One of the main advantages of PBS is that, unlike for records, site conditions are completely known. While the complexity of the small-scale variability of ground properties cannot be portrayed in detail, unless spatially correlated stochastic fields are applied to the average values of wave propagation velocities (see Paolucci et al., 2021, for an application to the PBS of ground motions from induced seismicity in Groningen, Netherlands), PBS are suitable to investigate site amplification effects from a variety of viewpoints, such as: (i) the variability of site amplification with respect to different outcropping bedrock stations; (ii) the comparison with the results from 1D and 2D simulations (see e.g. Smerzini et al., 2011, for an application to the Gubbio basin, Italy); (iii) their repeatability and scenario dependence both in the linear and non-linear ranges (see e.g., Stafford et al., 2017). Although SPEED allows for consideration of a relatively simple, albeit effective, non-linear visco-elastic model (Stupazzini et al., 2009), due to the relatively low levels of seismic excitation we will consider in this section only linear visco-elastic site amplification effects. To this end, the focus is on the cross-section shown in Fig. 15 (the azimuth of the cross-section is the same as the fault strike), where, velocity time histories at selected locations, are illustrated, on the top panel, both in the basin and at outcropping bedrock, and, on the bottom, at all receivers along the cross-section (the EW component was chosen as reference for these investigations, for simplicity). The latter plot allows to highlight the complexity, as well as the 3D nature, of seismic wave propagation in the basin. As clarified also from Fig. 8, the western portion of the cross-section is the one that first experiences ground motion due to the lower source-to-site distance, but afterwards the presence of the basin increases the complexity of the overall seismic wave field, with prominent amplification effects towards the basin center.
To quantify the basin-induced amplification, regardless of the reference station, a second PBS, with the same reference kinematic source model (see Section 3.2), was carried out but without the presence of the basin. In such simulation, referred to as “3D-C21-R” (where “R” means “rock”) in Table 4, the dynamic properties of the basin are replaced by those of the outcropping bedrock. In Fig. 16 (left), the acceleration time histories at D and C receivers (shown in Fig. 15) are plotted, clearly pointing out the increased amplitude, and elongated dominant period and duration of ground motion with respect to the case without basin. Such prominent amplification is clearly shown in terms of the corresponding acceleration response spectra, highlighting the significant long period amplification especially at the center of the basin.
The quantification of site effects is further explored in Fig. 17, where the Fourier Spectral Ratios (FSR) and Response Spectral Ratios (RSR) are considered, with reference to the receivers C and D: (a) label “3D” refers to the spectral ratios obtained by dividing the results of the simulation 3D-C21 over the 3D-C21-R; (b) label “1D” refers to the 1D theoretical amplification function with the local stratigraphy below the corresponding receiver; for the RSR, the accelerograms at C and D were computed by 1D convolution using as input motions the corresponding accelerograms computed in the without basin case (3D-C21-R); (c) labels “C/B” and “C/F” (and similarly for receiver D) refer to the spectral ratios computed from 3D-C21 run with respect to reference stations B and F, located on the left and right side of the basin respectively (see Fig. 15).
Several remarks can be made based on the inspection of Fig. 17:
- with some exceptions in relatively small frequency intervals, the FSR show that there is an overall good agreement between the 1D and 3D amplification functions, supporting the accuracy of the numerical results in a relatively broad frequency range;
- in agreement with studies aiming at quantifying the aggravation factors on the response spectra related to complex 2D/3D geological configurations (e.g., Chávez-García and Faccioli, 2000; Riga et al., 2016), the 1D solution tends to overestimate the 3D one close to the basin edge (receiver C), while the opposite occurs at the basin centre (receiver D). However, comparison of RSR at short periods suggests that PGA from 3D simulations tends to be smaller than in the 1D case;
- if site amplification functions are computed with respect to a reference station, the location of such station with respect to the basin is critical (as also shown in Smerzini et al. 2011): namely, spectral ratios with respect to receiver F show some sharp anomalies, since F lies on the other side of the Rhône basin with respect to the source, so that a part of the frequency content, including low and high frequencies, is filtered out by the presence of the basin; spectral ratios with respect to receiver B are instead closer to the 1D and 3D solutions.
More generally these results confirm that, when complex geological configurations lie in the vicinity of active faults, the main features of seismic response cannot be reliably captured by standard approaches owing to the variability of the source-to-site ray paths affecting wave propagation. In these conditions, especially in case of critical structures such as NPPs, PBS seem to be an effective way to predict the regional as well as the site-specific features of the seismic response.
Further investigations are planned, starting from this case study, aiming at evaluating the variability of site effects from different realization of earthquakes from the same source, with variable magnitude and slip distribution, and from other sources in the investigated area, with different distance and azimuth from the site.