###### Abstract
In the study area, velocity inversion was found to affect the seismic response at the lowest frequencies--close to the fundamental frequency of the deposit (f\({}_{0}\))--at one site. In contrast, at another location, it interacted with the complex stratigraphy and had a more pronounced impact at higher frequencies. A brief discussion is warranted regarding the use of 3D models for this case study. While 3D numerical models are powerful tools for the analysis of large-scale geological contexts--such as whole-basin effects and fault geometries--they require spatially extensive input data. Additionally, the high computational cost of 3D modelling is often mitigated by increasing the size of the mesh elements, which in turn reduces the numerical resolution, particularly at higher frequencies. Generally, 3D models are effective only up to frequencies of 2-3 Hz, making them inefficient for the objectives of this study. Given the high resolution and accuracy of the field experimental data, it was more appropriate to apply numerical methods that could capture small-scale variations in greater detail--namely, 1D and 2D approaches. In addition, the results were compared with theoretical models based on the assumption of an ideal viscoelastic homogeneous layer over a deformable substrate, in which the average Vs of the soil is considered. This comparison is relevant because the average velocity is similar to the equivalent shear wave velocity (\(V_{SEQ}\)) defined in the Italian Building Code 2018 (IBC2018). This parameter is used in simplified procedures to determine seismic action based on subsurface classification. \(V_{S,EQ}\) is defined as the shear wave velocity of the surface deposits averaged over their total thickness, i.e., down to the seismic bedrock--typically identified as a very stiff soil or rock formation with a Vs of at least 800 m/s. In practice, \(V_{S,EQ}\) tends to be slightly lower than the true average velocity, as it is the weighted average of the S-wave velocities in each layer from the foundation level, calculated according to the following relationship:  
\[V_{S,EQ}=\frac{H}{\sum_{i=1}^{n}\frac{b_{i}}{V_{s,i}}} \tag{1}\]  
where \(n\) is the number of layers identifiable in the investigated soil, each characterised by the thickness \(h_{i}\) and the wave velocity \(V_{S,i}\). However, this parameter may be unreliable, as it is often arbitrary and challenging to define the depth \(H\) of the profile. In many cases, \(H\) is established a priori--without sufficient knowledge of the actual geological setting--based on past investigations. Theoretically, \(H\) should correspond to the volume of soil significantly interacting with the structure. In seismic analysis, this 'domain of seismic interest' may encompass the entire valley deposit, rather than a fixed depth. In the earlier Italian Building Code (IBC2008), the reference depth was fixed at \(H\) = 30 m from the foundation level, leading to the commonly used V\({}_{\text{S},30}\) parameter. In contrast, IBC2018 leaves the determination of \(H\) to the discretion of the designer--hence, the 'EQ' (equivalent) notation. In practice, however, this often results in values that do not reflect the true seismic dimensions of complex valley systems. Under such complex subsurface conditions, simplifying the soil profile into a homogeneous model can lead to inaccurate estimates of resonance and amplification. These considerations are especially relevant for geotechnical earthquake engineering, as they support the development of seismically sustainable design solutions for geometrically irregular buildings. In these cases, it is particularly important to characterise the seismic actions affecting not only the fundamental structural mode but also higher modes of vibration.