Earth tides and polar motion

We establish a general theory that describes the rotational motion of a layered, oblate, elastic Earth under the influence of tidal forces when account is taken of the liquid outer core. We obtain a linearized version of the Navier-Stokes equation; within it not only have we retained the Coriolis and centrifugal acceleration terms, but also have included the nutational terms. We also make use of the Euler equation for angular momentum to analytically relate the nutational motion of the rotational axis with the oscillations of the liquid core and obtain a constraint for the nutational amplitude. Consideration of the Poisson equation for density variation completes our analytical model.We primarily discuss the equations of motion for the liquid core and present the solution as the sum of two terms: one being a component of the spheroidal displacement field, the other of the toroidal field. We also formulate the equations valid for the solid mantle when rotational effects are included, and establish the boundary conditions that must hold at the various interfaces in order that a complete integration of the differential system of equations be accomplished.We assume that the outer core consists of an inviscid fluid and ignore the existence of any boundary layer. We do not impose, however, any restriction on the stratification of the fluid. The dynamical coupling between liquid core and solid mantle is represented by a torque which is generated by the forced oscillations within the liquid core; these oscillations are in turn triggered by the diurnal tides.The expected influence of the liquid core/solid mantle boundary on the nutational motion is discussed in view of Poincare's results concerning a liquid core surrounded by a rigid shell. Comparison is finally made of our model with Molodenskii's 1961 theory for a neutral core and the 1976 Shen-Mansinha nutational theory for an unrestricted core.     

地磁Z分量低值时间位移与震源孕育体的可能联系

地震的孕育是一复杂的物理和力学过程。对于一球型震源体,则会有裂隙由核向外而后液体由外向核的双重扩散过程;与此同时,介质的电磁性质亦相应地发生扩散运动。本从定解问题入手,求得ε、μ、σ的扩散解。根据麦克韦电场理论、求得震源体各向异性介质中麦克斯韦的等价方程与电磁场的基本方程。由此得出震源体介质的似异体性质。对球型导体电磁感应的定解问题,对其频域解分离,得到在外源场作用下震源体中的分量解,即感应场、     

Dynamo macrodynamics in rotating stratified fluids

The linear solvability conditions are found for any field of force leading to steady motion in a stratified rotating medium. A general solution for such motion is determined. For the Lorentz force, it is shown that a unique relation between all axisymmetric poloidal and toroidal magnetic fields is specified. A path to solutions for the non-linear -dynamo stability problem compatible with these constraints is outlined.     

Magnetohydrodynamic oscillations due to precessional motion

Summary The motion of a non-viscous liquid medium with an ideal electrical conductivity, enclosed in the ellipsoidal cavity of an envelope subject to precessional motion, is investigated. Inside the cavity there is a toroidal magnetic field. It is proved that the precessional motion of the envelope generates forced oscillations of the medium with a period of 24 hours and two different types of eigen oscillations. Expressions for computing the amplitudes and frequencies of all types of oscillations are derived. The maximum values of disturbance fields are determined for geophysically acceptable parameters.     

基于弥散-黏滞型波动方程的地震波衰减及延迟分析

地震波的衰减、储层中的流体预测和4D流体监测技术是目前石油地球物理勘探领域十分有价值的热门研究课题.该文在基于一维弥散-黏滞型波动方程正演的基础上,根据含流体地层的弥散性与黏滞性,研究和模拟含流体地层对地震波的吸收衰减特征、低频伴影现象及其在流体预测中的应用;同时,模拟和分析了地震波在含流体地层中传播而导致的延迟特征.这些特征的检测与解释方法,为基于实际地震资料的储层流体预测及4D油气田开发监测提供技术思路与有效方法.     

Investigation of the dynamic interaction between a high-pressure pipeline and the moving liquid inside under seismic loading

The response of an open high-pressure pipeline containing moving liquid to horizontal seismic loading is investigated. The problem of the interaction between the pipe and the liquid inside it is solved after thorough kinematic analysis, involving two-stage application of the Coriolis theorem. The basic axial loading on the pipeline is also taken into account. As a result, the equation of motion of an arbitrary one-span part of the pipeline under seismic loading is obtained. The harmonic balance is used to find the solution. As an illustration to the theory a numerical example is given with the data of a real water power station pressure pipeline under a past earthquake record.     

空腔爆炸产生的地震波

本文首先讨论了压力空腔和爆炸中心的等价问题。计算层状介质中的空腔爆炸所产生的位移场时,可先求介质的单位脉冲响应,然后将其与等价的爆炸点源函数做褶积。对于均匀的半空间,自由面位移的暂态解是由三个无量纲的参数所决定的;由此可导出远场位移的精确解。本文也讨论了爆炸点附近的运动。最后还导出多层介质中空腔爆炸所产生的表面位移谱的形式解。     

2-D transient soil–surface foundation interaction and wave propagation by time domain BEM

This paper shows an effective implementation of the half-plane Green function for surface strip impulses (Lamb's problem), which was previously developed in a closed form by the authors, into the time-domain boundary element method for the analysis of related initial boundary value problems. The time-stepping algorithm utilizing Heaviside step function makes the solution process free from the Rayleigh wave front singularity. Illustrative analyses performed include that: First, the response due to an impulsive uniform strip loading is dealt with in order to check the accuracy of the present solution and to interpret the associated wave motion in the medium. Second, a rigid massless strip surface foundation is analysed when subjected to various impulsive loadings in vertical, horizontal and rotational directions to observe which wave is most concerned with the respective foundation motion. The field response is also of interest with respect to distance attenuation. Third, the dynamic cross-interaction between active and passive foundations through soil is investigated when multiple strip foundations are placed separately on a half-space with a certain distance.     

Closed form solution for a point force in a rotating stratified fluid

Summary The motion generated by an oscillatory point force in an inviscid incompressible rotating stratified fluid is studied, taking into account the effect of stratification on the inertia terms in the equations of motion. The solutions are obtained in closed form using Fourier transforms. The motion is axisymmetric (or not) according as the force acts along (or perpendicular to) the axis of rotation of the fluid. In the hyperbolic case, the motion is confined to the inner region of a cone with vertex at the origin. The solution when there is no rotation-no stratification-neither rotation nor stratification, is deduced and each case is found to differ from the case of rotating stratified fluid in many respects. The solution for a steady force is also deduced in the limit.     

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper. Based on the sealed system theory, the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported. In our work, wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefield and its characteristics are studied using the numerical finite element method. The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase. More specifically, the displacement decreases with increasing relaxation coefficient.     

On the inverse dynamo problem in a simplified mean-field model

Inverse dynamo theory seeks to gain information about the motion of a liquid conductor from measurements of the magnetic field in the surrounding vacuum. We consider here a highly simplified model problem, namely a steady α²-dynamo in plane geometry with an α-field varying only in the z-direction normal to the conductor–vacuum interface. Based on perturbation theory about constant-α solutions, we find as many integral conditions on α(z) as modes are present in the vacuum field. This result is corroborated by the complete solution of a special case.     

Dynamic response of a submerged hemispherical shell to earthquake motions

The dynamic response to ground motion of hemispherical shells in a fluid, medium is studied numerically. In the analysis, linear thin shell theory is used and the fluid is assumed to be compressible and inviscid. The effect of the duration of the ground motion on the dynamic response is studied using two forcing functions, one with a very short duration and the other in the form of a Heaviside function. As special cases, dynamic responses of the shell in vacuo and of a rigid hemisphere in the fluid medium are investigated. The results are valid also for a ring-stiffened complete spherical shell accelerating in an acoustic medium.     

双相介质中的地震波运动学特征

以 Biot理论为基础 ,推导了双相介质中弹性波的本构关系、运动方程及解。结果表明 :在均匀双相介质中可获得第一 P波、第二 P波和 S波。第一 P波近似于弹性介质中的 P波 ,第二 P波称为慢波 ,其速度一般小于 S波 ,但在个别介质模型中大于 S波。选择了合理的参数 ,对均匀双相介质中的波速进行了数值模拟     

Seismic response of reduced micropolar elastic half-space

This paper explores reduced micropolar theory to simulate ground motion during an earthquake. In this theory, rotational motions are kinematically independent of translational motions. Analytical expressions for ground displacement and rotational motions due to a buried seismic source are presented in this paper. This theory requires two additional material constants which characterise the microstructure of the medium compared with linear elastic theory. Ground motions are simulated for an earthquake of magnitude (M _w) 5.0. The sensitivity of ground motion to these new material constants is reported. It is observed that rotations are sensitive to microstructure of the medium. A comparison with recorded rotations of the M _w 5.2 Izu peninsula, Japan event is also presented in this article.     

EFFECT OF SLAB FLEXIBILITY ON INTERACTION BETWEEN TWO CIRCULAR FOUNDATIONS

The paper is aimed at investigating the effect of foundation rigidity on dynamic stiffness for two circular foundations on a viscoelastic medium. To generate the dynamic stiffness, a substructure technique is employed. For the substructure of a viscoelastic medium, the solution for wave motion reported in Reference 11 is used. For the substructures of two flexible foundations, classical plate theory with the inertial force neglected is employed to find the displacement fields of the foundation plates subjected to the interaction stresses. Then, the continuity condition for all the substructures is imposed implicitly by using the variational principle; then with the help of the reciprocal theorem the dynamic stiffness for the two flexible foundations can be obtained. For the numerical study, the boundary condition at the rims of both foundation plates is assumed to be a hinge connection to superstructures. Some numerical investigations are performed and the effect of foundation rigidity on dynamic stiffness is examined. Some discussions and conclusions are also made.     

Wavelet‐based non‐stationary seismic rocking response of flexibly supported tanks

The non‐stationary rocking response of liquid storage tanks under seismic base excitations including soil interaction has been developed based on the wavelet domain random vibration theory. The ground motion has been characterized through statistical functionals of wavelet coefficients of the ground acceleration history. The tank–liquid–foundation system is modelled as a multi‐degree‐of‐freedom (MDOF) system with both lateral and rocking motions of vibration of the foundation. The impulsive and convective modes of vibration of the liquid in the tank have been considered. The wavelet domain coupled dynamic equations are formulated and then solved to get the expressions of instantaneous power spectral density function (PSDF) in terms of functionals of input wavelet coefficients. The moments of the instantaneous PSDF are used to obtain the stochastic responses of the tank in the form of coefficients of hydrodynamic pressure, base shear and overturning base moment for the largest expected peak responses. Parametric variations are carried out to study the effects of various governing parameters like height of liquid in the tank, height–radius ratio of the tank, ratio of total liquid mass to mass of foundation, and shear wave velocity in the soil medium, on the responses of the tank. Copyright © 2003 John Wiley & Sons, Ltd.     

Investigation of nonlinear sloshing effects in seismically excited tanks

Nonlinear behavior of liquid sloshing inside a partially filled rectangular tank is investigated. The nonlinearity in the numerical modeling of the liquid sloshing originates from the nonlinear terms of the governing equations of the fluid flow and the liquid free surface motion as a not known boundary condition. The numerical simulations are performed for both linear and nonlinear conditions. The computed results using linear conditions are compared with readily available exact solution. In order to verify the results of the nonlinear numerical solution, a series of the shaking table tests on rectangular tank were conducted. Having verified linear and nonlinear numerical models, they are used for computation of near wall sloshing height at a series of real scale tanks (with various dimensions) under the both harmonic and earthquake base excitation. Finally, the nonlinear effects on liquid sloshing modeling are discussed and the practical limitations of the linear solution in evaluating the response of seismically excited liquids are also addressed.     

Dynamic response of rigid tanks with inhomogeneous liquids

A study of the response to horizontal ground shaking of a rigid cylindrical tank containing an inviscid liquid with a continuous vertical variation in density is presented. In addition to the free vibrational sloshing characteristics of the liquid, the responses examined include the vertical displacements at the free surface, and the impulsive and convective components of the hydrodynamic wall pressures and associated tank forces. The equations of motion for the system are formulated for an arbitrary variation in liquid density but the solutions presented are for a density that increases exponentially from top to bottom. Comprehensive numerical data are included which elucidate the underlying response mechanisms and the effects and relative importance of the various parameters involved. The solution for the continuous density variation considered herein is also compared with a previously reported solution in which the liquid was modelled as a multi-layered, discrete system.     

Conversion between solid and beam element solutions of finite element method based on meta-modeling theory: development and application to a ramp tunnel structure

In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.     

Dynamic response of an offshore pile to pseudo-Stoneley waves along the interface between a poroelastic seabed and seawater

A coupled model is developed to investigate the dynamic interaction between an offshore pile, a porous seabed and seawater when subjected to the pseudo-Stoneley wave along the seabed and the seawater interface. The pile and the seabed are treated as the porous medium governed by Biot's theory, while the seawater is considered as an acoustic medium and is described by the conventional Helmholtz equation. The free field solution of the incident pseudo-Stoneley wave is obtained using Biot's theory and the potential method. Based on the boundary element method (BEM) for the porous medium and the acoustic medium, three BEM formulations are constructed for the pile, the seabed and the seawater, respectively, which are combined together using the continuity conditions between the pile, the seabed and the seawater to formulate the coupled model for the system. As shown in numerical examples, when the system is subjected to the pseudo-Stoneley wave, the maximum pore pressure of the seabed usually occurs at the region near the interfaces between the seabed and the seawater.