On plane waves in thermo-viscoelastic solids deformed by magnetic fields

Summary In the present paper,Maxwell's electromagnetic equations together with the equation of motion of two types of viscoelastic solids have been used to deal with the propagation of magneto-thermoviscoelastic plane waves.     

The flow of a stratified viscous liquid down an inclined plane

Summary The problem of the flow of a viscous liquid layer down an inclined plane is analyzed in the case in which the local viscosity depends linearly upon the height above the plane. By an application ofYih's technique, the velocity of long waves is calculated and the criterion for their stability is established. These are then compared with the corresponding results for a homogeneous layer.     

Propagation of Love type waves in a non-homogeneous layer lying over a vertically semi-infinite homogeneous isotropic medium

Summary The aim of this paper is to study the propagation of love-type waves in a homogeneous half-space overlain by a heterogeneous crust with various types of heterogenety. Frequency equations are obtained in each of the cases and numerical calculations are done in some cases and the results thus obtained are compared with those done byJeffreys andMitra [3]²).     

On plane strain problems in magneto-thermo-visco-elasticity

Summary Plane strain problems on magneto-thermo-visco-elastic interactions in a parallel union of the Kelvin and Maxwell bodies are investigated using the basic equations of electrodynamics and thermo-visco-elasticity. Assuming that the applied magnetic field is transverse to the plane of deformation and that the material is a perfect conductor of electricity, it is seen that the heat sources and the potential part of the body forces produce longitudinal waves only and the rotational part of the body forces gives rise to transverse waves only. The effect of deformation on magnetic permeability is equivalent to an anisotropic rescaling of the primary magnetic field. The effect of the applied magnetic field on waves produced by a plane heat source is equivalent to increasing the value of the material constants which results in an increase in the speed of the waves.     

On the energy flux of Hide waves

Summary There are two ways to define the energy flux for Hide waves, one from its equations of motion and the other by multiplying its mean energy density by group velocity and these lead to different results FollowingLonguet-Higgins we point out that this is due to certain arbitrariness in the definition of the energy flux and that their difference is just a solenoidal vector.Dedicated to the memory of Dr.V. A. Wynne, 1945–1972.     

Periodic and aperiodic dynamo waves

Abstract

In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity.     

A note on specific variability of long surface gravity waves and drag coefficient in coastal upwelling zone

In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. UsingGent andTaylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.     

Magneto-elastic waves and disturbances in initially stressed conducting media

Summary The object of the present paper is to investigate magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, the theory of magneto-elastic surface waves in a conducting medium under an initial uniaxial tension has been deduced and then it has been employed to investigate the particular cases of surface waves such as Rayleigh, Love and Stoneley waves. Secondly, propagation of waves in an elastic layer has been considered using the fundamental equations of motion for magneto-elastic waves in conductors under an initial uniaxial tension or compression. This is followed by the case of plane Lamb's problem in a magneto-elastic semi-space under the same initial tension. The final results obtained in the above cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

在初始应力作用下磁热粘弹波的传播

本文研究在初始应力作用下导热导电粘弹体内平面波的传播.首先导出有初始应力存在时电磁场、位移场、温度场所满足的基本方程然后用它研究了流体静压力或张力及单轴压或张的初始应力条件下,磁——热——粘弹平面波的传播特性.讨论了弱耦合情况下,热效应磁场对波传播特性的影响.在无初始应力存在并略去热、磁耦合效应时,所得结果变成经典的粘弹波结果.      

饱和土中浅埋隧道耦合二维动力响应解答探讨

针对平面波耦合作用下饱和半空间中浅埋隧道二维动力响应的典型问题的解答进行探讨。首先基于Biot饱和孔隙介质理论建立饱和土场方程,并通过中间势函数的代入推导得到饱和土体中的快纵波、慢纵波及横波的Helmholtz势函数方程,随后引入柱坐标系下饱和土体和弹性衬砌的势函数通解,并代入边界条件中,建立以第n组参数为变量的多元一次齐次线性方程组。采用本文的推导思路,可以解决饱和土体中的浅埋隧道在地震作用时P波和S波耦合作用下的响应问题。     

Elastische Multipolwellen in einem Medium,das aus homogenen,isotropen, planparallelen Schichten besteht

Zusammenfassung Gegeben ist ein festes, elastisches Medium, das aus homogenen, isotropen, planparallelen Schichten aufgebaut ist. Im Innern einer Schicht wird ein punktförmiger Störungsherd von Multipolcharakter angenommen. Die Störung setzt zur Zeitt=0 ein. Unter Anwendung der Laplace-Transformation werden nach dem Verfahren vonCagniard «Exponentialkoeffizienten» und «Übertragungsfaktoren» berechnet, die gestatten, die elastischen Verschiebungen der an den verschiedenen Unstetigkeitsflächen reflektierten und gebrochenen Wellen zu bestimmen.

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Summary (Elastic waves of multiplet type in a solid consisting of homogeneous isotropic layers with plane parallel boundaries) — An unlimited elastic solid consists of homogeneous isotropic layers, separated by plane parallel boundaries. A point in the interior of one layer is a multiple source of elastic waves. The disturbance begins att=0. By aid of Laplace-transforms, «exponential coefficients» and «transmission factors» have been calculated according to the method shown byCagniard. By aid of the «transmission factors» we can determine the elastic displacements of the waves reflected and refracted at the boundaries.

     

用波函数展开法求解界面圆孔的SH波散射问题

研究了ＳＨ波绕界面圆孔散射的波函数展开理论。由入射,反射和透射波组成的自由波场与孔的散射场叠加成总波场。将定义于两个半平面的散射场按一定方式延拓到全平面。通过Ｈａｎｋｅｌ－Ｆｏｕｒｉｅｒ型积分来满足界面与孔缘处的边界条件,得到了确定特定系数的封闭代数方程组。给出了具体算例,计算了孔缘处的动应力系数分布。     

CodaQ as a combination of scattering and intrinsic attenuation: Numerical simulations with the boundary integral method

Numerical modelling ofSH wave seismograms in media whose material properties are prescribed by a random distribution of many perfectly elastic cavities and by intrinsic absorption of seismic energy (anelasticity) demonstrates that the main characteristics of the coda waves, namely amplitude decay and duration, are well described by singly scattered waves in anelastic media rather than by multiply scattered waves in either elastic or anelastic media. We use the Boundary Integral scheme developed byBenites et al. (1992) to compute the complete wave field and measure the values of the direct waveQ and coda wavesQ in a wide range of frequencies, determining the spatial decay of the direct wave log-amplitude relation and the temporal decay of the coda envelope, respectively. The effects of both intrinsic absorption and pure scattering on the overall attenuation can be quantified separately by computing theQ values for corresponding models with (anelastic) and without (elastic) absorption. For the models considered in this study, the values of codaQ ^–1 in anelastic media are in good agreement with the sum of the corresponding scatteringQ ^–1 and intrinsicQ ^–1 values, as established by the single-scattering model ofAki andChouet (1975). Also, for the same random model with intrinsic absorption it appears that the singly scattered waves propagate without significant loss of energy as compared with the multiply scattered waves, which are strongly affected by absorption, suggesting its dominant role in the attenuation of coda waves.     

Love waves in inhomogeneous and anisotropic earth — I

Summary The frequency equation is derived for the propagation of Love waves in the earth's crust, composed of transversely isotropic layers and overlying anisotropic and inhomogeneous mantle. The exact boundary value problem is solved for a single layer and extended to multilayered media by generalizing theHaskell's technique. In fact the problem of deriving the frequency equation has been reduced to finding out the solution of the equation of motion subject to the appropriate boundary conditions. To illustrate the method, the author has derived frequency equations of Love waves for linear, exponential and generalized power law variation of vertical shear wave velocity with depth in the half space overlain by transversely isotropic inhomogeneous stratum.     

Transient scattering of elastic waves by dipping layers of arbitrary shape. Part 2: Plane strain model

Scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity. The steady state displacement field is evaluated throughout the elastic medium for different incident waves so that the continuity conditions along the interfaces between the layers and the traction-free conditions along the surface of the half-space are satisfied in the least-squares sense. Transient response is constructed from the steady state one through the Fourier synthesis. The results presented show that scattering of waves by dipping layers may cause locally very large amplification of surface ground motion. This amplification depends upon the type and frequency of the incident wave, impedance contrast between the layers, component of displacement which is being observed, location of the observation station and the geometry of the subsurface irregularity. These results are in agreement with recent experimental observations.     

Onlamb's problem in a magneto-elastic initially stressed conducting medium

Summary The object of the present paper is to investigate the so-called planeLamb's problem in an initially stressed magneto-elastic semi-space bounded by a plane. The results obtained in this investigation are in agreement with the corresponding results of the classical planeLamb's problem when the semi-space is supposed to be initially unstressed and non-magnetic.     

Rocking vibrations of a rigid circular foundation on poroelastic half-space to elastic waves

A study is carefully conducted for the rocking response of a rigid circular foundation resting on a poroelastic half-space when subjected to seismic waves under the framework of Biot’s theory. The free-field waves, rigid-body scattering field waves and radiation scattering field waves are introduced to consider the complex behavior of the soil owing to the scattering phenomena caused by the existence of the foundation. The contact surface between the soil and the foundation is supposed to be perfectly bonded and fully permeable. Combining with the divided wave fields, two sets of dual integral equations elaborating the mixed boundary-value conditions are established, and then reduced to Fredholm integral equations. Therefore, with a semi-analytical method, the expressions of the rocking displacements are obtained. The numerical results of the rocking vibration of the foundation for incident P, SV and Rayleigh waves are presented. The influences of certain parameters, such as the permeability of the soil, the incident angle, Poisson’s ratio and the mass of the foundation, on the rocking vibration of the foundation are explored and studied. Different reactions are found when the foundation is excited by different waves.     

2012年江苏高邮、宝应交界MS4.9地震发震断层参数测定

基于一维单侧有限移动震源模式,根据地震波传播过程中的多普勒效应,分别利用P波和S波拐角频率的方位变化,反演2012年7月20日江苏高邮、宝应交界MS4.9地震的发震断层面参数。P波和S波拐角频率的反演结果一致显示:本次地震的断层面破裂方向为232°左右,破裂面呈NE-SW向;地震马赫数v/c为0.2左右,平均破裂速度小于S波速度,破裂长度较短,为0.2~0.3km左右。破裂面方位与震源机制解、宏观烈度调查和余震精定位的研究结果具有一致性,结合震区周边的地质构造背景,分析认为滁河断裂很可能是高邮、宝应交界MS4.9地震的发震构造。     

Marine seismic wavefield measurement to remove sea-surface multiples

We propose a new method for removing sea-surface multiples from marine seismic reflection data in which, in essence, the reflection response of the earth, referred to a plane just above the sea-floor, is computed as the ratio of the plane-wave components of the upgoing wave and the downgoing wave. Using source measurements of the wavefield made during data acquisition, three problems associated with earlier work are solved: (i) the method accommodates source arrays, rather than point sources; (ii) the incident field is removed without simultaneously removing part of the scattered field; and (iii) the minimum-energy criterion to find a wavelet is eliminated. Pressure measurements are made in a horizontal plane in the water. The source can be a conventional array of airguns, but must have both in-line and cross-line symmetry, and its wavefield must be measured and be repeatable from shot to shot. The problem is formulated for multiple shots in a two-dimensional configuration for each receiver, and for multiple receivers in a two-dimensional configuration for each shot. The scattered field is obtained from the measurements by subtracting the incident field, known from measurements at the source. The scattered field response to a single incident plane wave at a single receiver is obtained by transforming the common-receiver gather to the frequency–wavenumber domain, and a single component of this response is obtained by Fourier transforming over all receiver coordinates. Each scattered field component is separated into an upgoing wave and a downgoing wave using the zero-pressure condition at the water-surface. The upgoing wave may then be expressed as a reflection coefficient multiplied by the incident downgoing wave plus a sum of scattered downgoing plane waves, each multiplied by the corresponding reflection coefficient. Keeping the upgoing scattered wave fixed, and using all possible incident plane waves for a given frequency, yields a set of linear simultaneous equations for the reflection coefficients which are solved for each plane wave and for each frequency. To create the shot records that would have been measured if the sea-surface had been absent, each reflection coefficient is multiplied by complex amplitude and phase factors, for source and receiver terms, before the five-dimensional Fourier transformation back to the space–time domain.     

Numerical Simulation of the Effect of a DC Electric Field on Seismic Wave Propagation with the Pseudospectral Time Domain Method

We have modeled the effect of a direct current (DC) electric field on the propagation of seismic waves by the pseudospectral time domain (PSTD) method, based on a set of governing equations for the poroelastic media. This study belongs to the more general term of the seismoelectric coupling effect. The set of physical equations consists of the poroelastodynamic equations for the seismic waves and the Maxwell's equations for the electromagnetic waves; the magnitude of the seismoelectric coupling effect is characterized by the charge density, the electric conductivity, the Onsager coefficient, a function of the dielectric permittivity, the fluid viscosity, and the zeta potential. The poroelastodynamic vibration of a solid matrix generates an electric oscillation with the form of streaming current via the fluctuation of pore pressure. Meanwhile, fluctuating pore pressure also causes oscillatory variation of the electric resistivity of the solid matrix. The simulated poroelastic wave propagation and electric field variation with an existing background DC electric field are compared with the results of a physical experiment carried out in an oilfield. The results show that the DC electric field can significantly affect the propagating elastic energy through the seismoelectric coupling in a wide range of the seismic frequency band.