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.     

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.     

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.     

Excitation of Surface and Leaky Waves on a Solid Body – Gas Interface

We analyze excitation of bulk, leaky, and surface waves by a point time-harmonic forcing applied perpendicularly to a solid body – gas interface. The case where the sound speed in the gas is less than the Rayleigh-wave velocity on the solid surface is considered. Expressions for the radiation powers of longitudinal and transverse spherical waves in the solid body and of a Stoneley surface wave, averaged over their periods, are derived. Excitation of a spherical acoustic wave in the gas and a pseudo-Rayleigh leaky wave is analyzed. For the spatial region corresponding to zenith angles exceeding the arcsine of the ratio of the sound speed in the gas and the transverse-wave velocity in the solid body, where the leaky-wave energy is transformed into the acoustic wave, we derive formulas describing their summed radiated power.     

Excitation of seismoacoustic waves by a harmonic force source acting at the boundary of a liquid layer and an elastic halfspace

A problem on the excitation of seismoacoustic waves in a system of a homogeneous isotropic elastic halfspace covered with a liquid layer is solved in the case of action of a source of point harmonic force on the surface of an elastic medium. Integral expressions are obtained for the radiation powers averaged over a wave period for longitudinal and transverse waves in a solid. Mode excitation is analyzed in detail. Expressions describing parts of the mode powers radiated into a liquid layer and an elastic medium are obtained. Numerical analysis of radiation powers is conducted for spherical longitudinal and transverse waves as well as for the radiation powers of seismoacoustic modes in a solid halfspace and a liquid layer. It is determined that in the conditions characteristic of bottom rocks in the case, where the basin depth is several times and more larger than the sound’s wavelength, about 2/3 of the total power is radiated into a liquid.     

The radiation power of elastic waves excited in a solid half-space by a subsurface time-harmonic source

The method of Fourier transforms is used to solve the problem of excitation of longitudinal, transverse, and Rayleigh surface waves by a time-harmonic point source placed in a homogeneous isotropic, perfectly elastic half-space and acting along the normal surface. Expressions for the time-average radiation powers of the aforementioned waves are obtained by the method of radiation reaction without using any approximations. The distribution of radiation power over different types of waves depending on their velocities and the source’s depth is investigated in detail.     

分层半空间表面非线性瑞利波的激发*

针对非线性瑞利波在均匀分层半空间结构中的激发和传播规律进行研究。根据摄动理论和模态分解将分层半空间结构中瑞利波的二次谐波声场表示为二倍频瑞利波模式的线性组合,经由互易关系得到各模式的展开系数表达式。对不同分层半空间结构中瑞利波二次谐波的激发和传播特性进行讨论,结果表明相速度匹配的瑞利波模式其二次谐波分量随传播距离线性增长,非匹配模式的二次谐波分量则沿传播方向周期震荡传播。此外,文中定义非线性参数表征瑞利波模式产生的非线性程度,这有利于选择出具有明显非线性效应的匹配点,为后续检测工作提供理论依据,具有指导意义。     

Radiation of surface Stoneley waves by distributed force sources acting at the solid earth-atmosphere interface

Using the Fourier transform, we find an integral solution describing the excitation of seismoacoustic waves in the solid Earth and the atmosphere by time-dependent forces arbitrarily distributed over the interface between the media. The solid Earth and the atmosphere are modeled by an isotropic solid half-space and a homogeneous gaseous half-space, respectively. Depending on the types of the excited surface and bulk waves, classification of the corresponding force distributions is performed. In the case of harmonic sources, an expression for the period-averaged radiated power of the Stoneley wave is obtained. For arbitrary time dependence of the forces, we find an expression describing the the Stoneley-wave energy radiated during the entire time of the source operation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 7, pp. 624–637, July 2007.     

Parametric scattering of high-frequency elastic waves by a small spherical cavity oscillating under the action of a Rayleigh wave

Scattering of high-frequency transverse and longitudinal plane waves incident on a spherical cavity located at a small depth under the surface of a half-space is considered. The cavity oscillates as a whole in the field of a low-frequency Rayleigh surface wave, the oscillation vectors of the longitudinal, transverse, and surface waves being coplanar. The cavity radius is assumed to be small compared to the wavelengths of the sounding wave and the pumping surface wave. The scattered compression and shear waves at the combination frequencies ω±Ω are calculated in the dipole approximation. Expressions obtained describe the qualitative behavior of the combination-frequency signal levels produced at the outputs of horizontally and vertically oriented geophones moving over the free surface of the elastic half-space.     

含孔隙分层半空间中瑞利波的传播特性研究

为了研究含孔隙介质分层半空间中瑞利波的传播规律,分析孔隙介质参数对瑞利波频散曲线的影响,本文进行了数值模拟研究。采用传递矩阵算法,计算了含孔隙分层半空间中一定频率范围内瑞利波所有模式的频散及激发强度曲线,并与均匀弹性固体分层半空间情况作了类比分析,在含孔隙覆盖层的两层模型和含低速孔隙夹层的三层模型下,详细研究了孔隙度、渗透率、层厚度等参数对瑞利波各模式的影响,发现孔隙度及层厚度的变化对频散曲线影响较大,而渗透率的变化对频散曲线影响较小。      

Enhanced sound transmission from water to air at low frequencies

Excitation of acoustic radiation into the air from a low-frequency point source under water is investigated using plane wave expansion of the source spectrum and Rayleigh reflection/transmission coefficients. Expressions are derived for the acoustic power radiated into air and water as a function of source depth and given to lowest order in the air/water density ratio. Near zero source depth, the radiation into the water is quenched by the source's acoustic image, while the power radiated into air reaches about 1% of the power that would be radiated into unbounded water.     

Propagation of surface elastic waves in the Cosserat medium

The problem of surface elastic wave propagation in the Cosserat medium (half-space) is considered. The strained state is characterized by two independent vectors: displacement and rotation. Solutions to the equations of motion are sought in the form of wave packets specified by an arbitrary Fourier spectrum. It is shown that, if the solution is sought in the form of a three-component displacement vector and a three-component rotation vector dependent on time, depth, and longitudinal coordinate, the initial system splits into two systems, one of which describes the Rayleigh wave and the other corresponds to a transverse wave decaying with depth. For both waves, analytical solutions in terms of displacements are obtained. It should be particularly noted that, unlike the Rayleigh wave, the solution for the transverse surface wave has no analogues in the classical elasticity theory. The transverse wave solution is numerically compared with the Rayleigh wave solution.     

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

Field due to a point source in a layer over an inhomogenous medium

Summary A point source at an interface between a homogeneous layer of finite depth and an inhomogeneous half-space is considered. The transmitted wave and the dispersion relation for the Love waves is calculated analytically. The authors of this paper have agreed to not receive the proofs for correction.     

Low-frequency sound transmission through a gas-liquid interface

Typically, sound speed in gases is smaller and mass density is much smaller than in liquids, resulting in a very strong acoustic impedance contrast at a gas-liquid interface. Sound transmission through a boundary with a strong impedance contrast is normally very weak. This paper studies the power output of localized sound sources and acoustic power fluxes through a plane gas-liquid interface in a layered medium. It is shown that, for low-frequency sound, a phenomenon of anomalous transparency can occur where most of the acoustic power generated by a source in a liquid half-space can be radiated into a gas half-space. The main physical mechanism responsible for anomalous transparency is found to be an acoustic power transfer by inhomogeneous (evanescent) waves in the plane-wave decomposition of the acoustic field in the liquid. The effects of a liquid's stratification and of guided sound propagation in the liquid on the anomalous transparency of the gas-liquid interface are considered. Geophysical and biological implications of anomalous transparency of water-air interface to infrasound are indicated.     

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.     

激光超声检测带过渡圆角平板表面缺陷的数值研究

为了研究激光激发出的超声波在带过渡圆角的金属平板上的传播规律和检测表面缺陷的方法,采用有限元法模拟了该类平板中的激光超声现象,分析了表面波在圆角区域的传播规律和与表面缺陷的作用过程。数值结果表明:激光激发出纵波、横波和Rayleigh波等,其中Rayleigh波主要存在于表面mm量级,并且在过渡圆角处发生模式转换生成了直达波R′和模式转换波R_R等多种表面波;经过过渡区域后的声波在表面缺陷处发生了反射和透射现象,通过B扫图可以检测缺陷的位置。随着缺陷深度的增加,表面波的透射系数不断减小,且透射波R_t和R_st存在0.5 μs左右的到达时间差,该时间差与缺陷深度近似成线性正相关。数值结果为激光超声检测带过渡圆角的平板表面缺陷提供了有价值的参考。     

The reflection of bounded inhomogeneous waves on a liquid/solid interface

Fourier analysis and normal mode theory are used to describe the reflection of bounded inhomogeneous waves on a liquid/solid interface. Nonspecular reflection phenomena in the Rayleigh angle are studied in detail. In this way, an explanation is given for the Rayleigh dip phenomenon for positive inhomogeneity factors and the related result of a reflection coefficient larger than unity when the sign of the inhomogeneity factor is reversed. In the limit of large beamwidths, the reflection coefficient predicted by the infinite plane inhomogeneous wave theory is obtained. These results are entirely consistent with the experimental work published by Deschamps [J. Acoust. Soc. Am. 96, 2841-2848 (1994)]. The energy efficiency of Rayleigh wave excitation is investigated as well. It is shown that for large beamwidths, the energy efficiency for bounded inhomogeneous waves is considerably higher in comparison with Gaussian and square-profiled beams.     

Transition radiation of seismic waves at the atmosphere-earth interface

The method of contour integration is used for solving the problem of transition radiation of elastic waves by a mass source, which travels uniformly in a gas normal to the interface between homogeneous gaseous and elastic halfspaces and disappears at the time it touches the solid surface. We have obtained asymptotic formulas for the field of transition radiation, which hold true near the fronts of longitudinal and transverse spherical waves and a conical wave. An exact analytical expression for the field of transition radiation has been obtained for the observation points located on the source trajectory extension in a solid. The influence of interaction between longitudinal and transverse waves, which occurs on the surface of elastic medium, on the space distribution of the field of transition radiation is analyzed. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1210–1223, October, 1997.     

Wave radiation in lattice fracture

The square and triangular lattices are considered, where the uniform crack growth is accompanied by the wave radiation. The radiation energy and structure are studied. The energy radiated to the bulk of the lattice is found in a direct way. The radiation structure is described based on the crack problem solution and by means of the analysis of two-dimensional dispersion relations for the intact lattice. The mode III problem for square lattice is discussed in detail, whereas, in the case of the plane problem for the triangular lattice, the only those results are derived which follow from the two-dimensional dispersion relations. It is shown that there exists a finite crack-speed-dependent region of wavenumbers corresponding to the waves radiated to the bulk of the lattice. In the case of the triangular-cell lattice, in addition, one or several lattice Rayleigh waves are radiated. For the square lattice a complete solution for the wave field is presented with the crack-speed-dependent far-field asymptote. The latter is characterized by the wave amplitude asymptotically decreasing as the distance from the crack front in power −1/3. The asymptotically significant crack-speed-dependent direction of the radiation is determined. Such asymptotic results are also valid for the triangular lattice.