During this work, numerous ground models and parameterizations have been tried while developing the inversion software. In the next sections, the influence of the parameterization is illustrated through inversion examples with a common reference ground model. This latter one is made of three layers including the bottom half space. The properties of each layer are specified in table 4.1. The velocity profiles, the dispersion and the ellipticity curves are shown in figure 4.1.
The fundamental Rayleigh curve of figure 4.1(b) is considered in the next section as the data curve that would have been obtained by any of the experimental methods presented in chapter 1. Various inversion schemes are tried to retrieve the original velocity profiles. The other curves are used in chapter 5 where more specialized inversions are reviewed.
Contrary to synthetic curves that can be calculated on any arbitrary frequency interval, the experimental curves are generally available on a restricted frequency band. Because there is a close relation between the depth and the signal frequency content (section 3.1.8), the quality of inversion strongly depends upon the frequency range of the measured dispersion curve. Scherbaum et al. (2003) showed that the energy on the vertical component drastically decreases in the vicinity and below the fundamental frequency of the soil structure. Rayleigh dispersion curves are currently best measured on the vertical components, perpendicular to the free surface. It implies that the uncertainties on the apparent velocity determination below the threshold frequency are usually significant and limit the range of available dispersion curves. From the shape of the ellipticity (figure 4.1(d)), this effect is assumed to occur below 5.5 Hz. Actually, the ellipticity curve has two maxima at 2.5 and 5.5 Hz. Hence, the energy on the vertical component might be still sufficient below 5.5 Hz. In the absence of ambient vibration simulations for this case, we cannot predict the value of the peak frequency of the measured H/V and thus the magnitude of the high-pass filter effect. Hereafter, two cases are considered: a broad band (0.2 to 20 Hz) and a narrow band (5.5 to 15 Hz) dispersion curve. The second one is probably closer to frequency range obtained for real experiment with Rayleigh waves.
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profile. (b) Dispersion curve for the fundamental (solid) and the first higher mode (dots) of Love (grey) and Rayleigh (black). (c) 
profile. (d) Rayleigh fundamental ellipticity.