Seismic response of a hill: The example of Tarzana, California

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Abstract
The Northridge, California, earthquake that strongly shook the city of Los Angeles in January 1994, produced one of the highest ground accelerations ever recorded in an earthquake, at a site located on top of a small hill in Tarzana, about 6 km south of the epicenter. The subsequent study of aftershock recordings obtained by a dense seismic array deployed on the hill a few days after the earthquake showed the existence of a strong amplification at stations located at the top of the hill, relative to stations near the base (Spudich et al., 1996). Resonances and polarization rotations were also observed. We investigate in this study the role that the topography of the site played on the observed ground motions and accelerations. To this aim, we perform numerical simulations and study the response of the three-dimensional topography of the site to incident shear waves polarized in different directions. The method used is a boundary integral equation scheme in which the Green's functions are calculated by the discrete wavenumber method. The results obtained show that the topography of the site, though quite gentle (the hill is less than 20-m high), strongly affects the ground motions in the frequency range between 2 and 15 Hz. Many of the observed characteristics of the seismic response at Tarzana are explained in part by its topography: the consistent amplification of ground motion at and near the top of the hill, the directional seismic response of the hill that results in a strong amplification of the ground motion transverse to the direction of elongation of the hill, the existence of a fundamental transverse oscillatory resonance mode of the hill at 3 to 5 Hz, the rotation of the polarization of ground motion, and the spatial variation of amplification over the hill at the fundamental resonance mode. The seismic response of the topography, however, does not fully explain the amplitude of the effects observed. The three-dimensional geological structure of the site must in some way amplify the effect of the topography to produce the observed seismic response. In spite of not being as strong as the observed effect, the topographic effect of the site is considerable. The ground motion is amplified by factors ranging from 30% to 100% at some locations in the frequency range from 2 to 15 Hz. Rapid spatial variations of ground-shaking intensities can take place over distance scales of a few tens of meters at high frequency. Finally, the results of the simulation indicate that the topography of the site amplified the large east-west accelerations recorded there during the Northridge mainshock by 30% to 40%.