Statistical correlation of earthquake and ambient noise spectral ratios

The Horizontal-to-Vertical Spectral Ratio from earthquake (HVSR) and from
ambient noise (HVN) recordings realistically indicate the fundamental frequency of soil
response but, for the majority of the worldwide examined sites, they do not provide reliable
amplification curves as calculated by the earthquake standard Spectral Ratio (SSR). Given
the fact that HVSR and especially HVN can be easily obtained, it is challenging to search
for a meaningful correlation with SSR amplification functions for the entire frequency band
and to use the results for the SSR estimate at a further site where only noise measurements
are available. To this aim we used recordings from 75 sites worldwide and we applied a
multivariate statistical approach (canonical correlation analysis) to investigate and quantify
any correlation among spectral ratios. The canonical correlation between SSR and HVN
is then used to estimate the expected SSR at each site by a weighted average of the SSR
values measured at the other sites; the weights are properly set to account more for sites
with similar behaviour in terms of the canonical correlation results between HVN and SSR.
This procedure, repeated for all sites in turn, constitutes the basis of a cross validation. The
comparison between the inferred and the original SSR highlights the improvements of site
response estimation with respect to the use of ambient noise techniques. The goodness and
limitations of the reconstruction procedure are explained by specific geological settings.