The methods of complex variable function and Green’s function are applied to derive analytical solutions to the scattering of SH-waves induced by a buried elliptic inclusion near a vertical interface in the elastic half space. Firstly

the analytical model to be solved is divided into two rectangular domains along the vertical interface. The conformal mapping method was used to map the outer boundary of the elliptic inclusion into a unit circle in the domain I. Moreover

in these two domains

the method of images is applied to construct scattering wave fields and an applicable Green’s function satisfying boundary conditions of rectangular domains. Secondly

with the aid of interface ‘conjunction’ technique

infinite algebraic equations are established by adding an additional system of forces at the interface and then solved by truncation

which meets the displacement and stress continuity conditions at the interface. Finally

some specific examples are given to estimate surface displacement amplitudes. Numerical results show that incident wave

incident angle

the position of inclusion

material properties and vertical interface to some extent affect the distribution of ground surface displacement.