Stoneley wave generation by an external seismic point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation: Basic relationships

The method of integral transformations is used to obtain a long-wave solution to the problem of tube wave excitation by an external point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation. The external field that occurs in the formation gives rise to waves in the borehole fluid. The waves generated in the borehole include the lowest mode of the Stoneley wave (tube wave), which is the borehole eigenmode, and the qP-and qSV-waves. It is shown that the Stoneley wave is determined by the contributions of two poles in the complex plane of horizontal slowness. According to the asymptotic solution, the Stoneley wave can be described by one of three different waveforms depending on the relationship between the elastic parameters of the surrounding anisotropic formation and the borehole fluid. An analysis of the results of calculations shows that the shape and polarity of the Stoneley wave strongly depend on the sign of the nonellipticity parameter of the elastic medium, which offers a possibility of estimating the anisotropy of the borehole environment from observations of the waveform of the Stoneley wave.     

Quasidislocation stoneley wave and Eshelby dislocation Scholte wave

A quasidislocation (a dislocationlike entity described here for the first time) moves at the speed of a Stoneley surface wave that travels at the interface between two different elastic solids. An Eshelby glide edge dislocation moves at the speed of a Scholte surface wave that travels at the interface between a solid and an ideal liquid. The quasidislocation and the glide edge dislocation (that moves at the Eshelby velocity) are the Green's functions of their waves. Scholte waves are planar distributions of transonic moving glide edge dislocations. They are not Stoneley waves, although often called by that name, because Stoneley waves are planar distributions of subsonic moving quasidislocations.     

Stoneley (interfacial) waves between two magneto-electro-elastic half planes

We investigated the propagation properties of Stoneley waves between two magneto-electro-elastic half planes. Magneto-electro-elastic materials are assumed to possess hexagonal (6 mm) symmetry. Twenty-five sets of magneto-electrical interface conditions were adopted and generalized frequency equations were derived and solved numerically. It was found that, for each set of interface conditions, existing Stoneley waves are always non-dispersive. Numerical results further show that material properties have a significant effect on both the number and velocity of Stoneley waves, and that, although different magneto-electrical interface conditions could influence the existence of Stoneley waves, they have no effect on wave velocities.     

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.     

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.     

Investigation of solid/solid interface waves with laser ultrasonics

A new method for detection of the soild/soild interface wave with laser ultrasonics is introduced in this paper. Based on the interaction between the acoustic wave and the probe laser beam of an interferometer in a transparent solid, the Stoneley waves propagated along the quartz/steel interface are detected successfully. The dispersion properties of Leaky Rayleigh wave are studied when the boundary conditions are described by interface spring mode. The Leaky Rayleigh wave at Plexiglas/aluminum interface is also detected and the experimental results are in good agreement with the theoretical results. It shows that the interface wave should be a powerful technique for evaluation of the interface properties.     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

Tube-wave propagation in a fluid-filled borehole generated by a single point force applied to the surrounding formation

Propagation of tube waves in an infinite fluid-filled borehole, generated by a single-force point source placed in the elastic surrounding formation, is analyzed in the long-wave approximation. Integral representations of the precise solution are obtained both for fast and slow formations. An asymptotic analysis of tube-wave propagation in the fluid-filled borehole is performed on the basis of these two integral representations. The complete asymptotic wave field in the borehole fluid for a fast formation consists of P and SV phases and the lowest eigenmode of the Stoneley wave (tube wave). For a slow formation the conical Stoneley wave (Mach wave) is generated. It appears only behind the critical angle defined by the ratio of the S wave velocity in the formation to the low-frequency Stoneley wave velocity and decays weakly with an offset. Asymptotic wave forms are in good agreement with wave forms obtained by straightforward calculations.     

Attenuation of a Stoneley wave and higher Lamb modes due to the scattering by two-dimensional irregularities of the walls of a fluid-filled borehole

Attenuation of Stoneley waves and higher Lamb modes propagating along an irregular surface of a fluid-filled borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular surface of an empty borehole [10]. The technique used to evaluate the attenuation coefficient is based on the perturbation method (surface irregularity heights are considered to be small in comparison with the wavelength) and the mean field method. As a result, an expression is obtained for the partial coefficients of the eigenmode attenuation due to the scattering of eigenmodes by the irregularities of the borehole walls into the same or other eigenmodes, as well as into the bulk longitudinal and transverse waves. The frequency-dependent behavior of the partial attenuation coefficients of both Stoneley waves and higher modes is analyzed against the ratio between the irregularity correlation length and the borehole radius for different correlation functions of irregularities.     

随钻声波测井隔声体刻槽影响的数值模拟研究*

针对随钻声波测井中钻铤波干扰以及刻槽后散射波问题,该文 利用时域有限差分法模拟钻铤波在随钻隔声体中的传播规律,首先考察在无限大流体中钻铤波在凹槽分界面处的散射特征,利用波场快照直观显示了钻铤波会有一部分能量在刻槽的固液界面转化为斯通利波。同时在有地层时分别对比了均匀内刻槽和外刻槽对钻铤波的衰减效果,发现在选择均匀内刻槽还是外刻槽时结果不仅与频率范围有关,而且与刻槽的深度也有关系。最后对比了槽宽较大的均匀凹槽隔声体和槽宽较小的渐变凹槽隔声体。可以得出结论,在设计随钻隔声体时,在10 kHz以下选择均匀外刻槽方式相对于内刻槽隔声效果会更好。随着刻槽槽深增加,外刻槽在10 kHz以下相比于内刻槽隔声性能优势更加明显。渐变刻槽在满足衰减钻铤波幅度要求的同时,散射波对后续地层波和斯通利波影响也更小。     

Perturbation Analysis on Guided Waves in a Fluid-Filled Borehole Surrounded by a Cubic Crystal Anisotropic Medium

The perturbation method is employed to analyse the guided waves in a borehole surrounded by a cubic crystal medium for the first time. The cubic crystal medium is regarded as a reference unperturbed isotropic state added to the perturbation. The dispersion characteristics of Stoneley wave, pseudo-Rayleigh wave, flexural wave, and screw wave are investigated in detail. It is found that dispersion of the guided waves excited by monopole and dipole sources does not depend on the azimuth of the source, whereas the dispersion of screw wave excited by quadrupole source is significantly related to the azimuth of the source. Screw waves propagated along different azimuth in the borehole can be split. This is different from screw waves in transversely isotropic media （hexagonal crystal）, which have been widely studied.     

Thermodynamic compatible model of microfractured porous media and Stoneley waves

Nonstationary theory of two-velocity continuum describing the propagation of acoustic waves inmicrofractured porousmedia is based on general physical principles: the first law of thermodynamics, the conservation laws, the kinematic relationships in the metric tensor and the Galilean principle of relativity. As a physical application, the theory of the Stoneley wave in microfractured porous media is developed. The simulation results are compared with the results of physical measurement of the Stoneley wave parameters in the boreholes. It is shown that an additional fluid transport through fractures makes it possible to satisfactorily correlate the experimental and theoretical data. In general, the developed theory is a nonlinear physical model of fluid dynamics in fractured porous media.     

激光超声方法研究固-固界面波传播特性

对界面波的传播特性进行了理论及实验研究.首先探讨了界面波的求根问题，基于黎曼面分析，给出了求解界面波特征方程所有根的一般方法.理论上对三种常见的界面波——Stoneley波，Leaky Rayleigh及Leaky Interface波传播机理进行了分析，描述了三种界面波的波矢及位移势在两种介质中的状态.最后基于光弹效应原理, 利用全光学的激光超声手段对界面波进行了实验测量，实测结果与理论符合很好.     

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

<正>The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated.The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves,pseudo-Rayleigh waves,flexural waves,and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients.The corresponding acoustic waveforms illustrate their properties in time domain.The results are also compared with those based on generalized Biot's theory.The results show that the influence of non-Newtonian effect on acoustic guided wave,especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.     

国产的多极子阵列声波测井仪(MPAL)在油田开发生产中的应用

本文对国产的多极子阵列声波测井(MPAL)资料进行了分析,验证了仪器有较好的稳定性,测试结果表明:硬地层的纵波、横波、斯通利波波形清楚,幅度变化正常;通过其在岩性识别、裂缝识别、气层识别、岩石机械特性分析及各向异性的应用进行研究,能够较为准确地求取地层的纵波、横波、斯通利波的声波时差及幅度和衰减曲线,计算岩石力学参数,并进行地层各向异性评价。     

Reflection of spin and spin-elastic waves at the interface of a ferromagnetic half-space

This paper considers the reflection of pure spin and spin-elastic (or magneto-elastic) waves at the interface of a ferromagnetic half-space and a vacuum. For pure spin waves two cases are considered, with exchange effects, and without. It is shown that when exchange effects are taken into account, volume spin waves in the ferromagnetic half space incident at the boundary with the vacuum generate a reflected volume spin wave, and an accompanying compound surface wave propagating along the boundary and consisting of two partial inhomogeneous spin waves in the ferromagnetic half-space and a partial magneto-static inhomogeneous surface wave in the vacuum. When exchange effects are neglected the incident wave generates only a reflected volume wave in the ferromagnetic half-space.

Reflection and transmission of spin-elastic (or magneto-elastic) waves has been considered only in the case of the absence of exchange effects. An incident volume wave generates a volume spin-elastic reflected wave and one inhomogeneous magneto-static accompanying surface wave.

Excitations of the magnetic field are not transmitted into the vacuum in both cases when the exchange effect is neglected. In all cases the reflection of a spin wave has the character of a full internal reflection.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

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.     

Medium characterization from interface-wave impedance and ellipticity using simultaneous displacement and pressure measurements

The interface-wave impedance and ellipticity are wave attributes that interrelate the full waveforms as observed in different components. For each of the fluid/elastic-solid interface waves, i.e., the pseudo-Rayleigh (pR) and Stoneley (St) waves, the impedance and ellipticity are found to have different functional dependencies on Young's modulus and Poisson's ratio. By combining the attributes in a cost function, unique and stable estimates of these parameters can be obtained, particularly when using the St wave. In a validation experiment, the impedance of the laser-excited pR wave is successfully extracted from simultaneous measurements of the normal particle displacement and the fluid pressure at a water/aluminum interface. The displacement is measured using a laser Doppler vibrometer (LDV) and the pressure with a needle hydrophone. Any LDV measurement is perturbed by refractive-index changes along the LDV beam once acoustic waves interfere with the beam. Using a model that accounts for these perturbations, an impedance decrease of 28% with respect to the plane wave impedance of the pR wave is predicted for the water/aluminum configuration. Although this deviation is different for the experimentally extracted impedance, there is excellent agreement between the observed and predicted pR waveforms in both the particle displacement and fluid pressure.     

Excitation of Rayleigh and Stoneley surface acoustic waves by distributed seismic sources

Using the integral Fourier-transform technique, we obtain a solution in integral form to the problem of excitation of elastic waves in a homogeneous isotropic solid half-space and the bordering homogeneous gas by the time-dependent forces which are arbitrarily distributed in a solid over the plane parallel to the interface of the media. Different configurations of the force sources are analyzed from the viewpoint of excitation of different types of seismoacoustic waves. Expressions for the time-averaged radiated powers of the Stoneley wave at the gas–solid interface and the Rayleigh wave at the solid–vacuum interface as well as analytical expressions for the Rayleigh wave displacements, which are valid for large distances from the source, are obtained for the harmonic dependence of forces on time. Excitation of a Rayleigh wave by the point sources oriented vertically, i.e., along the normal to the surface of elastic half-space, and horizontally, i.e., parallel to this surface, is analyzed in detail. Analytical expressions for the Rayleigh-wave radiated power are obtained. The dependences of these powers on the source orientation and depth are derived. It is shown that the Rayleigh-wave radiated power decreases with distance between the point of the force application and the boundary and turns to zero for a source depth of about 17.5% of the wavelength of the transverse wave in the case of a horizontally oriented subsurface source and a medium with identical Lamé parameters λ and μ. This power increases and reaches a relative maximum when the source depth becomes equal to about 42.4% of the wavelength of the transverse wave and then exponentially falls off as the source depth increases. This maximum is about 5.5% of the surface-source radiated power.