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ON EVALUATION OF LAMB'S INTEGRALS FOR SEISMIC WAVES IN A THREE-DIMENSION ELASTIC HALF-SPACE

机译:三维弹性半空间中地震波的羔羊积分估计

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摘要

The analytical method such as the boundary integral (element) method or the series expansion method is usually used to solve the wave scattering problem. In these methods, the singular Green's function should be determined firstly; the main difficulty of the use of the Lamb's singular solutions in integral form to represent the diffracted fields is the numerical implementation for the evaluation of those improper integrals. The integrands of these integrals are highly irregular and oscillatory. In this paper, a technique is proposed to calculate the integral in wave-number domain based on the method of steepest descent. After replacing the original integration path by steepest decent path, the wave-number integral results in a Gauss-Hermite type quadrature, so the oscillating characteristics of the original integrand can be removed and results a non-oscillating integrand, it is very helpful in computing efficiency.
机译:通常使用诸如边界积分(元素)法或级数展开法之类的分析方法来解决波散射问题。在这些方法中,首先应确定奇异的格林函数;使用积分形式的Lamb奇异解来表示衍射场的主要困难是对那些不正确积分进行评估的数值实现。这些积分的被积是高度不规则和振荡的。本文提出了一种基于最速下降法的波数域积分计算技术。用最陡的体面路径替换原始积分路径后,波数积分会导致高斯-赫尔米特型正交,因此可以消除原始积分对象的振荡特性,从而得到非振荡积分对象,这对计算非常有帮助效率。

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