近年隨著地震學不斷發展，在地震發生不可預測的情況下，許多研究便朝向結構物強度提高與能量消散著手，並也開始出現有別於以往在結構物本身而是結構物以外的區域去設計，本文即是針對地層表面額外配置的導引層來達到先行減緩地震波的目的。材料異向性比較於各向同性的假設更貼近現實，並在性質上有所差異但也相對增加複雜性，而自然界地表常見的沉積岩層則是隨著深度方向變化，因此本文以橫斷面等向性的假設作為分析依據，並採用不同外加時諧點載重的形式，以同時考量產生的各種表面波。本文在計算推導上使用交換定理來處理複雜材料與分層結構，並得到表面波之解析解，再代入實際數值後發現較小的材料參數能有效放大位移場而釋放地震能量，尤其是縱向剪力模數影響最為明顯，最後結合新興領域之超材料的概念，結果表現出與橫斷面等向性材料相同的位移趨勢，且憑藉其極端特性而達到更好的效益。

This aim of this thesis is regarding the energy attenuation of seismic waves. In contrast to the conventional half-space medium, we consider an additional finite–thickness layer on the top of the half-space to serve as an additional layer with possible different material properties. In addition, we consider the material anisotropy effect. Specifically, we consider the media could be transversely isotropic, in simulation of the common sedimentary rock on the Earth's surface. Firstly, we investigate the surface wave subjected to a vertical and horizontal time-harmonic point load in the transversely isotropic layered medium. The surface wave fields generated by loads of other directions can be superposed by the two solutions of vertical and horizontal loads. Closed-formed solutions are derived from elastodynamic reciprocity theorem instead of the integral transform methods. Secondly, it is found by our numerical analysis that smaller values of elastic parameters will magnify the displacement fields for energy attenuation. Lastly, we consider the wave motion in the layered medium by using metamaterials with extreme properties. The results demonstrate similar phenomena as the transversely isotropic media, but will give better effect.

Achaoui, Y., Ungureanu, B., Enoch, S., Brûlé, S. and Guenneau, S., Seismic waves damping with arrays of inertial resonators, Extreme Mechanics Letters 8: 30-37 (2016).

Achenbach, J. D., Calculation of surface wave motion due to a subsurface point force: An application of elastodynamic reciprocity, J. Acoust. Soc. Am. 107: 1892-1897 (2000).

Achenbach, J. D., Lamb waves as thickness vibrations superimposed on a membrane carrier wave, J. Acoust. Soc. Am. 103: 2283-2286 (1998).

Achenbach, J. D. and Xu, Y., Use of elastodynamic reciprocity to analyze point-load generated axisymmetric waves in a plate, Wave motion 30: 57-67 (1999).

Achenbach, J. D. and Xu, Y., Wave motion in an isotropic elastic layer generated by a time-harmonic point load of arbitrary direction, J. Acoust. Soc. Am. 106: 83-90 (1999).

Achenbach, J. D., Wave Propagation in Elastic Solids, North Holland (1973).

Achenbach, J. D., Reciprocity in Elastodynamics, Cambridge University Press (2003).

Ammon, C. J., Velasco, A. A., Lay, T. and Wallace, T. C., Foundations of modern global seismology, Academic Press (2020).

Arfken, G. and Weber, H., Mathematical Methods for Physicists, Academic Press (2005).

Bertoldi, K., Vitelli, V., Christensen, J. and van Hecke M., Flexible mechanical metamaterials, Nat. Rev. Mater. 2: 1-11 (2017).

Betti, E., Teoria dell'elasticità, II Nuovo Cimento 7: 69-97 (1872).

Bose, J. C., On the rotation of plane of polarization of electric wave by a twisted structure, Proceedings of the Royal Society of London 63: 146-152 (1898).

Chao, C. C., Dynamical response of an elastic half-space to tangential surface loadings, J. Appl. Mech 27: 559-567 (1960).

Deutsch, W. A., Cheng, A. and Achenbach, J. D., Focusing of Rayleigh Waves: Simulation and Experiments, IEEE Transactions of Ultrasonics, Ferroelectrics, and Frequency Control 46: 333-340 (1999).

Kulkarni, S. S. and Achenbach, J. D., Application of the reciprocity theorem to determine line-load-generated surface waves on an inhomogeneous transversely isotropic half-space, Wave motion 45: 350-360 (2008).

Lamb, H., On the propagation of tremors over the surface of an elastic solid, Phil. Trans. R. Soc. A203: 1-42 (1904).

Lamb, H., On waves in an elastic plate, Proc. R. Soc. A93: 114-128 (1917).

Lang, H. A., Surface displacements in an elastic half-space, Z. angew Math. Mech. 41: 141-153 (1961).

Liu, Z. Y., Zhang, X. X, Mao, Y. W., Zhu, Y. Y., Yang, Z. Y., Chan, C. T. and Sheng, P, Locally resonant sonic materials, Science 289: 1734-1736 (2000).

Molina, O., Vilarrasa, V. and Zeidouni, M., Geologic carbon storage for shale gas recovery, Energy Procedia 114: 5748-5760 (2017).

Miller, G. and Pursey, H., The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid, Proc. R. Soc. A223: 521-541 (1954).

Miniaci, M., Krushynska, A., Bosia, F. and Pugno, N. M., Large scale mechanical metamaterials as seismic shields, New Journal of Physics 18: 083041 (2016).

Mitra, M., Disturbance produced in an elastic half-space by impulse normal pressure, Math. Proc. Cambridge Philos. Soc. 60: 683-696 (1964).

Pendry, J. B., Negative refraction makes a perfect lens, Physical Review Letters 85: 3966-3969 (2000).

Pekeris, C. L., The seismic surface pulse, Proc. Natl. Acad. Sci. U. S. A. 41: 469-480 (1955).

Phan, H., Cho, Y. and Achenbach, J. D., Application of the reciprocity theorem to scattering of surface waves by a cavity, Int. J. Solids Struct. 50: 4080-4088 (2013).

Phan, H., Cho, Y., Le, Q. H., Pham, C. V., Nguyen, H. T. L., Nguyen, P. T. and Bui, T. Q., A closed- form solution to propagation of guided waves in a layered half-space under a time-harmonic load: An application of elastodynamic reciprocity, Ultrasonics 96: 40-47 (2019).

Rayleigh, L., On waves propagated along the plane surface of an elastic solid, Proc. Lond. Math. Soc. 17: 4-11 (1885).

Rayleigh, L., Some general theorems relating to vibration, Proc. Lond. Math. Soc. 4: 366-368 (1873).

Santos, J., Catapang, A, N. and Reyta, E. D., Understanding the fundamentals of earthquakes signal sensing networks, Analog Dialogue 53(4) (2019).

Shelby, R. A., Smith, D. R. and Schultz, S., Experimental verification of a negative index of refraction, Science 292: 77-79 (2001).

Smith, D. R., Pendry, J. B. and Wiltshire, M. C., Metamaterials and negative refractive index, Science 305: 788-792 (2004).

Sokolnikoff, I. S. and Specht, R. D., Mathematical Theory of Elasticity, McGraw-Hill New York (1956).

Stoneley, R., Elastic waves at the surface of separation of two solids, Proc. R. Soc. Lond. A106: 416-428 (1924).

Veselago, V. G., The electrodynamics of substances with simultaneously negative values of ε and μ, Physics Uspekhi 10: 509-514 (1968).

Woods, R. D., Screening of surface waves in solids, Journal of the Soil Mechanics and Foundations Division 94: 951-979 (1968).

Xu, L., Wang, K., Su, Y., He, Y., Yang, J., Yuan, S. and Su, Z., Surface/sub-surface crack scattered nonlinear Rayleigh waves: A full analytical solution based on elastodynamic reciprocity theorem, Ultrasonics 118: 106578 (2022).

Yu, X., Zhou, J., Liang, H., Jiang, Z. and Wu, L., Mechanical metamaterials associated with stiffness, rigidity and compressibility: A brief review, Progress in Materials Science 94: 114-173 (2018).

郭典愷，洛夫波於橫斷面等向性介質與地震超材料之波傳互制行為，成功大學土木工程學系碩士論文 (2019)。

何瑞堂，具雷利波頻散效應之地震超材料於橫斷面等向性介質之設計與模擬，成功大學土木工程學系碩士論文 (2019)。

陳柏廷，表面波之位移場量在橫斷面等向性分層介質的行為探討，成功大學土木工程學系碩士論文 (2021)。