## 4 Field Tests of the GFZ-WISE
### Methodology of Surface-Wave Analysis  
Consistent and reliable estimates of parameters related to site effects from seismic noise measurements are commonly retrieved from the analysis of the horizontal-to-vertical (H/V) spectral ratio curve [e.g., 28,29], and the Rayleigh wave dispersion curves (RWDC) (e.g., [3,5,7,30-33]). Microtremors are highly variable and irregular assemblages of seismic waves (e.g., body waves, surface waves, and their related scattered and diffracted phases). Among them, surface waves (_i.e._, Rayleigh and Love waves) are considered to be the dominant and the most coherent component of microtremors. Therefore, when a network (array) of vertical seismometers is used for microtremor recordings, information on the Rayleigh wave propagation in the medium can be extracted. The great interest that seismologists reserved for these waves is mainly justified by the relationship existing between their velocity and the subsoil structure, and in particular the S-wave velocity. Hence, considering that Rayleigh waves sample portions of the subsoil proportional to their wavelengths, and that their phase velocities are strongly conditioned by the S-wave velocities of the layers sampled, they are used to deduce information on the subsoil structure, and in particular on the local S-wave velocity profile. The H/V curve is obtained by single station microtremor recordings. Similarly to the RWDC, also the H/V curves are related to the presence of surface waves in the seismic noise, and in particular to the particle motion, also known as ellipticity, of Rayleigh waves. Therefore, also the H/V provides information on the subsoil structure of a site. Specifically, H/V curves are strongly conditioned by the properties (depth and S-wave velocity contrast) of the interface between the soft sediment and the bedrock. [PERSON] _et al_. [34,35] confirmed that seismic noise H/V curves exhibit a good agreement with the H/V curves obtained from earthquake recordings, especially with regards to the value of the fundamental resonance frequency of the sedimentary cover, and hence provides some indication of the sedimentary cover thickness. Various processing techniques for estimating the Rayleigh and Love wave phase velocities have been proposed [e.g., see 4 for a complete review of methods]. Because of its relative simplicity, at this stage of the system's development, the traditional Extended Spatial AutoCorrelation (ESAC [1,3,4]) method using only the vertical component of ground motion is used for the estimation of the Rayleigh wave dispersion curve. A number of studies [e.g., 3,7,30] have shown that by using RWDC, thecharacterization of the local _S_-wave velocity profile can be obtained with a good accuracy, especially when a priori information about the total sedimentary cover thickness is available in advance. We followed the procedure described by [7] in order to compute the RWDC with the ESAC procedure [3]. Practically, the procedure consists of estimating at each angular frequency \(o\) the experimental, azimuthally averaged space-correlation values _g_(_o_) for every pair of stations by means of [3, 4]:  
\[\phi_{jn}(\omega)=\frac{\frac{1}{M}\sum_{m=1}^{M}\mathrm{Re}\left({}_{m}S_{j_{ m}}(\omega)\right)}{\sqrt{\frac{1}{M}\sum_{m=1}^{M}{}_{m=1}{}^{m}S_{j_{m}}(\omega)} \sum_{m=1}^{M}{}_{m=1}{}^{m}S_{m}(\omega)} \tag{1}\]  
where _m_S_j_m is the cross-spectrum for the _m_th segment of data, between the _j_th and the _n_th stations and \(M\) is the total number of used segments. The power spectra of the _m_th segments at station \(j\) and station \(n\) are _m_S_j_ and _m_S_m_, respectively.