1 Introduction

The Red Sea, an inlet located between Africa and Asia, holds profound importance due to its unique geographical and strategic attributes. The Red Sea is an essential conduit of maritime connections. It is bordered by Egypt, Saudi Arabia, Yemen, Sudan, Eritrea, and Djibouti, creating a nexus of cultures and nations along its shores (Fig. 1). This maritime thoroughfare plays a pivotal role in global trade and connectivity. Serving as a major shipping route. Some of the world’s oil and gas shipments traverse the Red Sea, underlining its status as a vital channel for energy transportation (Aliboni 2015). The Red Sea’s significance extends beyond trade and energy. Its crystal-clear waters and stunning coral reefs have transformed it into a popular tourist destination, attracting scuba divers and snorkelers from around the globe. This natural beauty bolsters local economies and highlights the need for environmental conservation efforts (Farid 2022).

The Red Sea region is part of a complex tectonic setting characterized by the spreading of the Earth’s crust along the Red Sea Rift. This geological activity gives rise to numerous earthquakes (EQs), varying in magnitude and frequency. Situated at the juncture of two plates (the Arabian and the African one), the region experiences a high level of seismicity. This seismic activity stems from the tectonic forces responsible for shaping the Red Sea Rift and various fault systems (Fig. 1a). Consequently, the area witnesses a range of EQs, from minor tremors to potentially destructive events, with potential implications for both infrastructure damage and population safety (Melville and Adams 1994; El-Isa and Shanti 1989; Moustafa et al. 2016; Baker 2008).

The seismic activity in the Red Sea region is acknowledged for its prominence, marked by a notable frequency of EQs. This seismic behavior holds significant ramifications for the countries in proximity, encompassing those situated along the coast of the Red Sea and the contiguous areas. In recent decades, numerous endeavors have been undertaken to enhance the precision of seismic parameter estimation and hazard assessment in the Red Sea and its neighboring areas (Badawy and Horváth 1999; Rehman et al. 2019; Kamel and Arfa 2020).

Seismic events in the Red Sea region have repercussions that extend beyond their immediate surroundings, impacting neighboring countries in multifaceted ways. An eminent concern revolves around the potential ground motion provoked by EQs. Robust seismic activities have the capability to generate ground shaking, directly endangering structures, infrastructure, and human lives, particularly in coastal zones. The magnitude of the EQ and its proximity to populated areas influence the intensity and duration of ground shaking, which can vary significantly (Abdalzaher et al. 2023, 2021, 2022, 2021; Moustafa et al. 2021). Beyond ground shaking, seismic events in the Red Sea region can trigger consequential hazards such as aftershocks. These subsequent tremors can exacerbate the effects on affected areas and complicate recovery endeavors. Aftershocks extend the period of heightened seismic activity and amplify the overall damage potential. Moreover, the seismicity in the Red Sea bears economic implications. This region serves as a pivotal maritime route for international shipping, boasting numerous ports and harbors along its coastline. EQs and the associated hazards they unleash, including tsunamis and submarine landslides, can disrupt maritime operations, culminating in economic setbacks and logistical complexities. Additionally, the Red Sea region holds strategic significance for offshore resource exploration, especially concerning oil and gas installations. These vital assets might be susceptible to seismic events, further underscoring the need for robust preparedness and risk mitigation measures (Moustafa et al. 2016; Kamel and Arfa 2020; Ruch et al. 2021).

Despite the evident seismic activity in an area of the Red Sea, there is a conspicuous shortage of comprehensive seismic hazard studies that adequately address the potential risks. Consequently, there exists a pressing need to conduct Probabilistic Seismic Hazard Assessment (PSHA) for this area. PSHA is a systematic approach that integrates geological, seismological, and geophysical data to quantify the likelihood of various levels of ground shaking occurring over a specified time frame. By conducting PSHA, we can gain a more accurate understanding of the seismic hazards in the Red Sea region (Moustafa et al. 2022). This assessment would provide insights into the expected ground shaking intensities, the frequency of strong seismic events, and the potential impact on structures, infrastructure, and population centers. Armed with this information, policymakers, urban planners, and engineers can make informed decisions regarding building codes, land use planning, and disaster preparedness measures (McGuire 2008). Given the economic significance of the Red Sea region, particularly its role as a critical maritime route and offshore resource exploration site, performing PSHA becomes imperative. It would not only safeguard human lives and property but also contribute to the resilience of vital economic activities. Investing in comprehensive seismic hazard studies and PSHA for the Red Sea area is a proactive step toward reducing vulnerabilities, enhancing disaster response capabilities, and fostering sustainable development in the face of seismic challenges Anbazhagan et al. (2017); McGuire (2008); Moustafa et al. (2021).

The majority of earlier research has concentrated on specific geographical areas or relied upon distinct classifications of faults prone to seismic activity, frequently characterized by subjective interpretations and constrained by data accessibility. In this paper, the smoothed seismicity (SS) technique is employ as introduced in Frankel (1995). The methodology demonstrates effectiveness in various other geographical contexts (Cao et al. 1996; Akinci et al. 2004; Kalkan et al. 2009; Khodaverdian et al. 2016). Its primary characteristic involves treating recorded EQs (instrumental and historical ones) as distinct point sources, rather than events integrated into a predetermined network of faults within a specific tectonic framework. In this regard, new technologies can play a significant role (Abdalzaher et al. 2022, 2023, 2023; Krichen et al. 2023). While we acknowledge that a probabilistic seismic hazard analysis rooted in fault systems can provide heightened realism and precision, our selection of the SS approach aims to diminish uncertainties linked to fault delineation, EQ pinpointing, and source mechanism determination (Fig. 1a). This approach also encompasses regions that might otherwise be undervalued or disregarded (Akinci et al. 2004; Abdalzaher et al. 2020; Elhadidy et al. 2021).

Moreover, comprehending and precisely determining seismicity parameters, including metrics like the magnitude of completeness (\(M_c\)), b-value, and maximum considered magnitude (MCM), hold paramount significance. These assessments play a pivotal role in evaluating the repercussions of seismic occurrences and devising efficacious approaches to minimize vulnerabilities and enhance the resilience of adjacent nations (Kárník 2012; Goda et al. 2013). In the realm of seismicity analysis, the parameters of \(M_c\), b-value, and MCM stand as vital components within the framework of the SS method. These parameters play a significant role in shaping the understanding of seismic activity, assessing potential hazards, and making informed decisions regarding risk mitigation strategies (Akinci et al. 2004; Abdalzaher et al. 2020).

\(M_c\) is a crucial parameter that delineates the threshold below which EQs might go unnoticed due to limitations in detection sensitivity. Determining \(M_c\) is vital because it forms the basis for accurately characterizing the seismicity distribution. Its estimation aids in filtering out insignificant seismic events, ensuring that only reliable data is utilized in subsequent analysis. A precise \(M_c\) value influences the calculation of seismic rates and has a direct impact on hazard assessments, contributing to the accuracy of seismicity models (Wiemer and Wyss 2000). The b-value represents another pivotal seismicity parameter. It quantifies the frequency of EQs and the magnitude relationship. A lower b-value indicates a higher frequency of larger EQs relative to smaller ones. Understanding the b-value assists in deciphering the underlying tectonic processes and potential fault behavior, which in turn aids in forecasting the likelihood of various magnitude events. This parameter serves as a cornerstone in probabilistic seismic hazard analysis, guiding the formulation of EQ recurrence models (Marzocchi and Sandri 2003; Lamessa et al. 2019). MCM carries significant weight in seismic hazard assessment. It designates the EQ magnitude top limit considered in the analysis. MCM is crucial for defining the scope of potential seismic events that need to be accounted for in hazard assessments, ensuring that the analysis encompasses the full range of possible scenarios. Accurate determination of MCM is essential for capturing worst-case scenarios and providing a comprehensive foundation for designing resilient structures and infrastructure capable of withstanding the most extreme seismic events (Kijko 2004; Anbazhagan et al. 2015). In essence, the \(M_c\), b-value, and maximum considered magnitude collectively contribute to the robustness of seismicity analysis and hazard assessment. Their accurate estimation not only enhances the reliability of seismicity models but also informs critical decision-making processes for risk reduction, disaster preparedness, and the development of resilient communities and infrastructure in seismic-prone regions (Anbazhagan et al. 2019; Moustafa et al. 2022).

Moreover, the development of smoothed seismicity models is of paramount importance for seismic hazard assessment in the Red Sea region, a zone characterized by significant tectonic activity due to the movements of the African and Arabian plates. These models are integral to producing more accurate seismic hazard maps, which are essential for identifying areas at greater risk and for the forecasting of seismic activity both spatially and temporally. This predictive capability is crucial for the design of resilient infrastructure, guiding engineers in creating structures that can withstand potential seismic events. In addition to aiding in infrastructure design, smoothed seismicity models serve as a key tool for insurance companies assessing risk, and for policymakers tasked with developing building codes and land-use plans. These models enhance our understanding of the tectonic processes that drive seismicity in the region and utilize historical seismic data to better estimate the likelihood of future earthquakes. This, in turn, supports the development of public safety programs, ensuring that communities are better prepared, and helps in the planning of efficient emergency response strategies. Moreover, the pursuit of these models drives scientific advancement by encouraging research in seismology and earthquake engineering and fostering cross-disciplinary collaboration that includes geology, physics, statistics, and engineering, thereby contributing to a holistic approach to disaster risk reduction in the Red Sea region.

The integration of Geographic Information Systems \(GIS\) with seismicity parameters and the SS method presents a potent synergy that can greatly enhance the understanding and accuracy of PSHA. Researchers and analysts may build complete geographic datasets that include EQ sites, magnitudes, depths, fault systems, and tectonic features by combining GIS with seismicity characteristics. This combination gives a platform for evaluating the geographical distribution of EQs and identifying prospective high-risk locations in addition to providing a visual depiction of seismic activity. Additionally, the use of GIS with the SS approach enables a more precise representation of seismicity rates across various geographical zones. With data sparsity and skewed EQ distributions as common problems, traditional seismicity analysis has certain inherent limitations that our integration helps to solve. By taking into account both regional tectonics and seismicity patterns, SS maps with GIS support offer a more accurate picture of seismic activity, improving the accuracy of hazard estimates. The combined approach offers a holistic overview of seismic hazards by incorporating geological, tectonic, and seismic data into a spatial context. This enriched perspective aids in identifying areas with varying levels of seismic risk, facilitating better-informed decision-making for land use planning, infrastructure development, and disaster preparedness strategies. Ultimately, the integration of \(GIS\) with seismicity parameters and SS significantly contributes to the robustness and reliability of Probabilistic Seismic Hazard Assessment, strengthening our ability to mitigate the impact of potential seismic events (Moustafa et al. 2022; Hamdy et al. 2022; Ghamry et al. 2021; Pancholi et al. 2022). The objectives of the article are:

  • To analyze the seismicity characteristics of the Red Sea region through the estimation of b-value and a-value using both raw and declustered EQ catalogs.

  • To investigate the spatial distribution of b-values and a-values across the Red Sea region using \(GIS\) techniques, considering the influence of declustering techniques.

  • To assess the impact of declustering techniques on seismicity analysis by comparing the seismicity patterns obtained from raw and declustered catalogs.

  • To evaluate the effectiveness of different declustering methods (e.g., window-based, distance-based) in improving EQ catalog quality and reducing the influence of aftershocks and foreshocks.

  • To quantify the changes in b-value and a-value estimates resulting from the application of declustering techniques and assess their implications for seismic hazard assessment in the Red Sea region.

  • To evaluate the impact of declustering parameters on b-value and a-value patterns, shedding light on seismotectonic processes.

  • To showcase the effectiveness of GIS for seismic data integration, declustering analysis, and visualization in the Red Sea region.

  • To enhance the understanding of seismic activity and EQ characteristics, contributing to seismic hazard assessment and risk mitigation decisions in the area, while acknowledging limitations and suggesting avenues for future research.

In summary, this research underscores the significance of utilizing GIS-based mapping to decipher the intricate nature of seismic events in the Red Sea area. Through this method, scientists can expand our understanding of EQ risks in the region, leading to improved risk mitigation strategies for coastal communities. The study’s results are anticipated to advance our comprehension of seismic activity in the Red Sea region and bolster the precision of seismic hazard evaluations. By incorporating the effect of declustering techniques and utilizing GIS tools, we can derive more reliable estimates of the b-value and a-value, facilitating a more comprehensive understanding of EQ behavior. Such insights will aid in the development of effective seismic risk mitigation strategies and inform decision-making processes to guarantee the protection and resilience of communities in the Red Sea region.

In the subsequent sections, we offer a more comprehensive overview of our focal geographical area, delve into its linked tectonic activities and seismic patterns, and furnish supplementary details about the methodology we’ve adopted. Noteworthy components of our study encompass the structure of the EQ dataset, involving both catalog comprehensiveness and the conversion of EQ magnitudes, the identification of a suitable attenuation relationship tailored to the region, and the calculation of the Gutenberg-Richter (GR) seismicity parameters.

2 Red Sea Seismicity and Tectonics

The Red Sea region, located between the Arabian Peninsula and Northeast Africa, is characterized by its complex tectonic setting and high seismic activity. It is influenced by the interactions of several major tectonic plates, including the Arabian, African, and Eurasian plates (Bosworth et al. 2019). There is a high amount of seismicity in the area as a result of the convergence and divergence of these plates, which have produced a range of tectonic features including transform faults, rift systems, and volcanic activity (Abou Elenean 1997; El-Isa and Shanti 1989).

Significant seismic activity is present in the Red Sea region, which is also located in a complex tectonic environment impacted by the Red Sea Rift. The distinctive geological characteristics of this area and the continuing plate tectonic processes that have moulded its seismicity characteristics are well recognized (Fig. 1b). Assessing possible seismic hazards and reducing risks in the vicinity need an understanding of the tectonics and seismicity of the Red Sea region (Melville and Adams 1994; El-Isa and Shanti 1989).

The process of continental rifting is the main cause of seismicity in the Red Sea region. The African Plate and the Arabian Plate are progressively separating along a divergent plate boundary known as the Red Sea Rift. Faults and cracks in the Earth’s crust arise as a result of tensional strains brought on by extensional forces along the rift. EQs are caused by the release of stored strain energy through these faults (El-Isa and Shanti 1989).

There are two main categories of seismicity in the Red Sea region: crustal seismicity and rift-related seismicity. The continuous extensional tectonic processes inside the Red Sea Rift are linked to rift-related seismicity (Fig. 1b). These EQs are distinguished by standard faulting processes and generally occur along the rift axis. These EQs can range in size from minor to moderate, with sporadic larger-magnitude occurrences (Bosworth et al. 2019; Ruch et al. 2021).

The larger tectonic framework and related forces are thought to be responsible for the crustal seismicity in the Red Sea region. The continuous movement of the Arabian Plate and the African Plate causes crustal deformation and stress to build up along pre-existing faults. This may cause EQs to occur outside the local rift zone. By the precise fault orientations and stress regimes, the region’s crustal seismicity is frequently defined by strike-slip or reverse faulting mechanisms (Bosworth et al. 2019).

One of the main fault systems in the Red Sea region, the Red Sea Rift, which is an extension of the East African Rift System, is characterized by complex tectonic processes involving several interacting fault systems. In order to accommodate the separation of the Arabian and African Plates, this rift has a number of segmented normal faults (Bosworth et al. 2019; Amjadi et al. 2020). The Dead Sea Transform Fault, which allows for left-lateral movement between the Arabian Plate and the Sinai Peninsula, and the Gulf of Suez Rift, an extension of the Red Sea Rift, both contribute to the complexity of the region’s tectonic structure (Delaunay et al. 2023). The Red Sea region’s seismic hazard is highlighted by the increased potential for seismic activity brought on by these variables.

The magnitude of EQs in this region can vary, with some EQs reaching substantial magnitudes that can cause ground shaking and other risks. The combination of rift-related and crustal seismicity, as well as the unique fault geometries and stress distributions, all have an impact on the region’s seismicity patterns (Rehman et al. 2019).

Fig. 1
figure 1

Seismicity and tectonics of the Red Sea and surrounding ar (Bosworth et al. 2019)

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3 Data Collection and Analysis

The amalgamation and rigorous analysis of seismicity catalogs from various sources provide a foundation for a well-informed and comprehensive Probabilistic Seismic Hazard Assessment. This approach enhances the accuracy and reliability of seismic risk evaluations, which are critical for informed decision-making, urban planning, and disaster preparedness.

3.1 Catalog Compilation

Compiling a seismicity catalog specific to the Red Sea region involves the systematic collection, and organization, of EQ data that have occurred in or around the Red Sea area. Such a catalog serves as a foundational dataset for conducting seismic hazard assessments in this region.

The initial essential stage in conducting a regional seismic hazard analysis involves creating a dependable seismic catalog that encompasses both EQs documented in history and those recorded with instruments. Presently, instrumental datasets can be readily obtained from global, regional, and local organizations. Conversely, historical data requires a more subjective interpretation. Noteworthy past endeavors to construct consistent EQ catalogs for Red Sea encompass, among others but not exclusively, the work of (Ambraseys et al. 2005; Ambraseys 2009; Poirier and Taher 1980; Maamoun et al. 1984; Riad et al. 1999; Badawy et al. 2010; Sawires et al. 2016). However, these investigations vary in terms of the magnitude scales they employ or the rules they use for converting magnitudes, as well as their level of acceptance of historical reports as credible data. As noted by Ambraseys et al. (2005) in his work, there exists an indication of EQs related to the 3rd millennium B.C., although certain reports from that time are challenging to decipher.

Here, the considered catalog is prepared for the Middle East (Mehdi et al. 2014) and the Red Sea (Babiker and Mula 2015) regions, along with data amalgamated from various sources by Gaber et al. (2018), Abdalzaher et al. (2020), which incorporates records from the Egyptian National Seismological Network (ENSN) spanning (1121 BC until 2022). We expand upon this dataset to suit our specific region of interest. This catalog holds particular significance due to its inclusion in the ongoing collaborative efforts of the Earthquake Model of the Middle East (EMME) project and the Global Earthquake Model (GEM) cooperation. This comprehensive compilation draws from more than 128 thousand entries derived from distinct datasets encompassing both historical and instrumental seismic events. The instrumental data integrates information gathered by international, regional, and local agencies and networks, including notable sources like bulletins from the International Seismological Centre (ISC), the National Earthquake Information Centre (NEIC) of the U.S. Geological Survey, and ENSN, among others. The historical information integrates datasets assembled over time by Ambraseys et al. (2005) and Ambraseys (2009). Regarding the magnitude scale, the recorded events underwent a conversion process from \(M_L\), \(M_s\), and \(m_b\) scales to \(M_w\). This conversion was executed using relationships established by Hussein et al. (2008); Babiker and Mula (2015); Moustafa et al. (2021). Table 1 shows the conversion equations.

Table 1 Empirical relationships between Mb, Ms, and Md with Mw established by Hussein et al. (2008); Babiker and Mula (2015); Moustafa et al. (2021)
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Fig. 2
figure 2

Temporal and Spatial Variations in EQ Data Collection within the Red Sea Region. Data has been compiled from different sources including the ENSN from 2200 BC to 2022

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Data preprocessing is crucial for preparing seismic data for \(GIS\)-based mapping. This involves steps like data cleaning, quality control, and standardization. Data cleaning eliminates errors, duplicates, and gaps, while quality control ensures accuracy and adherence to standards. To remove duplicates from the EQ catalog, a multi-window search method is used based on source parameters. Priorities are then established by the authors to retain catalog entries, with emphasis on data from the ENSN due to its authority. This approach ensures the catalog includes ENSN and regional data, reflecting their importance in assessing seismic activity. The study’s event set is depicted in figures showing spatial distribution and event characteristics. The number of events considered in this study is depicted in Fig. 2, which are spatially distributed within the designated area of the Red Sea for historical and instrumental selected occurrences.

4 Catalog Declustering and Completeness

Declustering techniques play a crucial role in seismic analysis, especially in regions with high levels of seismic activity. EQ catalogs often contain numerous aftershocks and foreshocks, which can significantly influence the estimation of seismic parameters and seismic hazard assessments. Declustering techniques aim to remove these secondary seismic events and isolate the mainshocks, which are the primary focus for studying seismicity characteristics. By implementing appropriate declustering methods, it is possible to improve the quality and accuracy of EQ catalogs, leading to more reliable estimates of seismicity parameters (Thomasvan Stiphout and Marsan 2012).

The window methods were among the pioneers of identifying the aftershocks (Gardner and Knopoff 1974; Uhrhammer 1986). According to the simplicity of these means, they are the commonly used ones. Indeed, the windowing scheme relies on a spatial-temporal window regarding the main event \(t_k, \lambda _k, \phi _k, h_k, \text {and} m_k\) that are determined by specific criteria as follows:

$$\begin{aligned} \begin{array}{c} 0< t-{{t}_{k}}< {{W}_{1}}\left( {{{m}_{k}}} \right) , \\ 0< r\left( {{{\lambda }_{k}},{{\varphi }_{k}};\lambda ,\varphi } \right) < {{W}_{2}}\left( {{{m}_{k}}} \right) , \end{array} \end{aligned}$$
(1)

where \(r(\lambda _k, \phi _k, \lambda , \phi )\) represent the inter-distance grid points on the surface of Earth, and \(W_1(mk)\) and \(W_2(mk)\) are the boundaries of the main shock magnitude.

In Gardner and Knopoff (1974), the windowing criterion is given as:

$$\begin{aligned} \begin{array}{c} T_{\text {norm}}= {\left\{ \begin{array}{ll} ({{t}_{k}}-{{t}_{i}}) \times {{10}^{{2.7389+0.032M}}},&{} M \geqslant 6.5\\ 10^{0.5409M - 0.547,} &{} \text {otherwise}, \end{array}\right. }\\ D_{\text {norm}} = 10^{0.983+0.1238M}. \end{array} \end{aligned}$$
(2)

where \(T_{norm} \le 10W\); \(D_{norm}\le 10W\) gets its standard when \(W = 0\).

While, the windowing methodology in Uhrhammer (1986) is given as:

$$\begin{aligned} \begin{array}{c} {{T}_{{{\text {norm}}}}} = ({{t}_{k}}-{{t}_{i}}) \times {{10}^{{1.2464-0.5316M}}},\; M \geqslant 6.5, \\ {{D}_{{{\text {norm}}}}} = {{10}^{{0.4447-0.3992M}}}. \end{array} \end{aligned}$$
(3)

where \(T_{norm} \le 10W\); \(D_{norm}\le 10W\) gets its standard when \(W = 0\).

In the context of PSHA, the prevailing approach involves the utilization of the windowing methodology introduced by Gardner and Knopoff (1974), as it yields a declustered seismic event catalog that bears semblance to a Poissonian dataset (Thomasvan Stiphout and Marsan 2012). An observation highlighted by (Luen and Stark 2012) posits that the preservation of temporal homogeneity in a Poisson process is achievable through the judicious removal of a substantial number of events from the catalog. In the present investigation, we adopt three distinct adaptations of the windowing technique, specifically those detailed in the works of (Gardner and Knopoff 1974), (Uhrhammer 1986), and (Thomasvan Stiphout and Marsan 2012), as delineated in Fig 3. The aggregate counts of EQs within the resultant declustered catalogs are presented in Table 2.

Fig. 3
figure 3

Seismicity and tectonics of the Red Sea and surrounding area

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Table 2 Descriptive statistics of original and declustered catalogs
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Fig. 4
figure 4

A comprehensive examination of catalog completeness utilizing the method in stepp (1972) for the Red Sea Region

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The evaluation of the completeness of historical EQ data has traditionally been a central concern in seismology, particularly within the realm of PSHA. To address this issue, statistical methods are employed to ascertain the time interval during which the dataset can be regarded as complete for seismic events above a certain magnitude threshold. Portions of the dataset preceding this established timeframe are deemed incomplete and therefore unsuitable for subsequent statistical analysis. This methodology enables the determination of the temporal extent during which a specific magnitude class can be considered complete. To achieve this objective, the seismic data has been categorized into six distinct classes (Fig. 4). It is worth noting that the inception of the statistical approach to completeness assessment can be attributed to the pioneering work of Stepp (1972).

The methodology introduced by Stepp (1972) provides a comprehensive and sophisticated approach to declustering seismic events, utilizing statistical models to differentiate between mainshocks and their aftershocks or foreshocks. It is also used to differentiate between instrumental earthquakes and historic earthquakes. This method is grounded in the application of the Epidemic Type Aftershock Sequence (ETAS) model, which categorizes earthquakes based on their nature as either background (spontaneous) or triggered events. A key aspect of their methodology is the estimation of background seismicity rates through maximum likelihood estimation techniques, enabling more precise identification of aftershocks by considering their spatial and temporal proximity to preceding seismic events. The iterative process employed refines the model parameters through successive iterations, ensuring the accuracy of the declustering and the stability of the parameters. Additionally, Stiphout et al. incorporate an uncertainty analysis to address the inherent uncertainties within earthquake catalog data and the stochastic nature of earthquake occurrences. This methodology not only significantly improves the declustering process, leading to more reliable calculations of b-values and enhanced seismic hazard assessments, but also offers insights into the mechanisms driving seismicity, thereby contributing to a deeper understanding of earthquake dynamics and risks. Its application improves the reliability of seismic hazard assessments, contributing to safer building practices, better-informed policy decisions, and a deeper understanding of earthquake phenomena. As seismic data continue to accumulate and computational methods advance, such sophisticated approaches to declustering will play an increasingly crucial role in mitigating the risks associated with earthquakes.

In this research article, methodology in Stepp (1972) has been employed to assess the completeness of declustered seismic catalogs. Subsequently, using a 10-year time interval, the average annual event count within each magnitude range has been calculated. If \(x_1, x_2,..., x_n\) represent the number of events per year within the considered magnitude range, then the sample’s mean rate can be expressed as:

$$\begin{aligned} X = \frac{1}{n} \sum _{i=1}^{n} x_i, \end{aligned}$$
(4)

where n represents the number of unit time intervals, and the variance (\(\sigma _x^2\)) is calculated as \(\frac{x}{T}\), T is the duration of the sample. If the variable X were to remain constant, the variance would vary proportionally with \( \frac{1}{\sqrt{T}} \). The standard deviation of the mean rate for the six magnitude intervals is graphed as a function of the sample length. These plots exhibit nearly tangent lines with a slope of \( \frac{1}{\sqrt{T}} \). The deviation of the standard deviation estimate of the mean from the tangent line provides insights into the length up to which a particular magnitude range can be considered complete.

The departure of the standard deviation of the mean estimate from the tangent line serves as an indicator of the extent to which a specific magnitude range may be regarded as finalized, as illustrated in Fig. 5, across the various magnitude ranges employed by each applied declustering algorithm.

Fig. 5
figure 5

Examination of the completeness of EQ data within the study region. Variation of (\(\sigma _x^2\)) concerning both the time intervals and magnitudes. This analysis yields lines characterized by specific slopes \( \frac{1}{\sqrt{T}} \), indicative of particular trends or patterns

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5 Spatial distribution of seismicity parameters

The research herein delves into an examination of the incompleteness inherent in EQ datasets, stemming from the temporal non-uniformity exhibited by seismic networks. This investigation is primarily conducted through the application of a GR model to the Frequency Magnitude Distribution (FMD). The FMD represents the intrinsic relationship between the frequency of EQ occurrences and their respective magnitudes, represented mathematically as:

$$\begin{aligned} \log N (M) = a - b (M), \end{aligned}$$
(5)

where \(N (M)\) signifies the count of EQs with magnitudes equal to or exceeding \(M\), ’a’ corresponds to the number of EQs surpassing a magnitude of zero, and ’b’ encapsulates the relative distribution characteristics between small and large EQs. It is imperative to underscore that the values of ’a’ and ’b’ are commonly ascertained through the fitting of empirical data samples. The cumulative EQ Count across magnitude ranges and temporal fluctuations in the b-Value as compared to the collected and declustered EQ catalogs in the Red Sea region is illustrated in Fig. 6.

This mathematical relationship has been corroborated not only within the global seismic context but also across various regional seismic zones, provided that the data series adheres to homogeneity. In such cases, Eq. 1 demonstrates a robust ability to yield a stable recurrence rate for EQs. However, practical constraints are encountered in real-world applications, as articulated earlier, where EQ catalogs frequently exhibit incompleteness, especially in capturing events of smaller magnitudes. This bias towards larger events skews the dataset.

To address this issue, the concept of the \(M_c\) is introduced. \(M_c\) is identified as the magnitude at which the lower end of the FMD deviates from the linear trend observable in log-linear. It is crucial to emphasize that this deviation is solely considered at the lower end of the FMD; deviations at higher magnitudes (upper end of the FMD) can be attributed to statistical fluctuations stemming from under-sampling or, alternatively, may signify a genuine departure from GR. Importantly, the \(M_c\) is a dynamic parameter that may vary over time due to evolving seismic data collection and network characteristics.

Fig. 6
figure 6

Cumulative EQ Count Across Magnitude Ranges (Figs. a, c, e and g) and Temporal Fluctuations in the b-Value (Figs. b, d, f and h): Comparing Collected and Declustered EQ Catalogs in the Red Sea Region

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6 Development of smoothed seismicity models

Zoneless or SS models have emerged as valuable tools in EQ source characterizations and probabilistic seismic hazard assessments, particularly for tectonically complex regions such as the Red Sea. These models depart from traditional seismic zoning approaches, which discretize the area of interest to predefined events source zones taking in consideration a continuous distribution of seismic activity across the entire region. In the context of the Red Sea region, characterized by complex tectonic interactions and varying seismicity patterns, zoneless models offer several significant contributions. Firstly, zoneless models accommodate the inherent spatial variability of seismicity in the Red Sea region. This variability arises from the intricate plate tectonics, including the interaction of the African and Arabian plates, as well as local fault systems. Unlike discrete zoning, which may oversimplify this complexity, zoneless models provide a more nuanced representation of seismic activity, allowing for a better understanding of the spatial distribution of EQ sources. Second, approaches of SS make it easier to include geological observations, instrument recordings, and historical EQ data in seismic hazard evaluations. These models decrease the noise that comes with sparse seismic catalogs and give a more reliable assessment of seismic event rates and magnitudes by taking into account the complete dataset and using statistical smoothing algorithms. This, in turn, leads to more accurate seismic hazard assessments for the Red Sea region. Furthermore, zoneless or SS models offer the advantage of adaptability. In an evolving tectonic setting like the Red Sea, where seismicity patterns can change over time, these models can readily accommodate updated data and evolving scientific understanding. This adaptability is crucial for maintaining the relevance and reliability of seismic hazard assessments (Akinci et al. 2004; Hagos et al. 2006; Abdalzaher et al. 2020).

In our current investigation, we partition the Red Sea area into a standardized grid composed of cells measuring 0.1\(^\circ \) in both longitude and latitude. In accordance with the method outlined by Frankel (1995), the quantity \(n_i\) undergoes a smoothing process facilitated by the normalized Gaussian function.

$$\begin{aligned} {\tilde{n}}_i = \frac{ \sum _{j} n_{j} \exp ( \frac{ -D_{ij}^{2} }{ c^2 } ) }{ \sum _{j} \exp ( \frac{ -D_{ij}^{2} }{ c^2 } ) } \,, \end{aligned}$$
(6)

where \({\tilde{n}}_i\) symbolizes the smoothed and normalized count of events within i-th cell, \(D_{ij}\) represents the distance between the \(i\)-th and \(j\)-th cells, and c corresponds to the correlation distance. The summations in Equation \(3\) are computed across the count of \(j\) cells situated within a radius of \(3c\) from the \(i\)-th cell. It’s important to emphasize that during this procedure, we transform the cumulative count of events into incremental values, as per the approach outlined by Herrmann (1977). Additionally, as suggested by Frankel (1995), regions with noteworthy quantities of events featuring magnitudes \(M \ge 3\) tend to experience moderate EQs. This aligns with our focus on enhancing the EQ catalog by incorporating events surpassing this magnitude boundary.

In fact, Eq. 6 represents a pivotal parameter in the process of seismicity smoothing reflecting the correlation distance denoted as \(c\). Prior research has showcased a range of \(c\) values, spanning from 10 to 50 kms. For instance, Frankel (1995) and Boyd et al. (2008) adopted a correlation distance of 50 km, while Foteva et al. (2006) employed 10 and 15 km, Barani et al. (2007) utilized 25 km, and Khodaverdian et al. (2016) employed 40 km. According to Mirzaei et al. (1997), the determination of an appropriate \(c\) value hinges on factors like the region’s crustal structure, station distribution, and the quantity and quality of available records.

7 Results and discussions

The northernmost region of the Red Sea is characterized by a relatively weak continental crust, whereas the southern portion exhibits primarily oceanic crustal characteristics, with exceptions along the coastal margins (Mitchell and Stewart 2018). It is hypothesized that the differential behavior of the crust in these two areas can be attributed to shear deformation occurring within the Levant fault zone. Indeed, the amalgamation of seismological data and geophysical data has been instrumental in yielding comprehensive insights into the tectonic processes at play within the northernmost segment of the Red Sea region.

This finding emphasizes the value of multidisciplinary techniques that integrate geological, geophysical, and seismological data to better understand the intricate tectonic events in the area. The different crustal traits in the Red Sea’s northern and southern halves, as well as the Levant fault zone’s contribution to these differences, are significant aspects of the area’s geology and tectonics. It may be possible to gain a deeper understanding of the geological dynamics in this area and their wider consequences for plate tectonics and continental development through more research and cooperation among specialists in these domains.

The outcomes of deep seismic soundings conducted in the mapped Red Sea, as reported by Makris and Rihm (1991), have revealed the presence of a relatively fine continental crust under both the western flanks and eastern ones of the region. These findings are further substantiated by a confluence of geophysical evidence. Notably, high seismic activity, coupled with the detection of dense crustal layers immediately beneath evaporate deposits (El-Bohoty et al. 2012), gradients of low seismic velocity (Le Pichon and Gaulier 1988), and the identity of shield rocks of Precambrian, collectively support the assertion that the Northern Red Sea area is over a fine continental crust. Additionally, certain secluded sites within this region have been associated with basaltic injection processes (Mitchell and Stewart 2018; Bosworth et al. 2020).

The absence of linear magnetic anomalies in the mapped Red Sea implies that the deposition of Miocene evaporites occurred upon a continental lithosphere that had undergone attenuation and experienced elevated temperatures (Moustafa et al. 2023). This observation may signify an early stage in the tectonic evolution of the region, marked by continental separation, rifting, and the thinning of the crust, preceding subsequent seafloor spreading as long as the development of oceanic crust (Mart and Hall 1984).

These multidisciplinary findings underscore the complex geological history of the Northern Red Sea, shedding light on the processes involved in continental rifting and the transition to oceanic crust formation, which are of paramount importance in the broader context of plate tectonics and the evolution of continental regions. Further research endeavors are warranted to delve deeper into the intricacies of this geological setting and to enhance our comprehension of its geological and tectonic significance. The region exhibits distinct heterogeneities within the crust and upper mantle, which are linked to the localized accumulation of stress resulting from the interplay between tectonic and magmatic processes.

The geographical area under investigation serves as an intrinsic natural laboratory, offering a valuable opportunity to gain insights into several geological processes occurring within a nascent continental plate boundary. These processes encompass the initial stages of continental rifting, the genesis of oceanic basins, and the intricate transformations of continental terrain due to the dynamic interplay of tectonic forces. This interplay is manifested through the concurrent activity of movements of divergence and convergence at the boundaries of the Arabian-Turkish plats and African-Arabian ones. Various tectonic interpretations posit that the process of rifting commenced in the Red Sea region, extending into the Suez Rift during the middle Miocene epoch, ultimately evolving into an incomplete continental rift within the Precambrian shield located to the south of Sinai. The present-day Gulf of Aqaba, marked by its ongoing tectonic activity, originated from the gap between the Arabian plate and the sub-plate of Sinai. This separation event is believed to have been initiated during the Middle Miocene orogeny and has persisted as an active geological process since that time. It is worth mentioning that the results obtained show the importance of the study area and the utilized methodology that has already been implemented in different active areas such as Mase (2020); Mase et al. (2023); Somantri et al. (2023); Mase (2022); Mase et al. (2021).

The phenomenon of underreporting in seismic events of lower magnitude within the earlier time periods of a 110-year EQ catalog presents a noteworthy observation in contrast to more recent records. A comprehensive analysis of data completeness indicates that the catalog exhibits completeness across the entire temporal span for seismic events of greater magnitude (\(M_w \; 7\)). Furthermore, seismic events falling within the magnitude ranges of \(M_w \; 6-6.9\), \(M_w \; 5-5.9\), and \(M_w \; 4-4.9\) may be deemed to have been adequately recorded since the years 1921, 1961, and 1991, respectively.

An essential attribute of the method in Stepp (1972) lies in its capacity to ascertain the temporal duration necessary to achieve a stable mean recurrence rate of seismic events across various magnitude classes. This capability enables the creation of an artificially homogenized and comprehensive dataset, thereby facilitating the conduct of rigorous statistical inquiries. In the present investigation, the stable mean recurrence rates for seismic events falling within the magnitude classes of \(M_w \; 4-4.9\), \(M_w \; 5-5.9\), \(M_w \; 6-6.9\), and \(M_w \; 7\) have been established as 10, 30, 40, and 90 years, respectively.

In order to enhance the accuracy of the b-value estimation, our study delved into the spatiotemporal fluctuations of the magnitude completeness (Mc) as illustrated in Fig. 7. A marked and abrupt shift was discerned, particularly evident after the year 1995, as depicted in Figures 5a and 5b. This observed alteration is likely attributable to an upsurge in the deployment of EQ monitoring stations within the area of interest. Therefore, this improved station coverage has resulted in a more consistent and steady rate of estimation fluctuation.

Fig. 7
figure 7

Geospatial mapping of magnitude completeness (a), b-Values (b), a-Values (c), and the maximum considered magnitude (d) using the Gardner and Knopoff (GK1974) declustering model. The study area was discretized into 0.1\(^\circ \times \) 0.1\(^\circ \) square grids, and seismicity parameters were computed at grid nodes positioned at 0.1\(^\circ \) intervals along both latitude and longitude axes

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Fig. 8
figure 8

Geospatial Mapping of magnitude completeness (a), b-Values (b), a-Values (c), and the maximum considered magnitude (d) of Uhrhammer’s (UH1986) declustering model. The study area underwent discretization following the same procedure as previously outlined

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Fig. 9
figure 9

Geospatial mapping of \(M_c\) (a), b-Values (b), a-Values (c), and the maximum considered magnitude d according to Van Stiphout’s (VS2012) declustering model. The study region was discretized using the same process as previously described

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The b-value represents a significant statistical parameter with the capacity to offer valuable insights into the seismotectonic characteristics and the potential seismic risks inherent to a specific geographic area (Gutenberg and Richter 1944). The value of b primarily hinges upon the prevailing tectonic conditions, the degree of crustal heterogeneity, variations in pore fluid pressure, and the state of stress within the geological context (Woessner and Wiemer 2005). In the context of seismic hazard assessment, the b-value is of paramount importance for accurately depicting earthquake frequency. The significance of the b-value lies in its capacity to quantify the relative likelihood of small versus large earthquakes within a given region, thereby informing risk assessments. A smaller b-value (\(<1\)) suggests a greater relative frequency of high-magnitude earthquakes, thus indicating a higher seismic hazard, while a higher b-value (\(>1\)) points towards a predominance of smaller seismic events. Therefore, the b-value is instrumental in shaping seismic hazard models, guiding the development of building codes, and informing disaster preparedness strategies, making it a cornerstone of both theoretical seismology and practical hazard mitigation efforts.

We employed the magnitude-frequency scaling (mbs) technique to quantitatively assess the b-value. To delineate the spatial variation of b-values, the geographical region under investigation was partitioned into square grids to ensure the coherent representation of data points. At each grid intersection, spaced at intervals of 0.1\(^{\circ }\) in both latitude and longitude, the b-value was computed. This calculation was carried out using the technique of weighted least-squares, with a prerequisite of \(N_{min} = 100\) seismic EQs for analysis. The bootstrap approach was used to assess the errors in b-values (Chernick 2011). The interpolated map of the b-value spatial distributions is shown in Fig. 8a. It is evident from the figure that b-values vary between 0.54 and 1.08. The reliability of b-value calculations was evaluated by the respective error estimations as shown in Fig. 8b.

Among the prominent parameters used to discern the crust and stress heterogeneity, is the parameter known as the (b-value), which can be calculated by analyzing the relationship between the frequency and the magnitude of seismic events. The variability in b-values can be attributed to several factors, including material heterogeneity as proposed by Mogi (1963), the stress state as postulated by Urbancic et al. (1992), and the effective stress as discussed by Wyss (1973). It is also noteworthy that thermal gradients may lead to an increase in b-values, as suggested by Warren and Latham in 1970.

In Mogi (1967), the authors primarily focused on the mechanical properties of rocks as a determinant of b-values, whereas Scholz (1968) speculated that b-values are significantly affected by the stress behavior more than the inherent heterogeneity of the rock material. Both (Scholz 1968; Wyss 1973) evaluated that low b-values are associated with periods characterized by an increase in shear stress or effective stress. On the other hand, elevated b-values are often associated with greater heterogeneity in rock mass or an increased density of cracks, a concept initially proposed by Mogi (1967). Additionally, the existence of resilient blocks known as "asperities" within rock formations has been observed to reduce b-values. These insights collectively underscore the multifaceted utility of b-values as a tool for comprehending the intricate structural and stress-related aspects of the Earth’s crust, offering valuable perspectives into the geological and geophysical processes at work beneath the surface.

Fig. 10
figure 10

Developed spatial SS distribution models of seismic events with magnitudes equal to or greater than M = 0, presented as the logarithm of annual event count, across geographical regions varying from 0.1\(^\circ \) to 0.1\(^\circ \). This investigation encompasses two distinct correlation distance settings: a c = 30 km and b c = 50 km. The seismic event catalog underwent preprocessing by UH1986

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The spatial variations in b-values are influenced by several factors, including material heterogeneity, stress accumulation, changes in pore fluid pressure, and thermal activities. In regions with different tectonic settings, b-values typically (0.5–1.5) across various magnitude scales, as observed by Wiemer and Katsumata (1999). In active volcanic areas where seismicity is driven by magmatic processes, b-values are expected to fall within (1.5–3.0), as suggested by McNutt (2005). Additionally, regions characterized by dense fractures and stress variations tend to exhibit b-values (1.0–2.5), as explained by Roberts et al. (2015). An in-depth analysis of the b-value distribution (see Fig. 8a) reveals significant variations ranging (from 0.4 to 2.5), marking different zones with low to high b-values, likely stemming from heterogeneities in either the stress field or material properties. The obtained b-value of 0.4 in the Red Sea region holds significant seismic implications, echoing findings from previous studies such as those by Al-Amri et al. (1998); Ali and Abdelrahman (2023), albeit these specific studies were not directly cited in the provided search results. The b-value, a crucial parameter in the GR relationship, serves as an indicator of the relative frequency of small to large earthquakes within a given region. Typically, a b-value around 1.0 suggests an equilibrium between the occurrences of small and large earthquakes, whereas a lower b-value, like the 0.4 observed in the Red Sea region, indicates a predominance of larger magnitude earthquakes over smaller ones. This deviation from the global average b-value of approximately 1.0 underscores a unique seismic risk profile for the area, highlighting the potential for significant seismic events. The consistency of this lower b-value across studies suggests a persistent tectonic stress regime conducive to generating larger earthquakes, underscoring the importance of incorporating such data into regional seismic hazard assessments and preparedness strategies. The critical nature of these findings, in line with the broader seismic activity characterizing the Red Sea region as detailed in the search results 1,2, emphasizes the need for ongoing monitoring and analysis to better understand and mitigate the seismic risks associated with this tectonically active area.

Notably, the Gulf of Aqaba, the Gulf of Suez, and the northernmost part of the Red Sea exhibit low b-values, consistent with previous findings by Al-Amri (1995). The geospatial mapping of Mc, b-Values, a-Values, and the maximum considered magnitude according to the declustering model (Thomasvan Stiphout and Marsan 2012) is presented in Fig. 9. Figure 10 shows the obtained smoothed seismicity based on the seismic event catalog that underwent preprocessing by UH1986. The results highlight the significance of b-values as a valuable tool for comprehending the intricate link between geological and geophysical processes in distinct tectonic zones and provide light on the dynamic nature of seismicity in various geological contexts.

8 Conclusions

The analysis of b-values, which are produced by relating the frequency and magnitude of EQs, sheds light on the complex geological and geophysical processes occurring in various tectonic zones. These b-values serve as markers for geographic differences in crustal and stress heterogeneity, revealing a complex interaction of elements including material characteristics, stress building, variations in pore fluid pressure, and temperature impacts. B-values varied widely across different magnitude scales and tectonic environments, from 0.5 to 1.5. B-values are anticipated to fall between (1.5 and 3.0) in active volcanic locations where seismic activity is predominantly driven by magmatic processes. Furthermore, areas with high-density fractures and stress heterogeneities typically have b-values (1.0–2.5).

The spatial distribution of b-values within the mapped Red Sea region shows substantial variability, ranging from 0.4 to 2.5. It is possible that the heterogeneity present in the stress field or the material qualities is the cause of this change, which appears as alternating patches with low to high b-values. Notably, the northernmost part of the mapped Red Sea, the Gulf of Suez, and the Gulf of Aqaba exhibit low b-values, consistent with previous research findings.

Overall, the diverse range of b-values observed across different regions underscores the importance of considering multiple geological and geophysical factors when interpreting seismic data. The application of b-values as a diagnostic tool enhances our understanding of seismicity and tectonic processes, providing valuable contributions to the field of EQ and geophysical research. Further investigations into the specific driving mechanisms behind these b-value variations will contribute to a deeper comprehension of the dynamic geological processes operating within these regions and their broader implications for seismic hazard assessment and mitigation strategies.

Finally, developing a smoothed seismicity model for the Red Sea region holds significant implications for enhancing earthquake risk assessment and mitigation strategies in this geologically complex area. By implementing such models, which incorporate spatially smoothed seismicity, there is potential for more accurately predicting future earthquake activity rates and their associated hazards. This advanced approach can lead to a better understanding of the seismic hazard distribution across different parts of the Red Sea region, particularly along the main tectonic features of the Red Sea rift systems. Consequently, this could inform more targeted and effective building codes, urban planning, and emergency preparedness measures, particularly in areas identified as having higher risks. Moreover, the smoothed seismicity maps produced could serve as critical tools for governments and disaster response agencies in prioritizing resources and efforts, not only to safeguard infrastructure but also to reduce the potential for human casualties in the event of seismic events. Ultimately, the adoption of such a model represents a proactive step toward reducing the vulnerability of communities and enhancing resilience against seismic threats in the Red Sea region.