近年來隨著地震學的成熟，學者開始遍尋能夠量化地震能量的方法，在認定地震必然發生的前提下，結合其他領域如地質學以評估各地的危害程度，此重要的依據即為本文探討的地震表面波。相較以往各向同性介質的波傳假設，自然界的沉積岩會隨著深度方向有所差異，因此本文以橫斷面等向性材料模擬廣大的地球表面，其中除了岩層的基底還包含了一層較鬆軟的土壤作為導引層，並考慮地震發生後是以點波源的形式，向四周發出時諧的擾動。本文首先透過交換定理，推導得出表面波的位移解，其遠場行為與既有文獻相比並無差異，接著藉由實際數值的材料參數，發現較大的彈性模數C33以及較小的彈性模數C13、C44皆能降低因垂直載重所引發之位移場，最後引入超材料的導引層進行分析，結果顯示即使是等向性的材料，仍可以憑著極端特性達到預期的目標。

We investigate the surface wave field generated by a time-harmonic point load, which is applied in a finite-thickness layer joined to a half-space. In this thesis, both the top layer and the semi-infinite space are considered to be transversely isotropic, in a simulation of sediments where seismic waves travel. Firstly, closed-formed solutions of surface waves are derived from elastodynamic reciprocity theorem. The far-field motion obtained by the method is identical to that of the existing literature. Secondly, the effects on the propagation of surface waves in a transversely isotropic domain are numerically analyzed. We find that a greater value of elastic modulus C33 and smaller values of elastic modulus C13, C44 are able to attenuate the displacement field caused by a normal load. Lastly, metamaterials with negative Poisson’s ratio and with extremely low shear rigidity are considered in the wave phenomena. The results suggest that even isotropic media can still achieve some desired objectives with a top layer of extreme properties.

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