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If I use the DINVER program to invert only HVSR data, as in my case, what are the inverted data?
Only the peak frequencies, as in the case of join inversion?
If so, what and how many parameters are used in the inversion?
I feel that all the space of parameters is inverted. Is it possible?
In my case, I can fix the thicknesses, which are known from drilling data. Is it necessary to fix also two more parameters (density and Poisson ratio) and
to invert only for one (S-wave velocity)?

There are two ways for inverting single station measurements:

1. Only the frequency of the HVSR peak
2. The shape of the curve interpreted as the Rayleigh ellipticity curve

The second option is only possible if a true Rayleigh ellipticity is extracted out of H and V signals. Simple techniques such as the one implement in geopsy HV module is not sufficient. A specialized module like HVTFA (based on wavelet transform) can extract the ellipticity is some cases. There are also methods like RayDec (Hobiger et al. 2009) to be implemented soon in geopsy. Only the first one is discussed here below though some recommendations may also be valid for the second one.

You can try to invert all the parameters you want like for a dispersion curve inversion. However, with only the peak of the HVSR, past studies have shown that there is a big trade-off between depths and velocities (Scherbaum et al. 2003). You cannot invert both with HVSR only. Density and Vp have almost no influence on ellipticity peak, so it's better to fix them to some realistic values.

Poisson's ratio is never inverted in Dinver. It is not a parameter like Vs, Vp and density. The limits you can set up in Dinver are just conditions, which means that Poisson's ratio is forced to be inside the specified range for all generated models. In future releases (currently only in the development branch), it is possible to fix Poisson's ratio to a constant value. In this case only, Vp is no longer a parameter but it becomes a condition as well.

This is normal behavior that all the parameter space is covered with equally good models. This proves that the inversion algorithm performs very well at exploring nearly all areas of the solution and that no resolution can be obtained without providing prior information (boreholes, dispersion curve,...).

If you have reliable data from drilling and if a clear contrast can be identified in the lithology which supports a drastic change in the shear wave velocity, then you can fix depths, eventually with a very small range. For instance from 22 to 23 m if you suspect some alteration layers or if you feel uncertain, better than a fixed 22.5.

References:

• Hobiger, Manuel, Pierre.-Yves Bard, Cecile Cornou, and Nicolas Le Bihan. "Single station determination of Rayleigh wave ellipticity by using the random decrement technique (RayDec)." Geophysical Research Letters 36, no. 14 (July 2009): 0-4. doi:10.1029/2009GL038863.
• Scherbaum, Frank, Klaus.-G. Hinzen, and Matthias Ohrnberger. "Determination of shallow shear wave velocity profiles in the Cologne/Germany area using ambient vibrations." Geophys. J. Int. 152 (2003): 597-612.