Analyses of scattreing waves due to a scattering object embedded deep site of the layered medium by means of the spectral representaion of Green's function

利用格林函数的光谱表示分析层状介质深层散射物体引起的散射波

• 批准号: 10650469
• 负责人: TOUHEI Terumi
• 金额: $ 1.34万
• 依托单位: Science University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650469/
• 关键词: Green's function; Spectral theory; scattering waves; スペクトル分解; Hyperfunction

This research deals with the spectral representation of Green's function for a layered medium and its application to the scattering problem. Regarding the layered scalar wave field, the procedure for obtaining the spectral representation is rather simple. On the other hand, as for a 3-D layered medium, the precedure of deriving Green's function is not very simple due to the inability of establishing the orthogonality relations of the Rayleigh wave modes. Nevertheless, the concept of the Hyperfunction is found to be applicable to derive the spectral representation of Green's function.The boundary integral equation method as well as the spectral representation of Green's function are introduced to the scattering problem in that the scattering waves are caused by the interaction between a scattering object in a layered medium and a plane wave. The spectral representation of Green's function enables us to introduce a viewpoint of eigenvalue problems into the boundary integral equation method. The scattering waves are decomposed into oeigenfunctions for the point and continuous spectra via interchanging the order of the boundary integral and the spectral integral or summation. As a result, an understanding of scattering waves becomes possible by means of the eigenfunctions for a layered medium.

本文研究分层媒质中绿色函数的谱表示及其在散射问题中的应用。对于分层标量波场，获得谱表示的过程相当简单。另一方面，对于三维层状介质，由于无法建立瑞利波模式的正交关系，推导绿色函数的过程并不十分简单。本文利用超函数的概念导出了绿色函数的谱表示，并将边界积分方程方法和绿色函数的谱表示引入到分层介质中散射体与平面波相互作用的散射问题中。绿色函数的谱表示使我们能够将本征值问题的观点引入边界积分方程方法。通过交换边界积分和谱积分的阶数或求和，将散射波分解为点谱和连续谱的本征函数。因此，散射波的理解成为可能，通过本征函数的分层介质。

项目成果

東平 光生: "Hyperfunction の概念による成層弾性波動場のGreen関数の分岐組積分核の分解について"土木学会論文集. No.640. 231-236 (2000)

Mitsuo Tohira：“利用超函数的概念分解分层弹性波场的格林函数的分叉集积分核”，日本土木工程学会论文集，第 640 期。231-236（2000 年）。

東平光生: "スカラー成層波動場のGreen関数のスペクトル測度を用いた表現"応用力学論文集. vol.1. 585-594 (1998)

Mitsuo Tohira：“使用标量分层波场格林函数的光谱测量表示”《应用力学杂志》第 1 卷（1998 年）。

"Concept of the Hyperfunction to derive the spectral representation of Green's function for a scalar wave field."Journal of Applied Mechanics. vol.2, (in Japanese). 485-493 (1999)

“超函数的概念推导出标量波场格林函数的光谱表示。”应用力学杂志。

東平光生: "離散および連続スペクトルの固有関数を用いた成層弾性波動場のGreen関数の表現"土木学会論文集. No.605. 171-185 (1998)

Mitsuo Tohira：“使用离散和连续光谱的本征函数表达分层弹性波场的格林函数”日本土木工程师学会学报第 605 期。171-185（1998 年）。

"Representation of Green's function for an elastic layered medium in terms of eigenfunctions for the point and continuous spectra."Journal of Structural Mechanics and Earthquake Engineering, (JSCE). No.605, (in Japanese). 171-185 (2000)

“用点和连续谱的本征函数表示弹性层状介质的格林函数。”结构力学与地震工程杂志（JSCE）。