Study on the Sh-Waves Scattering and Focusing by a Semi-Elliptical Mountain

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Project title

Code/計畫編號

NSC98-2221-E019-019

Translated Name/計畫中文名

半橢圓形山峰引致SH波散射及聚焦之研究

Project Coordinator/計畫主持人

Deng-How Tsaur

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=1914744

Year

2009

Start date/計畫起

01-08-2009

Expected Completion/計畫迄

01-07-2010

Bugetid/研究經費

474千元

ResearchField/研究領域

土木水利工程

"關於凸起地形對地震波的影響，過去有很多研究者採用不同的方法研究過幾種不同的地形，例如：半圓形、圓弧形、三角形、矩形、半橢圓形、半正弦形…等等。就我們所知，針對半橢圓形凸起地形的研究並不多，目前所知的有採用直接邊界元素法以及複變函數法來求解任意凸地形者，其中有半橢圓形凸起地形的計算例而已，還沒有人以理論解析的方式來求解這個問題。再者，根據法國學者Semblat 研究沖積山谷的經驗，以及我們研究圓弧形凸起地形的經驗發現，會有地下聚焦的現象，此一現象可能會對地下結構物產生重要的影響。因此，本研究將採用領域媒親法及波函數展開法來分析半橢圓形山峰的SH 波散射以及可能產生的聚焦現象。首先，我們引入一個半橢圓形輔助邊界，其將整個求解領域分割成一個橢圓領域和一個半無限領域，然後各領域的位移場以 Mathieu 函數展開來表示，由於Mathieu 函數是橢圓座標系統下的波函數，所以，藉由它來分析半橢圓形山峰的問題是最適合的。接著再以滿足輔助邊界上的連續條件，以及山峰表面的無曳引力邊界條件來建立聯立方程式，即可決定各領域的未知係數。最後，我們將針對不同參數，計算半橢圓形山峰的地表位移振幅、地下位移振幅的譜變化及地下位移場的分佈，並進行討論其散射及聚焦的情形，以供地震工程研究之參考。" "Concerning the effect of convex topography on the seismic waves, many researchers have used different methods to study the topographies in different shapes, such as semi-circle, circular arc, triangle, rectangle, semi-ellipse and semi-sine. To our knowledge, the investigations on the convex semi-elliptical topography are rare. Such a shape is only one of numerical cases in the studies of arbitrary shaped topographies in which the direct boundary element method and the complex variable method are used. Up to now, none applies the theoretical analysis method to deal with this problem. Furthermore, according to the experience of Semblat, who is the researcher in France, in analyzing alluvial basins and our experience in studying the convex circular-arc topography, the phenomenon of subsurface focusing will occur, which may have significant influence on underground structures. Therefore, in this work, the SH-waves scattering and focusing by a semi-elliptical mountain will be investigated via the region-matching technique and the method of wavefunction expansion. At first, the entire domain is decomposed into an elliptical domain and a semi-infinite domain by introducing a semi-elliptical auxiliary boundary. The displacement field of each domain is expressed in terms of an expansion of Mathieu functions. Since Mathieu functions are the wavefunctions in the elliptical coordinate system, using them to analyze the problem of semi-elliptical mountains is very feasible. After imposing the matching conditions on the auxiliary boundary and the traction-free condition on the mountain surface, the unknown coefficients in each domain can be determined. Finally, the surface displacement amplitudes, spectral variation of underground motions and the distribution of underground wavefields will be calculated for different parameters. The phenomena of scattering and focusing will be also discussed. We deeply hope this work can be taken as references for other studies in the field of earthquake engineering."

Keyword(s)

SH 波
山峰
散射
聚焦
SH waves
mountain
scattering
focusing

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Study on the Sh-Waves Scattering and Focusing by a Semi-Elliptical Mountain

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