## 3 Modeling Results and Discussion
### The Response of Soft Clay Layer at the Black Sea Offshore Site
The observed resonant frequency corresponds to the value 3.6 Hz, calculated by the well-known empirical equation [47]:  
\[f=\ \frac{V_{S}}{4H} \tag{19}\]  
where \(H=\) a thickness of the layer. A slight shift between simulated and observed spectra may be due to uncertainty in determining the thickness of the soft clay layer under the seismograph because the dominant frequency in response spectra depends on the layer thickness [48; 49]. Figure 9 shows results at the OBS site with a soft clay layer of 14 m thickness, which is similar to those shown in Figure 8. The synthetic and experimental responses are also largely consistent with each other. The main observed resonant frequency also corresponds to the value 1.4 Hz, calculated by the Equation (19). In Figure 9, it can be seen that resonant spikes are more pronounced in the modeled spectra rather than experimental ones. This may be due to the excessive contrast boundary between the flysch bedrock and the soft clay layer in the synthetic soil profile. In real settings, some impedance gradients might be observed. In this case, the simulated response spectrum would be smoother, as is the case with the spectra of the observed signals. Figure 8: Modeling results for the Black Sea shelf site with soft clay layer of 5.5 m thickness: (**a**) response spectra SA(T, 5%) obtained by different modeling methods and real record; (**b**) stress–strain curves at the surface of the layer. In addition, it is necessary to take into account the nonlinear behavior of the soil, including such effects as S-wave signal saturation when ground motion amplitudes stop increasing with an increase of macroseismic intensity and damages [50,51]. At high values of macroseismic intensity, loose soils begin to collapse by seismic waves, plastic behavior and soil flow, cracks, etc., appear. On one hand, collapsing soils lose their bearing capacity: they can no longer serve as a basement for buildings and structures. On the other hand, a high-amplitude wave cannot propagate through weak soil. The weaker the soil (the lower its impedance), the lower the maximum wave amplitude that can be observed on its surface [51]. It is mainly about accelerations but not displacements (see below). The spectra in Figure 9 (for 14 m thickness) lie lower than the spectra in Figure 8 (for 5.5 m thickness). It could be due to the attenuation of the S-waves and also due to the described mechanism causing S-wave amplitudes saturation. This behavior is seen in both observed and synthetic spectra. In Figure 10, the approximating curves are shown for the simulated peak ground accelerations (PGA), peak ground velocities (PGV) and peak ground displacements (PGD) on the surface of a soft clay layer with different thickness (3 m, 10 m and 14 m), while different input accelerograms on the bedrock are applied. The amplitude saturation effect is clearly seen. First, the larger thickness of the soft clay layer, the faster saturation occurs. In turn, for calculating macroseismic intensity increase, the mean impedance is used calculated for the soil thickness of 10 or 30 m [24]. Thus, the larger thickness of the soft clay layer, the lower the mean impedance of the upper 10 or 30 m of the soil profile. Second, the saturation effect is less distinguished for velocities than for accelerations, while the displacements, in this case, are in accordance with macroseismic intensity and level of damages. Figure 10: Modeled dependences (polynomial approximation) of peak ground acceleration (PGA) (**a**), peak ground velocities (PGV) (**b**) and peak ground displacements (PGD) (**c**) on the surface of the soft clay layer. Figure 9: Modeling results for the Black Sea shelf site with soft clay layer of 14 m thickness: (**a**) response spectra SA(T, 5%) obtained by different modeling methods and real record; (**b**) stress–strain curves at the surface of the layer.