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1.
圆弧状凹陷地形对平面P波的散射:高频解答 总被引：2，自引：1，他引：1
利用波函数的Fourier-Bessel级数展开,推导了具有不同深宽比的圆弧状凹陷地形对入射平面P波二维散射问题的解析解.与现有解析解不同之处在于,为了使该解析解适用于更高的入射波频率,本文利用了柱函数的渐进性质,使得散射波的待定系数可以直接确定,避免了线性方程组的求解以及相关的数值计算问题,从而拓展了该解析解适用的频带范围.通过与现有解析解的比较,论证了该解析解的正确性,进而在一个较宽的频带范围内分析了圆弧状凹陷地形对入射平面P波的散射效应. 相似文献
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利用波函数的Fourier-Bessel级数展开法,推导出了含任意多个圆弧状沉积层的谷地在平面SV波入射下稳态动力响应的解析解,并分析了该级数形式的解析解随着截断项数的收敛问题.其结果表明,该级数解能够在一个非常宽的频带范围内收敛;通过在简化条件下与现有其他解析解的比较,验证了该解析解的正确性;并利用该解析解,以稳态地面运动的位移幅值和相位差为基本参数,在一个较宽的频带范围内讨论了谷地中沉积介质的成层性对地面运动的影响,其结果表明对于多层谷地而言,当入射波频率较高时,散射波之间的干涉显著并且出现了能量聚焦现象. 相似文献
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圆弧状凹陷地形在平面SH波入射下的动力响应：高频解答 总被引：1，自引：0，他引：1
利用波函数的Fourier-Bessel级数展开法和外域型Graf加法公式,推导了圆弧状凹陷地形对平面SH波二维散射问题的解析解。与现有其他解析解不同的是,该解析解的获得无须求解线性方程组,从而避免了高频波入射下方程组系数矩阵可能出现的病态问题。因此,既使在入射波频率很高的情况下,该解析解也能够收敛。利用该解,在一个非常宽的频带范围内讨论了凹陷地形的几何形状对地面运动的影响。 相似文献
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利用波函数的Fourier-Bessel级数展开法,推导了具有不同深宽比的圆弧状凹陷地形对入射平面SV波二维散射问题的解析解。区别于现有其他解析解,利用柱函数的渐近性质,使得散射波的待定系数得以直接确定,避免了线性方程组的求解以及相应的高频波入射下的数值计算问题,从而拓展了解析解适用的频带范围。通过与已有解析解的比较论证了该解析解的正确性,并在一个较宽的频带范围内研究了圆弧状凹陷地形对入射平面SV波的散射效应。 相似文献
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Introduction The effect of local topographies on seismic wave propagation is one of the most attractive topics in seismology. It may be resolved by either an analytical method or a numerical method. Here, the analytical method is the wave function expansion method; numerical methods include the finite difference, finite element, boundary integration equation, and discrete wave number method, etc. The advantage of these numerical methods is that they can be applied to local inhomogeneity and ir… 相似文献
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Yushan Zhang 《地震科学（英文版）》2010,23(2):157-165
By expressing the wave functions in the form of Fourier-Bessel series,the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary number of circular-arc-shaped layers is presented firstly.And then,the convergence of the proposed series solution with the truncation number of terms is discussed,which demonstrates that the analytical solution can converge even for very high frequencies of the incident P wave.Finally,using this solution,the influences that are imposed on the stationary ground motion by the number and the sequence of alluvial layers,as well as the stiffness of soft interlayer contained in the canyon,are studied. 相似文献
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Scattering of SH waves induced by a symmetrical V-shaped canyon: a unified analytical solution 总被引：2，自引：1，他引：1
This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering. 相似文献
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This paper presents an analytical solution for two-dimensional scattering and diffraction of plane P waves by circular-arc alluvial valleys with shallow saturated soil deposits. The solution is based on Biot's dynamic theory for saturated porous media, and derived by employing Fourier–Bessel series expansion technique. In this analysis, soil deposits in the circular-arc valley are modeled as saturated porous media based on Biot's dynamic theory, and the circular-arc valley is assumed to be imbedded in an infinite half-space, filled with elastic single-phase media. Numerical results from this solution show that the amplitudes of displacement at the surface of an alluvial valley are mainly relative to the angle of incidence, the dimensionless frequency of incident P wave, the degree of saturation and porosity of soil deposits, and the stiffness and Poisson's ratio of the solid skeleton of the soil deposits. Furthermore, the proposed solution is compared with the previous solution, in which the soil deposit was modeled as an elastic single-phase solid. 相似文献
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Scattering of plane P waves by circular-arc layered alluvial valleys: An analytical solution 总被引：1，自引：0，他引：1
IntroductionThe site effect of local inhomogeneity and irregularity on seismic wave propagation is one of the most attractive topics in seismology. The problem may be resolved by either analytical method or numerical method. Here, the analytical method is the wave function expansion method; numerical methods include the finite difference, finite element, boundary integration equation, and discrete wave number method, etc. Although these numerical methods can be applied for sites of arbitrary s… 相似文献
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A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section in a half-space is studied using the wave functions expansion method. The solution is reduced to solving infinite linear algebraic equations using the Graf's addition theorem in an appropriate form. Numerical results of the solution are obtained by truncation of the infinite equations and accuracies of the truncation are checked by the extent to which the numerical results fit the boundary condition and by convergence of the numerical results with the truncation order. Complicated effects of the depth-to-width ratio of the canyon on surface ground motion are shown by the numerical results for typical cases. 相似文献
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利用Fourier Bessel级数展开法，给出了表面具有覆盖层的圆弧形凹陷地形对入射平面SV波散射问题的一个解析解，并利用该解分析了不同深宽比凹陷地形表面覆盖层刚度和厚度对入射SV波的影响．结果表明，凹陷地形表面覆盖层的存在，即使厚度很薄，也会显著增加对入射SV波的放大作用，该放大作用可达到单一凹陷地形的2.5倍以上．覆盖层刚度和厚度的变化对入射平面SV波也具有很大影响． 相似文献
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利用波函数的FourierBessel级数展开法,给出了含任意多个圆弧状沉积层的谷地在平面P波入射下稳态动力响应的解析解.并以具有三个沉积层的谷地为例,在宽频范围内,利用稳态地面运动幅值的空间分布,讨论了谷地中沉积介质的成层性对地面运动的影响. 相似文献
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圆弧形有水河谷场地对平面P波的散射 总被引：1，自引：0，他引：1
利用波函数展开法,在频域内给出了圆弧形充水河谷对平面P波散射问题的解析。并分析了入射波波长、入射角对充水河谷地形地面运动的影响。 相似文献
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Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored. 相似文献
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A closed-form wave function analytic solution of two-dimensional scattering and diffraction of incident plane SH-waves by a fl exible wall on a rigid shallow circular foundation embedded in an elastic half-space is presented. This research generalizes the previous solution by Trifunac in 1972, which tackled only the semi-circular foundation, to arbitrary shallow circular-arc foundation cases, and is thus comparatively more realistic. Ground surface displacement spectra at higher frequencies are also obtained. As an analytical series solution, the accuracy and error analysis of the numerical results are also discussed. It was observed from the results that the rise-to-span ratio of the foundation profi le, frequency of incident waves, and mass ratios of different media(foundation-structure-soil) are the three primary factors that may affect the surface ground motion amplitudes near the structure. 相似文献
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An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill. 相似文献
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Diffraction of plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space 总被引：7，自引：0，他引：7
Jianwen Liang Zhenning Ba Vincent W. Lee 《Soil Dynamics and Earthquake Engineering》2006,26(6-7):582-610
An analytical solution for the scattering and diffraction of incident plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space is derived by the wave function expansion method. The solution is utilized to analyze the dependence of the computed surface motions on the incident frequencies, incident angles, porosity, boundary drainage and Poisson's ratio. It is shown that, depending on the incident angles, the surface displacement amplitudes around a canyon in a dry poroelastic half-space and saturated poroelastic half-space can be very different. The surface displacement amplitudes of an undrained saturated poroelastic half-space are close to those of a drained saturated poroelastic half-space. For low porosity, the surface displacement amplitudes of a saturated poroelastic half-space are almost identical to those of a dry poroelastic half-space, and drainage condition has little influence on the surface displacement amplitudes. But for high porosity, the effect of drainage condition becomes significant, and for the same porosity, the displacement amplitudes of an undrained saturated half-space will be larger than those of a drained saturated half-space. Poisson's ratio is also an important factor affecting the surface displacement amplitudes around the canyon, both in drained and undrained conditions, but leads to larger effects for an undrained saturated half-space than for a drained saturated half-space. Large pore pressures are found around the canyon and their amplitudes depend on the incident angles and frequencies. Below the surface, the amplitudes of pore pressures are less than they are at the surface, especially for high frequencies. 相似文献
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Rayleigh波在浅圆凹陷地形附近的散射:高频解答 总被引：4，自引：1，他引：4
利用波函数展开法给出了Rayleigh波在浅圆凹陷地形附近散射的一个高频解析解，并分析了入射频率、凹陷地形宽度和深度等因素对波散射的影响。数值结果表明，由于Rayleigh波幅值随深度而衰减，凹陷地形表面位移幅值整体上较小，且随着凹陷地形深度的增加而减小；由于Rayleigh波幅值还随频率而衰减，随着入射频率的升高，凹陷地形表面位移幅值逐渐减小；由于凹陷地形的屏障作用，在人射波的近端，地表位移分布变得相对复杂，地表位移峰值出现在左角点附近，而在入射波远端，地表位移分布相对简单，地表位移峰值出现在距凹陷地形较远的地方。 相似文献