A study on the scattering field of SH-waves in a topographical area consisting of a semi-cylindrical hill and a subsurface horizontal hole

Abstract

This research intends to investigate the scattering field of SH-wave in a half-space containing a semicylindrical hill and a subsurface horizontal hole. A mathematical model is established in a two-dimensional plane on the basis of the characteristics of SH-waves, the ‘division-conjunction’ concept, the complex function, and moving-coordinate methods. The whole domain considered is divided into two subdomains, and the wave expressions are assumed in each subdomain. In the cylindrical subdomain, the wave function is constructed with the satisfaction of the zero-stress condition on the hill's surface automatically. In the other subdomain, the solution of the scattering waves is postulated under the stress-free condition on the horizontal surface. The analytical solutions of themodel established are obtained through a series of infinite linear algebraic equations, under the conditions that both the stress and displacement across the conjunction interface of the two subdomains are continuous. The numerical solutions are developed by truncating the infinite linear algebraic equations. The numerical simulations are performed for quantifying the displacements of the horizontal and semicylindrical hill surfaces subjected to incident SH waves, and the numerical results are verified with a comparison to the existing results of a case without subsurface hole.