A Literature Review of Seismic Analysis of Topographic Features Subjected to Incident SH-Waves

There are different methods for seismic analysis of topographic features which include analytical، semi-analytical and numerical methods. In the analytical methods extracted from matched asymptotic expansion of wave and Bessel/Hankel functions، responses are presented in terms of summation limit as closed-form solutions. Based on the semi-analytical methods، the problem is decomposed into two primary and secondary parts، which can be solved analytically and numerically. According to what is observed in the nature، the responses of analytical or semi-analytical methods have high accuracy، various types of arbitrarily shaped topographic features cannot be applied for modeling in reality. It results in the development of numerical methods which have good flexibility. These methods can be divided into three types including volumetric، boundary and mixed methods، This paper presented the most important studies that have been conducted in the past half-century (1960-2011) on the mentioned topics. The above mentioned studies are classified based on the used methods، prepared model type and publication year. Despite the development of volumetric methods، such as finite element method (FEM) or finite difference method (FDM) and their simple formulations، the whole body including the inside and boundaries must be discretized in order to model the topography features. This process requires too much time and data. As a result، special attention has been given to the Boundary Element Method (BEM) among the various existing numerical methods during the recent two decades. In this method، only the boundaries of the media need to be discretized in order to analyze an elastic continuous media. Two BEM formulations have been proposed to be used in modeling، including full-plane and half-plane. First، the formulas are classified and the governing boundary integral equations are presented. Then، the related studies based on the full-plane and half-plane fundamental solutions are reviewed. It is worth mentioning that out-of-the-plane wave (SH wave) has been considered as the case study in all studies investigated in this paper.