Introduction

The modeling of ground motion through the deterministic technique, employing an empirical approach or instrumental methods, relies on macroseismic data of earthquakes and is contingent on local site effects within heterogeneous media. Several studies have been dedicated to advancing deterministic ground motion modeling, with a specific focus on incorporating site effects (Babayev et al. 2019; Babayev et al. 2020a; Bulajic and Manic 2006; Frankel and Stephenson 2000; Gurboga and Sarp 2013; Kanlı 2010; Kanli et al. 2006; Kanli et al. 2008; Olsen et al. 1997; Panza et al. 2001, 2011).

In this study, the primary focus in seismic hazard assessment lies in the application of the deterministic approach, which aims to outline a scenario for the “maximum earthquake.” This scenario is designed to illustrate the most potent ground motion at the site. The approach involves computing peak ground acceleration and intensity values, taking into account detailed local site effects.

Theoretically, probabilistic seismic hazard assessment explores the likelihood and recurrence intervals of large events (Deif et al. 2013). Both deterministic and probabilistic methods necessitate substantial databases encompassing geology, tectonics, and seismicity for estimating attenuation and amplification characteristics, respectively. However, for engineering dynamic analysis, it is crucial to focus on individual earthquakes that have the most significant impacts (Deif et al. 2013).

The conservative deterministic seismic hazard analysis undertaken in this research allows for the identification and definition of seismic sources that may influence the studied area. Subsequently, the analysis evaluates the maximum potential earthquake effects on the area from each of these sources. This approach ensures a comprehensive understanding of the seismic risk posed by individual significant events, contributing valuable insights for engineering considerations and risk mitigation strategies.

In the present approach to ground motion modeling, the methodology does not explicitly incorporate forces and stresses that initiate ground motion on the fault plane. Instead, it heavily relies on actual earthquake events and their impact on the study area, taking into account local site conditions. The site effects can significantly influence the amplitude, frequency, composition, and duration of ground shaking (Santulin et al. 2012). Considering the integrated interplay of seismic waves and the lithological characteristics of soil and rock deposits is of paramount importance.

Various techniques, both empirical and theoretical, are available to estimate site effects (Kawase 2003; Pitilakis 2004; Santulin et al. 2012). The current research predominantly relies on the application of geotechnical parameters of local site conditions, incorporating computational techniques. These techniques are developed to model the seismic source process and the propagation of seismic waves in heterogeneous media, employing analytical or numerical 1D, 2D, or 3D models (Igel et al. 2009; Panza et al. 2001; Santulin et al. 2012).

Acknowledging the limitations, especially the lack of essential information about the geological deep structure, laboratory tests of soil deposits, and rock masses for estimating their physical-mechanical characteristics, often leads to the adoption of simplified approaches. In this paper, a proposed methodology aims to compute local- and near-field ground motion, emphasizing the importance of considering the vertical propagation of seismic motion in heterogeneous media from bedrock to the surface. This involves incorporating amplification with various soil physical-mechanical properties, and in practical terms, considering one dimension, depth, while assuming that the layers are infinitely extended in the other two dimensions (Santulin et al. 2012).

Theoretically, the significant amplification of seismic waves stems from the impedance contrast among various soil layers, encompassing subsoil content and bedrock. In investigating the response of soil content, we utilized the technique of a 1D code (PSHAKE: Sanò and Pugliese (1991)).

The algorithm for generating the soil model has been tested and demonstrates its capability to perform rapid computations of ground motion, specifically for the purpose of seismic hazard mitigation. The chosen study area is the southeastern slope of the Greater Caucasus mega-anticline in Azerbaijan (Fig. 1). Within this region, our focus is directed towards the Ismayilli-Shamakhi zone and specific sites characterized by diverse ground conditions where previous earthquakes have resulted in significant damage.

Fig. 1
figure 1

Map of surface geology in and around the research region (Bochud 2011) with geometric figure showing the study area

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This study area stands out for having the highest seismicity in Azerbaijan (Babayev et al. 2020a; Babayev et al. 2020b; Telesca et al. 2013; Telesca et al. 2017; Tibaldi et al. 2020; Yetirmishli et al. 2015). Given the crucial role of lithological conditions in this context, the modeling of 1D site effects is deemed essential, offering an effective means to assess the impact of local soil conditions on ground shaking.

The area under investigation represents a singular seismogenic zone within the context of three primary blocks (Babayev et al. 2020a; Tibaldi et al. 2021), each characterized by distinct tectonic structures (Alizadeh et al. 2016; Kangarli and Akhundov 1988) contributing to the seismic hazard of the eastern slope of the Greater Caucasus in Azerbaijan. The prevailing contemporary stress situation is marked by extension, predominantly featuring normal fault and normal fault with strike-slip element (Agayeva and Babayev 2009; Babayev et al. 2020b; Jackson et al. 2002; Telesca et al. 2017; Tibaldi et al. 2020).

This region has witnessed some of the most potent earthquakes, reaching intensity levels of IX (MSK-64) in Azerbaijan (Babayev 2010; Babayev et al. 2020a, 2020b; Babayev and Telesca 2014; Kadirov 2004; Telesca et al. 2013, 2017; Yetirmishli et al. 2013). Notably, the most substantial contemporary event recorded in this part of Azerbaijan occurred on February 5, 2019.

We conducted calculations for the peak ground acceleration resulting from two hypothetical earthquake scenarios. The first scenario involved the 1902 Shamakhi earthquake with a magnitude of M = 6.8, considered a local-field event. The second scenario focused on the 2000 Baku-Caspian earthquake with a magnitude of Mw = 6.5 (treated as a single shock with an accepted average magnitude of 6.5), regarded as a near-field event. These scenarios represent the potential maximum magnitudes anticipated in the region (Babayev et al. 2010; Babayev et al. 2020a; Babayev and Telesca 2014; Telesca et al. 2017).

The magnitude of the 1902 Shamakhi earthquake was initially estimated as 6.9 ± 0.2 (Kondorskaya and Shebalin 1982). However, considering the duration of ground shaking, approximately 30–40 s, and the length of the ruptured area, about 80 km (Boghdanovitch 1904; Levitski 1902), its magnitude could potentially be as high as 7.3.

In the final step of our analysis, we computed intensities based on the values of peak ground acceleration derived from these scenarios.

Geological and seismo-tectonic context

The Ismayilli-Shamakhi seismogenic zone represents an intricate geological structure in the southeastern section of the Greater Caucasus, distinguished by a complex system of anticlines and synclines exhibiting significant deformation with various fault regimes (Alizadeh et al. 2016) (see Fig. 1).

The Greater Caucasus, situated entirely within an intraplate setting on the Eurasian plate, features a southern slope characterized by two primary mountain ranges (Alizadeh et al. 2016). These mountains extend across the region between the Black and Caspian Seas (Babayev et al. 2020a).

The geological characteristics of the examined region have been significantly shaped by the historical evolution of the Greater Caucasus and the remnants of ancient formations. The area is encompassed by a diverse range of volcanic and sedimentary rocks spanning from the Middle Jurassic to the Holocene period (Alizadeh et al. 2016).

In general, the geological formations within the study area can be categorized into three distinct layers. The first layer pertains to relatively ancient formations, specifically the Middle Jurassic sediments. This layer comprises a basalt-sedimentary structure, predominantly characterized by alternating layers of tuffite, tuff siltstone, tuff sandstone, tuff-gravel, tuff-breccia, and tuff-conglomerate. The second layer, dating back to the Early Cretaceous, is primarily composed of tuffites, tuff sandstones, and limestone, with occasional intrusions of clay, argillites, and marls (Alizadeh et al. 2016; Rzayev et al. 2019). The third layer, representing the Quaternary surface and subsurface soil, is a sedimentary stratum with a thickness ranging from 0.5 to 30 m. This layer is composed of alluvial-deluvial fine-coarse clays, sands, shales, argillites, limestone, and sandstones.

The seismic activity in the Ismayilli-Shamakhi area is characterized as moderate to strong, primarily concentrated along several NE-SW and N-S faults (Babayev et al. 2020b). Most earthquakes are clustered within fault zones, forming linear sources, although noteworthy seismic events have also been observed in polygonal sources (Tibaldi et al. 2021).

Historically, the city of Shamakhi, located approximately 110 km westward from the capital of Azerbaijan, Baku, experienced a powerful earthquake with a magnitude of 6.9 on February 13, 1902 (known as the Shamakhi earthquake). This event reached an intensity of IX in Shamakhi and Ismayilli cities (Veber 1904). Earlier seismic events shook the city in 1191, 1667, and 1859, with magnitudes ranging from 6.0 to 6.9 (Veber 1904; Kondorskaya and Shebalin 1982). These earthquakes were felt at the epicenter with an intensity of IX on the MSK-64 scale (Babayev 2010; Babayev et al. 2010; Babayev et al. 2020a; Babayev and Telesca 2014; Telesca et al. 2013; Telesca et al. 2017; Yetirmishli et al. 2013). Additionally, earthquakes with a magnitude around М~5.0 occurred in the region, reaching an intensity of VII at the epicenter on the MSK-64 scale (Babayev et al. 2020a). The most recent significant earthquake in the zone took place on February 5, 2019, with a magnitude of Мw = 5.2.

Methodology

Two primary approaches are commonly employed for seismic hazard analysis: deterministic (DSHA) and probabilistic (PSHA). Deterministic seismic hazard assessment (DSHA) involves the delineation of earthquake scenarios. DSHA relies on geotechnical properties (Bommer 2002; Krinitzsky 2003) in conjunction with macroseismic parameters specific to the study area. On the other hand, in probabilistic seismic hazard assessment (PSHA), the key considerations are earthquake statistics and numerical calculations (Cornell 1968; Kijko and Öncel 2000; Musson and Henni 2001; Sokolov et al. 2001).

In the current study, a dynamic procedure is implemented to compute peak ground accelerations (PGA) at bedrock and surface for each target earthquake with the maximum expected magnitude (Mmax) from both local and near seismogenic zones to the study area. Two specific events were chosen for analysis: the 1902 Shamakhi earthquake, categorized as local-field with a magnitude of M = 6.8 and an intensity of VIII-IX, featuring a focal depth h = 15 km (Babayev et al. 2020a); and the 2000 Baku-Caspian earthquake with a selected magnitude of M = 6.5, defined as an extreme event and classified as near-field with a focal depth h = 35 km in the deep-water part of the Middle Caspian (Babayev and Agayeva 2021) (see Fig. 2).

Fig. 2
figure 2

Base map and meshing of the study area (scale is 1:500,000). Green and blue circles (and star) represent local- (1902 Shamakhi) and near-field (2000 Baku-Caspian) target earthquakes, respectively. Note: The red triangles indicate the sites of drilled boreholes; the geological and geophysical data from these boreholes were used in this study (see Table 1 for the lithology and physical description of ground unit parameters for the study area). Source: Khain and Alizadeh 2005

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To evaluate the anticipated ground motion at both bedrock and surface with 1D site effects, the initial step involves computing path effects using the stochastic approach (Boore 2005, 2009; Motazedian and Atkinson 2005). Subsequently, a soil column is determined at specific sites, and the 1D response is calculated using PSHAKE (Sanò and Pugliese 1991). Finally, the expected peak ground acceleration and intensities for each Mmax are estimated, and distribution patterns are simulated.

The study area boundaries are defined based on the geological map of Azerbaijan (Alizadeh 2008; Alizadeh et al. 2016), considering specific geological context (Khalilov et al. 1987) and tectonic features with a few deep faults in the area (Kangarli and Akhundov 1988; Khain and Alizadeh 2005). The area, covering approximately 6053 km2, is discretized using ArcGIS (ESRI) software based on the geological and tectonic configuration, and the Ismayilli-Shamakhi zone is divided into 33 cells with a step size of 15.5 × 15.5 km2 (see Fig. 2).

Ground motion from source to bedrock

The objective here is to implement a ground motion prediction equation at bedrock, representing it as a function of source and path, subsequently incorporating site parameters (Bommer et al. 2009; Bora et al. 2014; Lee and Green 2014). The stochastic algorithm operates under the assumption that the motions to be simulated are S waves, which are deemed the most critical for seismic hazard assessment (Boore 1983, 2009; Motazedian and Atkinson 2005). The motion initiates at the hypocenter and propagates kinematically through each layer with various physical-mechanical parameters, ultimately reaching the surface. The bedrock ground motion prediction equation integrates the ground motion amplitude spectrum with earthquake magnitude and the distance from the source (Aptikayev and Kopnichev 1979). Path effects are modeled through geometrical spreading, non-elastic attenuation, and ground motion duration effects (Boore 2009).

For calculation path (propagation) effect from source to bedrock, ground motion prediction Eq. (1) was applied:

$$\log {A}_{BR}=0.28\ M-0.8\log R+1.7$$
(1)

with ABR—peak ground acceleration (in gal = 10−2 m s−2), M—magnitude, and R—hypocentral distance (in km).

The Eq. (1) that is an empirical function to compute PGA (Aptikayev and Kopnichev 1979), is the best-fitting empirically-derived equated function for predicting ground motion for Azerbaijan and, therefore, for the study region (Babayev et al. 2020a).

1D site effects

The PSHAKE software (Sanò and Pugliese 1991) represents an enhanced version of the SHAKE program (Schnabel et al. 1972) and was employed in the current study for evaluating 1D site effects. In essence, it computes the response of a layered half-space traversed by shear waves propagating in the vertical direction (Santulin et al. 2012). Within the PSHAKE program, shear modulus and damping points were utilized in the algorithm. The shear modulus (G/G0) and damping (%) dependencies on shear deformation were applied for each lithological material of the layer, incorporating specific mean dynamic property curves sourced from the literature (Seed et al. 1969; Seed et al. 1986). The damping curve characterizes a scenario where the damping factor is contingent on the amplitude of strain deformation, indicating that damping increases with higher levels of strain deformation. Conversely, the shear modulus ratio decreases with an escalation in the strain deformation level.

The computation initiates with bedrock ground motion, specifically the peak acceleration. It takes into account the input of physical-mechanical parameters for each layer of the sedimentary section at the site, encompassing thickness, density, shear wave velocity, damping, and the content of each layer. In this study, laboratory test values of shear wave (S-wave) velocity for the examined soils (lithological layers) are not available; hence, P-wave velocity values were extracted from the literature (Babayev et al. 2020a). An empirical relationship between S-wave velocity and P-wave velocity was employed (Eq. 2) to calculate amplification factor coefficients (Eq. 3) for each layer in each cell (Table 2):

$${V}_S={V}_P/\left(4.34-0.49{V}_P\right)$$
(2)

where VS is the shear wave velocity, and VP is the P-wave velocity (Seed et al. 1969).

Amplification factor is estimated with the following Eq. (3) for hard rocks (Midorikawa et al. 1992) and with PSHAKE software for soft rocks (Sanò and Pugliese 1991).

$$\log {A}_{AMP}=1.11-0.42\log {V}_S$$
(3)

with AAMP being the amplification factor and VS the shear wave velocity (in m/s).

Lithological content of each cell was defined through geological base map (Alizadeh et al. 2016).

The bedrock, situated at significantly varying depths (Table 1), comprises cemented aleurolite and marlstone with a shear wave velocity (Vs) of approximately 2.82 km/s. The sedimentary cover remains relatively consistent across the study area, characterized by a superficial layer of variably consolidated silts and sands underlaid by alternating limestone (Rzayev et al. 2019), marlstone, and sandstone with a Vs of 350 m/s (Table 1).

Table 1 Lithology and physical parameters of ground units for the study area
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Results

The PGA for the surface was computed through the following equation:

$${A}_{SR}={A}_{BR}\ast {A}_{AMP}$$
(4)

where ASR is the surface PGA (in gal = 10−2 m s−2), ABR is the peak ground acceleration at bedrock (in gal = 10−2 m s−2), and AAMP is the amplification factor.

The amplification factor is specific at the site and mainly interlinked with the local conditions and causes the propagation effects.

Tables 2 and 3 show the PGA results.

Table 2 The estimated PGA at bedrock predicted from the effective selected different earthquakes at the researched area, applying the Eq. (1)
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Table 3 Modeling parameters used for simulation of surface acceleration
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In Table 2, A represents the local-field earthquake corresponding to the 1902 Shamakhi event, while B represents the near-field earthquake associated with the 2000 Baku-Caspian event. Additionally, R denotes the hypocentral distance, measured in kilometers, calculated for events A and B by estimating the d value. The d value signifies the distance from the epicenter of events A and B to each mesh, measured in kilometers. PGA(BR) indicates the peak ground acceleration at bedrock for events A and B (in gal = 10^-2 m s^-2), computed from Eq. (1). As a final step, the parameters used for simulating surface acceleration were modeled. In Table 3, PGA(SURF)A and PGA(SURF)B represent the peak ground accelerations at the surface for selected events A and B, which are among the most energetic events that occurred in the study area. Additionally, I(A) and I(B) denote the intensity values for events A and B in each mesh.

The final surface ground acceleration values for each selected earthquake were compared with the intensity values (Table 4) (Murphy and O’brien 1977; Trifunac and Brady 1975).

Table 4 Conversion between PGA (gal) and intensity (MSK-64) (Murphy and O’brien 1977; Trifunac and Brady 1975)
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The distribution of amplification factor throughout the investigated site characterizing the local ground effects is shown in Fig. 3.

Fig. 3
figure 3

Distribution of the estimated amplification factor throughout the investigated area

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Figure 4 shows the surface PGA distribution for the Ismayilli-Shamakhi study area from the chosen local- (Fig. 4a) and near-field (Fig. 4b) earthquakes.

Fig. 4
figure 4

Surface PGA distribution for the Ismayilli–Shamakhi investigated area (scale of the map is 1:500,000). a PGA computed according to the local-field earthquake parameters. b PGA computed according to the near-field earthquake parameters

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Figure 5 depicts the intensity (MSK-64) distribution for the Ismayilli-Shamakhi study area based on the correlation with surface PGA values from the parameters of the local- (Fig. 5a) and near-field (Fig. 5b) earthquakes.

Fig. 5
figure 5

Intensity (MSK-64) distribution through the Ismayilli-Shamakhi study area (scale of the map is 1:500,000). a Intensity derived from the comparative scale PGA-MSK for the selected local-field earthquake; b Intensity derived from the comparative scale PGA-MSK for the selected near-field earthquake

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For validation reasons, peak ground motions derived from the synthetic signals were compared with those obtained from the actual recordings from BAKU station with EW and NS components (Fig. 6). The figures demonstrate that these signals are in good agreement.

Fig. 6
figure 6

Comparison of time histories and FAS of synthetic (blue line) with real data (green lines—EW component, red lines—NS component) for the November 25, 2000 Baku-Caspian earthquake at the BAKU station

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Discussions

As is commonly understood, seismic hazard assessment involves the analysis of the regional potential for future earthquakes using two approaches. In this study, a deterministic seismic simulation of peak ground acceleration (PGA) was employed for seismic hazard assessment. To conduct this analysis, it is crucial to estimate the magnitude of the largest earthquakes that a specific seismic source might generate. In this study, efforts were made to generate earthquake scenarios by predicting the distribution of surface PGA throughout the investigated area, estimated from the effective target earthquakes originating from both local and near seismogenic zones.

The peak ground acceleration (PGA) at bedrock, site amplification, surface PGA, and intensity in the eastern part of Azerbaijan were evaluated based on the influence of two distinct seismogenic zones within and around the area of interest. The findings clearly illustrate the impact of local ground conditions on the estimated ground motion. The maximum magnitude for the selected earthquakes was estimated by adding 0.3–0.5 magnitude units to the largest known magnitude in the zone.

In this study, the distribution of estimated surface peak ground accelerations (PGAs) (Fig. 4a, b) resulting from the two local- and near-field target earthquakes indicates that the highest accelerations are observed in sites with soft soil. Consequently, the assessment of ground motions should always consider the analysis of a variety of ground conditions.

The site amplification (Fig. 3) exhibits significant heterogeneity, with high values exceeding 0.8 in the southern part, contributing to a substantial local lithological impact on the expected surface ground motion. Moderately high amplification, with nearly 0.7 value, is observed in the southeastern and southwestern parts. In the central part of the investigated area, lower amplification with a value of 0.5 is evident. The northern part of the study area shows sites with sharp changes in amplification factor from medium to moderately high values, indicating high heterogeneity in local soil and rock conditions.

The scenario surface PGAs for the Shamakhi 1902 and 2000 Baku-Caspian earthquakes (Fig. 4a, b, respectively) exhibit a consistent trend. The local-field PGA scenario estimates a value range of 77–328 gal, corresponding to MSK-64 intensity at VII–IX range, respectively. The seismic hazard level in the region was assessed as high in the southern and southeastern parts, with moderately high levels in the southwestern sites of the study area, indicating these areas as the most hazardous parts of the researched region.

In this study, despite the substantial amount of input data and materials, it is important to note that estimating the nonlinear amplification capability of local ground conditions and computing the parameters using the latest empirical correlations were influenced by the scarcity of records or the absence of detailed soil information at some sites.

Comparing the results obtained in this study with previous ones (Babayev et al. 2020a; Telesca et al. 2017), it is evident that the computed peak acceleration values in this study exhibit a similar behavior, regardless of the scenario sources. Specifically, Babayev et al. (2020a) previously identified that the Ismailli-Shamakhi zone is characterized by a high amplification factor, and this characteristic is clearly reflected in the results obtained in the present study.

Conclusion

In this paper, a simplified approach to compute the expected ground motion in the Ismayilli-Shamakhi seismic region, situated on the southeastern slope of the Greater Caucasus in Azerbaijan, was presented. The analysis focused on peak acceleration and intensity values generated by two selected target earthquakes originating from the local and near seismogenic zones. The study involved an assessment of 1D site effects and a detailed classification of various local soil and rock conditions. The research area, marked by moderate to high seismic activity, has experienced several historically significant and damaging earthquakes, both felt and recorded instrumentally.

The selection of target events for this study was based on the analysis of the strongest earthquakes in the region’s past and an estimation of the expected maximum magnitude, specifically a 6.8 magnitude earthquake in the Shamakhi source and a 6.5 magnitude event in the Caspian Sea source. The comparison of peak ground acceleration and intensity values derived from this scenario reveals a consistent trend in the southern, southeastern, and moderately similar conditions in the southwestern part of the study area.

For the local-field scenario, the peak ground acceleration ranges from 77 to 328 gal, corresponding to MSK-64 intensity levels of VII–IX. In the near-field scenario, the peak ground acceleration varies from 28 to 62 gal, aligning with MSK-64 intensity levels of VI–VII. The approach employed in this study proves effective in analyzing 1D site effects through the use of dedicated software, offering a flexible tool for deterministic seismic hazard assessment with detailed information about local ground conditions.

Given that the study area encompasses critical infrastructure such as oil and gas terminals, energy corridors, and strategic cities with historical monuments, the results of this research can be invaluable for engineers, planners, and decision-makers. Additionally, the study provides crucial information for areas related to tourism and recreation in Azerbaijan.