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.     

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.     

Energy losses of dipoles traveling relative to a moving medium

We consider the radiation from nonoscillating dipoles traveling with constant velocity directed parallel or antiparallel to the velocity of a homogeneous transparent moving medium. It is assumed that the medium in its rest frame is isotropic and has no spatial dispersion. We obtain expressions for the radiative energy losses and estimate the polarization energy losses of electric and magnetic dipoles of different orientations. In particular, it is shown that the energy loss of a source is negative if it moves in the direction of the medium motion and the source velocity is less than the medium velocity. Estimates for the energy losses of dipoles in the cases of an electron beam and a flow of a weakly dispersive medium are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 502–512, June 2006.     

The Role of a Specific Response of Media in the Vavilov-Cherenkov Effect

It is shown that the condition υ > υ_p (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.     

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.     

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.     

Influence of a Dielectric on the Radiated Energy of a Charge Moving in a Vacuum Channel

We study the radiation from a charged particle moving along the axis of a vacuum channel in a dielectric with resonance frequency dispersion. In particular, it is shown that the maximum of the spectral density of the radiated energy shifts from a resonant frequency towards lower frequencies with increasing channel radius. The obtained results are compared with the corresponding results for the case of a nondispersive dielectric. It is noted that for the sufficiently high velocity of the charge, the radiated energy in a dispersive dielectric is usually much less than that in a nondispersive dielectric. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika,Vol. 48, No. 4, pp. 327–330, April 2005.     

Study of low-temperature ordering and crystal structure in FePtBi/Au nanocomposite films

We investigate the frequency behavior of a half-wave dipole antenna placed very close over a 2LC uni-planar compact electromagnetic bandgap (UC-EBG) structure. A very compact and high-gain antenna is realized at 1 GHz. The air distance between the dipole element and the UC-EBG surface is ∼λ ₀/100. We analyse the structure by using the optical model of Hansen, full-wave electromagnetic simulations (EM) and experimental characterizations. The analytical model of Hansen describes accurately the UC-EBG phase contribution to the total radiated field below 1 GHz. Above this frequency, the Hansen analytical model is in discrepancy with the measurements and full-wave simulations, which show split in the radiation patterns. We show that this phenomenon is induced by the power leakage of the fast-wave UC-EBG surface excited by the dipole source inside its leaky wave region. We propose an original model based on the Hansen optical analysis that takes into account the overall phenomena. The model includes the contribution of the weighted fields radiated by the cells of the UC-EBG. This model leads to very good agreements with measurements and full-wave simulations.     

线阵波束形成声强缩放方法估算声源的辐射声功率

为了解决波束形成声源识别过程中声源辐射声功率定量计算的问题,给出了阵型简洁、便于组合的线阵声强缩放模型。通过推导线阵的声强缩放系数,建立起线阵波束输出结果与声源辐射声功率之间的换算关系。无论是线阵还是平面阵的声强缩放方法,对于偏离阵列中心位置较远处的声源进行辐射声功率估算时都存在较为明显的误差。通过理论推导和仿真模拟计算,研究了同一单极子点声源在不同位置处的声功率估算偏差随频率、幅度的变化规律,发现该估算偏差只与声源偏离位置有关,而与声源自身的强度信息无关的结论,据此给出了相应的声功率估算修正方法。半消声室实验结果和声压法测量结果对比表明:修正后的线阵声强缩放方法用于中高频声源的辐射声功率计算时,单频声源的估算误差不超过1.0 dB,宽带声源的估算误差不超过1.8 dB。      

环境因素对海-气界面低频异常声透射的影响研究

针对海中声源在海-气界面低频异常声透射问题, 根据两层媒质声传输模型, 分析了大气声速和密度与气压、气温、湿度及海水中声速和密度与海温、盐度间的关系, 研究了低频声透射和传输受温度、气压、盐度、湿度等因素的影响, 分析了各因素对声透射和传输的影响程度. 结果表明: 1) 声透射到大气中的声功率与气温、湿度负相关, 与海温、盐度、气压正相关; 2) 单极子与水平偶极子声源辐射到海中的声功率与海温、盐度负相关, 而垂直偶极子声源辐射到海中的声功率与海温、盐度正相关; 3) 声透射指向性与海温正相关, 与气温负相关; 4) 低频声透射受温度影响最大, 其次是盐度, 受气压和湿度影响较小, 垂直偶极子声源的声透射受温度影响大于水平偶极子和单极子声源.     

Features of Radiation Fields of Some Sources in a Subluminal Flow of a Nondispersive Medium

We study radiation fields of various dipole sources as well as of a source of bisphere type moving in a nondispersive medium with velocity less than the speed of light in this medium. In particular, it is shown that in certain cases, there is a displacement of the angular pattern of a source in the direction opposite to the medium flow. Expressions for energy losses of the considered sources are obtained. It is pointed out that the radiation power of both a bisphere and a toroidal dipole increases with increasing velocity of motion of the medium more rapidly compared with the ordinary dipoles.     

Exact results of statistical analysis of multichannel adaptive systems with continuous gradient algorithms

We obtained some exact expressions for the power of the output signal of adaptive systems with continuous gradient adjustment algorithms. It is shown that fluctuations of weight coefficients result in a decrease in the signal power at the adaptive-system output as compared with the output-signal power in the absence of fluctuations of the weight coefficients. The “overcompensation” phenomenon is explained by the presence of a non-Gaussian statistical relation between the weight- coefficient and input-signal vectors. N. I. Lobachevskii State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 914–921, September, 1999.     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

Energy Characteristics of Wave Fields Radiated from Elementary Oscillators in a Nondispersive Medium Moving with Subluminal Velocity

We study the energy characteristics of fields radiated from electric, magnetic, and toroidal dipoles in a nondispersive medium moving with velocity lower than the speed of light in this medium. The angular dependences of Abraham's energy-flux density of electromagnetic field are analyzed. In particular, it is shown that if the medium velocity is high enough, then the radial component of the vector of energy-flux density is negative in a certain angular range. Expressions for the electromagnetic energy flux through a sphere of large radius are obtained. It is shown that if the velocity of a moving medium is high enough, then the energy flux is negative and its absolute value can exceed the energy losses of sources.     

The overall phase shift and lens effect calculation using Gaussian boundary conditions and paraxial ray approximation for an end-pumped solid-state laser

In this work, the inhomogeneous equation of heat conduction was exactly solved by applying inhomogeneous boundary conditions for laser crystals of aspect ratio=1 (aspect ratio=radius of the laser rod/length of the laser rod). We have shown that the paraxial ray approximation leads the solution to be a function ofr ² , that is, the approximation is equivalent to a situation in which a homogeneous pump source is used. The solution was then used to derive expressions for the overall phase shift, focal length of the thermal lens and the end effect induced curvature of the end face. The expressions were then applied to Nd:YAG laser medium. The result shows a meaningful correction of the order of 0.001 cm to the focal length of Nd:YAG rod for 3 W source power and beam waist of 100 μm.     

On transition radiation

Summary A treatment of transition radiation between two dielectric media is presented which is based on the exact expressions for the fields of the particle in the two media. Expressions for the spectral distribution of the energy emitted forward and for that emitted backward are derived. The results are in accord with experimental findings for ultra-relativistic particles. In the asymptotic region the energy spectrum becomes discrete. It is indicated how the treatment can be extended to the case of a plate and to that of a wave guide, as well as to emission by a monopole. The case of the simultaneous emission of transition radiation and Čerenkov radiation is considered and the relationship between them is clarified. In particular, it is shown that, when the particle can emit Čerenkov radiation in the forward medium, it will also emit an interference signal. This is several orders of magnitude smaller than the usual transition radiation and is concentrated in the forward direction. It is also found that the Čerenkov wave emitted by the particle in the backward medium will be partially reflected and partially refracted into the forward medium, after the particle crosses the boundary between the two media. The linear energy density for the refracted wave is calculated and it is shown that under certain feasible conditions this is amenable to experimental verification. This work was done while the author was a summer visitor at Stanford Linear Accelerator Center, Stanford University. It was supported by the U.S. Department of Energy, contract DE-AC03-76SF00515.     

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.     

Superradiation in ensembles of classical electron oscillators under conditions of group synchronism

We consider the cyclotron superradiation of a moving electron bunch under conditions of group synchronism when the forward velocity of the bunch is equal to the group velocity of the electromagnetic wave. It is shown that this mode of operation makes it possible to increase the increment of superradiant instability and raise the peak radiated power.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 292–297, March–April, 1995.     

Energetic analysis of an actively controlled one-dimensional acoustic waveguide

The aim of this work is to show the energetic behavior when an active noise controller is applied in a one-dimensional waveguide, namely an ideal duct under the first critical frequency. In order to model the duct, a spectral element method, which is shown to be more practical for analyzing pipe networks than other commonly used analytical models, was used. The model used here consists of a duct with two sources, the primary source at one end of the duct, and the secondary source at the middle section. The error sensor was placed downstream from secondary source, and the other end of the duct was open with no flange. Three optimal control methods were applied: minimization of the potential energy density, minimization of the active intensity, and minimization of the total acoustic power radiated by the sources. It was observed that the three control methods achieved the same final result, and when the volume velocity of the secondary source was driven to the optimal volume velocity, neither the primary source nor the secondary source radiated any acoustic power. Furthermore, the controlled duct was equivalent to a duct opened-ended at the secondary source position with radiation impedance equal to zero.