Numerical and Experimental Seismic Characterization of Byblos Site in Lebanon

Abstract

Geological and topographic site effects lead to variations in the spatial distribution of ground motion during large earthquakes. Despite the impact of such phenomena, they remain poorly understood. There is a lack of joint studies of numerical predictions and experimental observations on the geomorphological site effects. Therefore, a comparison between well-constrained models and experimental field observations is needed. Byblos is a seismic region in Lebanon surrounded by faults that historically generated destructive earthquakes. Its geological and geomorphological settings are interestingly characterized by fractured rocks and anthropic deposits altering seismic ground motions. Field surveys in Byblos gathered ambient vibration recordings and surface waves. It identified multiple resonant frequency peaks, suggesting impedance contrasts and lateral variations in subsurface stiffness, using Horizontal-to-Vertical Spectral Ratio (HVSR) and directivity. It also revealed soft, shallow layers with low velocities, indicating potential resonance during earthquakes, using Multichannel Analysis of Surface Waves (MASW) and 2D seismic arrays. Thus, our study on Byblos is a first step for seismic microzoning of the area that evaluated its heterogeneous subsoil, soft surface layers, and anthropic deposits. Finally, combining geophysical data and field measurements with a numerical model allowed a better understanding of Byblos seismic hazards and enhanced its resilience and sustainability.

1. Introduction

Earthquakes have always been among the most dangerous natural disasters worldwide, underscoring the importance of safe construction practices in earthquake-prone regions. The consequences of such phenomena are observed in direct effects, such as the destruction of housing, damage to structures and infrastructure, and loss of human life. As for the indirect effects, they include landslides, liquefaction, changes in topography, and tsunamis. While it is impossible to predict when the next destructive earthquake will occur, countries can adopt building codes that better assess risks, structural vulnerability, and community resilience and anticipate future disasters. For example, strengthening construction techniques and designing structures capable of withstanding specific levels of shaking are crucial steps to protect lives, buildings, bridges, and infrastructure [1,2,3,4,5,6,7,8,9,10,11,12,13]. This is especially vital in high-risk seismic zones.

During historical earthquakes, varying levels of damage have been observed across various locations, even during the same event [14]. This variation is due to site effects [15,16], and it describes seismic waves’ interaction with local geological irregularities (e.g., sedimentary basin fill effects) [17] and topography [18].

Geological or stratigraphic effects have been well documented in studies, such as those by [19,20]. Stratigraphic amplification is critical in explaining the uneven distribution of damage observed after earthquakes, as highlighted by [21,22]. Recognizing its importance, seismic building codes incorporate requirements for these effects, recommending stronger frequency-dependent designs for structures on soft sediment sites than those on bedrock. Another aspect of localized effects originates from topographical features (e.g., relief-induced site effects) such as hills and mountains. Seismic waves begin to reflect and refract until all their energy dissipates, consequently amplifying or de-amplifying seismic ground motion response. Topographic effects are often evident during destructive earthquakes, with damage [23] typically more severe on hilltops than at the hills’ bases. This phenomenon has been widely documented in earthquake reports, such as those by [21,24]. Scientific studies, including those by [25,26], have consistently highlighted the amplification of ground motion at the peaks of topographic features. This amplification is attributed to the constructive interference of seismic waves as they converge and interact at ridge tops, as [27] noted.

The most notable example of such site effects is the 1985 Mexico City earthquake. Despite the epicenter being over 350 km away, Mexico City was extensively destroyed, with more than 35,000 fatalities. The city is situated in a sedimentary basin that resonated, amplifying seismic waves and worsening the disaster [23]. The soft lakebed sediments beneath the city contributed to this unexpected amplification, leading to extensive damage. As for topographical site effects, observations from earthquake events have shown increased damage on hill crests compared to their bottom. It is the case of the 1909 Lambesc earthquake in France [28], and later, the earthquakes in California [29], such as the San Fernando earthquake in 1971 [30], the Whitter Narrow earthquake in 1987 [31], the Northridge earthquake in 1994 [32,33], and the Loma Prieta in 1989 [34]. Similarly, Taiwan has experienced significant earthquakes [35,36], such as the Chichi earthquake in 1989 [37]. Ref. [33] documented one of the earliest cases of topographical effects in Los Angeles, where seismic amplifications during the Northridge aftershocks varied significantly from hilltop to bottom. Geological and topographical site effects play crucial roles in shaping earthquake impacts, often amplifying seismic waves and resulting in much more damage than the distance from the epicenter alone might predict. Understanding these effects [38] is essential for accurate seismic hazard assessments, guiding construction practices, and protecting lives and infrastructure in seismically active regions. Moreover, as pointed out many times by the scientific community, one of the surprising facts related to geomorphological site effects comes from the gap between the numerical predictions and the experimental observations. Therefore, it is mandatory to carefully compare modeling and experimental field observations to improve our understanding of such phenomena.

Seismic hazard and risk assessment studies rely on accurately characterizing the seismic source, path, and site effects to estimate the ground motion parameters and predict the potential damage to structures. Advances in instrumentation, data processing, and numerical simulations have led to advancements in our understanding of seismic events and site effects. However, there is still much to learn in this field. Ongoing research and monitoring of seismic activity and site conditions are critical for improving our ability to mitigate the effects of earthquakes and protect people and infrastructure from seismic hazards. To do so, understanding the mechanical characterization of the subsoil is a must. It is generally obtained from expensive and destructive geotechnical tests and is limited to a small investigated volume. That is the reason why geophysical methods are currently increasingly used for subsurface imaging due to their non-destructive nature and speed. Microtremor recordings provide a cost-effective approach to estimating site characteristics, particularly for resonance frequency and amplification. They are widely applicable in urban zones for mapping fundamental resonance frequencies and supporting microzonation. Multichannel Analysis of Surface Waves (MASW) complements these studies by efficiently obtaining Vs profiles for shallow structures. Combining MASW with the 2D seismic array method, which uses ambient noise, generates reliable shear wave velocity profiles and deeper subsurface imaging down to bedrock, enhancing our understanding of S-wave velocity distributions, known as one of the fundamental factors influencing the stratigraphic amplification effect at the site of interest [20]. The mechanical characterization of soils is typically obtained from geotechnical tests, limited to a small, investigated volume, whether in situ (drillings, penetration tests) or in the laboratory. Additionally, these tests do not provide a comprehensive understanding of the lateral variability of the subsurface. Therefore, the two families of techniques are highly complementary, and empirical relationships between geotechnical and geophysical parameters have been proposed in the literature.

However, few studies have compared the results from geophysical and numerical methods for a specific region. These different approaches were implemented on the experimental site of Byblos in Lebanon. The aim, herein, is to conduct a study that serves as a starting point for Byblos, complementing other studies initiated in different regions of Lebanon: this includes a careful comparison between results from numerical modeling of site effects and field observations and recordings on this experimental site. For this purpose, Section 2 discusses Lebanon’s seismicity, where Byblos is located. Section 3 presents the Byblos case study. Then, in Section 4, site investigations were performed to acquire the geological and seismic data necessary for the simulations and to perform microzoning on the site. The coherence of recorded signals will be evaluated using the Multichannel Analysis of Surface Waves and Horizontal-to-Vertical Spectral Ratio (H/V). In Section 5, building a model as realistic as possible using the acquired experimental data and a real topographic profile chosen from the Byblos region and conducting a numerical study using Flac 2D 8.0 software allows for comparing results from numerical simulations with the H/V instrumental data in terms of the spatial distribution of the soil, as well as consequences in terms of amplification factors and slope stability. Finally, Section 6 discusses the results, and Section 7 concludes.

2. Lebanon’s Seismicity

Lebanon, a country with moderate to high seismicity, is crossed by the great Levant Fault, also called the Dead Sea Fault, one of the major fault systems of the Mediterranean Sea, extending from Syria to Mozambique [39]. In Lebanon, this fault is divided into three major branches that have already generated many destructive earthquakes of magnitudes greater than seven on the Richter scale [40]. Although the seismicity recorded in recent years is only moderate, paleo-seismic studies show that the faults of Yammoune and the fault of Mount Lebanon are now sufficiently stress-loaded to generate new ruptures. The latest events in 2023 in Turkey, Syria, and Lebanon [41,42,43,44] and the surrounding region prove that Lebanon is an interesting country to be studied seismically, primarily with its historical seismicity [45]; one of the largest earthquakes in recorded history occurred in the region of Beirut in 551 AD, with an estimated magnitude of 7.6. On the other hand, Lebanon is a small country with a high population density, especially in urban areas. This means that even moderate seismic events can significantly impact people and infrastructures.

Remarkably, Lebanon’s first seismic building code only dates to 2005. According to this code, Lebanon was considered a single seismic zone with a minimum horizontal ground acceleration of 0.2 g. However, it was not applied in designing structures until after the earthquake of 2008 with a magnitude above 5, which caused damages to houses, especially in south Lebanon. Since then, the government has been encouraged to enforce the application of seismic codes imposed by the board of engineers in 2005 [46]. Nevertheless, no measures were taken or proposed regarding re-evaluating the PGA in these codes, until the 2012 revision slightly increased this value to 0.25 g. However, studies suggest this assessment is inaccurate: [47] showed a PGA varying between 0.15 g and 0.3 g across the territory, which considers a recurrence probability of 50 years, while [48] updated these values and showed a PGA that varies between 0.2 g and 0.8 g over the territory. This indicates that Lebanon has moderate to high seismicity.

Moreover, Lebanon, a strategic region in the Middle East, has a complex landscape, immense historical heritage, and cultural sites prone to earthquakes. Seismic studies can provide valuable insights into how the country can prepare for and respond to seismic events and how seismic activity may impact its infrastructure and economy. These studies can also be used to improve our understanding of earthquake hazards in the region and to develop measures for mitigating their effect. Several studies have already discussed the impact of the region’s seismicity on the Byblos built environment and structural, human, and economic potential losses [46,49,50,51,52,53]. Despite this, there were no microzonation studies or risk assessments for major Lebanese cities until recently. Previous studies in Beirut [54,55,56,57] highlighted the importance of detailed evaluations of local site effects, especially in areas with complex surface layers that influence seismic response. However, no microzoning map is available for the Byblos region yet. Thus, the results of the loss estimations to the built environment can be improved if such refined maps are accounted for.

3. Byblos Case Study

The coastal city of Jbail (40,000 inhabitants) in Lebanon, also known as Byblos, is the largest in the Mount Lebanon Governorate. It is believed to have been first occupied between 8800 and 7000 BC and continuously inhabited since 5000 BC, making it one of the oldest continuously inhabited cities in the world. The old town of Byblos is a UNESCO World Heritage Site. The ruins of successive cities had formed a mound about 12 m high covered with houses and gardens. The ancient site was rediscovered in 1860 by the French orientalist and historian Ernest Renan, who surveyed the area. The extensive excavations and the remaining ruins made Byblos one of the most important archaeological sites in the area, which was mainly studied by [58], a prominent French archaeologist and was followed later by Lebanese efforts. Byblos historical city is about 5 km², located in the coastal area of Jbail’s district with an altitude between 0 m (sea level) and about 90 m. It is an almost flat old town with very gentle slopes with an inclination of less than 17°. Although the old part of Byblos lacks prominent relief features (studies showed that the relief should be at least 25° to show a significant amplification of the signal on the surface [59,60], part of the city, especially the old town (Figure 1), is built on artificial deposits, anthropic layers, and fractured rocks. From a geological point of view, the region is made of limestones and marly limestones from the Cenomanian and Turonian ages. The coastal area is made from scraps of marine and fluvial terraces (Quaternary) that reach the sea to the ancient port of Byblos and sink into it. An anthropic deposit has covered the coastal quaternary layer during the past years. It covers the ancient Byblos city with a thickness reaching about 15 m to 20 m. This kind of deposit of fractured rocks, often heterogeneous, can modify the mechanical properties of the subsurface, leading to amplification or attenuation of ground motion at certain frequencies known as seismological site effects [61]. Byblos is in a region with increased seismic hazard on the Mediterranean Sea [48]. However, despite the historical importance of this city and how it is crucial to protect the industrial and cultural heritage buildings and structures from all kinds of natural disasters, including the seismic hazard, no seismic microzoning of the urban area has been performed so far to quantitatively assess the effects of the local geological structures on seismic ground motion. Given Byblos’ geological and geographical location, the city is susceptible to earthquakes occurring with moderate and great magnitudes. Therefore, ancient and modern structures, including historical monuments and contemporary infrastructure, must be designed to withstand this seismic threat.

4. Location and Acquisition Characteristics of the Geophysical Tests

To determine the fundamental frequency of the subsoil and characterize the subsurface structure, a field campaign was held during the summer of 2020 in the old town of Byblos. Seventy-one microtremor measurements (the locations are shown in Figure 1) were performed in the old town area of 0.8 km² with a 50–100 m spacing between the points. The grid of measured points is, therefore, quite uneven. In this urban environment, avoiding the influence of buildings and traffic in all the measurement locations was impossible because free-field space is rare. Microtremor or ambient vibration HVSR measurements were performed using a three-component Lennartz sensor on the ground surface connected to a CitysharkTM acquisition unit [62]. Thus, ambient wave field vibration was recorded in the north–south, east–west, and vertical directions. Generally, the minimal total duration of ambient vibration recordings depends on the lowest frequency that is desired to be reached. For example, according to the SESAME project [63], a total recording duration of 30 min is required to reach a fundamental frequency of f₀ = 0.2 Hz, while a 10-min recording duration is needed for 1 Hz. Nonetheless, it should be considered that sometimes, noisy windows must be removed from the recorded signal before computation. Hence, a longer recording time is required to fulfill all the criteria recommended by the SESAME Project, as explained further in this section. It should be noted that the longer the recording is on a site with low f₀, the more cycles can be captured, and the easier the peak frequency can be determined. Hence, in this study, the sampling frequency was 200 Hz, and the recording length at each point was 20 min, allowing for the detection of resonance frequencies down to 0.5 Hz [64]. The experimental conditions of microtremor measurements (e.g., [64]) were usually unfavorable. The main difficulties occurred from the low-frequency traffic, anthropic noise, nearby structures such as underground pipelines and buildings, and the poor in situ soil–sensor coupling due to stiff artificial soils (cement, asphalt, pavement, etc.). The Horizontal-to-Vertical Spectral Ratio of microtremors (MHVSR), also known as (HVSR) or the (H/V) was then analyzed using the open-source software package Geopsy (http://www.geopsy.org (last accessed on 1 December 2024)) developed during the SESAME (European Site Effects Assessment using Ambient Excitations project; http://sesame-fp5.obs.ujf-grenoble.fr/ (accessed on 21 November 2024)) and the NERIESJRA4 projects (Network of Research Infrastructures for European Seismology; www.neries-eu.org) [63,65].

In September 2016 and the summer of 2021, two field campaigns were held in the region of Byblos. As a result, three MASW profiles and three 2D seismic arrays were investigated (yellow lines and yellow, blue, and purple arrays in (Figure 1)). A heavy sledgehammer (e.g., 5 kg) was used on an impact rubber plate. The recording’s duration for each shot was 2 s, plus 0.1 s before the sledgehammer hit the plate. Stacking multiple (around 20) impacts was applied to improve the signal-to-noise ratio in the urban area. Twenty-four vertical low-frequency geophones (4.5 Hz) were typically used to acquire Rayleigh waves. The spacing between the receivers was equal to 3 m, leading to three 69 m long profiles. This procedure, therefore, determines the shallowest resolvable depth of investigation (Zmin ≈ 0.3 λmin). In practice, however, the minimum and the maximum investigated depth (Zmin and Zmax) in our survey were limited due to the lack of space for putting in place a longer profile. Thus, the investigated depth ranges between 1 m and 10 m based on the wavelengths (λ = V/f) obtained from the different dispersion curves, which depend on the profile and the source location.

For the 2D seismic arrays, each array was composed of 10 three-component Güralp CMG40Ts connected to Nanometric Taurus digitizers. It was used in a 2D circular geometry, as strongly advised because it has no preferred direction [66], and in ambient vibration wavefields, the locations of the sources are usually unknown. Thus, the arrays were deployed in a circular shape with one station at the center surrounded by nine stations (Figure 1).

Knowing that the depth of penetration and the resolution of the measurement near the ground surface is affected by the receiver spacing, measurements were recorded with different array radiuses (15 m, 50 m, 130 m) while keeping the central station in the same position during the recording session. In this study, we consider the results of the 15 m array due to the limited resolution in the results of the other two. Each recorded time series was divided into numerous frequency bands between 0.5 and 50 Hz. Likewise, each frequency band was subdivided into shorter time windows varying between 50 and 100 times the central period. This subdivision was automatically performed using the gphistogram tool implemented in Geopsy after defining the frequency bands and time windows within the tool.

5. Field Data Analyses and Results

5.1. Multichannel Analysis of Surface Waves—MASW

To estimate the shallow shear wave velocity structure of Old Town Byblos, we analyzed the linear data using the software package Geopsy (http://www.geopsy.org). The software program implements the active F-K technique, constituted of a two-dimensional Fourier transform over time and space. A detailed assessment of the F-K method for analyzing surface wave data to derive subsurface shear-wave velocity profiles is provided by [66]. In the FK domain, there is a two-dimensional spectrum, the amplitude and the phase spectrum, but usually, only the phase spectrum is displayed for clarity reasons. The phase spectrum is then represented with a color intensity map used to show the amplitude of the data at different frequencies and wave number components. The data analysis herein was performed in the frequency domain. The basic idea of the beamforming technique is to sum the energy propagating concerning a particular wave number k and to keep the azimuths and phase velocities producing the maximum energies [67]. The dispersion curve can be obtained by performing a double Fourier transform to represent the signal information in the frequency–wavenumber (f-k) space [68], which is the algorithm used here and described above. The FK space is then transformed into the frequency–velocity (f-v) space using the following relationship:

$$\mathrm{V}={\displaystyle \frac{1}{\mathrm{P}}}={\displaystyle \frac{2\mathrm{\pi }\mathrm{f}}{\mathrm{k}}}$$

(1)

where V is the phase velocity, and P is the phase slowness of the surface wave at frequency f and corresponding wavenumber k.

The last step before picking the experimental dispersion curve is to stack the obtained results for each recording. The latter helps to eliminate the random noise and improves the data quality. When all the records have been evaluated and stacked, the fundamental mode is selected by picking points in the highest energy area. These points represent the experimental dispersion curve used during the inversion process, aiming to compare them with theoretical dispersion curves.

Two velocity inversions were computed for MASW profile 1. The first case was for the forward shot 3 m away from the first geophone. The shortest wavelength detected by Dinver (the tool implemented in Geopsy and used to resolve the inversion problems on the extracted Rayleigh DC) was equal to about 9.5 m, and the longest wavelength was equal to about 16 m. Hence, according to the limitations cited previously, the maximum depth that can be explored using the forward shot results of profile 1 was approximately 4.8 m, and the shallowest depth is around 2.8 m. The inversion was conducted in a one-layer uniform medium laying above a half-space, with interface depths ranging from 2.8 m to 4.8 m. Considering a range of values based on the geology of the area, we set the shear wave velocity (Vs) to vary between 250 and 1000 m/s, while the default values for the Poisson’s ratio (0.2 to 0.5) and the density (2000 kg/m³) of the layer material remained unchanged. The results were derived from 10,000 theoretical model computations.

The second case corresponds to the reverse shot 3 m away from the first geophone. The shortest wavelength detected by Dinver on the picked Rayleigh DC was equal to about 4.8 m, and the longest wavelength reached was approximately 16.5 m. Hence, according to the limitations cited previously, the maximum depth that can be reached is equal to around 5 m, and the shallowest depth is approximately 1.5 m. The inversion was then computed in a one uniform layer medium laying over a half-space with an interface set between 1.5 m and 5 m depth. The Vs variations, the Poisson’s ratio, and the density were kept the same as in the previous case. The results were also obtained after 10,000 theoretical model computations.

The phase velocity diagrams in Figure 2a,d show monotonical energy variation with an experimental dispersion curve whose velocity decreases with the frequency without any peculiarity in its shape. This behavior commonly happens in stratified underground soil layers because shear wave velocity increases with depth in such medium. The misfit between the best theoretical dispersion curve (in grey) in Figure 2b,e and the picked observed DC (in black) for the forward (first case) and the reverse (second case) shots are approximatively equal to 0.0039 and 0.0041, respectively. The two extracted dispersion curves show slight incoherence. They are not compatible on a small scale. Generally, two different extracted DCs for a forward and a reverse shot indicate the existence of lateral variation due to the medium’s heterogeneity. This is not the case for the results of profile 1 because the two dispersion curves seem parallel and have a small variation of about 150 m/s in velocity.

After inverting the curves, the obtained velocity profiles in Figure 2c,f are represented in Figure 3. The evaluated S-wave velocity profiles in Figure 3 (red profile) show a shallow low-velocity layer down to 3.5 m, with Vs equal to 370 m/s. In the lower half-space, the velocity increases to approximately 590 m/s. On the other hand, the shear wave velocity profile in Figure 3 (dashed blue profile) presents a shallow low-velocity layer down to 3.5 m. It has a quite similar behavior as the first case, with Vs equal to 390 m/s, which increases to approximately 530 m/s in the lower half-space. Thus, Figure 3 shows minimal variation between the velocities, proving the coherence of the two extracted DCs on a large scale. These variations are expected in inversion problems and can be due to differences in signal quality.

Another field campaign was held in the summer of 2021. Two MASW profiles (MASW profiles 2 and 3 in Figure 1) were performed. For Downtown Byblos (MASW profile 2 in Figure 1), located above a quaternary formation according to the geological cross-section, the results (Figure 4) show abrupt contrast (sharp slope in the DC curves) at depth (low frequency) and a possibility that a stiff layer exists on the top layer. This conclusion is based on comparing our results with the example by [66]. In their example, they describe stratigraphic conditions where higher modes may be dominant, and the apparent dispersion curve may jump from one mode to the other.

We tested this theory by performing an inversion of the extracted DC, first by imposing a fundamental mode (Figure 4a) and then by imposing a first higher mode (Figure 4b). The inversion was carried out between 3 m and 10 m, as the lowest and highest detected wavelengths were approximately 11 m and 27 m, respectively, using a one-layer over half-space model. The misfit value in case (a) was higher than in case (b), indicating that the error was lower when imposing the higher mode. Both velocity profiles show a strong contrast between the first and second layers. In the first case, the boundary between the two layers was identified at 8.5 m, while in the second case, it was detected at 5 m. The first layer’s velocity was around 650 m/s in the first case, jumping to 3000 m/s, while in the second case, the velocity was around 350 m/s, increasing to 1200 m/s. These results suggest that imposing a higher mode during the inversion is more reliable and produces results that are more consistent and aligned with those obtained from the inversion of the DC from profile 1.

For Hboub (MASW profile 3 in Figure 1), located on the C5 formation, were not conclusive either. No proper dispersion curves leading to a realistic shear wave velocity profile can be extracted from the shots. For both profiles 2 and 3, the geophones could not be embedded in the soil; instead, they were positioned on the surface of a rigid layer using tripods. This placement limited the coupling and might have influenced the results, potentially introducing lower data quality that cannot be interpreted with great confidence.

Hence, the shear wave velocity profile generated using data of the reverse shot at 3 m for the MASW profile 1 was adopted. Compared with the locations of other measurements (HVSR and 2D seismic arrays), the positioning of profile 1 renders the analysis and interpretation of extracted information in the old city of Byblos more pertinent since all the other measurements were conducted on the same geological formation. Further geophysical depth investigations are presented next.

5.2. The 2D Seismic Array

Intending to reach deeper layers to produce the shear wave velocity structure of Old Town Byblos, we used the results of the passive 2D seismic array method. The low frequencies allow for investigating deeper layers. Thus, the inversion of the dispersion curve extracted from ambient vibration data should show the structure of the subsoil deeper than the subsoil investigated using the MASW profile.

In this section, we analyzed the data provided by the smaller array with an aperture of 15 m (the yellow circular array in Figure 1). The passive F-K method was applied [66]. The key difference between the active and passive techniques is due to the nature of the recorded waves. In the case of the passive technique, all types of waves, including ambient noise and naturally occurring seismic waves, are analyzed. In the passive F-K (frequency–wavenumber) method, signals are recorded using a 2D array of sensors. Because these signals originate from various directions, their wavenumbers are first projected onto the x and y axes in the transformation from the time–space domain to the frequency–wavenumber domain. Once this projection is completed, the resultant wavenumber at each point in space is calculated. This resultant wavenumber is then used to compute the phase velocity as a function of frequency, following Equation (1). The corresponding velocity diagrams are represented in Figure 5. We can notice that the maximum energy is concentrated between 10 Hz and 35 Hz (the green dots in Figure 5). For these data, the lowest wavelength (λmin = Vmin/fmax) detected on the picked Rayleigh DC was equal to 11 m, and the largest wavelength (λmax = Vmax/fmin) reached was equal to 140 m (Figure 5). Hence, the maximum depth that can be reached is equal to 46 m, and the shallowest depth is 3.5 m. So, the inversion was computed using three-layer mediums, laying over half-space (

Table 1. The first set of input parameters used in Dinver for the inversion of the dispersion curve.

Layer Number	Poisson’s Ratio	Vs Range m/s	Bottom Depth Range	Vs Variation	Visited Models	Minimum Misfit Value
Layer 1	0.2–0.5	200–1000	3.5–40	Uniform	20,107	0.88
Layer 2	0.2–0.5	200–1000	3.5–40	Uniform
Layer 3	0.2–0.5	200–1500	3.5–40	Uniform
Half space	0.2–0.5	1000–3500	-----	Uniform

). The Vs was set to vary between 250 and 2500 m/s. The default values for Poisson’s ratio (range between 0.2 and 0.5) and the density equal to 2000 kg/m³ were kept the same. The results were obtained after 10,000 theoretical model computations. After the inversion, the best velocity profile (Figure 6) shows a shear wave velocity value equal to about 250 m/s above the layer of velocity 450 m/s to a depth of 12 m. This velocity increases to 800 m/s up to 36 m, then abruptly increases to 1400 m/s. The velocities of 250 m/s and 450 m/s of the first two upper layers are consistent with those obtained from MASW.

An additional test was conducted, and the inversion was performed by imposing non-uniform variations on the layers using the linear increase option. The outcome of this inversion is illustrated in Figure 6b. The shear wave velocity profile aligns with the findings from the inversion conducted using uniform layers with one slight difference in the last detected layer, herein exhibiting a velocity of 1400 m/s.

5.3. Combination of Active and Passive Extracted Dispersion Curves

The inversion for these combined dispersion curves was computed using four medium layers, laying over half-space. The parameterizations tested are described in

Table 2. The input parameters used in Dinver for the inversion of the combined dispersion curve.

Layer Number	Poisson’s Ratio	Vs Range m/s	Bottom Depth Range	Vs Variation	Visited Models	Minimum Misfit Value
Layer 1	0.2–0.5	50–3500	1.5–10	Uniform	50,107	0.32
Layer 2	0.2–0.5	50–3500	1.5–20	Uniform
Layer 3	0.2–0.5	50–3500	10–30	Uniform
Layer 4	0.2–0.5	50–3500	10–50	Uniform
Half space	0.2–0.5	1000–3500	-----	Uniform

.

After inversion, the best velocity profile (Figure 7) shows a shear wave velocity value equal to about 350 m/s up to a depth of 2 m. This velocity increases to the value of 500 m/s down to approximately 12 m, then increases to 850 m/s down to around 38 m in depth. Based on the thickness of the Quaternary layer shown on the geological cross-section (discussed later in Section 5.5,), the three layers correspond to the anthropic and the quaternary layers. The small differences in the interface’s depth and the shear wave velocity reached at each depth for each inversion case may be due to the range of uncertainties that come with inversion problems. At 38 m, a sudden increase of the velocity up to around 2000 m/s was present, and this should correspond to the fractured limestone rock layer C5. From the estimated velocities, the average shear wave velocity can be computed according to Equation (2):

$${\mathrm{V}}_{\mathrm{S}\mathrm{Z}}={\displaystyle \frac{\mathrm{Z}}{{\sum }_{\mathrm{i}}{\mathrm{h}}_{\mathrm{i}}{/\mathrm{V}}_{\mathrm{i}}}}$$

(2)

where Z is the thickness of the layers; h_i and V_i are the thickness and velocity of each sublayer, respectively. This formula allows computing the Vs30 for z = 30 m. This parameter is one of the main parameters used in estimating site effects.

It should be noted that the Vs₃₀ computed using the minimum misfit Vs profile is approximately ≈600 m/s. According to the EC8 soil categories (2004), the class of this soil is clay, the same type B for which a weak to moderate stratigraphic amplification is expected.

No studies have been conducted on Byblos before, except for the tests conducted near the municipality. A soil sample was collected at a depth of 6 m in an area adjacent to the Byblos municipality during a field campaign carried out through Notre Dame University in Lebanon. The results were published in [69]. The collected samples were used to characterize the soil and determine its properties, such as plasticity index, cohesion, and friction angle. According to the USGS, the soil is a Clayey Sand SC, or a poorly graded clayey soil A-7-6 (6) type according to AASHTO was identified. It is a clayey soil of high plasticity and a high water table with an internal friction angle of =25° and a cohesion of 6 kPa. It is worth noting that soils with high plasticity have a small damping and a relatively wide range of linearly elastic behavior, which are prerequisites for resonance. Therefore, the results from the MASW and the 2D seismic array data inversion appear realistic because they match the study’s results in 2017.

5.4. Experimental Horizontal-to-Vertical Spectral Ratio of Microtremors (HVSR) or (H/V)

The aim of single-station measurements is the estimation of the fundamental resonance frequencies of the Old Town Byblos. First, each recorded time series was divided into stationary shorter time windows varying from 20 to 50 s without overlapping. Then, in each window, signals were 5 percent cosine tapered and transformed into the frequency domain using a Fourier transformation. All the Fourier spectra were smoothed using the Konno–Omachi algorithm with a width value set to 40 [70]. The HVSR or H/V results are analyzed and interpreted according to the SESAME project criteria [63] in the frequency range between 1 and 20 Hz. The analysis excludes both the range below 1 Hz because it may be impacted by the weather conditions [71,72,73] and the range higher than 20 Hz, which reflects the very shallow sublayers uninteresting for engineering studies.

5.4.1. HVSR Results

The most notable aspect of the obtained results is the heterogeneity observed, as the behavior of the curves differed even between stations located very close to each other. This highlights the variability of the subsurface. According to the SESAME Project [63], the analysis of the H/V curves showed that 62% of the recordings fulfilled the criteria for reliability measurements, but only a few showed clear peaks. In some curves, the noise persisted during the total measurement duration, which was predictable because Byblos is an urban environment. In most reliable H/V measurements, no high amplitudes were registered, and the standard deviation, represented in dashed lines on the HVSR curves, was sometimes greater at low frequencies and became narrower at high frequencies. Such behavior is mainly due to the noise generated by the traffic in the area. Usually, if enough criteria are fulfilled according to the suggestions of the SESAME project [63], and the H/V curve shows a clear peak, this peak frequency is the fundamental frequency of the first subsurface layer of soil. When the peak has stratigraphic origins, it appears on the Fourier spectrum as a detachment of the horizontal and vertical components, forming as eye-shape pattern (black arrow in Figure 8). But it is recommended to always make sure this peak has no anthropic origins. In this study, most of the H/V curves corresponding to the 71 measurements showed a narrow peak at approximately 1.5 Hz (red circle on R051, curve in Figure 8c). Because all the recordings were performed in an urban environment, it was recommended to check if this perturbation was due to site effects or had an industrial origin. Thus, the random decrement technique [58] suggested in the SESAME project and implemented in Geopsy was applied at the frequency band between 1 Hz and 2 Hz. A cosine taper was applied. This resulted in a sustained frequency with damping below 5%. Additionally, the Fourier spectra curves for all three components exhibit a sharp peak at this frequency (Figure 8). Both results suggest with very high confidence that this frequency peak corresponds to a forced ambient vibration induced by low-frequency anthropic noise and should not be considered in this study. On the other hand, a clear HVSR or H/V peak was obtained at the frequency range between 4 and 6 Hz on curve R051. This result shows a high impedance contrast between the subsoil and bedrock in this area, detected with 20 min of recording.

The measurements were registered on artificial soil because of the impossibility of finding natural soil in this urban old town, and high levels of noise were noticed during the whole recording session. Therefore, the criterion of clarity for these curves was not fulfilled, and no fundamental frequency can be determined according to the SESAME project. Many complex H/V curves were obtained during this campaign, where no clear peaks were identified in the curves in the frequency range between 1 and 20 Hz. Instead, broad peaks and plateau-like shapes (Figure 8a) of low amplitude were detected. For these H/V curves, the peak frequency is defined as the frequency cut-off of the “plateau”. These shapes are obtained in the case of strong lateral material thickness variation (3D structure beneath the surface) [74], and they were observed in complex subsoil structures studied by [75]. However, it was still possible to determine the resonant frequency of the subsoil layer because the curves satisfied the reliability criteria [63]. That is why we analyzed the spectral ratio curves and by relying on the interpretations by [76]. Other peculiar shapes, such as flat curves with amplitudes between 1 and 2 or curves with amplitudes below 1 (Figure 8b) due to the velocity inversion, and multiple-peak curves (Figure 8d) were also detected.

5.4.2. Results Comparison

The analysis of the different complex cases with various scenarios of the H/V curves and the picking of the fundamental frequencies on curves were achieved according to the interpretations done by [76] and the SESAME project.

The distribution of detected frequencies for the 63 measurement points is illustrated in Figure 9. From this plot, it is evident that there are consistent results at low frequencies and a close distribution at intermediate frequencies. Such consistent distribution is typically observed in sedimentary basins with symmetrical shapes. Therefore, in the case of the old town of Byblos, there is no obvious distribution of the subsurface geology concerning the geographical position. The fundamental frequencies range between 3 and 20 Hz. At certain points, two different frequencies were detected at different scales, and in some other cases, three frequencies were detected. The green dots, representing frequencies of the shallow subsurface layer, are widely scattered across a frequency range of 8 to 20 Hz. In contrast, the blue and red dots, reflecting frequencies of deeper layers, show more consistency, with values varying within narrower ranges. This suggests that the frequencies of the blue points indicate a coherent state of the deeper layer. By calculating the thickness of this layer using an average shear wave velocity Vs30 = 600 m/s, we estimate the thickness of the quaternary layer to be approximately 42 m, which aligns with the values reported in the literature. As for the frequencies of the red points, they show the heterogeneity of the intermediate subsurface layer. Conversely, the scattering of the green points indicates variation in the shallowest subsurface layer over short distances. This is due to the difference in the types of materials that cover the urban area on the surface.

5.5. Numerical HVSR or H/V Curve

To assess numerical H/V on Byblos and compare it with experimental curves, we conducted a series of numerical simulations using the FLAC 2D 8.0 finite difference software program. Building an accurate model requires setting the grid size to less than one-tenth to one-eighth of the wavelength of the input wave’s highest frequency, preventing numerical distortion. In our case study, the highest frequency of the injected signal was 7 Hz, and the softest layer shear wave velocity was 600 m/s. Thus, the grid element size was set to 8.5 m. The rheological model for all layers was linear elastic, involving parameters such as density (ρ), Poisson’s ratio (ϑ), and Young’s modulus (E), which relate to shear a wave velocity (Vs) based on Equation (3):

$${\mathrm{V}}_{\mathrm{S}}=\sqrt{{\displaystyle \frac{\mathrm{E}}{2\left(1+\mathrm{\vartheta }\right)\ast \mathrm{\rho }}}}$$

(3)

Shear wave velocities Vs of the layers were determined based on the profiles obtained from MASW and 2D passive seismic methods. ϑ was fixed to 0.25, and ρ was determined according to the theoretical values for different types of soils and rocks [77]. The E was then computed accordingly using Equation (3). The geomechanical parameters of the materials are presented in

Table 3. Geomechanical parameters of the materials for the different studied cases. The shear wave velocity value Vs was obtained from the shear wave velocity profile. Parameters E, ρ, and ϑ were computed accordingly.

Materials	E × 106 (Pa)	ρ (kg/m3)	ϑ	Vs (m/s)
Material 1 (qt)	1600	1800	0.25	600
Material 2 (C5)	16,200	2000	0.25	1800
Material 3 (C4)	29,100	2200	0.25	2300

.

The compressional wave velocity Vp of the bedrock corresponding to the C4 layer was computed using the following Equation (4):

$$V_P=\sqrt{{\displaystyle \frac{2(1-\vartheta )}{1-2\vartheta }}}{V}_S$$

(4)

With ϑ equal to 0.25 and Vs equal to 2300 m/s according to Table 3.

Given that multiple sublayers in the 40 m thick quaternary soil layer would require fine meshes, we used representative single layers to simplify simulations. The model’s boundary conditions were set to mimic an infinite formation: fixed displacements at lateral boundaries and the base (X and Y directions) and initial gravity-induced stresses were applied. Before any dynamic calculations, FLAC ensured equilibrium under static conditions; we then reset displacements to isolate seismic-induced deformations. To prevent reflected energy, the model employs Lysmer and Kuhlemeyer’s “quiet boundaries”, using normal and tangential dampers on the base and lateral edges. Regarding the dynamic excitation, a synthetic accelerogram (Ricker waveform) was applied at the base, with a peak acceleration between 0.1 g and 0.3 g. The seismic signal was applied as normal $\sigma n$ and shear stresses $\sigma s$ given by the following equations:

$$\mathsf{\sigma }\mathbf{n}=2 \ast \mathsf{\rho } \ast \mathbf{V}\mathbf{p} \ast {\mathbf{v}}_{\mathbf{n}}$$

(5)

$$\mathsf{\sigma }\mathbf{s}=2 \ast \mathsf{\rho } \ast \mathbf{V}\mathbf{s} \ast {\mathbf{v}}_{\mathbf{s}}$$

(6)

where ${\mathrm{v}}_{\mathrm{n}}$ and ${\mathrm{v}}_{\mathrm{s}}$ represent the velocity normal and tangential components at the boundary, ρ is the mass density, and Vp and Vs are the P and S wave velocities, respectively. A Rayleigh damping, effective for a frequency-independent response, was set at 2% with a 5 Hz resonant frequency to control energy dissipation.

Four points were picked on the quaternary layer (Figure 10), spaced approximately 40 m apart, and are represented in Figure 11 with a thick red arrow. The chosen location corresponds to the projection of four experimental H/V measurements recorded along the profile E-W in ancient Byblos (Figure 10). Vertical and horizontal signals were recorded at the surface of the model. Using Geopsy, we plotted the H/V curves at these four points (Figure 12a). A peak at a resonance frequency between 4 and 5 Hz can be seen for all four points. To validate this, we examined the Fourier spectra of the vertical and horizontal response components (Figure 12b), confirming the presence of an eye shape between 4 and 5 Hz, corresponding to the resonance frequency peak. Considering the thickness of the layer beneath based on the geological cross-section, this result confirms that the average velocity Vs in the zone is approximately 600 m/s. This result is consistent with the experimental results discussed in Section 5.3.

These curves can be compared to the experimental H/V curves recorded in Byblos City at points close to the chosen profile (Figure 12c). We can observe that between 2 Hz and 6 Hz, the behavior of the curves is similar and shows a peak between 4 and 5 Hz. As for the amplitude of the numerical H/V curve, it is greater than the amplitude of the experimental curves. This is logical since, in the numerical model, no artificial surface soil was included, which, as previously explained in earlier paragraphs, affects the amplitude values of the H/V curves.

6. Discussion

This article aims to study the numerical and experimental seismic characterization of the Byblos site in Lebanon. The analysis results of all the field records show that Byblos presents a very heterogeneous subsoil made of stiff and soft materials. They also show huge lateral variation, confirmed by the analysis of recorded data.

An H/V measurement was performed next to the municipality, at the same location where the soil sample was collected in 2017, during a field campaign of the research team at Notre Dame University in Lebanon [69]. A clear peak at the frequency of 6 Hz was detected with a relatively high amplitude. The measurement was performed on the natural soil on this site, as 6 m of the surface layers were excavated. Given that the quaternary geology should be consistent across the entire area of the old town, all the H/V curves should show clear peaks. However, this was not the case for all the measurements in this study; instead, some curves displayed very low amplitude. This suggests that the low amplitude observed in many H/V measurements was likely due to artificial soil on the ground surface where the measurements were taken. On the other hand, S-wave velocity profiles have shown the presence of different quaternary layers that may not have enough velocity contrast to show multiple peaks on the H/V curves.

According to this result and in case thick layers exist, the extracted curves should resemble 1D structures. It is worth noting that curves presenting broad peaks or plateau-like shapes imply the presence of a 2D subsurface structure. Hence, they should not be used for deriving any quantitative information on average shear wave velocity or average sediment thickness using the simple f_0i = Vs/4h relation (generally used for 1D structures). However, in our case, we used the 1D f₀ formula because we are trying to determine the potential thickness of the subsoil underneath Byblos (Figure 13). As for the fundamental frequencies in 2D scenarios, the selected H/V peak frequency aligns within +/− 20% of the theoretical 1D resonance frequency in the flat part of the soil structure, where clear peaks are found [74]. Thus, the fundamental frequency range for the 2D structure in Jbail should be between 4.5 and 7.5 Hz, corresponding to +/− 20% of 6 Hz. This range aligns with the intermediate fundamental frequencies f₀₂ extracted from the recordings in this study (Figure 9b).

These frequencies are likely associated with the heterogeneous middle layer with a shear wave velocity of Vs = 450 m/s (Section 5.3). The depth of this layer varies between 12 and 26 m (Figure 13). This variation may be attributed to several factors, such as natural erosion, the deposition of other materials due to anthropogenic activities, or the alteration of the soil needed to build or construct infrastructure in the old town.

Additionally, a numerical model was built based on real and experimental data to develop an initial representation of the subsurface of Byblos. Simulations using a model with a quaternary layer having an average shear wave velocity of 600 m/s overlying a bedrock revealed a resonance frequency of approximately 4.5 Hz. This result aligns with the experimental findings, confirming that the average shear wave velocity of the subsurface in the old city of Byblos is approximately 600 m/s, with a total thickness of the quaternary layer ranging between 40 and 50 m. The region has undergone erosion over time. Thus, part of the quaternary layer has been removed, revealing the deeper C5 layer closer to the coast. The non-uniform variations in the thickness observed are consistent with reality. Although the geological cross-section along the dip direction shows a uniform increase in thickness towards the sea, the actual situation is more complex. Therefore, finding thinner quaternary layers near the sea seems logical and supports the hypothesis of the erosion of the surface quaternary layer, which explains the low thickness of the quaternary layer on the west side. A second hypothesis suggests that the upper boundary of the C5 layer has undergone significant deformation, resulting in irregularities and, consequently, a change in the thickness of this layer before the appearance of the quaternary layer.

7. Conclusions and Perspectives

This article aims to study the numerical and experimental seismic characterization of the Byblos site in Lebanon. The analysis results of all the field records show that Byblos presents a very heterogeneous subsoil made of stiff and soft materials with huge lateral variations. In this geological context, the analysis of recorded data confirmed the presence of soft and fractured rocks, as suggested by Dubertret, with a resonant frequency of approximately 4.5 Hz.

The topography of the measurement area in Byblos presents a very shallow slope and does not exhibit distinctive features, as the slope angle does not exceed 10°. Additionally, topographic effects generally do not significantly impact H/V results. Hence, the latter reveals that, in our case, the HVSR measurements effectively reflect the geological heterogeneity of the area. Additionally, the shear wave velocity profile extracted from the data of profile 1 revealed the presence of a soft material directly beneath the surface, with a low shear wave velocity of about 250 m/s and an average shear wave velocity of Vs₃₀ = 600 m/s.

Regarding the thickness of the first soil layers, we combined the results of the extracted fundamental frequencies from the H/V curves with the obtained shear wave velocities. It allowed for us to identify a potential range of layer thicknesses varying between 12 and 50 m.

Despite these advancements in this research that focused on simplified 2D models, further studies will consider three-dimensional models to provide a more accurate representation of the seismic hazards in Byblos. This would involve integrating more detailed data on the geological structures beneath the city and conducting additional field studies to refine the models. More in-depth geotechnical studies would offer a clearer understanding of how these deeper layers interact with the surface layers, particularly in identifying the water table level, determining the mechanical properties of the various layers, and assessing their potential impact on seismic wave propagation. Moreover, non-linear soil behavior under high-intensity seismic loading will be studied in future research.

The aim of these suggested perspectives will allow for the development of microzoning maps for earthquake hazards and risks in Byblos: an invaluable tool for urban planners, architects, and engineers.