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It is well known that ground surface with irregular topographic features causes complicated seismic responses. The complex seismic response is mainly caused by wave scattering. In this study, for a homogeneous, isotropic, linearly elastic half-space, the formulation of a two-dimensional SH-wave field based on the direct boundary element method and Neumann series expansion is developed. By discretizing the ground surface to boundary elements, the boundary integral equation is formulated into a general matrix form. This general matrix form is then reduced to a more efficient form, which considerably reduces the size of the computational matrices using Neumann series expansion. For this purpose, a Fortran computer program is developed, whose accuracy and feasibility in the frequency domain is shown by some numerical analyses conducted for grounds with semicircular convex and concave, and symmetrical V-shaped canyon topographical configurations. Comparing the results of the present study with those available in the literature shows the accuracy of the present study by just considering two first terms of Neumann series expansion. The minor differences of the results of the present research with other reseach results may be assigned to the number of terms of Neumann series expansion and the order of used boundary elements. In other words, if the number of terms of Neumann series expansion and the order of used boundary elements incease, the accuracy of the numerical results may enhance. Based on the results of the present research for various parameters of different two-dimensional canyons, the following conclusions may be obtained: When the exciting frequency increases, the wave-length decreases. As a result, the violence effects of incident wave due to canyon effects may be significant for a given canyon. Moreover, the displacement field of various canyon points follows more complicated pattern. On the other hand, for smaller exciting frequencies with larger wave-lengths, the canyon effects as the main cause of disturbation source are not so remarkable, and the displacement field of various canyon points are smoother. The effects of incident wave angle is also remarkable on the disturbation patterns of displacement field of different canyon points. When the angle increases, the triangle canyons experience more complicated patterns compared to semicircular canyons. Analyses'''' results show important effects of shape and depth of various canyons. These effects are more considerable when depth''''s variations are remarkable in comparison with the wave-length of incident wave. Furthermore, the mentioned effects are functions of frequency and angle of incident wave.

Keywords: Topographical effects, Neumann series expansion, Direct boundary element method, Seismic wave propagation, Forward solution

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