An extension of the Aki-Larner technique to vertically inhomogeneous media is presented, so that vertical velocity gradients may be taken into account in two-dimensional models. Only SH waves are considered here, but the theory is valid for P and SV waves as well.

This method is applied to investigate the seismic response of two-dimensional sedimentary deposits with large velocity gradients. Three different cases are considered: a shallow, high-contrast valley, a deep, high-contrast valley, and a deep, low-contrast valley. In each case, a comparison is performed with the results of a two-dimensional model taking into account only homogeneous sediments and a one-dimensional model taking into account the vertical inhomogeneity of sediments.

The presence of a large velocity gradient does not change a lot the qualitative behavior of a two-dimensional deposit: local surface waves and/or two-dimensional resonance patterns are observed as in the case of homogeneous sediments. Nevertheless, the surface waves are much more dispersive with lower phase and group velocities and larger amplitudes. Only very deep valleys give rise to the development of two-dimensional resonance.

On the other hand, the amplifications obtained in such deposits may reach much larger values than those predicted with either two-dimensional, homogeneous models or one-dimensional, inhomogeneous models. Since these results have been obtained for realistic values of valley geometrical and mechanical considerations, they should find some application in earthquake engineering or seismic microzonation studies.

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