The effect of rainfall on the fundamental frequency and shear wave velocity profile is limited. Various articles have been reviewed on the effect of saturation or non-saturation on shear wave velocity and fundamental frequency. yang 2001, yang 2006 has investigated that the effect of full saturation and partial saturation on the shear wave velocity is negligible, and on the other hand, the compressive wave velocity can be significant.

Another recent reference directly addressing the topic of impact of rainfall of S-wave velocity : Roumelioti, Z., Hollender, F., & Guéguen, P. (2020). Rainfall‐induced variation of seismic waves velocity in soil and implications for soil response: What the ARGONET (Cephalonia, Greece) vertical array data reveal. Bulletin of the Seismological Society of America, 110(2), 441-451, with the main results in the abstract below:

"We apply interferometry by deconvolution to compute the shear-wave velocity in shallow sediments (0–83.4 m) based on earthquake records from a vertical accelerometric array (ARGOstoli Network [ARGONET]) on Cephalonia Island, Greece. Analysis of the time varia- tion of measured values reveals a cyclical pattern, which correlates negatively to rainfall and a soil moisture proxy. The pattern includes a sharp reduction in velocity at the beginning of rainy seasons and a gradual rise toward dry periods, the overall variation being around 20%–25% within the shallowest depth interval examined (0–5.6 m) and estimated to reach 40% within the top 2 m. The variation itself and its amplitude are verified by surface-wave dispersion analysis, using ambient vibration data. Synthetic standard spectral ratios suggest that this seasonal effect leaves an imprint on soil response, causing differences in the level of high-frequency ground motion between dry and rainy seasons, and this is verified by earth- quake records. Furthermore, the near-surface velocity decrease due to soil saturation can be of the same order of magnitude as the nonlinear coseismic variation, masking the physical process of the nonlinear response of the site due to weak-to-strong-motion shaking. Thus, seasonal variations of seismic-wave velocities in shallow sediments may be important for a number of site-effect related topics, such as high-frequency ground-motion variability, soil anisotropy, kappa measurements, nonlinear site response, and so on."

I think after rainfall velocity decrease about 20-30% only for first layer of soil and no change in velocity for deeper layers and of course no change in fundamental resonance frequency but we could see change in amplitude.

It may be of your interest the next couple of papers relating the Topic and the references they cite :

Article On the use of the microtremor HVSR for tracking velocity cha...

Article HVSR Analysis of Rockslide Seismic Signals to Assess the Sub...

When we studied the variability of the HVSR curves in an urban site with a high level of enthropic noise sources during 35 recording days, we noticed that after heavy rainfall, the amplitude of the fundamental peak frequency seriously decreased for about a week, but after that the trend of the HVSR curves became normal as on the other recording days. This means that rainfall affects the fundamental frequency as well as the velocity profile for a period.

You can reffer to our work [Benkaci et al 2018: During the heavy rainfalls that occurred from day 22 to day 28, cumulating 82 mm of rain (Figure 4d), the stadium construction stopped. During this period, peak1 amplitude is consistently lower than usual between 6:00 am and 6:00 pm, while peak2 amplitude remains the same (Figure 4)].

Fundamental frequency is related to the frequency of resonator. For thick layers (e.g. > 40-50 m) you need the variation of physical properties of the entire soil column. In term of water content this means that water should disappear or fill all with a rainfall event. I don't think that rainfall can produce this kind of effect in a thick layer so rapidly. Instead, in the upper 1-2 m rainfall can change physical properties and then it is possible to observe variation in the H/V amplitude at high frequency (e.g. > 8-9 Hz). In my opinion, the variation of H/V amplitude at low frequency (e.g. < 8-9 Hz), if observed, it is mainly due to the variation of noise wavefield composition (activation or de-activation of local or regional sources). For instance, from summer to winter in some places it is possible to observe some H/V peaks in more clear way (effect of ocean storms or other long period sources). Therefore, I suggest to refer always to the range of frequencies for which you are observing changes due to rain.

We use the bootstrapping method to estimate the uncertainty and variations in the horizontal-to-vertical spectral ratio in different seasons. Although the predominant frequency does not show any seasonal variation, the amplitudes reveal a slight dependence, Ref. Singh et al. 2019, Investigation of spatial and temporal variability of site response in the Arunachal Himalaya using ambient seismic noise and earthquake waveforms, Near Surface Geophysics, 17(4), 427-445

We conducted a single-station microtremor survey using TROMINO at different site locations in Jammu and Kashmir to get resonance frequency and shallow depth shear wave velocity. We observed changes in the HVSR curve due to topographic variation while moving from the Indo-Gangetic plains of Jammu to Kashmir Himalayas. But, no change in the HVSR curve was observed due to the change to the ground water table.