Characterization of the Sedimentary Cover in the City of Aïn Témouchent, Northwest Algeria, Using Ambient Noise Measurements

Abstract

The city of Aïn Témouchent, located in northwest Algeria at the westernmost part of the Lower Cheliff Basin, has experienced several moderate earthquakes, the most significant of which occurred on 22 December 1999 (Mw 5.7, 25 fatalities, severe damage). In this study, ambient noise measurements from 62 sites were analyzed using the horizontal-to-vertical spectral ratio (HVSR) method to estimate fundamental frequency ($f_0$) and amplitude ($A_0$). The inversion of HVSR curves provided sedimentary layer thickness and shear wave velocity (Vs) estimates. Additionally, four spatial autocorrelation (SPAC) array measurements refined the Rayleigh wave dispersion curves, improving Vs profiles (150–1350 m/s) and sediment thickness estimates (up to 390 m in the industrial zone). Vs30 and vulnerability index maps were developed to classify soil types and assess liquefaction potential within the city.

1. Introduction

Northern Algeria is characterized by moderate seismic activity, with the occurrence of few strong earthquakes, resulting from the collision between the African and Eurasian tectonic plates. Most of the seismic activity is located at the margins of the northern Neogene Basin [1,2].

Understanding local site effects is crucial in seismic hazard assessment, especially in sedimentary basins where ground motion amplification can significantly impact infrastructure. Various methods, including the HVSR technique [3] and array-based seismic surveys, have been used globally to characterize subsurface structures and assess seismic vulnerability (e.g., [4]). While several studies have focused on urban areas in high-risk seismic zones (e.g., [5,6]), northwest Algeria remains very little explored in this regard. To address this gap, this study investigates the sedimentary cover of the city of Aïn Témouchent using ambient vibration single station and array methods, providing new insights into the soil characteristics of the Lower Cheliff Basin.

Aïn Témouchent is a city located at the westernmost part of the Lower Cheliff Basin, the largest of the Neogene basins of northern Algeria [7]. It stretches for 450 km in an EW direction and it is divided into 3 sub-basins: Upper, Middle, and Lower Chelif Basin (e.g., [8]). The city of Aïn Témouchent is built on a small plain (the Aïn Témouchent Plain), located between the Mleta Plain, the Tessala Mounts, and the Tlemcen Mounts (Figure 1).

In the Lower Chelif Basin, northwest Algeria, the seismicity is also moderate. The most important earthquakes were the 1790 Oran earthquake, with an intensity I₀ = VIII (European Macroseismic Scale, EMS-98) [9]; the 1999 Aïn Témouchent earthquake, with a moment magnitude of Mw = 5.7 ([10,11]); and the 2008 Oran earthquake, with a moment magnitude of Mw = 5.4 [12]. The 1999 Aïn Témouchent earthquake (Figure 1) was caused by a reverse fault oriented NE–SW, located around 20 km west of the city center [10]. The final toll from this earthquake was 25 dead and 174 injured. The total number of people affected was around 25,000. More than 600 houses were destroyed and more than 1200 others were severely damaged.

The Aïn Témouchent region has undergone several geological (e.g., [13,14]) and geotechnical studies (e.g., prospections carried by the LTPO (Laboratoire des Travaux Publics de l’Ouest) and the LNHC (Laboratoire National de l’Habitat et de la Construction)). After the 1999 earthquake, more studies were conducted in the region, including the city of Aïn Témouchent. In the first place, several studies have used seismological [10] and InSAR [11] data to characterize the surface rupture and propose an underground fault model. After that, several studies focused on the geotechnical characteristics of the soils in the city of Aïn Témouchent. For example, the study carried out in [15] led to the elaboration of a geotechnical map of the city using the geographic information system (GIS). The most important was the seismic hazard assessment study carried out mainly by Geomatrix ([16], unpublished report).

It is well known that each region and structure react differently during an earthquake. The fundamental frequencies of the soils and buildings are the main elements involved in this case, so it is crucial to understand their behaviors in the case of a strong earthquake [17,18,19]. Several methods based on the analysis of ambient noise data have been developed to study the shear wave velocity structure in shallow sedimentary layers, which is likely to be a factor of amplification during earthquakes. Among these methods, the horizontal-to-vertical spectral ratio (HVSR) technique [3] is one of the most widely used. It has a number of advantages over other approaches, particularly in urban environments, due to its quick implementation and the low cost of the equipment required for data acquisition.

The HVSR technique has proven its reliability for estimating ground fundamental frequencies, as confirmed by several research studies [20,21,22,23,24,25]. Examples of its application can be found all over the world [26,27,28,29,30] and even outer space (e.g., [31]) The Lower Cheliff Basin has been the subject of few studies using ambient noise data to characterize the sedimentary cover (e.g., [32,33]).

HVSR analysis can be complemented by other geotechnical data as well as ambient noise array measurement techniques, both active and passive, such as frequency-wavenumber (f-k) [34,35,36,37], spatial autocorrelation (SPAC) [38,39], extended spatial auto-correlation (ESAC) [40,41] and refraction microtremor (REMI) [42] techniques. Passive methods offer the possibility of modeling deeper Vs structures than active techniques, since seismic waves generated by passive sources (natural sources) are richer in low frequencies than the energy spectra of active sources [43,44].

To analyze the influence of sedimentary structure on ground motion, it is essential to well characterize the soil structure. Some geophysical, geotechnical, and geological properties of the soil have to be determined: for example, the P- and S-wave velocity structures (Vp and Vs), the density ($\rho$), and the thickness of sedimentary deposits. The Vs structure of the surface layers can be obtained in several ways, for example, by inversion of the HVSR or/and surface wave dispersion curves extracted from ambient noise recordings.

The main purpose of this study is to assess the site effects and sedimentary structure beneath the city of Aïn Témouchent using ambient vibrations data in order to enhance the seismic hazard assessment in the region. For this purpose, ambient noise was recorded at 62 sites inside the city, using single station measurements. In addition, array recordings were performed at 4 potential sites. The HVSR technique was applied to single-station recordings to estimate the fundamental frequency of the soil ($f_0$), the corresponding amplitude ($A_0$), and the vulnerability index ($Kg$). The inversion of HVSR curves was used to estimate the shear wave velocity in sedimentary layers. In addition, the SPAC technique was applied to array measurements to retrieve the dispersion curves of the fundamental mode of Rayleigh waves. The inversion of dispersion curves was performed separately to estimate more constrained Vs profiles, particularly at shallow layers. Based on the inversion results (Vs profiles) and available borehole data, which were also used as input to the inversion process, different cross-sections were established to track the lateral evolution of sedimentary layers in the area. Finally, several maps showing the variation in$f_0$,${ A}_0$,$Kg$, soil class based on Vs30, and bedrock depth are proposed. This work contributes to existing studies in the region, with the aim of helping to assess the region’s seismic hazard.

2. Geological Framework

The Cheliff Basin is the largest Neogene basin in northern Algeria [7]. In its major part, the sedimentary cover is made up of marine, continental, and sometimes lacustrine sedimentary rocks of the Neogene and Quaternary ages. However, in the plain of Aïn Témouchent, which is located in the westernmost part of the Lower Cheliff Basin, the context is somewhat different, with the subsoil being characterized by the strong presence of eruptive rocks of the Quaternary and Miocene ages [13]. In fact, the western part of the Lower Cheliff Basin has been the site of two distinct volcano episodes: the first, of Calco-Alkaline type, took place in the Messinian (Upper Miocene); while the second, of alkaline basaltic type, occurred in the Quaternary [13,14]. These deposits were only slightly affected by the NS to NW–SE compressive phase of the Quaternary, which may explain why seismic activity is relatively low compared to other areas of the Tellian Atlas [10,13].

The plain of Aïn Témouchent is bordered from the east and south by the Tessala Mountains, from the north by the Mleta Plain, and from the west by the Tlemcen Mountains (Figure 1). The city of Aïn Témouchent is located in the central part of the plain. From a lithological point of view, although the city is located in the central part of the plain, the soil structure is highly diversified (Figure 2). In most of the city, the soil is made up of Messinian formations (Upper Miocene), composed of several layers of silty clay, marl, limestone, and gravel [13]. These layers are thick, and according to the boreholes provided by LNHC and LTPO laboratories (

Table 1. Layer structure from the available borehole information.

Borehole	Quaternary [m]	Pliocene [m]		Miocene [m]
F1	14.0	>13	0.0	–
F2	14.0	7	0.0	78	0.0
F3	14.0	7	0.0	78	0.0
F5	7.5	>10	0.0	–
F6	1.0	–		>35	0.0
F7	1.0	–		>19	0.0
F8	2.0	>9	0.5	–
F9	2.0	17	0.0	>2	0.0
F10	4.0	>5	0.5	–
F11	4.0	>5	0.5	–
F14	1.0	4	0.0	>11.0
F17	8.0	>10	0.0	–
F21	2.0	–		>20	0.0
F26	1.0	–		>7	0.0
F30	7.5	>10	0.0	–
F34	>12.0	–		–

), their thickness can exceed 100 m. The Messinian clays and marls are less developed in the plain of Aïn Témouchent than in the Oranie plain, where their thickness reaches 400 m [45]. Quaternary and Miocene eruptive formations outcrop to the NW and S of the city, reaching maximum thicknesses of 46 m and resting on Messinian clays. Some recent alluvial and calcareous deposits are found at the city’s extremities. In the western part of the city, the Quaternary formations rest directly on the Miocene sediments. To the east, a thin layer of Pliocene sand and sandy silt separates them. According to the available boreholes, the thickness of the sandy layers does not exceed 17 m.

These sedimentary and eruptive deposits lie on Mesozoic bedrock, sometimes composed of Cretaceous marl and sometimes of Jurassic pelite and sandstone [13]. Both formations outcrop to the north and east of the town. However, the exact nature of the bedrock in the city of Aïn Témouchent is not clear.

3. Data and Methodology

3.1. Applied Techniques

3.1.1. Horizontal-to-Vertical Spectral Ratio Technique

The horizontal-to-vertical spectral ratio, HVSR, or H/V technique enables retrieving the fundamental frequency of the soil and the corresponding amplitude using ambient noise recordings. This method was initially proposed by [46] and became widely used after some improvements carried out by Nakamura [3]. It is now widely acknowledged for its efficiency in estimating soil fundamental frequency [3]. Nevertheless, the scientific community maintains a degree of skepticism regarding the accuracy of the technique in estimating amplification factors, primarily due to the complex contributions of various seismic waves to the wave field. At present, the quantification of the ratio between body and surface waves remains a challenging undertaking. A previous study [20] demonstrated that when there are significant impedance contrasts between bedrock and sediments, the HVSR curve is predominantly influenced by surface waves. The relatively low amplitude of body waves renders them insufficient for providing precise estimation of the amplification factor. Furthermore, the authors of [47] demonstrated that the HVSR peak amplitude can fluctuate over time. It was therefore recommended that the amplitude of the frequency peak obtained using the HVSR technique in this study be regarded as a relative indicator rather than an exact representation of the amplification factor.

3.1.2. Spatial Autocorrelation (SPAC) Technique

Spatial autocorrelation (SPAC) analysis is an array-based technique that allows for the use of simultaneous recording of ambient noise to calculate the dispersion curve of surface waves [38]. This technique is mainly based on the assumption that the wave field exhibits stochastic, stationary behavior in both spatial and temporal dimensions [38]. In theory, the SPAC method identifies a single-phase velocity for each frequency within a specified range by fitting the SPAC coefficient to a Bessel function. In the case of a circular array, the Bessel function represents the mean cross-correlation between station pairs as a function of their separation distance. The authors of [38] demonstrated that, at a given frequency, the SPAC coefficient aligns with the 0th order Bessel function. The SPAC method is optimized using a circular array with a centrally placed sensor, as attested by Okada [41]. However, a previous study [39] introduced a modification to this approach, enabling the SPAC method to be applied to arrays with non-circular configurations. This adaptation replaces fixed radius values with rings of finite thickness, thereby affording greater flexibility in array design. In the present work, the modified SPAC (MSPAC) technique proposed in [39] was utilized.

3.1.3. Vulnerability Index $\mathrm{K}\mathrm{g}$

The issue of liquefaction is of critical importance. It is often induced by an earthquake and the consequences of such a phenomenon can be catastrophic (case of 1964 Nigata earthquake, [48]). This phenomenon is particularly prevalent in sedimentary basins, especially when sandy formations are present at shallow depths. One approach to assess the liquefaction risk is through the use of the $Kg$ vulnerability index, as proposed by Nakamura [49]. Nakamura’s studies [49,50] demonstrated that regions susceptible to liquefaction and landslides often display markedly elevated $Kg$ values. The index is calculated using the fundamental frequency of the ground and its corresponding amplitude, as expressed in Equation (1):

$$Kg={\displaystyle \frac{{\left(A_0\right)}^2}{f_0}}$$

(1)

where $f_0$ represents the fundamental frequency and $A_0$ its corresponding amplitude

3.1.4. Vs30 Values and Soil Classification

The shear wave velocity for the uppermost 30 m, often denoted as Vs30, can be determined using the Vs profile obtained by inversion of the HVSR and dispersion curves. The Vs30 value is determined using Equation (2) (Eurocode 8, [51]):

$$\mathrm{V}\mathrm{s}30={\displaystyle \frac{30}{\sum _{i=1}^N\frac{H_i}{V_i}}}$$

(2)

Here, $H_{i }$denotes the thickness of the $i$th layer in meters, $V_i$represents the shear wave velocity of the $i$th layer in meters per second (m/s), and N indicates the total number of layers from the surface down to a depth of 30 m.

Different contour maps have been generated by linear interpolation to represent the different key factors related to site effects, including f₀, A₀, Kg, depth to bedrock, and Vs30. In the case of Vs30 values, the generated contour map serves as a basis for site classification according to the National Earthquake Hazards Reduction Program (NEHRP) code [52]. Three-dimensional and 2D geo-models constitute valuable tools for representing multisource data retrieved from boreholes, seismic measurements, etc. [53,54,55,56].

3.2. Data Acquisition and Processing

3.2.1. Single-Station Measurements

An ambient noise measurements campaign was conducted in the city of Aïn Témouchent in 2024. Ambient noise was recorded at 62 sites (Figure 2), at night and under calm weather conditions, in accordance with the recommendations of the Site Effects Assessment using Ambient Excitations (SESAME) project [57]. The standard acquisition time was 16 min. However, in the industrial zone located northeast of the study area, the recording time was extended to 20 min due to the influence of human activity. The additional recording time ensured that the obtained spectral ratios were representative of the actual characteristics of the site and were not significantly affected by short-term disturbances. Besides, previous experimental tests showed that the HVSR curves were stabilized after 15–20 min at these sites, minimizing possible errors. The equipment used for the recordings was a SARA short-period triaxial velocity station, with a natural frequency of 1 Hz and a sampling frequency of 100 Hz.

The HVSR processing was carried out using GEOPSY software (release 2.10.1) [58]. First, the recording was divided into windows of a predefined duration. In this study, a duration of 30 s for each window was used. Then, an anti-triggering algorithm was applied, which ensured that only stationary windows were selected for the required processing. The spectrum of each component was calculated for each window, and the results were smoothed using the Konno–Ohmachi [59] technique to obtain the spectral amplitudes of each component (NS, EW, Z) for each window using a smoothing coefficient equal to 40. Subsequently, the horizontal spectrum was calculated as the quadratic mean of the NS and EW spectra. Thereafter, the H/V spectral ratio was determined for each window. Finally, a geometric mean of the H/V spectral ratio was calculated in the frequency band between 0.5 and 15 Hz. As a result, the HVSR curve, with amplitude as a function of frequency, was obtained.

3.2.2. Array Measurements

Ambient noise was also recorded using an array measurement technique at four potential sites within the city (Figure 2). The measurements were carried out using seven SARA (https://www.sara.pg.it/, accessed on 1 March 2025) short-period seismographs distributed over two concentric equilateral triangles with a station in the middle (Figure 2), with each side of the triangle measuring 30 m. The ambient noise was recorded for a period of 40 min at each of the four sites. The acquisition was carried out following SESAME project recommendations. The seven stations were connected to a GPS system in order to homogenize the time base.

For data processing, only the vertical components of each sensor were considered, discarding the effects of Love waves, which are only present in the horizontal field. Therefore, only Rayleigh waves were considered. The SPAC method was implemented using Geopsy software (https://www.geopsy.org/, version 2.10.1). First, the theoretical wavenumber limits (kmin, kmax) were obtained by introducing the coordinates of each of the seven sensors into the WARANGPS module (from Geopsy package, release 2.10.1) [58]. Then, they were processed using the SPAC toolbox for the definition of the ring parameters. Following the input of the coordinates of each sensor, the software automatically generated spatially distributed sensor pairs, typically comprising 21 pairs derived from seven sensors. Subsequently, the pairs were allocated to one or more rings by defining the inner and outer radii, thereby ensuring optimal pairing. In accordance with the recommendations set forth by [39], each ring should comprise a minimum of two pairs, with the inclusion of as many rings as feasible to enhance resolution. The recorded signals were divided into 50 s windows, which were selected using an anti-triggering algorithm to ensure the maintenance of data quality. Subsequently, spatial autocorrelation curves were calculated for each ring. Spac2Disp (from Geopsy package, release 2.10.1 [58]) facilitated the visualization of phase velocity histograms based on the calculated autocorrelation values. The final dispersion curve was derived by identifying the Rayleigh wave phase velocity values that significantly contributed to the curve within the defined Kmin and Kmax ranges.

3.2.3. Inversion of HVSR and Dispersion Curves

The analysis process involved separate inversion of the HVSR and dispersion curves. Thanks to the inversion of the HVSR curve, it was possible to generate a detailed 1D model of seismic wave velocities (Vp, Vs) and densities. The depth of the investigation for HVSR inversion was limited by the fundamental frequency ($f_0$), whereas for array applications it was influenced by the array configuration (maximum aperture and inter-station spacing). The ambiguity of the inversion process (multiple models can provide the same response) makes it necessary, especially in the case of HVSR curves, to have some prior knowledge regarding the possible ranges of velocity and thickness of the sedimentary layers that allows constraining of the solution space. These essential data can be obtained from borehole analysis, geological section interpretation, or seismic refraction methods, all of which provide critical constraints on the initial model (Table 1). The Vs and Vp velocity ranges were taken from works previously carried out on the Lower Cheliff and Middle Cheliff Basins also using ambient noise data [6,32,45]. The close synergy between all of the collected data (experimental measurements, geologic surveys, boreholes, and seismic surveys) allowed for a further reduction of uncertainties during the data inversion.

There are several inversion methods available. The authors of [60] summarized the different interpretations suggested in previous studies and proposed a new theory for the HVSR technique and the inversion of its curve to obtain a soil profile based on the diffuse field assumption (DFA). Whichever method is used, the inversion process does not produce a single definitive solution. Instead, it produces several models, each one characterized by a different degree of misfit between the observed HVSR curve and the theoretical Rayleigh wave ellipticity curve. The velocity model with the lowest degree of misfit is considered the most representative. There is a similarity in shape between the HVSR curve and the fundamental mode of the Rayleigh wave ellipticity curve [61].

In this study, the inversion process was performed using the Sesarray package (release 2.10.1) in Dinver software (https://www.geopsy.org, version 2.10.1) [58], which implements the neighborhood algorithm [62]. The input parameters for the inversion, including Vp, Vs, and the density range, are shown in

Table 2. Input parameters for the inversion, including the number of layers and the ranges of Vp, Vs, and density.

Sedimentary Layers	Vp Range [m/s]	Vs Range [m/s]	Density Range [kg/m3]
Quaternary	150–1200	100–400	1600–2000
Pliocene	450–1650	300–550	1800–2100
Upper Miocene	600–2700	400–900	1900–2200
Lower Miocene	1200–4200	800–1400	2000–2400
Bedrock	2000–7000	1300–2750	2200–2800

. The number of layers and their thicknesses were derived from the data obtained from 16 boreholes (Table 1). These borehole data were provided by the “Laboratoire National de l’Habitat et de la Construction” (LNHC). A Poisson’s ratio between 0.2 and 0.5, representative of typical soil values, was used [63]. The maximum number of iterations was set at 300, with 100 models generated per iteration. For each site, the experimental HVSR curve was compared with the theoretical ellipticity curve using a misfit value [64], and the Vs model with the lowest misfit was selected.

4. Results and Discussion

4.1. Fundamental Frequency Peaks and Corresponding Amplitudes

The fundamental frequencies and corresponding amplitude variations obtained from the HVSR analysis are mapped in Figure 3 and Figure 4, respectively. The fundamental frequencies vary between 0.8 and 4.8 Hz. The outcrop of Upper Miocene clays and marls 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.

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 f₀ = 0.8 Hz suggests that the sedimentary cover in Aïn Témouchent is thinner than in other areas in the Lower Chelif Basin, as in the city of Oran (lowest frequency f₀ = 0.2 Hz [41]) and the city of Chlef (lowest frequency f₀ = 0.3 Hz [28]). This is probably due to the fact that the city of Aïn Témouchent 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.).

4.2. The Vulnerability Index ($Kg$)

The vulnerability index ($Kg$) is used to assess soil instability and earthquake-induced phenomena such as liquefaction and landslide. In our study area, the vulnerability index was used to identify areas prone to liquefaction, as an alternative to other geotechnical-based analyses (e.g., [65]). The calculated $Kg$ values range from approximately 3 to 50 (Figure 6). According to [49], sites with higher $Kg$ values ($Kg$ ≥ 10) are at greater risk of liquefaction. The results of our analysis suggested that the overall potential for liquefaction in the area is relatively low. However, certain regions, notably the industrial zone NE of the city and to the south of the hospital, show a higher $Kg$ value, suggesting higher susceptibility. The boreholes show that in the industrial zone, thick sandbanks (≥7 m) are observed at shallow depths. Also, the piezometric wells indicate the presence of ground water at shallow depths [16]. The presence of sand banks and groundwater at shallow depths indicates a high risk of liquefaction. This led the industrial zone to be considered as an area with high potential of liquefaction, as already mentioned in the Geomatrix report [16].

The range of the vulnerability index for Aïn Témouchent (0–50) is slightly lower than the one calculated for the city of Oran (5–75 [41]). This variation is mainly attributed to differences in the lithology and local geological conditions, with the presence of eruptive hard rocks in Aïn Témouchent. Also, the thickness of the sedimentary cover directly influences the vulnerability index of the soils, as the $Kg$ value is inversely proportional to the f₀ value, and since the f₀ value in Aïn Témouchent is higher than that in Oran, this could explain the difference in the vulnerability index.

4.3. Rayleigh Wave Dispersion Curves

The dispersion curves generated for each array measurement site using the SPAC method are presented in Figure 7 (panel a). The aforementioned curves are illustrated within the theoretical wavenumber limits (kmin, kmax), which were obtained by introducing the coordinates of each of the seven sensors into the WARANGPS module (from Geopsy package, release 2.10.1) [58], encompassing a frequency range of 3.5 to 12 Hz and a velocity range extending from 400 to 680 m/s. The Rayleigh wave phase velocity values are within the same range with those obtained previously in a similar investigation in the Middle Cheliff Basin [33]. In their research, the same geometry was employed, as well as a 30 m aperture, resulting in reported frequency values within the range of 5 to 12 Hz. Furthermore, in another study [45] carried out in the city of Oran, 80 km NE of Aïn Témouchent, array measurements were performed using the same geometry but with apertures of 30 and 50 m. The dispersion curves were obtained within frequency ranges between 5 and 12 Hz (for apertures of 30 m) and between 2.7 and 14 Hz (for apertures of 50 m). The variation in frequency range is mainly due to local geological conditions between the two cities. It also could be attributed to different apertures.

4.4. Shear Wave Velocity Models

The inversion of the HVSR and dispersion curves allowed for estimating the shear wave velocity in the soil sedimentary layers. The inversion process relied on borehole data (Table 1), geological information (Figure 2), and velocity values derived from previous studies conducted in the same basin [6,32,33,45].

Figure 7b and Figure 8 (right panel) show the shear wave velocity profiles obtained from the best-fit 1D Vs model through the inversion of the dispersion and HVSR curves, respectively. The observed HVSR curve was compared to the theoretical Rayleigh wave ellipticity curve for each model, using a misfit value. The plots depict the model with the best fit (minimum misfit), represented by a black line, as an indicator of the confidence associated with the results. The dark gray area outlines solutions within 10% of the minimum misfit, while the light gray curves illustrate the other models considered during testing.

As a result of the inversion of the HVSR and dispersion curves, the thickness and velocity of each layer were obtained. These results allowed for plotting six cross-sections, as shown in Figure 9a. In addition, Figure 9b shows the correspondence between the fundamental frequency and the HVSR points, as a function of the corresponding amplitude. The lithological boreholes revealed four sedimentary layers corresponding to Quaternary, Pliocene, Upper Miocene and Middle Miocene deposits. Vs models derived from HVSR curves were used to estimate the thickness and shear wave velocities (Vs) of these layers within the soil column. In addition, the dispersion curves were used to determine the sedimentary thickness and Vs values for the upper 30 m of the soil profile.

Figure 9 presents three cross-sections oriented WNW–ESE and 3 others oriented SSW–NNE (a, c, e, g, i, k). These cross-sections indicate good agreement between the depth of the sedimentary layers and their corresponding frequency peaks, represented by the contour maps (b, d, f, h, j, l). Note that a low frequency indicates a deep sedimentary layer. This figure also demonstrates a clear increase in the depth of the sedimentary layer following the SSW–NNE direction.

The uppermost layer is composed of alluvium and limestone belonging to the Quaternary, with a corresponding thickness ranging from 1 to 10 m. The maximum thickness of this layer is located at P10 (Figure 2). These layers have a Vs value ranging between 150 and 350 m/s. This velocity range is in agreement with the one obtained for the city of Oran (200–380 m/s) [66] and in the Middle Chelif Basin (210–350 m/s) [6]. The composition of this formation is approximately similar for the whole Chelif Basin.

The second layer, attributed to Pliocene deposits, is mainly sandy with occasional clay interbeds. Its thickness varies from 1 to 39 m. The maximum thickness of this layer is reached in point 49 (Figure 2) in the industrial zone. Its velocity ranges between 350 to 500 m/s. This variation is probably related to lateral and vertical facies transitions between sands and clays. In addition, the boreholes show that the Pliocene formations are not present in the western parts of the city, where the Quaternary deposits lie directly over the Upper Miocene layers. It should be noted that in the Middle Chelif Basin, the velocity range for the Pliocene formation is between 405 and 630 m/s. The difference is mainly linked to the lithology, where the hard sandstones are predominant within this formation in the Middle Chelif Basin [6].

The third layer from the top, which represents deposits from the Upper Miocene (Messinian), consists of silty clay, marl, limestone, and gravel. The thickness of this layer varies from 5 to 85 m in the industrial zone (P46 in Figure 2), with Vs values ranging from 500 to 850 m/s, which agrees with the Vs values obtained in Oran (460–880 m/s [41]). The deepest layer corresponds to the Middle Miocene (Serravallian) sediments, composed mainly of sandstone and marl. Its thickness varies between 45 and 280 m in P36 (see Figure 2), with Vs values between 850 and 1380 m/s. This range is in accordance with the one obtained in the city of Oran (730–1300 m/s [45]). The wide Vs range probably reflects lateral variability between the sandstone and marl deposits.

These sedimentary and eruptive formations are underlain by a Mesozoic substratum that varies regionally. In some areas, it consists of Cretaceous marl, in others it consists of Jurassic pelite and sandstone. The shear wave velocity of this formation ranges from 1400 to 2600 m/s, probably reflecting the lateral transitions between the Cretaceous marl and the Jurassic sandstone. The velocity range is similar to the ones obtained in the city of Oran [45] and in the Middle Cheliff Basin [32,33].

The sedimentary column reaches a maximum thickness of 390 m in the industrial zone (point P36 in Figure 10). The thickness of the sedimentary cover significantly decreases toward the southern part near the hospital and at point P07 in the city center (Figure 10). This variation is clearly depicted in the cross-sections shown in Figure 9a.

4.5. Vs30 and Soil Classification

The present study addresses verification of average seismic shear wave velocity from the surface to a depth of 30 m (Vs30) as a suitable proxy for a seismic amplification e.g., [67]. The Vs30 map (Figure 11) was calculated by applying Equation (1) at the surface layers derived from the shear wave velocity profiles estimated from the inversion of the HVSR and dispersion curves. The Vs30 values range from 240 to 680 m/s and are divided into two main classes (

Table 3. NEHRP codes for soil type and classification [52].

Vs (m/s)	Soil Type	Classification of Soil
Vs > 1500	Hard rock	A
760 < Vs ≤ 1500	Rock	B
360 < Vs ≤ 760	Very dense soil and soft rock	C
180 < Vs ≤ 360	Stiff soil	D

). Class C (very dense soil and soft rock), with Vs30 values between 360 and 680 m/s, is the dominant classification in the region, in accordance with NEHRP standards [52]. Class D (Stiff soil), with Vs30 values between 240 and 360 m/s, is also observed, particularly in the industrial zone where the Pliocene layer (mainly composed of sand) is present. It is also observed in the hospital zone and to the north of the hospital zone (AR03). The same soil classes were obtained in the city of Oran [45] and in the cities of El-Abadia, El-Attaf, and Ain-Defla in the Middle Chelif Basin [33].

4.6. Correlation Between Bedrock and Frequency

In this section, the bedrock depth values derived from the obtained Vs models were analyzed as a function of their fundamental frequency $f_0$ (e.g., [45,68]). The resulting relationship, illustrated in Figure 12, is nonlinear and can be described mathematically by Equation (3):

$$D\left(f_0\right)=a\ast f_0^b$$

(3)

where $a$ and $b$ are the regression coefficients, $f_0$ is the fundamental frequency, and D is the bedrock depth.

The best fit is given by Equation (4), with a correlation coefficient of 0.91:

$$D\left(f_0\right)=271.63\ast f_0^{-1.158}$$

(4)

4.7. Technical Limitations

Ambient noise methods offer indirect measurements and require calibration with ground truth data to enhance accuracy. The detection of low-frequency signals (<1 Hz) demands prolonged recording durations and expansive sensor arrays, whereas high-frequency noise (>20 Hz) is naturally attenuated by surface and subsurface conditions, limiting the resolution of deeper structures [69].

Interpretation of ambient noise data depends on assumptions regarding wave propagation and subsurface heterogeneity, which can introduce errors, particularly in geologically complex settings where variations in subsurface materials and bedrock composition significantly influence results [70].

Furthermore, HVSR inversion can face challenges in mode identification, leading to interference between Rayleigh and Love waves and potential inaccuracies in velocity estimations. In urban environments, increased high-frequency noise further reduces penetration depth, making deep structure characterization more difficult [71].

5. Conclusions

The study provides fundamental frequencies and Vs profiles for the city of Aïn Témouchent, offering essential data for seismic hazard assessment and risk mitigation. The identification of fundamental frequency ($f_0$) and vulnerability index ($Kg$) enables the detection of areas where seismic amplification effects are likely to occur, which is critical for earthquake-resistant building design. The city holds particular importance as a seismic hazard study zone, having been severely impacted by the 1999 earthquake. While this study provides valuable insights into the subsurface structure and site effects in Aïn Témouchent, certain limitations must be acknowledged. First, the HVSR method, although widely used, does not provide absolute site amplification factors, requiring additional validation through numerical modeling or direct ground motion recordings. Moreover, the resolution of shear wave velocity profiles is constrained by the depth penetration of ambient noise waves, which could be improved by combining passive seismic techniques with active-source methods.

The research aims to improve the understanding of site effects and provide a more detailed characterization of the subsoil. The key findings and conclusions are summarized as follows:

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Environmental noise analysis: Using the HVSR method to analyze ambient environmental noise, the study identifies predominant single-peak curves across the study area, with the fundamental frequency ($f_0$) ranging between 0.8 and 4.8 Hz. In areas with Quaternary deposits, two frequency peaks are observed. The secondary frequency peak (6–15 Hz) corresponds to impedance contrasts at shallow depths between Quaternary and Mio-Pliocene deposits.

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Stratigraphic model: The HVSR and dispersion curve inversion reveals a five-layer stratigraphic structure for the city. The Quaternary layer, at the surface, exhibits shear wave velocities of 150–350 m/s and thicknesses ranging from 1 to 14 m. Beneath this is the Pliocene layer, with shear wave velocities of 350–500 m/s and thicknesses of 1 to 43 m. Below the Pliocene, the Miocene layer is identified, characterized by shear wave velocities of 500–850 m/s and thicknesses of 10 to 124 m. Deeper still, the Lower Miocene sediments show velocities of 850–1350 m/s and thicknesses of 47 to 284 m. At the base of the sequence lies the Mesozoic basement, composed of Cretaceous and/or Jurassic materials, with shear wave velocities ranging from 1400 to 2600 m/s.

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Lateral variations: The inversion of HVSR curves highlights significant lateral variations in both shear wave velocity and sediment thickness across Aïn Témouchent. The resulting shear wave velocity models offer valuable insights for simulating ground motions in the far western region of the Lower Cheliff Basin.

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Soil and liquefaction potential: The area is predominantly composed of very dense soils and soft rocks, with stiff soils concentrated in and south of the industrial zone. The vulnerability index ($Kg$) shows a marked increase in the industrial zone, indicating a higher potential for liquefaction.

These findings can be directly integrated into local seismic microzonation studies and to help urban planners and engineers adopt suitable construction techniques in high-risk areas. Additionally, the shear wave velocity models and sediment thickness estimations can improve numerical simulations of ground motion and refine liquefaction susceptibility maps. Finally, the obtained results could be used to update the Algerian seismic code and inform urban planning and construction practices in the region.