An analytical solution to the scattering of cylindrical SH waves by a partially filled semi-circular alluvial valley: near-source site effects

The earth's surface irregularities can substantially affect seismic waves and induce amplifications of ground motions. This study investigates whether and how the source characteristics affect the site amplification effects. An analytical model of a line source of cylindrical waves impinging on an alluvial valley is proposed to link the source and site. The analytical solution to this problem proves one aspect of the strong effect of source on site amplification, i.e., the wave curvature effect. It is found that the site amplification depends on the source location, especially under conditions of a small source-to-site distance. Whether the displacement is amplified or reduced and the size of the amplification or reduction may be determined by the location of the source. It is suggested that traditional studies of site responses, which usually ignore the source effect, should be further improved by combining the source with site effects.