  We address the problem of the response to a seismic wave of an urban site
consisting of a large and infinite number ($N\_{b}$) of identical, equispaced
blocks overlying a soft layer underlain by a hard substratum. The results of
the theoretical analysis, appealing to a space-frequency mode-matching (MM)
technique, are compared to those obtained by a space-time finite element (FE)
method. The two methods are shown to give rise to much the same prediction of
seismic response for $N\_{b}=10$. The MM technique is also applied to the case
$N\_{b}=\infty$, notably to reveal the structure and natural frequencies of the
vibration modes of the urban site. The mechanism of the interaction between
blocks and the ground, as well as that of the collective effects of the blocks,
are studied. It is shown that the presence of a large number of blocks modifies
the seismic disturbance in a manner which evokes, and may partially account
for, what was observed during many earthquakes in Mexico City. Disturbances at
a much smaller level, induced by a small number of blocks are studied in the
companion paper.
