論含孔隙導電彈性介質之轉換矩陣之建立 及研析震電波散射問題之應用

On formulation of a transition matrix for electroporoelastic medium and application to analysis of scattered seismoelectric wave

陳思妙(Szu-Miau Chen)

指導教授 ： 葉超雄

國立臺灣大學/工學院/土木工程學研究所/博士(2007年)

https://doi.org/10.6342/NTU.2007.00511

摘要

Pride (1994) 理論藉由融合了Biot (1956) 對於孔隙彈性材料的理論，馬克斯威爾方程式，和通量/力傳輸方程式而來。本論文係基於此理論，並將Pao(1978) 對於彈性介質的推演，和Yeh et al. (2004) 對於彈性多孔隙介質的推導，而建立孔隙導電彈性介質的轉換矩陣。在推導的過程中，將耦合的運動方程式解耦為兩個部份：一部分描述膨脹(dilatational)(縱(longitudinal))波，另一部份描述轉動(rotational)(橫(transverse))波。上述的縱波包括Biot (1962) 理論的快波和慢波，而橫波包括力學剪力波和電磁波。在論文中，也利用Wronskian公式，證明解析形式的基函數具有正交的關係。為了顯示用轉換矩陣法解析震電效應的結果，文中建立一例：在孔隙導電彈性介質中，埋置一異質圓球狀導電孔隙彈性介質，分析當它承受平面入射壓力波時，波的散射現象。

關鍵字

震電波 ； T-矩陣

並列摘要

On the basis of Pride’s theory (1994), which couples Biot’s theory for poroelastic medium (1956) and Maxwell equations via flux/force transport equations, we extend Pao (1978) and Yeh et al. (2004) approaches for elastic medium and poroelastic medium, respectively, to develop a transition matrix for electroporoelastic medium. During the process of derivation, we decouple our motion equations into two parts; one is dilatational (longitudinal) wave and the other is rotational (transverse) wave. The above mentioned longitudinal wave includes the fast wave and slow wave components. Regarding with transverse wave, it includes shear wave and electromagnetic wave. In this thesis, we also utilize the Wronskian formula to prove that our analytical base functions have orthogonality. To illustrate the application, we consider a simple case of the scattering problem of a spherical electroporoelastic inclusion, embedded within the surrounding electroporoelastic medium subjected to an incident plane compressional wave.

並列關鍵字

seismoelectric wave ； transition matrix

參考文獻

施博仁(2004). 向量多極之傅氏譜表示式及其在彈性和孔隙彈性半空間散射問題分析之應用, 國立台灣大學土木工程學研究所博士論文.

Abramowitz, M., and Stegun, I. A. (1964). Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series Vol. 55 (National Bureau of Standards, Washington, DC), Eq. (10.17), 437 pp.

Berryman, J. G. (1985). “Scattering by a spherical inhomogeneity in a fluid-saturated porous medium,” J. Math. Phys. 26, 1408-1419.

Biot, M. A. (1962). “Mechanics of deformation and acoustic propagation in porous media,” J. Appl. Phys. 33, 1482-1498.

Block, G. I., and Harris, J. G. (2006). “Conductivity dependence of seismoelectric wave phenomena in fluid-saturated sediments,” J. Geophys. Res. 111, B01304.