1 Introduction

The Gulf of Aqaba, as a part of the Dead Sea transform fault zone, has a long history of major tectonic activity (Ben-Avraham et al. 1979; Alamri et al. 1991; Ben-Avraham et al. 2008). The Gulf of Aqaba represents the southern part of the Dead Sea transform fault that connects with the rifting region in the northern Red Sea to the south. Tectonically, the gulf is controlled by the relative motions between the African, Arabian, and Eurasian plates, as well as the anticlockwise rotation of Sinai Peninsula (Fig. 1). These relative motions might be responsible for the occurrence of seismic activities in the Gulf with dominant strike-slip to infrequent dip-slip mechanisms (Pinar and Turkelli 1997; Klinger et al. 1999; Hofstetter 2003; Hofstetter et al. 2003; Shamir et al. 2003; Abdel-Fattah et al. 1997, 2006, 2016). The coupling of extensional to shear movements is currently accommodated along the plate boundaries demarcated in the region (Fig. 1). The extensional stress regime is thought to be imparted from the opening of the Red Sea with a spreading rate of 1 cm/year at 25.5° N (Chu and Gordon 1998). Moreover, the shear deformation is presumably activated by an anticlockwise rotation of the Arabian plate relative to Africa with a rate of 1 cm/year at an angle of 6° (Girdler 1966; Garson and Krs 1976).

Fig. 1
figure 1

Map showing three types of plate tectonic boundaries and relative plate motions in the Middle East region. The acronyms represent the following: GA the Gulf of Aqaba, GS the Gulf of Suez, DST Dead Sea transform, EAF East Anatolian Fault. The fault traces in the Gulf of Aqaba (upper right map) are adopted after Ben-Avraham (1985) and Darkal et al. (1990)

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The intense seismicity in the Gulf of Aqaba is triggered as isolated sequences (Abdel-Fattah et al. 1997). Three distinctive earthquake sequences have been reported on 1983 (M w = 4.9, using the equation of Mohamed et al. (2012)), 1993 (M w = 6.0), and 1995 (M w = 7.1) for different faulting mechanisms. For instance, the 1993 earthquake exhibited pure normal faulting mechanism while the 1995 earthquake showed strike-slip focal mechanism (Pinar and Turkelli 1997; Abdel-Fattah et al. 2006). As a matter of fact, the sinistral shear slip along the strike is accommodated along the main fault trend slip of NNE orientation, while the dip slip is accommodated along the conjugate fault trend. The moment tensor summations obtained by Abdel-Fattah et al. (2016) showed average source mechanisms of pure sinistral strike-slip solutions along Aqaba-Dead sea fault.

The determination of the source mechanism, focal depth, and moment magnitude for small- to moderate-sized earthquakes is of great importance to provide insights on the ongoing stress in the region. Using different methods based on inversion and modeling techniques, the source mechanism solutions and focal depths can be determined. The solutions mainly depend on how the one-dimensional velocity model (used for computing synthetic seismograms) is adequate to reflect the simulation of true heterogeneities for low-frequency signals. This problem is resolved by computing synthetic seismograms in the frequency band lower than 0.1 Hz, giving insensitive estimates of focal depths. The region in the vicinity of the Gulf of Aqaba is characterized by different structural settings: the Dead Sea rift valley northward, the Arabian Shield eastward, the Sinai sub-plate westward, and the Red Sea rifting southward. To overcome the complex structure in the region, Abd el-aal and Badreldin (2016) retrieved the source mechanism of the respective earthquake using moment tensor inversion and regional waveform data recorded by seismic stations located within an azimuth beam of about 30° west. However, this narrow azimuth beam might influence the adequate estimation of the moment tensor solution.

In order to determine a precise focal depth in the present study, the focal mechanism solutions over a range of focal depths were investigated by using the waveform modeling for teleseismic P wave in a frequency band of 0.02–1 Hz. Within the distance range 30°–90°, no upper mantle triplication affects the P waves. The focal mechanism based on P wave onsets was used to constrain the focal mechanism retrieved from the waveform modeling. Considering the fault trends in the Gulf of Aqaba, the identification of the causative fault is of great importance for the seismic hazard assessments. For this purpose, the aftershock hypocenters were relocated using the double-difference technique. The source parameters were quantified using the spectral analysis technique.

2 Tectonic settings

From the geological and geophysical viewpoints, the shear deformation is accommodated along the Gulf of Aqaba-Dead Sea transform fault zone between the Arabian and African plates, advocating to be initiated less than 20 Ma bp (Freund et al. 1970; Garfunkel 1981). This tectonic process forms the complex structure in the Gulf of three successive pull-apart basins of NNE-SSW strike associated with normal to shear seismic deformations (Abdel-Fattah et al. 2016). Although the recent focal mechanism solutions and GPS studies reveal that the southern part of the Gulf undergoes extensional deformation, no direct evidence of oceanic crust has been observed.

The Gulf is structurally characterized by two main faults of NNE-SSW and ESE-WNW strikes as recognized by Ben-Avraham (1985), Lyberis (1988), and Bayer et al. (1988). The faults are arranged as an echelon transverse structure, as shown in Fig. 1. The NNE-SSW fault trends control the Gulf structure with sinistral strike-slip movement that presumably initiated during the Late Miocene. The ESE-WNW faults probably originated due to the ENE-WSW extensional stress regime that began in the Late Burdigalian age (Lyberis 1988).

The source region has experienced historical earthquakes and recent seismic activities. The historical earthquakes in 600 bc, 28 bc, and 1778 are reported to have epicenters close to the center of the Red Sea (Ambraseys et al. 1994). The most recent destructive earthquake of 22 of November 1995 of M w 7.1 is the largest earthquake that occurred along the Dead Sea transform fault and was widely felt in Egypt, Israel, Jordan, and Saudi Arabia (Abdel-Fattah et al. 2006). On the basis of GPS measurements, the average slip rate is 4.4 ± 0.3 mm/year of left-lateral deformation developed along the Gulf of Aqaba and Wadi Araba, as revealed by Mahmoud et al. (2005) and Reilinger et al. (2006). Using the moment tensor summation, the seismic slip rate showed an extensional deformation of 0.011 mm/year along ENE-WSW trend and compression of 0.007 mm/year along the NNW-SSE direction with an average focal mechanism having a strike of 204°, a dip of 62°, and a slip of −9° and similar to the focal mechanism of the 1995 earthquake (Abdel-Fattah et al. 2016).

The seismicity and seismotectonic settings of the Gulf of Aqaba were investigated by numerous authors (El-Isa et al. 1984; Alamri et al. 1991; Shapira and Hofstetter 1993; Abdel-Fattah et al. 1997; Klinger et al. 1999; Hofstetter 2003; Salamon et al. 2003; Abdel-Fattah et al. 2006; El-Isa 2013). For earthquakes with m b ≥ 3.0, the moment magnitude was unified using the equation of Mohamed et al. (2012):

$$ {M}_{\mathrm{w}}=1.16{m}_{\mathrm{b}}-0.9 $$
(1)

The seismicity in the Gulf of Aqaba from the period of 1964 to 2015, as reported by the International Seismological Center (ISC), is shown in Fig. 2. It is obvious from the figure that the hypocenter distribution shows an intensive seismicity at focal depths ranging from 5 to 20 km. The straight lines at shallow depths are probably defined by the location algorithm when the calculation provides too shallow depth. Moreover, the regional velocity model is not well calibrated in the region.

Fig. 2
figure 2

The epicentral distribution map showing the earthquake data compiled from ISC in the period from 1964 to 2015. The upper left panel shows the spatial distribution of epicenters while the upper right panel and the bottom panel show the hypocenter distributions along the latitude and longitude, respectively. The legend classified the earthquakes with different colors based on the moment magnitude range. The stars denoted the mainshock locations of the earthquake sequences occurred in 1983, 1993, 1995, and 2015. The equation of Mohamed et al. (2012) was used to unify the moment magnitude

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Recent focal mechanism solutions satisfied the sense of motion along the NE-SW and WNW-ESE fault trends (Abdel-Fattah et al. 1997, 2006; Pinar and Turkelli 1997, Klinger et al. 1999, Hofstetter 2003; Hofstetter et al. 2007). Figure 3 shows the available focal mechanisms that were determined by international centers (Harvard, MED_RCMT, RCMT, and ZUR_RMT) based on the assumption of double-couple point source using the moment tensor inversion technique. The parameters of the focal mechanisms are listed in Table 1. Most of the earthquakes showed normal to strike-slip faulting mechanisms. Due to the usage of different waveform dataset, it is noteworthy that the solution of MED-RCMT displayed different focal mechanisms, from all other solutions, that showed an inconsistent mechanism with the left-lateral strike-slip mechanisms along the NNE strike.

Fig. 3
figure 3

The spatial distribution of locations (open circles) and focal mechanism solutions (green beach balls) for earthquakes listed from 1 to 9 in Table 1. The map also shows the average fault plane solution in the Gulf of Aqaba (red beach ball), as estimated from the moment tensor summation by Abdel-Fattah et al. (2016). The location (purple stars) and focal mechanism (purple balls) of the 2015 earthquake are displayed, as determined by the USGS (www.usgs.gov), GCMT (www.globalcmt.org), MED_RCMT (www.bo.ingv.it/RCMT/), and GFZ (www.gfz-potsdam.de). The numbers corresponded to the focal mechanism listed in Table 1

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Table 1 The fault plane parameters for the focal mechanisms shown in Fig. 3
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3 Data and methodology

The teleseismic P waves recorded by the broadband seismic stations were retrieved from the Data Management Center of the Incorporated Research Institutions for Seismology (IRIS). The waveforms were used to determine the focal mechanism, focal depth, and moment magnitude for the mainshock. The mainshock location used in the present study, as taken from the International Seismological Center (ISC), and the broadband stations are shown in Fig. 4a. The waveform data obtained from the seismic stations in Fig. 4a were used to determine the focal mechanism depending on polarities. The recordings of the seismic stations within the epicentral distance of 30°–40°, for keeping good signal-to-noise ratio, were used to determine the focal mechanism using waveform modeling. The waveform data of P wave were filtered in the frequency band of 0.02–1.0 Hz. In the solution based on P wave polarities, a total number of four stations (KONO, KURK, MSEY, and PAB) are lost as their readings are less clear. On the other hand, a total number of six stations of hypocentral distances smaller than 30° were not included in the waveform modeling.

Fig. 4
figure 4

Map showing the distribution of seismic stations used in the present analysis. (a) The location of the 2015 earthquake (star) and the distribution of the recorded broadband IRIS seismic stations. All stations (solid circles and open squares) are used to determine the focal mechanism using the first P wave polarities while the stations denoted by solid circles were used in waveform modeling. The area enclosed by open rectangle represented the map showed in (b) that displayed the distribution of local stations used to relocate hypocenters and to estimate source parameters. The solid-triangle stations belong to ENSN, and the open-square stations are for the SSN. Station codes are also written

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To determine the source parameters of the mainshock and its larger aftershocks, the waveform data recorded by the Egyptian National Seismographic Network (ENSN) and the Saudi Seismographic Network (SSN) were used (Fig. 4b). The networks are operated by the National Research Institute of Astronomy and Geophysics in Egypt and the Saudi Geological Survey in Saudi Arabia, respectively.

4 Focal mechanisms

Two methods were used to retrieve the focal mechanism solution from first onset P wave polarities and waveform modeling. Firstly, the normalized waveform modeling technique incorporated with grid search technique was applied. The normalized waveform modeling for teleseismic P wave of frequency range lower than 1.0 Hz is used to show a reliable depth determination and stability in focal mechanism solutions. The green’s functions were calculated using the Hudson (1969) technique and the AK135 spherical earth model of Kennett et al. (1995). Using the software developed by Herrmann and Ammon (2004), the grid search method over the strike, dip, and rake was followed to obtain the double-couple solution and the optimum focal depth. A weighted L1 norm was summed over all stations to measure the misfit between the observed and synthetic seismograms. Secondly, the focal mechanism was determined based on P wave polarities. The theoretical travel time of the first P wave polarity was calculated using the AK135 spherical velocity model (Kennett et al. 1995) and the TauP software (Crotwell et al. 1999). The DRAWFM software program of Abdel-Fattah (personal communication), running under Linux with GUI environment, was used to project the nodal planes separating the quarters of different polarities.

The focal mechanism solutions, based on polarities and waveform modeling, showed two similar solutions of a strike-slip faulting mechanism with minor normal dip-slip component (Fig. 5). The results reflect stability in the focal mechanism solutions at different focal depths. The focal mechanism solutions, retrieved from waveform modeling, were determined at a set of focal depths through gross and fine grid searches at increments of 10° and 2°, respectively, in strike, dip, and rake. The fine grid search showed a minimum RMS value at a focal depth of 15 ± 1 km, as shown in Fig. 5. The resulted focal mechanism solution derived from waveform modeling is 354° ± 11° for strike, 61° ± 8° for dip, and −12° ± 5° for rake. Over the grid search of the double-couple solution, the standard deviation in the best-fitting solution was measured from the solutions having errors ranging from the minimum value to 10% confidence level above the minimum value. The range along the strikes, dips, and rakes is used to measure the solution uncertainty. According to the waveform modeling result, the fault plane solution is calculated by using polarities at a focal depth of 15 km. The polarity method shows a strike of 356°, a dip of 80°, and a rake of −11° (Fig. 6).

Fig. 5
figure 5

Plot showing the distribution of focal mechanism solutions at different focal depths as estimated from teleseismic P wave modeling using the Hudson technique with a dislocation grid search method. The optimum solution represents the optimum focal mechanism obtained at a focal depth of 15 km and a triangle STF of 1.0s rise time

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Fig. 6
figure 6

The focal mechanism solutions of the mainshock as retrieved from a the first arrival of P wave polarities and b P wave waveform inversion at a focal depth of 15 km, plotting without the stations of hypocentral distances lower than 30°. The focal mechanism retrieved from the waveform modeling displayed nearby the NS plane unmatched readings that are less clear than the other stations. The downward and upward polarities are given by open and solid circles, respectively. The center of the beach ball is denoted by the cross symbol. Station codes are written nearby each polarity

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5 Double difference location

A total number of 15 aftershocks of moment magnitude larger than 2.9 were relocated using the double-difference technique (Waldhauser 2001). The differential travel time measurements of P and S waves and the velocity model of Rodgers et al. (1999) were used to relocate the events. The differential travel time was measured from the seismic stations that are shown in Fig. 4b. The distribution of relocated epicenters, with respect to the mainshock location, showed a distribution aligned in NE-SW direction, as shown in Fig. 7. The relocated hypocentral parameters are listed in Table 2.

Fig. 7
figure 7

The spatial distribution of the relocated aftershocks (open circles) with respect to the location of mainshock (red stars) as obtained using the double-difference algorithm. The locations (red stars) of 1983, 1993, and 1995 earthquakes are shown. The dashed line is the suggested extension of one of fault segments that is consistent with the aftershock distributions and with one of the nodal planes of focal mechanism solution obtained from the present analysis

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Table 2 The location of the largest aftershocks using the double-difference algorithm
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The spatial distribution of relocated aftershocks is approximately aligned along the NS orientation in consistence with one of fault segments in the Gulf and with one of the nodal planes obtained by the fault plane solution, suggesting that the causative fault produced the 2015 Gulf of Aqaba sequence.

6 Spectral analysis

The spectrum amplitude was computed using fast Fourier transform (FFT) for the mainshock and largest aftershocks. Fourier amplitude spectrum vectorially combined the three components in the frequency domain. Assuming a circular source model of the Brune model (Brune 1970), the least square technique was used to recover the model parameters, the corner frequency, and the low-frequency spectral amplitude. The spectrum amplitude was determined using time window lengths of 2–3 and 4–6 s for P and S waves, respectively.

The estimated source parameters for the mainshock and the analyzed aftershocks are listed in Table 3. Figure 8 shows the amplitude spectra of velocity waveform data. The estimated moment magnitude, fault radius, and stress drop of the mainshock are 5.0 ± 0.02, 2.48 ± 0.26 km, and 1.14 ± 0.17 MPa, respectively. The standard deviations of the source parameters were calculated by following Archuleta et al. (1982). Figure 9 shows the relationship between the seismic moment and fault radius, illustrating approximately constant stress drops. The plot is based on the dataset of mainshock and 15 aftershocks in the moment magnitude range from 3.0 to 5.0. Estimates of source parameters showed seismic moments of 3.34E+13 to 3.98E+16 Nm, fault lengths of 0.29 ≤ L ≤ 2.48 km, and stress drops of 0.14 to 1.14 MPa, indicating a source scaling similar to the tectonic earthquakes related to plate boundaries.

Table 3 Averaged source parameters (seismic moment Mo, fault radius r o, stress drop Δσ, and moment magnitude M w) for the mainshock and largest aftershocks of the 2015 earthquake sequence
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Fig. 8
figure 8

Plot showing the velocity spectra and the corresponding synthetic spectra (black lines) for selected stations and events for P wave (red lines) and S-wave (blue lines). A grid search technique, combined with an assumption of circular source model, was applied to find the best-fit source spectra over the space parameters: long period spectral level and corner frequency assuming the asymptotic high-frequency falloff of 2. The station code and the event ID are written on the upper right for each panel. The event ID corresponded to the event serial number listed in Table 3

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Fig. 9
figure 9

Seismic moment versus fault radius of the mainshock and a total number of 15 aftershocks. Solid lines showed constant stress drops around 0.1 and 1 MPa. For the events of small fault radius, the stress drops are essentially below 1 MPa, while for those having larger fault radius, the stress drops are approximately closed to 1 MPa

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7 Discussions and conclusions

In this study, two methods are used to retrieve the source mechanism solution of the 2015 Gulf of Aqaba earthquake. Firstly, the normalized waveform modeling that revealed strike-slip faulting mechanism of a strike of 354° ± 11°, a dip of 61° ± 8°, and a rake of −12° ± 5°; indicating an extensional stress of 13° that plunged horizontally towards N38° E and an average compressional stress of 28° that plunged towards N316° E. Secondly, the pattern of P wave polarities showed a strike-slip faulting mechanism with a strike of 350°, a dip of 80°, and a rake of −2°, indicating an extensional stress of 6° that plunged horizontally towards N34° E and a compressional stress of 9° that plunged towards N305° E.

It is noteworthy that the fault plane solution obtained from waveform modeling differs in the dip of one of the nodal planes from the pattern of the fault plane solution from the polarities (see Fig. 6). Despite the difference in the dip along the NS plane, both fault plane solutions are consistent with the regional stress pattern. The distribution of maximum and minimum compressive stresses shows mainly strike-slip stress regime with a slight extension component (horizontal NW-SE σ 1 and NE-SW σ 3). The focal mechanism solutions retrieved in the present analysis implied that the respective earthquake was the typical consequence of crustal deformation due to current tectonics, reflecting the NE-SW extension and NW-SE compression along the Gulf of Aqaba (Lyberis 1988; Bajous and Mikbel 1990; Abdel-Fattah et al. 1997; Lunina et al. 2005; Hussein et al. 2013; Abdel-Fattah et al. 2016). Under this stress regime, the dominant compatible focal mechanisms are strike-slip faulting types with fault planes dipping at a nearly vertical angle.

The present results incorporated with those obtained from earthquake focal mechanism analysis in previous studies indicate that the Gulf of Aqaba is influenced by the NW-SE compression and NE-SW extension (Abdel-Fattah et al. 1997; Hofstetter 2003; Abdel-Fattah et al. 2006, 2016). For instance, the 1995 earthquake exhibited source mechanism solution similar to that obtained in the present study, reflecting a maximum compressive stress axis of NW-SE orientation (Abdel-Fattah et al. 1997). Moreover, the 1993 earthquake that has occurred onshore of the eastern coast of the Gulf of Aqaba had a well-determined maximum compressive stress axis striking due NW-SE (Abdel-Fattah et al. 2006). The crustal deformation analysis based on moment tensor summation revealed that the present-day stress field in the Gulf is dominated by the NW-SE compression and NE-SW extension, whose azimuths are 135° and 45°, respectively (Abdel-Fattah et al. 2016), and is consistent with the results derived from the stress tensor inversion analysis by Hussein et al. (2013). The results are almost compatible with the geological evidence, ERS-SAR interferometry, and the GPS observations (Klinger et al. 1999, 2000; El-Fiky 2005; Mahmoud et al. 2005).

Compiling the focal mechanism solution of the mainshock and the aftershock relocations, as obtained by the double-difference technique, the NS trending fault plane is considered as the causative fault that produced the 2015 earthquake sequence, coinciding with one of the fault segments in the Gulf. The distribution of aftershocks along the NS plane, as retrieved from the focal mechanism, suggests a reactivation of sinistral high-angle fault by the contemporary NE horizontal extensive stress, corresponding to the regional stress regime. It is noteworthy that the aftershocks are spatially distributed to the south of the mainshock epicenter.

Assuming the Brune model (Brune 1970), the estimates of source parameters exhibited fault radius of 0.3–2.42 km and the corresponding stress drops 0.14–1.14 MPa. The results reflected stress drop values similar to the tectonic earthquakes occurring along the plate boundaries, as suggested by Scholz (1990). It is noteworthy that the moment magnitude (M w = 5.0) of the mainshock determined by spectral amplitudes for P and S waves is smaller than that published by Abd el-aal and Badreldin (2016) of 5.2, GCMT (5.6), MED_RCMT (5.5), GFZ (5.5), and USGS (5.6) using regional and teleseismic waveform inversions. The significant difference may be due to the usage of different datasets and techniques and the uncertainties in the preliminarily determinations by the international centers.