Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green’s functions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of fictitious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary...     

Antiplane response of isosceles triangular hill to incident SH waves

In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill‘s peak on ground motion are discussed.     

Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green’s functions of compressive and shear wave sources are derived based on Biot’s theory. The scattered waves are constructed using fi ctitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verifi cation of the accuracy is performed by: (1) checking the satisfaction extent of the boundary c...     

Seismic reflection and transmission coefficients at an air-water interface of saturated porous soil

Based on the modified Biot＇s theory of two-phase porous media, a study was presented on seismic reflection and transmission coefficients at an air-water interface of saturated porous soil media. The major differences between air-saturated soils and water-saturated soils were theoretically discussed, and the theoretical formulas of reflection and transmission coefficients at an air-water interface were derived. The characteristics of propagation and attenuation of elastic waves in air-saturated soils were given and the relations among the frequency, the angle of incidence and the reflection, transmission coefficients were analyzed by using numerical methods. Numerical results show that the propagation characteristic of the wave in air-saturated soils is great different from that in water-saturated soils. The frequency and the angle of incidence can have great influences on the reflection and transmission coefficients at interface. Some new cognition about the wave propagation is obtained and the study suggests that we may carefully pay attention to the influence of air on the dynamic analysis of seismic wave.     

Time-domain solution for transient dynamic response of a large-diameter thin-walled pipe pile

The propagation of stress waves in a large-diameter pipe pile for low strain dynamic testing cannot be explained properly by traditional 1D wave theories. A new computational model is established to obtain a wave equation that can describe the dynamic response of a large-diameter thin-walled pipe pile to a transient point load during a low strain integrity test. An analytical solution in the time domain is deduced using the separation of variables and variation of constant methods. The validity of this new solution is verifi ed by an existing analytical solution under free boundary conditions. The results of this time domain solution are also compared with the results of a frequency domain solution and fi eld test data. The comparisons indicate that the new solution agrees well with the results of previous solutions. Parametric studies using the new solution with reference to a case study are also carried out. The results show that the mode number affects the accuracy of the dynamic response. A mode number greater than 10 is required to enable the calculated dynamic responses to be independent of the mode number. The dynamic response is also greatly affected by soil properties. The larger the side resistance, the smaller the displacement response and the smaller the refl ected velocity wave crest. The displacement increases as the stress waves propagate along the pile when the pile shaft is free. The incident waves of displacement and velocity responses of the pile are not the same among different points in the circumferential direction on the pile top. However, the arrival time and peak value of the pile tip refl ected waves are almost the same among different points on the pile top.     

Dynamic responses of a sediment-filled valley with a fluid layer subject to incident waves

The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteristics may be significant and should be carefully considered when designing long span bridges with high piers. The method of analysis adopted in the paper is to decompose the problem into an interior region and an exterior region. In the exterior region, the scattered wave fields are constructed with the linear combinations of two independent sets of Lamb’s singular solutions, i.e., the integralsolutions for two concentrated surface loads in two directions; and their derivatives are used to represent the scattered wave fields. A technique is proposed to calculate the integrals in the wave-number domain based on the method of steepest descent. For the interior region, the wave fields for the fluid layer and soft soil deposit are expressed in terms of wave functions which satisfy the equation of motion. The continuity condition at the interface of the media is satisfied in the least square sense. The effects of geometric topography, soil amplification and fluid layer subject to different types of incident harmonic plane waves are analyzed and discussed..     

A process-based model for sediment transport under various wave and current conditions

The purpose of this study is to investigate the capability of a newly developed process-based model for sediment transport under a wide variety of wave and current conditions.The model is based on the first-order boundary layer equation and the sediment advection-diffusion equation.In particular,a modified low Reynolds number k-e model is coupled to provide the turbulence closure.Detailed model verifications have been performed by simulating a number of laboratory experiments,covering a considerable range of hydrodynamic conditions such as sinusoidal waves,asymmetric waves and wave-current interactions.The model provides satisfactory numerical results which agree well with the measured results,including the time-averaged/dependent sediment concentration profiles and sediment flux profiles,as well as the time series of concentration at given elevations.The observed influences of wave orbital velocity amplitude,wave period and sediment grain size are correctly reproduced,indicating that the fundamental physical mechanisms of those processes are properly represented in the model.It is revealed that the present model is capable of predicting sediment transport under a wide range of wave and current conditions,and can be used to further study the morphodynamic processes in real coastal regions.     

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅰ): Formulation

This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green’s functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot’s theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of ...     

The mechanism of the effects of the upwelling mean on the ENSO event mature phase locking

The mechanism of the effects of the upwelling mean on the ENSO event mature phase locking is ex-amined by using a mixed-mode model. The results show that the positive feedback process of the ef-fects of the seasonal variation of the upwelling mean on the Kelvin wave is the mechanism of the locking of the event mature phase to the end of the calendar year. The memory of the Rossby waves for the sign-shifting of the sea surface temperature anomaly from positive to negative 6 months before the cold peak time is the other mechanism of the locking of the La Nia event mature phase to the end of the calendar year. The results here are different from previous ones which suggest that the balance between cold and warm trends of sea surface temperature anomaly is the mechanism involved. The cold trend is caused by the upwelling Kelvin wave from upwelling Rossby wave reflected at the western boundary, excited by the westerly anomaly stress over the central Pacific and amplified by the seasonal variation of the coupled strength in its way propagating westward. The warm trend is caused by the Kelvin wave forced by the western wind stress over the middle and eastern equatorial Pacific. The cause of the differences is due to the opposite phase of the seasonal variation of the upwelling mean to that in the observation and an improper parameterization scheme for the effects of the seasonal varia-tion of the upwelling mean on the ENSO cycle in previous studies.     

Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel

A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semicylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations. Fourier expansion theorem with the form of complex exponential function and cosine function is used. Numerical solutions are obtained by truncation of the infinite equations. The accuracy of the presented numerical results is carefully verified.     

多次透射公式在衰减波场中的实现

在多次透射公式的基础上，引进一衰减系数，用来模拟外行的衰减波，将透射公式推广到考虑衰减波入射时的情形；并对衰减波入射时两种极限情形下(理想稳态和理想暂态情形)的反射系数进行了分析. 结果表明, 多次透射公式对弱衰减波仍可适用，对于强衰减波则需应用加衰减系数的多次透射公式进行透射．最后，通过两相介质两个数值实验, 验证了该边界条件在模拟衰减波时的精度．      

多人工波速优化透射边界在谱元法地震波动模拟中的应用

将作者最近发展的多人工波速优化透射边界(记为ca j-MTF)应用于高精度谱元法的地震波动模拟中,并与经典的廖氏透射(MTF)边界、完美匹配层(PML)边界、黏弹性边界以及一阶旁轴近似边界进行了比较分析.结果显示:①ca j-MTF边界与MTF边界在形式上非常接近,它继承了后者公式简单、易于实现、精度可控、计算量低以及...     

透射边界高频耦合失稳机理及稳定实现——SH波动

就大型近场波动的高效数值模拟而言,稳定实现高阶人工边界是一个尚未圆满解决的问题.本文针对使用多次透射公式的SH波动集中质量有限元模拟,依据GKS定理的群速度解释,进一步阐明了人工边界与内域离散格式耦合所导致高频失稳的机理,即两者支持群速度指向内域的外行高频平面谐波,波动能量自发地从人工边界进入內域,从而导致失稳,而这类谐波是由集中质量有限元离散引入的.本文提出了消除此种耦合失稳的一种方法:通过修改有限元刚度阵来改变内域离散格式,并保证修改格式的精度不低于原有格式的精度.理论分析和数值实验表明此法能稳定实现透射边界.本文研究结果具有推广应用前景.     

热弹性介质中波传播特征

深层-超深层油气地震勘探涉及高温介质地震波传播问题,热弹介质参数对地震波传播有重要影响.含弛豫时间修正项的Lord-Shulman双曲型耦合热弹波动方程从理论上预测了热弹性介质中存在快纵波、慢纵波(一种准静态慢纵波,简称热波)和横波的传播,两个纵波为热耗散衰减波而横波不受介质热特性的影响.本文结合平面波频散分析和格林函数法数值模拟,详细研究两个热耗散衰减波的频散和衰减特征,着重分析热导率、热膨胀系数及比热的变化对波速和衰减的影响.研究表明热导率作为主要参数决定了波速与衰减的临界变化,热膨胀系数对波速和衰减的幅度有明显影响,比热则兼顾了前两个热弹系数的影响特征.最后,利用热弹性动力学频率域的二阶格林函数进行波场快照数值模拟,展示热弹性介质中纵波、横波和热波的传播行为.     

Arbitrary-order Taylor series expansion-based viscoacoustic wavefield simulation in 3D vertical transversely isotropic media

Taking the anisotropy of velocity and attenuation into account, we investigate the wavefield simulation of viscoacoustic waves in 3D vertical transversely isotropic attenuating media. The viscoacoustic wave equations with the decoupled amplitude attenuation and phase dispersion are derived from the fractional Laplacian operator and using the acoustic approximation. With respect to the spatially variable fractional Laplacian operator in the formulation, we develop an effective algorithm to realize the viscoacoustic wavefield extrapolation by using the arbitrary-order Taylor series expansion. Based on the approximation, the mixed-domain fractional Laplacian operators are decoupled from the wavenumbers and fractional orders. Thus, the viscoacoustic wave propagation can be conveniently implemented by using a generalized pseudospectral method. In addition, we perform the accuracy and efficiency analyses among first-, second- and third-order Taylor series expansion pseudospectral methods with different quality factors. Considering both the accuracy and computational cost, the second-order Taylor series expansion pseudospectral method can generally satisfy the requirements for most attenuating media. Numerical modelling examples not only illustrate that our decoupled viscoacoustic wave equations can effectively describe the attenuating property of the medium, but also demonstrate the accuracy and the high robustness of our proposed schemes.     

Modeling of nonmigrating tides in the middle atmosphere

On the basis of calculations using the general circulation model of the middle and upper atmosphere, the relative role of sources of nonmigrating tides distributed in atmosphere has been investigated. It is shown that in winter, when planetary waves in stratosphere are well developed, the main contribution to the generation of nonmigrating tides is caused by nonlinear interaction between migrating tides and a quasi-stationary planetary wave with zonal wave number 1 (SPW1). Taking into account the longitudinal ozone inhomogeneities in the model leads to the occurrence of additional sources of nonmigrating tides caused by longitudinally inhomogeneous heating of the atmosphere, the contribution of which can be comparable to that from nonlinear interaction under an attenuating amplitude of SPW1 in the stratosphere.     

基于混合有限元格式的完美匹配层与多次透射公式人工边界比较研究

介绍了完美匹配层(PML)人工边界可以吸收不同频率和任意角度入射波的原理以及PML人工边界的构造方法. 在此基础上,将PML人工边界应用于地震波动数值模拟的速度应力混合有限元格式中,探讨了PML应用的可行性,并通过数值试验研究了PML人工边界的反射率,比较了PML人工边界与多次透射公式(MTF)人工边界应用于体波和面波模拟中数值反射的差异,对两种边界的透射效果进行了分析. 结果表明, 尽管数值离散后PML人工边界不再保持完美匹配特性,但PML人工边界在近场波动数值模拟中可获得比MTF人工边界更为理想的吸收效果,在角点透射、大角度掠射情形下尤为明显;PML人工边界在混合有限元格式的数值算法中,未见失稳等不良反应,比MTF人工边界有更好的稳定性;在合理选择参数的情况下,PML人工边界的运算量可接受.      

Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation

The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construc- tion process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investi- gated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in corner and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computa- tional efficiency of PML boundary is only a little lower than MTF boundary.     

Research Note: Overpressure prediction from C‐wave seismic data

Recently, mode converted shear waves (C‐waves) have been shown to enable overpressure prediction in media where primary wave acquisition is inhibited by gas and fluid effects – C‐wave moveout is analysed and a long standing relationship between differential stress and primary‐wave (P‐wave) velocity is modified and employed. Though pore‐pressure prediction based on C‐waves is supported by empirical evidence from laboratory and field experiments, a theoretical justification has yet to be developed. In this research note, we provide a supporting algebra for the original relationship between pore pressure and C‐wave velocity.     

Thermal Generation of Alfvén Waves in Oscillatory Magnetoconvection: Diffusively Modified Modes

Thermal instabilities in the form of oscillatory magnetoconvection representing diffusively modified Alfvén waves in an electrically-conducting Bénard fluid layer of rigid walls in the presence of a vertical magnetic field are investigated. Emphasis of the article is on the transition from a nearly undamped Alfvén wave to diffusively modified Alfvén waves, and on the effect of physically realisable magnetic field boundary conditions on magnetoconvection. It is found that the extra magnetic dissipation in the magnetic Hartmann boundary layers can enhance oscillatory magnetoconvection in the form of strongly modified Alfvén waves. Oscillatory magnetoconvection produced solely by the Alfvén wave mechanism can be the most unstable mode even in the presence of a strong viscous effect. This article also represents the first study on the effect of an electrically conducting wall on magnetoconvection which is associated with a nonlinear eigenvalue problem. We find that the electrically perfectly conducting condition does not yield a good approximation for magnetoconvection with an electrically highly conducting wall. The size of oscillation frequency with an electrically highly conducting wall can be more than a factor of 2 larger than that obtained using the perfectly conducting condition.