## 4 Results and Discussion  
### Fundamental Frequency Peaks and Corresponding Amplitudes  
The fundamental frequencies and corresponding amplitude variations obtained from the HVSR analysis are mapped in Figures 3 and 4, respectively. The fundamental frequencies vary between 0.8 and 4.8 Hz. The outcrop of Upper Miocene clays and marks could explain this large lateral variation. Indeed, in Figure 3, it can be observed that higher frequencies (between 2 and 4.8 Hz) are present in the central, southeastern, and western parts of the city, where the Marly formations of the Upper Miocene outcrop, suggesting a thinner sedimentary cover. On the other hand, low frequencies are observed in the southern and northern parts of the city, where the soil is composed of Quaternary sedimentary and eruptive formations. The lowest frequencies are observed in the industrial zone, NE of the city, suggesting a deeper bedrock.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Sedimentary Layers** & **Vp Range [m/s]** & **Vs Range [m/s]** & **Density Range [kg/m\({}^{3}\)]** \\ \hline Quaternary & 150–1200 & 100–400 & 1600–2000 \\ \hline Pliocene & 450–1650 & 300–550 & 1800–2100 \\ \hline Upper Miocene & 600–2700 & 400–900 & 1900–2200 \\ \hline Lower Miocene & 1200–4200 & 800–1400 & 2000–2400 \\ \hline Bedrock & 2000–7000 & 1300–2750 & 2200–2800 \\ \hline \end{tabular}
\end{table}
Table 2: Input parameters for the inversion, including the number of layers and the ranges of Vp, Vs, and density.  
Figure 3: Variation map of the fundamental frequency peaks (\(f_{0}\)) identified using the HVSR technique.  
Two types of HVSR curves were obtained (Figure 5). Some HVSR curves (P15, P19, P35, P36, P37, P38, P39, P40, and P51) exhibit a second frequency peak at higher frequencies (between 6 and 15 Hz). This second peak is observed only where the soil is composed of Quaternary deposits. This led us to infer that this peak is probably caused by the impedance contrasts at shallow depth between the Quaternary eruptive rocks and the Miocene sediments (clays and marls). The available boreholes (Table 1) and the geological map of the area led us to assume that the fundamental frequency peak is related to impedance contrasts between the Middle Miocene (Serravallian) and the Mesozoic bedrock. The corresponding amplitudes range between 2 and 6.6 (Figure 4). Higher amplitudes are observed mostly in the northeastern areas of the city, in and around the industrial zone and at two other points (P05, P22). This could indicate a higher amplification factor in these areas. It is important to note that ambient noise data do not constitute the appropriate data for consistently determining the extent of ground amplification, but can, however, give an idea of the degree of impedance contrast and the distribution of the relative amplification factor.  
In order to determine the nature of the frequency peaks, all of the measurement points were examined using a spectral analysis of the three components (NS, EW, and Z). The obtained results indicated that all of the peaks are of lithological origin.  
The lowest fundamental frequency of f\({}_{0}\) = 0.8 Hz suggests that the sedimentary cover in Ain Temouchent is thinner than in other areas in the Lower Chelif Basin, as in the city of Oran (lowest frequency f\({}_{0}\) = 0.2 Hz [41]) and the city of Chlef (lowest frequency f\({}_{0}\) = 0.3 Hz [28]). This is probably due to the fact that the city of Ain Temouchent is located within the southwestern margins of the Lower Chelif Basin. The amplitude range (2-6.6) is almost similar with the one obtained in the city of Oran (2-5.6 [41]), which is explained by the similitude in the impedance contrasts between the Middle Miocene sediments and the Mesozoic bedrock in both cities. It is important to notice that the variation in frequency range could be attributed to differences in local geological conditions between the cities (e.g., different outcrops, change in facies, erosions, etc.).  
Figure 4: The corresponding amplitude variation map (\(A_{0}\)) obtained by HVSR analysis.