本文主要探討彈性波在含兩相流體孔隙介質中折射與反射特性之理論研究，根據Lo et al. (2005) 推導得到的孔彈性理論為基礎並首先加入Lo et al. (2010) 所提出之膨漲運動模式(dilatory motional modes)進而得到在兩個不同的孔隙介質介面中入射低頻震波(P1波或SV波)所產生之折射與反射波的物理特性理論模式。進一步模擬彈性波通過兩層含兩相非混合流體之未壓密土壤，並代入孔隙介質中所包含之兩個流體比例(飽和度)和其孔隙率等土壤相關參數，計算得到不同折射(3個P波和一個SV波)和反射(3個P波和一個SV波)波的振幅比和能量比。結果顯示折射與反射波的振幅比明顯受到入射角的影響，而在每一個入射角度中其所有入射與反射波的能量比總和為1。前人的研究中因為沒有加入膨漲運動模式的概念，會在某些例子中可能得到能量比總和超過1的狀況。當入射SV波時，反射和折射P1波分別會在31和33度出現臨界角度，即各別超過此兩角度時反射和折射P1波的能量比會變成0，此結果與前人的研究相符。最後，觀察折射和反射波的振幅比與水飽和度的關係，並討論影響振幅比變化的重要影響參數。在每一個不同的水飽和度中其能量比總和也等於0，表示沒有能量的損失。很明顯地，反射與折射波的物理特性會受到上層與下層不同水飽和度的影響。

A theoretical model for the analysis of the reflection and refraction of incident elastic waves upon a plane interface between two semi-infinite porous elastic half-spaces respectively saturated by two different fluid mixtures is developed in the present study based on the poroelasticity theory of Lo et al. (2005) and the normal coordinates derived by Lo et al. (2010) for dilatory motional modes. The amplitude and energy ratios of the reflected and refracted waves that simultaneously account for the effect of inertial and viscous couplings are in turn determined theoretically for the first time with respect to the angles of incidence of either an incident P1 (the first dilatational wave) wave or an incident SV (the shear wave polarized in the vertical plane) wave. A numerical simulation is conducted for Lincoln sand permeated by an air-water mixture in the lower half-space and Columbia fine sandy loam permeated by an air-water mixture in the upper half-space as a representative example. Our numerical results indicate that regardless of the type of fluid mixtures and porous media, the sum of the energy ratio of the refracted and reflected waves induced by either an incident P1 wave or a incident SV wave is always equal to unity, a result that can not be achieved if the normal coordinates for dilatory motional modes is not incorporated to represent the Helmholtz potential of elastic waves. It is also shown that the amplitude and energy ratios of the reflected and refracted waves are significantly affected by the angle of incidence of elastic waves. Further, we found that there exists a critical angle of 31 and 33 degrees respectively for the reflected and refracted P1 waves due to an incident SV wave upon the interface while the critical angle is not observed for the case of an incident P1 wave. Lastly, the amplitude and energy ratios of the reflected and refracted waves were computed as functions of water saturation for an illustrative example with Lincoln sand containing an air-water mixture in the lower half-space and Columbia fine sandy loam containing an oil-water mixture in the upper half-space. The result shows that the amplitude ratio of the refracted and reflected P waves was affected by the different physical parameters. The sum of the energy ratio at the each water saturation is also equal to unity. Evidently, the water saturation at either upper half-space or lower half-space affects the behavior of the reflected and refracted waves.

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