Rayleigh wave attenuation due to the scattering by two-dimensional irregularities of the walls of an empty borehole

Attenuation of the Rayleigh waves propagating along an irregular surface of an empty borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular boundary of a half-space. The technique used to evaluate the attenuation coefficient is based on the perturbation method and the mean field method. As a result, an expression is obtained that relates the partial attenuation coefficients of the surface Rayleigh wave to the scattering by the irregular surface of an empty borehole into the bulk longitudinal and transverse waves (the R → P and R → S processes) and into the surface Rayleigh waves (the R → R processes). The frequency-dependent behavior of the partial attenuation coefficients is analyzed for different correlation functions of irregularities.     

Attenuation and scattering of axisymmetrical modes in a fluid-filled round pipe with internally rough walls

The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.     

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.     

Berkhoff approximation in a problem on surface gravity wave propagation in a basin with bottom irregularities

The problem of the propagation of small-amplitude surface gravity waves in a basin of constant mean depth with one- and two-dimensional bottom roughness is solved in the framework of the Berkhoff model by a mean-field method. In both cases the solutions obtained are compared with the solutions of sets of exact linearized equations of the hydrodynamics of an incompressible fluid. The comparison of the exact and approximate mean-field attenuation coefficients has shown that the Berkhoff approximation is appropriate for the solution of this problem in the case of shallow water for an arbitrary correlation length of bottom irregularities and in the case of arbitrary depth and large-scale irregularities. An explanation is given for the limits of applicability of the Berkhoff approximation which are connected with the weak variability of the vertical structure of the wave field in shallow water and in a basin with large-scale depth fluctuations. The mean-field attenuation coefficients reach their maximum values in the region k_oh_o≥1 (where k_o is the wavenumber of the surface gravity wave in a basin of constant depth h_o). The location of these maxima is practically independent of the correlation length of the bottom irregularities. For the case of one-dimensional irregularities the effect of bottom roughness on the surface gravity wave velocity is investigated. It is shown that the surface wave in a basin with an uneven bottom may propagate more slowly, as well as faster than the wave in a basin with an even bottom, depending on the relations between the wavelength, depth and correlation length of the bottom imperfections.     

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.     

Nonlinear resonance of plasma waves in the thermal irregularities of ionospheric plasma

We study the effect of striction plasma density disturbances on the generation intensity of longitudional cold and plasma oscillations due to polarization of the magnetic field-aligned ionospheric plasma irregularities with δN_o<0 by a powerful radio wave. It is assumed that the plasma density level inside the irregularity intersects the upper-hybrid resonance level, in the vicinity of which the cold oscillations excited directly by a powerful radio wave are transformed to shorter-wave plasma oscillations. We consider the short plasma wave limit to reduce the problem to a system of two coupled equations for the cold wave induction and plasma wave electric field. The first equation is supplemented by a local source equal to the integral of the plasma wave electric field in the resonance region. The second equation involves the cold wave induction at the resonance point and describes the electric field of interacting waves in the resonance vicinity. We use simplifications connected with the small absorption of plasma waves propagating inside the irregularity and weak radiation of these waves outside the irregularity. These conditions correspond to the generation of eigenmodes of plasma oscillations trapped in the irregularity. We have obtained a resonance-type nonlinear equation for the electric field intensity (or energy flux) of eigenmode plasma waves with allowance for striction disturbances of the plasma density profile in the resonance region. It is shown that the striction expulsion of plasma is responsible for the occurrence of coefficients describing the change in the intensity of excitation and radiation of plasma waves at the irregularity boundary. Such an expulsion leads to variations of the efficient generation band of plasma eigenmodes with the total phase increment of the wave in the irregularity. It also leads to a change in the phase shift of the plasma wave reflected from the resonance. These coefficients and the nonlinear phase shift are expressed in terms of real wave functions of the nonlinear Airy equation which describes the electric field of the excited waves in the resonance vicinity when the dissipation is absent. Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 270–297, March, 1998.     

Determination of the Phase Shift of a Plasma Wave Reflected from the Edge of a Small-Scale Irregularity

In our papers [1,2], a nonlinear theory has been developed for excitation of plasma-wave eigenmodes inside field-aligned small-radius inhomogeneities in experiments on ionospheric heating by powerful radio waves. This theory takes into account the striction effects of plasma expulsion near the plasma resonance level where a trapped wave is reflected from the edge of the irregularity. The results of this theory depend strongly on the phase of the linear (i.e., weak-field) reflection coefficient. In this paper, we calculate this parameter for irregularities of different shapes.     

Propagation of Lamb waves in an immersed periodically grooved plate: Experimental detection of the scattered converted backward waves

Guided waves propagation in immersed plates with irregular surfaces has potential application to detection and assessment of the extent, depth and pattern of the irregularity. The complexity of the problem, due to the large number of involved parameters, has limited the number of existing studies. The simplest case of irregularities of practical interest is the two-dimensional corrosion profile. Even this case is in general so complex, that one can extract several amplitude dominant periodic surfaces only by using a Fourier spectrum of the surface. Guided waves in plates, with one or both free surfaces having periodic perturbations of different shapes, have been presented in specialized literature.     

On a Modification of the Scintillation Method

We solve the problem of diffraction of fluctuating radiation by an optically thin irregular layer (phase screen) with developed turbulent structure. It is shown that in the case of diffraction of radiation with saturated fluctuations and a narrow-band frequency spectrum by a weakly turbulent moving phase screen, the measured frequency spectrum of intensity fluctuations in the observation plane allows one to obtain information on the form of the spectrum of irregularities of an optically thin irregular layer in a wide size range significantly exceeding the size of the first Fresnel zone. Similarly to the well-known phase method of diagnostics of randomly irregular media, the conventional scintillation method modified in such a way yields undistorted information on the form of the irregularity spectrum. However, in contrast to the phase method, it also allows one to obtain data on the drift velocity of irregularities in the studied irregular layer.     

Dynamics of an optical signal in a multimode waveguide structure

A mathematical model of linear dynamic distortions of average signal power in a planar optical waveguide stemming from the intermodal coupling and dispersion of waveguide modes caused by macroscopic bends and irregularities of the optical waveguide surface has been developed on the basis of pulse intermodal scattering matrix. It is shown that the elements of this matrix are determined at a waveguide segment whose length greatly exceeds the correlation scale of the field of irregularities but is much smaller than the normalization length of waveguide modes and are described by rectangular functions with a duration proportional to the relative velocity of the corresponding modes. The dependences of the pulse intermodal scattering matrix on the intensities of absorption, Rayleigh scattering, and optical signal scattering from waveguide irregularities have been established. It is shown that, at waveguide lengths exceeding the normalization length, the optical signal shape becomes almost stable and can be expressed in terms of the pulse characteristic of an integrating circuit. It has been established that irregularities of the film in a bent optical waveguide lead not only to additional attenuation but also to enhancement of multimode distortion. A matrix method is proposed for taking into account these distortions, which is based on the effect of equalization (scrambling) of the signal energy over the spectrum of the bent waveguide modes. The model developed was used to process the experimental data on the dynamics of a signal in a weakly guiding multimode polymer optical fiber in order to estimate the parameters of attenuation and irregularities of the waveguide surface.     

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.     

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.     

Propagation characteristics of guided waves in a rod surrounded by an infinite solid medium

The dispersion and excitation characteristics of the guided waves in a rod surrounded by an infinite solid medium (cladding) are investigated. First, the bisection technique is employed to find all the roots of the dispersion function on the basis of theoretical analysis and to obtain the complex phase and group velocity dispersion curves of the guided modes. Second, according to their different dispersion characteristics, the guided modes are divided into two categories: normal modes and Stoneley modes. And it is concluded that the normal modes merely exist in the “hard cladding” model in which the cladding’s shear velocity is larger than the rod’s; while the Stoneley modes in cylindrical interface are highly dispersive and merely exist in the model whose acoustical parameters satisfied the existence condition of the Stoneley waves. Third, the seldom discussed issue, the excitation mechanisms of the guided waves, excited by three source models: symmetric point source, axial and radial force sources, are simulated respectively. Attention is paid on the dominant mode which has better excitation sensitivity and the suitable excitation frequency range. Moreover, the propagation characteristics of the Stoneley modes, ignored in previous references, are analyzed and compared with those of the normal modes.     

Study of the Effect of Pulsed-Periodic Electric Field and Linearly Polarized Laser Radiation on the Properties of Liquid-Crystal Waveguide

Integrated-optical waveguides with a nematic liquid-crystal 4-cyano-4’-pentylbiphenyl (5CB) waveguiding layer have been investigated for different polarizations of incident laser radiation and under a pulsed-periodic electric field. A dependence of the damping coefficient of waveguide modes and the sizes of quasi-steady-state irregularities of nematic liquid-crystal layer on the linear polarization of laser radiation and the strength of pulsed-periodic field has been found experimentally. The correlation length is estimated for waveguiding layer irregularities. The waveguide scattering method has provided a resolution in correlation length exceeding the classical resolution limit by approximately an order of magnitude. The observed decrease in the damping coefficient of waveguide modes and irregularity sizes under external field is explained by the decrease in the correlation length of director fluctuations.     

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.     

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.     

Leaky Stoneley waves at a moving interphase boundary

The possibility of the existence of a leaky Stoneley wave at a uniformly moving interphase boundary defined as a jump in the acoustic parameters of an isotropic elastic medium is discussed. It is shown that the motion of the interphase boundary exerts dissimilar effects on the orientation of the wave normals of partial waves forming the Stoneley wave, and this results in different Doppler shifts of the frequencies of the partial waves in the laboratory frame of reference.     

Application of the method of nonstationary waveguide equations to simulating pulsed processes in irregular transmission lines

The potentialities of the model of nonstationary waveguide equations for describing pulsed processes in irregular transmission lines are studied using planar lines as an example. The problem of high-accuracy controllable-error numerical simulation is discussed. Typical examples of simulating ultra-wide-band electromagnetic pulses with an initial TEM structure in terms of time-domain representation are presented with emphasis on the interaction of the pulses with irregularities, including their transformation into longitudinal waves. Both lumped and distributed irregularities are addressed: deep corrugations that cover 90% of the transmission line’s aperture (distributed irregularities) and these corrugations in combination with sharp kinks at the boundary surfaces and permittivity steps at the boundaries of the dielectric filling (lumped irregularities). It is shown that a relative rms error involved in the calculated field intensity of no higher than 10⁻⁴ is easy to achieve.     

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。     

Low-frequency radio wave propagation in the earth-ionosphere waveguide disturbed by a large-scale three-dimensional irregularity

In this paper, we develop further the analytical and numerical method of solving three-dimensional problems in the theory of radio wave propagation, including three-dimensional local inhomogeneities (ionospheric disturbances or Earth’s surface irregularities). To model the Earth-ionosphere waveguide, we use the surface impedance concept, by which the irregularity extending beyond one waveguide wall has an arbitrary smooth shape, and its surface can be described by the impedance. In the scalar approximation, this problem is reduced to a two-dimensional integral equation for the irregularity surface, which, by asymptotic (kr ≫ 1) integration over the coordinate transverse to the propagation path (with allowance for terms of the order of (kr)⁻¹), is reduced to a one-dimensional integral equation, in which the integration contour is the linear contour of the irregularity. The equation is solved numerically, combining the inversion of a Volterra integral operator and successive approximations. By reducing the computer times, this method enables one to study both small-scale and large-scale irregularities. The results of numerical simulation of radio wave propagation in the presence of a powerful three-dimensional ionospheric disturbance are presented as an example. State University, St. Petersburg, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 5, pp. 588–604, May, 1998.