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The scattering of water waves by bottom-mounted vertical circular cylinders is solved by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In the implementation, the null-field point can be exactly located on the real boundary owing to the introduction of degenerate kernels for fundamental solutions. An adaptive observer system of polar coordinates is considered to fully employ the properties of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradients is carefully considered. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Neither hypersingularity in the Burton and Miller approach nor the CHIEF concept was required to deal with the problem of irregular frequencies. Five advantages of free of calculating principal value, well-posed algebraic system, convergence rate of exponential order, meshfree and elimination of boundary-layer effect, are achieved by using the present approach. Numerical results are given for the forces and free-surface elevation around the circular boundaries. Also, the near-trapped behavior arisen from the physical resonance is detected. A general-purpose program for water wave impinging several circular cylinders with arbitrary number, radii, and positions was developed. Several examples of water wave structure interaction by vertical circular cylinders were demonstrated to see the validity of the present formulation. 相似文献
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B.A. Mamedov 《New Astronomy》2012,17(3):353-355
A simple evaluation algorithm for calculation of the fermions and bosons relativistic thermodynamic functions with high accuracy is presented. This method is based on the use of the binomial expansion theorems and incomplete Gamma functions. The importance of this result is that it enables a series analytical formula to determine the thermodynamic functions of fermions and bosons in cases of degeneracy and relativity. The formulas obtained are numerically stable for ψ < 0. Examples of comparative calculations are given. Numerical results verify the effectiveness of the present approach and they are in good agreement with literature. 相似文献
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复杂构造地震成像主要取决于叠前地震数据品质、偏移速度可靠性和偏移算子成像精度. 库车坳陷异常复杂的近地表条件导致极低信噪比的地震采集数据. 该区逆冲推覆高陡构造刺穿盐体大面积分布, 盐层厚度变化大、顶底面形态复杂, 盐下断裂带破碎、小断块发育, 形成异常复杂的地震成像问题. 本文重点研究三个关键环节:(1)精细的叠前地震预处理研究: 根据该区地震地质复杂性和地震资料特征, 采用一些新的方法技术和技术组合从振幅与时移的大、中、小尺度变化三个层次来解决资料信噪比问题, 重建深部反射信号; (2)三级偏移速度分析研究:利用库车坳陷盐刺穿逆冲推覆构造建模理论及变速成图配套技术解决叠前时间偏移速度场时深转换问题,利用井约束低频速度地震迭代反演技术解决连井层速度场与偏移速度场的融合问题,实现从DMO速度分析、叠前时间偏移速度分析到叠前深度偏移速度分析的有机衔接,建立拓扑结构相对保持的叠前深度偏移速度模型;(3)基于退化Fourier偏移算子的半解析波动方程叠前时间和深度偏移研究, 极大地改善了地震偏移过程中高波数波的成像问题. 通过对库车坳陷大北、博孜、却勒、西秋4和西秋10等复杂高陡构造的叠前时间和深度偏移地震成像处理,取得了较好的应用效果. 相似文献
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现有的全球大规模空间数据可视化系统主要侧重于影像和地形数据的综合表达,针对矢量与地形的集成可视化能力相对较弱。该文以球面退化四叉树格网(Degenerate Quad-tree Grids,DQG)为基础,通过DQG格网的三角化过程构建了地表DEM模型,并提出了从矢量线对象到地形格网表面的映射方法。采用GTOPO30数据集和国界矢量数据进行了相关实验,结果表明:该方法能实现矢量数据与多分辨率DEM的无缝集成,并能有效地避免矢量对象"悬浮"和"入地"等现象。 相似文献
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Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach 总被引：1，自引：0，他引：1
Jeng-Tzong Chen Po-Yuan Chen Chia-Tsung Chen 《Soil Dynamics and Earthquake Engineering》2008,28(1):58-72
In this paper, the degenerate kernels and Fourier series expansions are adopted in the null-field integral equation to solve the exterior Helmholtz problems with alluvial valleys. The main gain of using degenerate kernels in integral equations is free of calculating the principal values for singular integrals by locating the null-field point exactly on the real boundary. An adaptive observer system is addressed to fully employ the property of degenerate kernels for circular boundaries in the polar coordinate. Image concept and technique of decomposition are utilized for half-plane problems. After moving the null-field point to the real boundary and matching the boundary conditions, a linear algebraic system is obtained without boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a “semi-analytical” solution since error only attributes to the truncation of Fourier series. Earthquake analysis for the site response of alluvial valley or canyon subject to the incident SH-wave is the main concern. Numerical examples including single and successive alluvial valleys are given to test our program. Limiting cases of a single canyon and two successive canyons are also addressed. Amplification of soft basin is also observed in this study. The validity of the semi-analytical method is verified. Our advantages, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence and mesh-free, by using the present method are achieved. 相似文献
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波动方程宽角抛物逼近得到的通常是非常系数的单程波传播算子,其系数是速度横向变化的函数,因此需要利用有限差分(FD)进行数值实施. 通过对Lippmann Schwinger单程波动积分方程的退化核逼近,本文研究了一类宽角退化算子的偏移成像. 这种退化偏移算子只用快速Fourier变换进行波场延拓,将常规的Fourier分裂步地震偏移方法(SSF)推广适应强速度横向变化介质和大角度传播波场. 退化的Fourier偏移算子通过在两个分裂步项之间作波数域线性插值来实现波场延拓,每延拓一层需要比常规的SSF地震偏移方法多一次快速Fourier变换(FFT). 通过SEG/EAGE盐丘模型和实际地震资料的应用表明,退化Fourier偏移算子能很好地对盐下的陡倾角断层和实际地震剖面上的复杂小断块和大断裂地质构造成像. 相似文献
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