While using the big circle method, Fourier Bessel series expansion technique, and the coordinate conversion of Graf's addition formula, an analytical solution for the scattering of non concentric arc layered alluvial valleys subjected to plane primary waves was derived. Then the precision of the numerical result was checked up and analyzed. Finally, by using the analytic solution, the surface displacement was analyzed at different shear wave velocity of covering layer. The analysis results show that shear wave velocity change has little effect on the crest value of displacement at lower frequency incidence, however the influence becomes significant with the increase of incident frequency. In general, lower the shear wave velocity is, higher the crest value of displacement will be. Compared with the existing conclusions, the covering thickness variation has little effect on the influence of shear wave velocity change on the scattering of elastic waves.
