Scattering of SH waves by a semi-cylindrical bump in an inhomogeneous half-space

The wave propagation in an inhomogeneous half space with a semi-cylindrical surface bump is investigated by the means of complex function method. With the origin of the coordinate system as the center, the density of the medium changes radially. To solve the Helmholtz equation with variable coefficients caused by the inhomogeneous of the medium, a conformal transformation technique based on the theory of complex variable functions is adopted. Then, by adjusting the inhomogeneous parameters and comparing with the published analytical results, the correctness of the method in this paper is verified. Finally, the displacement amplitudes of typical observation points on the surface and inside are given, and the effects of incident wave angle,