Two-dimensional ground motion at a soft viscoelastic layer/hard substratum site in response to SH cylindrical seismic waves radiated by deep and shallow line sources - I. Theory

We consider, using theory (herein) and associated synthetic seismograms (in a companion paper), the seismic response of a site comprising a horizontal, homogeneous, soft viscoelastic layer of infinite lateral extent overlying, and in welded contact with, a homogeneous, hard elastic substratum of half-infinite radial extent. We show that for shear-horizontal motion: (1) coupling to Love modes is all the stronger the closer (in the vertical direction) the source (modelled as a line, assumed to lie in the substratum) is to the lower boundary of the soft layer, (2) all anomalous features (such as long duration) of the seismic wavefield, including those for regional earthquakes, are primarily the result of strong excitation of Love modes, (3) 1-D (body wave) type of response is: non-resonant, obtained for deep sources and usually characterized by relatively short durations, (4) for shallow sources and hypocentral distances that are not very large, the response results from a complex interplay of Love mode and body wave contributions, which requires a numerical description (furnished in the companion paper).