圆弧状凹陷地形对平面P波的散射:高频解答

Scattering of Plane P Wave in Circular-arc-shaped Canyon Topography:High-frequency Solution

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。

An analytical solution to the two-dimension scattering problem of incident plane P wave in the circular-arc-shaped canyon topography with different depth-to-width ratio is deducted from the Fourier-Bessel series expansion of wave functions. Different from the other existing analytical solutions, and with view to ensuring the analytical solution to be valid for higher frequency of incident wave, this paper introduces the asymptotic properties of cylindrical functions to directly determine the unknown coefficients of scattering waves and avoid the solution of linear equation system and the corresponding numerical issues, and thus expands the frequency band in which the analytical solution is valid. A comparison with other existing analytical solutions demonstrates the correctness of the proposed analytical solution. The scattering effects of the circular-arc-shaped canyon to the incident plane P wave are further analyzed in a comparatively broad frequency band.