The theoretical response of sedimentary layers to ambient seismic noise

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Abstract
For over thirty years, attempts have been made to gain information about sediment amplification during earthquakes from observations of ambient seismic noise. While the results of several feasibility studies have been encouraging, theoretical support for the technique is scant. We present a model for the response of sedimentary layers to ambient seismic noise. The noise sources are modeled as a random distribution (in time and space) of point forces located on the Earth's free surface. This model is applied to a site where observed noise spectral ratios, relative to a rock site, have previously been shown to reveal the fundamental resonant frequency of a soft clay layer. Approximating the sediment site as a single layer over a half‐space, the horizontal noise spectrum predicted by our model reveals the fundamental resonance and first harmonic of the layer. We also examine an estimate of site response proposed by Nakamura (1989), which is formed by dividing the horizontal‐component noise spectrum by that of the vertical component. Nakamura's estimate applied to both observed and predicted noise‐spectra was also successful in identifying the fundamental resonance, with a slight (<10%) shift toward lower frequencies. Future work is needed to determine the generality of our results, and to elucidate the influence of the simplifying assumptions.