Site effects can generate large ground motion amplification during earthquakes

and it is important to study the wave field characteristics of layered soil. A new model was presented to compute the diffraction of P and SV waves by a valley embedded in multi-layered half-space. Based on the theory of soil-structure-interaction

the response of scattered wave field could be achieved by the response of free wave field. The layered half-space could be decomposed into near field (the generalized structure

composed of the structure itself and its surrounding soil) and far field (the infinite layered half-space with regular boundaries). The near and far fields of multi-layered half-space were modeled by scaled boundary finite element method (SBFEM) and high-accuracy precise integration method (HPIM)

respectively. The dynamic flexibility coefficients of the far field were solved in the frequency-wave number domain by using the precise integration method and then the results were transformed by the inverse fast Fourier transform within the frequency-space domain. The dynamic stiffness of near field was solved by a continued-fraction-based high-order transmitting boundary of SBFEM. Numerical examples were provided to validate the accuracy and efficiency of the proposed approach. In order to give perspective on the range of effects caused by the trapezoid valley embedded in the soft interlayer site

some examples were presented as well.