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Layer model description of the SH seismic response in anisotropically-idealized cities

ABSTRACT A city, modeled as a periodic (along one direction) assembly of blocks, infinitely long along another direction, covering a soft layer over a hard half space, lends itself to a rigorous theoretical analysis of its shear-horizontal (SH) response to a seismic body wave. This theory gives rise to two sets of linear equations, the first for the amplitudes of the waves in a generic block, and the second for the amplitudes of the waves in the hard half space. The first set is solved numerically to furnish reference solutions. The second set is submitted to low-frequency, dense city, approximation procedure whereby the displacement fields are just those for a site/city configuration in which the city is a homogeneous layer of the same thickness as the height of the blocks in the city. A simple formula is derived for the constitutive properties of this layer in terms of those of the blocks. The homogeneous layer model displacement transfer functions and spectral absorptance reproduce quite well the corresponding rigorous numerical functions throughout the generic block or surrogate layer of the city. Due to its simplicity, the homogeneous layer model enables theoretical predictions of key features of the site/city seismic response.