀层基底界面波的传播特性

理论分析了脉冲激光激发的流体-分层固体结构声场,在此基础上数值计算了流体-慢层快底固体和流体-快层慢底固体结构液-固界面Scholte波的频散特性与瞬态响应.数值结果显示,对于流体-慢层快底结构,Scholte界面波呈现出正常频散特性;而对于流体-快层慢底结构,Scholte波在较小的频厚积范围呈反常频散特性.理论瞬态信号也显示了同样的特性.采用脉冲激光激励,用水听器接收的方式进行了Scholte界面波的实验测量.实验测量和分析结果与理论结果有很好的一致性.此工作可为水浸检测条件下镀层与薄膜材料参数的超声无损表征、海底沉积物参数反演等应用提供理论基础.     

变声速弹性沉积层下压缩波与剪切波的耦合影响

针对压缩波声速n²线性分布、剪切波声速平方线性分布的变参数弹性海底沉积层中声场建模问题,建立了关于压缩波与剪切波本征函数的偏微分耦合方程组,基于微扰法,通过逐次微分给出了本征函数的近似解析解.理论分析表明,只有剪切波声速平方的梯度不为零的情况下,沉积层中的压缩波才会与剪切波产生耦合.压缩波与剪切波耦合的影响会带来本征值的变化,其对近场声传播的影响较小,但远距离声传播损失的预报在考虑耦合后与实测数据符合得更好.此外,耦合还会导致沉积层中本征函数及其导数的变化,使得耦合与非耦合情况下沉积层中质点位移场不同.通过与商用声场软件COMSOL计算结果的对比分析检验了本文方法的正确性,且本文方法计算时间远小于COMSOL软件运行时间.     

Excitation of the acoustic and leaky waves in the atmosphere by a sub-surface seismic source

We study excitation of acoustic, leaky, and surface waves by a time-harmonic force source located in a homogeneous isotropic elastic half-space contacting a homogeneous gas. The force acts in the normal direction to the interface between the media. We consider the case where the sound velocity in the gas is less than the velocity of the Rayleigh wave propagating along the surface of the solid. An expression is derived for the period-averaged radiation power of the surface Stoneley wave. The total radiation power is calculated for the acoustic wave in the gas and for the leaky pseudo-Rayleigh wave. Variations in the radiation powers of the surface and leaky waves are analyzed as functions of the source depth. If the velocities of compressional and shear waves in the elastic medium significantly exceed the sound velocity in the gas, then the radiation power of the Stoneley wave turns out to be a factor of 10⁶–10⁸ smaller than the radiation powers of other waves. The radiation power of the Stoneley wave decreases monotonically with increasing source depth, and the decrease becomes more pronounced with the increase in the difference between the acoustic impedances of the contacting media. If the shear-wave velocity in the solid is close to the sound velocity in the gas, then the radiation power of the Stoneley wave is comparable with the radiation powers of other waves and exhibits maximum at a certain source depth. For some parameters of the gas and the solid, and for certain source depths, the Stoneley wave carries away more than a half of the total radiation power. It is shown that, for certain relations between the parameters of the media, the radiation power of the Stoneley wave increases due to redistribution of the radiated power from the pseudo-Rayleigh leaky wave. The total power of these waves remains approximatly constant and, with accuracy of the order of 10⁻³, is equal to the radiation power of the Rayleigh wave at the vacuum-solid interface. It is shown that the acoustic-wave power which can be transmitted to the upper layers of the atmosphere during an earthquake does not exceed 0.01% of the total power radiated at a given frequency. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 577–592, July 2006.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot’s system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space–time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.     

Nonlinear waves in porous media saturated with live oil

A nonlinear equation is obtained for waves propagating in porous media of arbitrary consolidation (relative rigidity) saturated with live (i.e., air-bearing) oil. The equation describes the evolution of fast and slow Biot-Frenkel longitudinal acoustic waves propagating in both directions and allows one to analyze the reflected waves and their interaction. For a wave of the second kind, the diffusion coefficient is determined. The dependences of the dispersion and dissipation parameters on the rigidity of the oil pool structure and on the depth of the oil pool occurrence are analyzed.     

Surface-to-volume wave conversion in shallow water with a corrugated bottom

Acoustic transmission between points onshore or in very shallow water and points in deep water is strongly influenced by the shear rigidity of marine sediments, which control the parameters and the very existence of seismoacoustic surface waves. Previously, it was found that coupling between acoustic modes and the seismoacoustic surface waves is normally weak, although not negligible in the case of a gently sloping seafloor and soft sediments. In this paper, the previous work is extended by accounting for the small-scale roughness of the seafloor. The significant role of roughness in coupling between volume and surface waves is demonstrated. The combined effect of bottom topography, roughness, and wave attenuation in soft marine sediments on the sound propagation between points in shallow and deep water is discussed. Published in Russian in Akusticheskiĭ Zhurnal, 2008, Vol. 54, No. 3, pp. 400–407. The article was translated by the author.     

A solution to diffraction biases in sonoelasticity: the acoustic impulse technique.

Several methods have been proposed to estimate the viscoelastic properties of soft biological tissues using forced low-frequency vibrations (10-500 Hz). Those methods are based on the measurement of phase velocity of the shear waves (approximately 5 m/s). It is shown in this article that the measurements of velocity as well as attenuation are subjected to biases. These biases are related to reflected waves created at boundaries, to the nonnegligible size of the piston source which causes diffraction effects and to the influence of a low-frequency compressional wave. Indeed, a theoretical analysis of the field radiated by a point source explains how mechanical vibrations of a piston generate a shear wave with a longitudinal component and how this component can interfere with a low-frequency compressional wave. However, by using a low-frequency transient excitation, these biases can be avoided. Then the precise numerical values of elasticity and viscosity can be deduced. Experiments in phantoms and beef muscles are shown. Moreover, a relative hardness imaging of a phantom composed of two media with different elasticities is presented.     

Surface-to-volume wave conversion in shallow water with a gently sloping bottom

Marine sediments support seismoacoustic surface waves, which can propagate along the seafloor, in deep and shallow water, and even onshore. Because of the strong attenuation of compressional and especially shear waves in the sediments, the surface waves can significantly contribute to the acoustic field far from the shore only through their coupling with volume waves in the water. We theoretically study the excitation of acoustic normal modes by seismoacoustic surface waves in a shallow-water waveguide with a sloping bottom consisting of unconsolidated marine sediments. It is found that the coupling primarily occurs in the vicinity of a modal cutoff. The effects of geoacoustic parameters and stratification of soft marine sediments on the efficiency of surface-to-volume conversion are investigated. Published in Russian in Akusticheskiĭ Zhurnal, 2007, Vol. 53, No. 6, pp. 809–816. The article was translated by the author.     

Approximate expressions for viscous attenuation in marine sediments: relating Biot's "critical" and "peak" frequencies

Simple approximate relations are proposed for the viscous attenuation per cycle of the fast compressional and shear waves in the low-to-intermediate frequency range. Corresponding closed-form formulas are derived for frequencies at which maximum viscous attenuation per cycle occurs according to the Biot-Stoll theory of elastic wave propagation in marine sediments. In the new formulas, Biot's approximation [M. A. Biot, J. Acoust. Soc. Am. 34, 1254-1264 (1962)] for the frequency-dependent viscosity correction factor F(f) and the assumption of relatively low specific loss (Q(-1)<(0.2) [J. Geertsma and D. C. Smith, Geophysics 26(2), 169-181 (1962)] are used to provide an accurate representation of the fast compressional and shear wave attenuation from low frequencies through a transition region extending to two or three times Biot's critical frequency f(c). The approximate viscodynamic behavior of marine sediments for the fast compressional and shear waves shows similarities to that of a "homogeneous relaxation" process for an anelastic linear element [A. M. Freudenthal and H. Geiringer, Encyclopedia of Physics (Springer-Verlag. 1958), Vol. 6].     

流体/准饱和多孔介质中伪Scholte波的传播特性

研究流体/多孔介质界面Scholte波的传播特性对于水下勘探、地震工程等领域具有重要意义.本文基于Biot理论和等效流体模型,采用势函数方法,推导了描述有限厚度流体/准饱和多孔半空间远场界面波的特征方程和位移、孔压计算公式.在此基础上,分别以砂岩和松散沉积土为例,研究了流体/硬多孔介质和流体/软多孔介质两种情况下,可压缩流体层厚度和多孔介质饱和度对伪Scholte波传播特性的影响.结果表明：多孔介质软硬程度显著影响界面波的种类、相速度、位移和水压力分布;有限厚度流体/饱和多孔半空间界面处伪Scholte波相速度与界面波波长和流体厚度的比值有关;孔隙水中溶解的少量气体对剪切波的相速度的影响不大,对压缩波相速度、伪Scholte波相速度和孔隙水压力分布影响显著.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Features of radiation of the surface Stoneley wave by a harmonic force acting at the gas-solid interface

The solution is found for the problem of radiation of the surface Stoneley wave by a point harmonic force acting normally to the interface between uniform solid and gaseous half-spaces. We consider the case where the sound velocity in the gas is less than the Rayleigh-wave velocity on the surface of the solid. Expressions for the partial powers of the Stoneley wave radiated into the solid and the gas are obtained. The dependences of these powers on the parameters of the contacting media are analyzed. It is shown that if the velocities of the compressional and shear waves in the solid are significantly greater than the sound velocity in the gas, then almost all power of the Stoneley wave is concentrated in the gas. If the velocity of the Rayleigh wave in the solid half-space is close to the sound velocity in the gas, then the Stoneley-wave power radiated into the solid can be greater than the power radiated in the gas. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 304–313, April 2008.     

凹面相控阵聚焦声场在液固界面上的反射和折射

开展了凹面线性相控阵列辐射声场在液固界面上的反射和折射特性研究,利用射线近似方法,得到了凹面相控阵聚焦声场在液固界面上反射和折射后的声场渐近解析表达式,对声波在液固曲面上的反射和折射声场进行了分析和讨论. 利用这个解析表达式,对凹面线性聚焦声场在液固平界面和液固圆柱界面情况下固体中折射纵波和折射横波的相控阵声场进行了分析和讨论,发现凹面线阵声场在液固圆柱界面下比液固平界面具有更好的聚焦效果. 关键词： 凹面阵列 超声相控阵 反射与折射     

Surface gravity waves in deep fluid at vertical shear flows

Special features of surface gravity waves in a deep fluid flow with a constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to a nontrivial modification of the dispersive characteristics of surface gravity wave modes. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study show that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. The generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the latter wave is generated more effectively for high shear rates. From the mathematical standpoint, the wave generation is caused by non-self-adjointness of the linear operators that describe the shear flow.     

孔隙地层井壁上的声波首波及其诱导电磁场的原因

声波测井时孔隙地层中的声波首波平行于井轴沿井壁传播，它既有轴向位移分量，又有垂直于井壁的位移分量.这种以快纵波速度传播的波, 不仅含有由快、慢纵波势给出的梯度场,而且还含有由横波势给出的旋度场.慢纵波势的梯度是渗流位移首波的主要构成成分, 也是声电效应测井响应中存在伴随声波首波电场的主要原因.首波包含有旋度位移场，是存在伴随声波首波磁场的原因. 关键词： 孔隙介质 声波首波 诱导电磁场 测井     

Effect of anisotropy on acoustoelastic birefringence in wood

The ultrasonic velocity of shear waves propagating through radial direction of a wood plate specimen, transversely to the loading direction, was measured. By rotating an ultrasonic sensor, the oscillation direction of the shear waves was varied with respect to the wood plate axis and loading direction. The relationship between shear wave velocity and oscillation direction was examined to discuss the effect of anisotropy on the acoustoelastic birefringence in wood. The results obtained were summarized as follows. When the oscillation direction of the shear wave corresponded to the tangential direction of the wood specimen regardless of the stress direction, shear wave velocity decreased markedly and the relationship between shear wave velocity and rotation angle tended to become discontinuous. That is, when the shear waves oscillated in the anisotropic axis of the wood, the shear wave velocity peaked unlike in the case of oscillation in the stress direction. In an isotropic material (acrylic, aluminum 5052), on the contrary, when the shear waves oscillated in the stress direction of the specimen, the shear wave velocity peaked regardless of the main-axis direction of the specimen. On the basis of the discussion of these results, the ultrasonic shear wave propagating in wood under stress is confirmed to be polarized in the anisotropic axis of the wood.     

Effect of drifting carriers on longitudinal electro-kinetic waves in ion-implanted semiconductor plasmas

We present an analytical study of wave spectra of electro-kinetic waves propagating through semiconductor plasma, whose main constituents are drifting electrons, holes and non-drifting negatively charged colloids. By employing the hydrodynamical model of multi-component plasma, a compact dispersion relation for the same is derived. This dispersion relation is used to study slow electro-kinetic wave phenomena and resultant instability numerically. We find some important modifications in the wave spectra of the slow electro-kinetic branch. It is found that the drift velocities of electrons and holes are responsible for converting two aperiodic modes into periodic ones. The applied dc electric field increases the phase velocities of contra-propagating modes. The amplification coefficients of propagating modes can be optimized by tuning the amplitude of applied electric field and wave number. It is hoped that the results of this investigation should be useful in understanding the wave spectra of slow electro-kinetic waves in ion-implanted semiconductor plasma subjected to a dc electric field along the direction of wave propagation.     

Rayleigh wave and detection of low-velocity layers in a stratified half-space

The excitation and propagation of the guided waves in a stratified half-space and a Rayleigh wave exploration method in shallow engineering seismic exploration are studied in this paper. All the modes of the guided waves are calculated by the bisection method in the case where the low velocity layers are contained in a stratified half-space. Cases when the formation shear wave velocity gradually decreases from the top to the bottom layers are also studied. The dispersion curves obtained in actual Rayleigh wave exploration are usually noncontinual zigzag curves, but the dispersion curves given by the elastic theory for given modes of the guided waves are smooth and continual curves. In this paper, the mechanism of zigzag dispersion curves in Rayleigh wave exploration is investigated and analyzed thoroughly. The zigzag dispersion curves can give not only the possible positions of the low-velocity layers but also the other information on the formation structure (fractures, oil, gas, etc.). It is found that the zigzag dispersion curves of the Rayleigh wave are the result of the leap of the modes and the existence of low velocity layers in a stratified half-space. The effects of the compressional wave velocity, shear wave velocity, and density of each layer on zigzag dispersion curves and the relationship of the low velocity layers to zigzag dispersion curves are also investigated in detail. Finally, the exploration depth of the Rayleigh wave is discussed. The exploration depth of the Rayleigh wave is equal to the wavelength multiplied by a coefficient that is variable and usually given by the work experience and the formation properties of the local work area.