Modulation of whistlers

Analysis of the experimental data obtained at Paratunka observatory (53.02° N, 158.65° E; L = 2.3) has revealed a nonstandard form of whistlers involving spectral lines that are symmetric with respect to the whistler. We have shown that this form is most likely due to the amplitude modulation of whistlers by electromagnetic pulses with a length of around 1 s and carrier frequency of around 1.1 kHz. We have suggested that these pulses could be emitted by the auroral electrojet modified by heating radiation from the HAARP facility (62.30° N, 145.30° W; L > 4.2).     

Sources of microseismicP waves

Summary Origin ofP waves detected earlier in microseisms of very quiet locations in the USSR is discussed in detail. It appears that the most pronounced sources ofP waves are tropical cyclones over the Pacific. The amplitude of the force in the source for a medium power typhoon is found to be of the order of 10¹⁶ dynes. The effective source area is estimated as 10⁴–10⁵ km² approximately. The shape of the amplitude spectrum ofP wave corrected for the absorption in the mantle does not contradict with the standing wave theory of microseisms generation. Results of observations at various epicentral distances give strong evidences of the predominant attenuation of the fundamental Rayleigh mode as compared with higher Rayleigh modes andP waves in the frequency band of 0.3–0.15 cps.     

Boundary-reflected waves and ultrasonic coda waves in rock physics experiments

Ultrasonic coda waves are widely used to study high-frequency scattering. However, ultrasonic coda waves are strongly affected by interference from by boundary-reflected waves. To understand the effect of boundary-reflected waves, we performed ultrasonic experiments using aluminum and shale samples, and the rotating staggered-mesh finite-difference method to simulate the wavefield. We analyzed the wavefield characteristics at the different receiving points and the interference characteristics of the boundary-reflected waves with the ultrasonic coda wave, and the effect of sample geometry on the ultrasonic coda waves. The increase in the aspect ratio of the samples delays the interference effect of the laterally reflected waves and reduces the effect on the ultrasonic coda waves. The main waves interfering with the ultrasonic coda waves are laterally reflected PP-, PS-, PPP-, and PPS-waves. The scattering and attenuation of the high-frequency energy in actual rocks can weaken the interference of laterally reflected waves with the ultrasonic coda waves.     

Response of pile foundations to rayleigh waves and obliquely incident body waves

The paper presents results of a study on the harmonic response of piles and pile groups embedded in a halfspace to various forms of seismic waves. These include the Rayleigh wave as well as obliquely incident P, SV and SH waves. The pertinent mixed boundary value problems of pile-soil-pile interaction are solved by a numerical model of the boundary integral nature. All modes of foundation vibrations, i.e. translational, rocking and torsional, are included in the model. The results presented are used to highlight the salient features of the seismic response of piles. In addition, the influence of certain pile-soil parameters, such as pile rigidity and pile spacing, on the seismic behaviour of pile foundations is investigated.     

Migrating sand waves

A simple mathematical model is described, which reproduces the major features of sand waves' appearance and growth and in particular predicts their migration speed. The model is based on the linear stability analysis of the flat configuration of the sea bottom subject to tidal currents. Attention is focused on the prediction of the complex growth rate that bottom perturbations undergo because of both oscillatory fluid motions and residual currents. While the real part _r of controls the amplification or decay of the amplitude of the bedforms, the imaginary part _i is related to their migration speed. Previous works on the migration of the sand waves (Németh etal. 2002) consider a forcing tide made up by the M2 constituent (oscillatory period equal to 12 h) plus the residual current Z0 and predict always a downcurrent migration of the bedforms. However, field cases exist of upcurrent-migrating sand waves (downcurrent/upcurrent-migrating sand waves mean bedforms moving in the direction of the steady residual tidal current or in the opposite direction, respectively). The inclusion of a tide constituent characterized by a period of 6 h (M4) is the main novelty of the present work, which allows for the prediction of the migration of sand waves against the residual current Z0. Indeed, the M4 tide constituent, as does also the residual current Z0, breaks the symmetry of the problem forced only by the M2 tide constituent, and induces sand-wave migration. The model proposed by Besio etal. (2003a) forms the basis for the present analysis. Previous works on the subject (Gerkema 2000; Hulscher 1996a,b; Komarova and Hulscher 2000) are thus improved by using a new solution procedure (Besio etal. 2003a) which allows for a more accurate evaluation of the growth rate for arbitrary values of the parameter r, which is the ratio between the horizontal tidal excursion and the perturbation wavelength. Responsible Editor: Jens Kappenberg     

Magneto-elastic love waves

Summary The propagation of Love waves under the influence of an externally applied magnetic field is studied. The general phase velocity equation is derived and two special cases when the magnetic field is aligned with and transverse to the direction of wave propagation are discussed. in these cases, it is found that the magneto-elastic problem in hand can be reduced to the corresponding problem in pure elasticity.     

Refraction of elastic waves into a medium of lower velocity — Pseudospherical waves

Summary An irregular wave group (here called pseudospherical), the existence of which is connected with the velocity boundary at which the velocity decreases discontinuously, is investigated. A schlieren modelling device was chosen for a model investigation of this wave since it permits the investigation of wave fields inside the measured models. The model consisted of two layers of transparent gels, the source lay in the layer of higher velocity. The measurements have shown that an irregular wave in the layer of lower velocity exists only in a certain region along the boundary; its wave front has a spherical form and its intensity decreases rapidly with increasing distance of the source from the boundary. The wave always comes only after the regular refracted wave which conforms with the ray theory. These properties correspond to the properties of a wave first described byOtt [1]³) andBrekhovskikh [2]. In the conclusion of the present paper the possibilities of recording pseudospherical waves in seismology are outlined.     

Multiple scattering of seismic waves in fractured media: Velocity and effective attenuation of the coherent components ofP waves andS waves

We show that the multiple scattering by small fractures of seismic waves with wavelengths long compared to the fracture size and fracture spacing is indistinguishable from multiple-scattering effects produced by regular porosity, except for an orientation factor due to fracture alignment. The fractures reduce theP-wave andS-wave velocities and produce an effective attenuation of the coherent component of the seismic waves. The attenuation corresponds to 1000/Q of about unity for a Gaussian spectrum of fractures, and it varies with frequencyf asf ³. For a Kolmogorov spectrum of fractures of spectral index the attenuation is an order of magnitude or so larger and varies with frequency asf ^3-v The precise degree of attenuation depends upon the matrix properties, the fracture porosity, the degree of fracture anisotropy, the type of fluid filling the fractures, and the incidence angle of the wave.For fracture porosities less than about 15% theP-wave andS-wave velocities are decreased by the order of 5–10% with a lesser dependence on the type of fluid filling the fractures (gas, oil, or brine) and with a dependence on both the degree of anisotropy and the incident angle made by the wave. The tendency of fractures to occur perpendicularly to bedding suggests that the best way to measure seismically fractured rock behavior in situ is by using the travel-time delay and reflection amplitude. As both the offset and the azimuth of receivers vary from a shot, the travel-time delay and reflection amplitude should both show an elliptical pattern of behavior—the travel-time delay in response to the varying seismic speed, and the reflection amplitude in response to angular variations in the multiple scattering. Observations of attenuation at several frequencies should permit (a) determination of the spectrum of fractures (Gaussian versus Kolmogorovian) and (b) determination of the contribution of viscous damping to the effective attenuation.     

Nonlinear wave propagation on a sphere: Interaction between Rossby waves and gravity waves; stability of the Rossby waves

Abstract

An analytical spectral model of the barotropic divergent equations on a sphere is developed using the potential-stream function formulation and the normal modes as basic functions. Explicit expressions of the coefficients of nonlinear interaction are obtained in the asymptotic case of a slowly rotating sphere, i.e. when the normal modes can be expressed as single spherical harmonics.     

井间透射-反射波场分离方法及应用

近十几年来,井间地震在石油勘探领域发挥着重要作用.然而井间地震波极其复杂,给同相轴拾取、层析成像、偏移成像等工作带来了困难.因此,波场分离成为井间地震数据处理的一项重要内容.目前,不少学者研究了井间上下行波分离,纵横波分离等多种方法,但尚未出现相关文献研究透射波和反射波的分离方法.本文根据井间透射波和反射波在不同道集(共炮点集或共接收点集)中视速度极性的差异,首次提出了一种"透射.反射"波场分离方法.该方法首先在不同道集中利用τ-p变换进行视速度分离,得到反射上行波、反射下行波、透射上行波、透射下行波四个波场,然后选择对应的波场叠加,从而得到透射波和反射波.其中,透射波为井间层析成像提供了相对清晰的初至同相轴,尤其是横渡初至同相轴,以便进行到时提取;所得反射波为井中偏移成像提供了可靠的反射波数据,比人工切除透射波方法更为准确有效.本文通过理论模型试验和实际数据处理,证明了该方法的有效性和实用性.此外,在本文基础上,再进行纵横波分离处理可以得到更多的波场分量,为井间成像提供更有效的数据.     

The transformation of magnetoacoustic waves into Alfvén waves inside the magnetosphere

A mechanism for the transformation of a magnetoacoustic wave into an Alfvén wave is proposed. During the compression of the magnetosphere by the solar wind the inner edge of the plasma sheet and the contours of B=const move in different ways. In the case of asymmetrical compression, the contours of B=const will cross the inner edge of the plasma sheet. To close the drift currents - that flow in the plasma sheet along the contours of B=const - the appearance of the field-aligned currents is necessary. This appearance corresponds to the generation of the Alfvén wave.     

台湾及邻区Mb≥4．0地震受月相调制的时空统计研究

本文分析了台湾及邻近地区(116°～126°E,18°～28°N)地震活动与月相角的相关关系.所用目录来自Engdahl E.R.等(1998)修正后的全球地震目录,挑选1964年1月1日至1999 年12月31日Mb≥4.0地震目录共2611条.将历次地震的GMT发震时刻转换成月亮黄经λm和太阳黄经λs,得到发震时刻的月相角D=λm-λs,其中λm采用105阶多项式展开.统计D±0.5°(D=0.360°)范围内发生在台湾及邻近地区的地震频次,结果显示,地震频次高于均值的2倍标准偏差的月相角大约在D≈50°、D≈50°90°和D≈50°+180°上.这3个角度大约对应第4、12、19太阳日,比上弦、望以及下弦大约偏离了 50°.统计分析显示,地震频次在月相角上的分布有较尖锐的波峰出现,即台湾地区地震活动与月相角明显相关.从朔起算,以12°为一太阳日,统计每个太阳日及其前后1日内每个0.5°×0.5°子区域中的发震概率和地震蠕变释放概率,结果发现,在人口密集聚居的台湾岛上,造成重大灾害的中强地震在从朔起算的第4个太阳日附近发生的概率是其余时段的4倍.特殊地区对月相角的强烈响应为防震减灾和地震预测提供了背景性依据,也使准确的发震时刻预测更加艰难.     

Transhorizon propagation of decameter waves

Solutions to the problem of the point source field in a spherically layered medium are analyzed. For a three-layer waveguide model, a solution in the form of the Watson integral was used. A consideration of the singularities in the plane of the integration variable made it possible to represent the integral as a superposition of three waves. Two of them are connected with the interaction of the primary spherical wave with the lower convex and upper concave interfaces. The third wave is connected with the alternate action with both interfaces. The fourth wave is caused by the interaction between the primary wave and random inhomogeneities of the external medium (the ionosphere). Here, simulation was carried out based on Green equations. The considered unique data of flight measurements of the point source field strength indicate the efficiency of simulating the transhorizon propagation of decameter waves based on the superposition of all four aforesaid wave packets.     

On coda waves of earthquakes

Summary Coda waves viz. the tail portion of an earthquake record have been observed and analysed byCarder, Macelwane and others. They showed that the periods of such waves increase with the increase of epicentral distances.Carder observed that these waves have very little transverse component so that these may be considered as of the type of Rayleigh waves. RecentlyOmote showed that the Coda waves contain three periodsT ₁,T ₂,T ₃ of whichT ₁ increases with epi-central distances as observed by previous observers. ButT ₂,T ₃ remain constant for all earthquakes from different epicentral distances.Omote tried to explain this phenomenon by considering that the surface of the earth consists of several layers andT ₂,T ₃ are free oscillation periods of the surface layers.T ₁ period has been explained bySezawa and also byJeffreys which has been shown byGutenberg. The author has attempted to explain the periodsT ₂,T ₃ by considering passage of cracks at the focal region. The Rayleigh wave character of Coda waves and low velocity of such waves have been explained.     

Study of ultralow-frequency electromagnetic waves

The paper presents a brief review of problems of physics of ultralow-frequency electromagnetic waves studied by the author at the Borok Geophysical Observatory (BGO) Schmidt Institute of Physics of the Earth, RAS, in the period from 1964 through 1980. Some problems solved by the author in close cooperation with BGO staff members in the subsequent years are also briefly considered.     

Space-Time scales of internal waves

Abstract

We have contrived a model E(αω) α μ^?1ω^?p+1(ω ²?ω _i ²)^?+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber α extending to some upper limit μ(ω) α ω ^r-1 (ω ²?ω _i ²)^½, and frequency ω extending from the inertial frequency ω _i to the local Väisälä frequency n(y). The spectrum is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(α, ω) = 2παE(α₁, α₂, ω), with α₁, α₂ designating components of α. Certain moments of E(α₁, α₂, ω) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement η(t),…, yield the frequency spectra F _(u,η,…)(ω) = ∫∫ (U ², Z ²,…)E(α₁, ∞₂, ω) dα₁ dα₂, where U, Z,… are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber spectrum F _(…)(α1) = ∫∫… dα₂ dω. (iii) Moored measurements horizontally separated by X yield the coherence spectrum R(X, ω) which is related to the horizontal cosine transform ∫∫ E(α1, α2 ω) cos α₁ Xdα₁ dα₁. (iv) Moored measurements vertically separated by Y yield R(Y, ω) and (v) towed measurements vertically separated yield R(Y, α₁), and these are related to similar vertical Fourier transforms. Away from inertial frequencies, our model E(α, ω) α ω ^?p-r for α ≦ μ ω ω ^r, yields F(ω) ∞ ω ^?p, F(α₁) ∞ α₁ ^?q, with q = (p + r ? 1)/r. The observed moored and towed spectra suggest p and q between 5/3 and 2, yielding r between 2/3 and 3/2, inconsistent with a value of r = 2 derived from Webster's measurements of moored vertical coherence. We ascribe Webster's result to the oceanic fine-structure. Our choice (p, q, r) = (2, 2, 1) is then not inconsistent with existing evidence. The spectrum is E(∞, ω) ∞ ω ^?1(ω ²?ω _i ^{2 ?1}, and the α-bandwith μ ∞ (ω ²?ω _i ²)⁺ is equivalent to about 20 modes. Finally, we consider the frequency-of-encounter spectra F([sgrave]) at any towing speed S, approaching F(ω) as S ≦ S _o, and F(α₁) for α₁ = [sgrave]/S as S ≧ S _o, where S _o = 0(1 km/h) is the relevant Doppler velocity scale.     

The discovery of magnetohydrodynamic waves

The discovery of magnetohydrodynamic waves was a major breakthrough in plasma physics and its applications to space physics and fusion research. The waves were discovered by Hannes Alfvén and are therefore also called Alfvén Waves. The discovery was typical of Alfvén's outstanding ability to derive results of great generality from analysis of specific problems—in this case, the sunspots and the sunspot cycle. It was also typical of his electrodynamic approach to astrophysical problems. It took a long time before his discovery was generally accepted, partly because of the contemporary lack of means to verify the waves experimentally. The experimental verification of the magnetohydrodynamic waves came gradually many years later, beginning with experiments in liquid metals. It was not until the end of the 1950s that experiments were performed in plasmas. These clearly and conclusively demonstrated the existence and properties of magnetohydrodynamic waves, in excellent agreement with the theoretical prediction of Alfvén. The discovery of the magnetohydrodynamic waves opened a whole new field of physics—magnetohydrodynamics, which is of profound importance especially, but not only, in plasma physics. At the same time as the magnetohydrodynamic waves, Hannes Alfvén also discovered another magnetohydrodynamic concept, the frozen-in magnetic field.