An approximate solution is presented for the surface ground motion on a class of alluvial valleys under incident SH waves. It is based on the existence of a complete family of rays supported by the basin's boundaries. It is approximate, as diffraction is neglected.

This method is developed initially for rigid bases and extended to consider deformable boundary and arbitrary incidence angles. Comparison of results with a more rigorous solution shows very good agreement at a much lower computational effort. Time domain results are presented for different property contrasts and incidence angles.

The method is suited to study time domain resonse of a family of alluvial deposits, due to its low cost and practically no upper frequency limit.

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