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SUMMARY Topographies have significant effects on seismic waves. The wavefunction expansion method has been frequently employed to study the topographic effect because this method can reveal the physics of the wave scattering and can testify the accuracy of numerical methods. The 2‐D scattering and diffraction of plane SH waves induced by a non‐symmetrical V‐shaped canyon is examined here by using the wavefunction expansion method. Through a new domain decomposition strategy, the half‐space containing a V‐shaped canyon is divided into three subregions. Then the wavefield for every subregion is constructed in terms of an infinite series of wavefunctions with unknown coefficients in three coordinate systems, respectively. After that, three wavefields are all represented in the same coordinate system using the Graf addition theorem. The unknown coefficients are obtained by satisfying the continuity conditions of the auxiliary boundary. The proposed series solution of wavefunctions for a non‐symmetrical V‐shaped canyon can be reduced to a symmetrical case. Results in this study for the symmetrical case agree very well with those in the published literature. To show the effects of the non‐symmetrical‐geometry topography on the surface ground motion, a parametric study is carried out in the frequency domain. Surface and subsurface transient responses in the time domain demonstrate the phenomenon of wave propagating and scattering. Finally, the proposed model is successfully applied to two idealized cross sections of Pacoima canyon and Feitsui canyon.

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