The coda of earthquake motions and microtremors are sometimes referred to as diffuse-wave fields. They are generated by the multiple scattering due to the complexity of the Earth. It is accepted that the average cross correlation between the diffuse-field motions at pairs of receivers, in the frequency domain, is proportional to the imaginary part of the Green’s function between these locations. The average autocorrelation of a single receiver is also proportional to the imaginary part of the Green’s function when both the source and receiver are the same. In this study we explored the application of diffuse-field concepts to analyze earthquake records at a site when its site effect can be described using a 1D model. We derived a corollary of Claerbout’s result for a 1D layered medium. We found that the imaginary part of the Green’s function at the free surface is proportional to the square of the absolute value of the corresponding transfer function for a plane, vertically incident wave. We considered a set of incoming plane waves (of P, SV, and SH types) with varying azimuths and incidence angles. After summing up a few hundred synthetics with inclined incidences we obtained horizontal-to-vertical (H/V) spectral ratios that match the ratios estimated from the simple theory of diffuse field. By using observed records in Japan, we found that the earthquake H/V ratios are quite stable and converge rapidly regardless of what part of the waveform is used, except the P-wave part. We also found that their spectral characteristics can be reproduced well by the velocity structures estimated in previous studies. However, theory and observation were not in perfect agreement, which in turn means that the inversion of a 1D structure could be accomplished by adopting the proposed theory for earthquake H/V spectral ratios.

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