SH waves in a moon-shaped valley

The analytical solution of a two-dimensional moon-shaped alluvial valley embedded in an elastic half-space is analyzed for incident plane SH waves, using the wave function expansion and the Discrete Cosine Transform (DCT). A series of solutions with different depth-to-radius ratios have been computed, analyzed, and discussed. It is shown that amplification of incident motions along the thinning valley segment can be significant. The phenomena of combined action of the waves resulting from (a) turning (reversing the direction of propagation), (b) focusing, and (c) diffraction from the half space into the valley have been examined with an emphasis on the significance for surface-motion amplification and the power to damage man-made structures.