A new hybrid two-step method for computation of P-SV seismic motion at inhomogeneous viscoelastic topographic structure is presented. The method is based on a combination of the discrete-wavenumber (DW), finite-difference (FD), and finite-element (FE) methods. In the first step, the DW method is used to calculate the source radiation and wave propagation in the background 1D medium. In the second step, the FD-FE algorithm is used to compute the wave propagation along the topographic structure.

The accuracy of the method has been separately tested for inclusion of the attenuation and for inclusion of the free-surface topography through numerical comparisons with analytical and independent numerical methods.

The method is a generalization of the hybrid DW-FD method of Zahradník and Moczo (1996) for localized structures with a flat free surface.

Numerical computations for a ridge, sediment valley, and the ridge neighboring the sediment valley show that a ridge can considerably influence the response of the neighboring sediment valley. This means that the neighboring topographic feature should be taken into account even when we are only interested in the valley response.

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