A method is presented for fast calculations of SH-wave propagation in a class of homogeneous alluvial valleys that can be divided into simple elements for which the scalar Green's functions are determined. Assembling the set of elements allows the analysis of the whole valley. The formulation, exact for rigid bases, is extended to consider deformable boundary and arbitrary incidence angles.

The method was successfully tested for valleys of triangular shape with both analytical and numerical solutions, showing in the latter case a substantial saving of computer time.

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