Introduction

The 2010 Beni-Ilmane seismic sequence occurred on a complex faulted fold in the Biban region in the southern part of the Tellian Atlas (Fig. 1a, b). The region is bounded to the south by the northern front of the Hodna basin and to the north by the Soummam River valley. The epicentral area of the Beni-Ilmane seismic sequence is located at the boundary of two distinct geological domains: the Alpine Mountains and the Tellian Sub-Bibanique nappe in the north and the pre-Atlasic domain in the south (Yelles-Chaouche et al. 2014 ; Beldjoudi et al. 2016). The seismic sequence hits the Beni-Ilmane region between May 14 and 23, 2010. Three moderate shocks and 1431 aftershocks were recorded and located until May 31 (Table 1). The first shock with a moment magnitude of 5.5 Mw and seismic moment of 1.8 × 1017 Nm (Fig. 1c) occurred either on a dextral plane oriented [Strike1, Dip1, Rake1: 254°, 74°, 175°] or on sinistral plane oriented [Strike2, Dip2, Rake2: 345, 85, 16]. The second shock hit the region with a moment magnitude Mw of 5.1 and seismic moment 5.5x1016 Nm, occurred on a reverse fault oriented [Strike, Dip, Rake: 250°, 55°, 120°] and the third shock occurred on a left-lateral fault [Strike, Dip, Rake: 12°, 57°, 12°] with a moment magnitude Mw 5.2 and a seismic moment 7.4x1016 Nm (Beldjoudi et al. 2016). In this work, I will try to understand the interaction between these three moderate events which occurred on three neighboring unconnected faults. A seismotectonic model of the seismic sequence is presented in Fig. 1c.  I shown in this study that the fault F1 oriented NE-SW is the fault plane related to the first shock (Fig. 1c). Many studies concerning fault interactions and Coulomb stress changes modeling were conducted in the north of Algeria. Lin et al. (2011) studied the interaction of the fault of the Zemmouri-Boumerdes earthquake with two seismogenic structures in the border of the Mitidja basin: the Sahel Anticline and the Blida Structure. At a regional scale, Kariche et al. (2017), tried to explain the relationship in term of Coulomb stress changes between the major events which occurred in the North of Algeria during two century. On a local scale, Dabouz and Beldjoudi (2019) studied the fault interaction following the Mont Chenoua earthquake (Ms 6.0) on nearby fault structures in the epicentral area.

Fig. 1
figure 1

a Location of the epicentral area at a regional scale, b location of the epicentral area at a local scale, and c seismotectonic map of the epicentral area. Stars show the location of the main events and their relative focal mechanisms. Red dots are aftershocks for the first period (May 14–16), green dots are aftershocks for the second period (May 16–23), and blue dots are aftershocks for the third period (May 23–31). F1, F1’, and F2 are the identified faults close to the location of the main event

Full size image
Table 1 Source parameters of the main events
Full size table

Seismic sequence

The 2010 Beni-Ilmane seismic sequence consists of three main moderate magnitude earthquakes that ruptured strike-slip, reverse, and strike-slip faults in the Biban region (Beldjoudi et al. 2016; Yelles-Chaouche et al. 2014). The shallow sequence started on May 14 with Mw = 5.5. A second shock hit the region on May 16 with Mw = 5.1, and a third shock hit the region again on May 23 with Mw = 5.2. The three shocks are at a depth of 6 km (Beldjoudi et al. 2016). The largest events of the sequence are listed in Table 1. The aftershock sequence has been recorded by a dense temporary network between May 14 and 31 (Yelles-Chaouche et al. 2014). A total of 1403 events have been relocated with a horizontal error ERH ranging between 0.5 km and 1 km and a vertical error ERZ ranged between 0.5 km and 2 km. The duration magnitude Md ranged from 1.3 to 4.9. The epicenters are shallow and located between 0.3 and 11.08 km (Yelles-Chaouche et al. 2014). Relocated aftershocks drew two seismogenic volumes that are oriented NNE and EW (Fig. 1).

The aftershocks scenario can be divided into three episodes. The first episode started from the first shock (May 14, 12 h 29 min) until the occurrence of the second shock (May 16, 06 h 52 min); here, 118 events were relocated; the epicenters show diffuse seismicity with a semblance of orientation NE-SW; four shocks with a magnitude greater than 4 are located (Yelles-Chaouche et al. 2014). During the second period which started from the second shock until the third shock (May 23, 13 h 28 min), two main clusters can be shown. One cluster oriented E-W located North of the second shock and extent ~ 12 km. The other cluster located SE of the second shock. During the third period (May 23 to 31), 591 events were relocated. In this period two main clusters were well identified: one oriented E-W and the other oriented NNE-SSW. Focal mechanisms of the mainshocks obtained by waveform modeling (Beldjoudi et al. 2016) show a strike-slip regime for the first shock, a reverse fault for the second shock, and a strike-slip for the third shock (Fig. 1). The spatial distribution of the main epicenters and spatio-temporal distribution of the aftershocks point out several peculiarities. First, the seismic sequence occurred in a faulted fold with faults oriented in all directions. Second, the three main shocks are located on unconnected faults of the fold with different FM. Third, the aftershocks are oriented in two orthogonal directions: NNE-SSW and E-W.

Seismicity of the Beni-Ilmane region

The Beni-Ilmane region belongs to the Hodna-Biban area. The seismicity of the region dates to the Zemmoura-Guenzet earthquake on February 9, 1850, with a maximum observed intensity (Io) of VII (European Macroseismic Scale, EMS) assigned by Harbi and Maouche (2009). Other earthquakes occurred in the region for the period (1850–1973), their intensity were greater than VII near the following localities: (1) M’sila on 1885 and 1965 (Harbi et al. 2003; Hatzfeld 1978; Rothé 1950); (2) Mansourah on 1887, 1943, and 1973 (Harbi et al. 2003; Hatzfeld 1978; Rothé 1950); (3) Berhoum on 1946; (4) Beni-Ilmane (formerly Melouza) on 1960; and (5) M’sila on 1885 and 1965 (Fig. 2). During the instrumental era, the Mansourah region has recorded the largest earthquake with magnitude of up to 4.9 during the period 1973–1974; also on May 5, 2012, an earthquake of Mw 4.9 hit the region of Bordj Bou Arreridj (northeast of Mansourah). Historical and instrumental catalogs (Mokrane et al. 1994, Harbi and Maouche 2009) show that the Hodna-Biban region is seismically active; the seismicity is distributed on numerous active structures. The maximum observed intensity (Io) values of VIII–IX have been observed in the area of Mansourah (Roussel 1973; Bezzeghoud et al. 1996; Boughacha et al. 2004).

Fig. 2
figure 2

Historical seismicity in the Hodna-Biban region from February 9, 1850, to May 13, 2010. White open squares show the main earthquakes (historical) reported in the region. Open circles show instrumental seismicity. Open stars show the main events of the seismic sequence. Black solid squares indicate cities and villages in the region

Full size image

Coulomb stress changes

I calculate Coulomb stress changes (∆CFF) using the Coulomb 3.3 software (Toda et al. 2005a, b; Lin and Stein 2004). The static stress changes caused by an earthquake are computed using the Coulomb failure assumptions (King et al. 1994; Hodgkinson et al. 1996; Harris 1998; Cocco et al. 2000). The variation of the Coulomb stress changes (∆CFF) is defined as (Stein et al. 1992; Harris 1998)

$$ \Delta \mathrm{CFF}=\Delta \uptau +\upmu\ \left(\Delta \upsigma +\Delta \mathrm{P}\right) $$
(1)

where ∆τ is the change in shear stress, ∆σ is the change in normal stress (positive for extension), μ is the friction coefficient, and ∆P is the change in pore pressure. This latter term can be expressed in terms of the Skempton’s coefficient B as follows (Harris 1998; Cocco et al. 2000):

$$ \Delta \mathrm{P}=-\mathrm{B}\frac{{\Delta \upsigma}_{\mathrm{kk}}}{3} $$
(2)

where ∆σkk is the volumetric stress change and σkk is the sum of the normal stresses (σkk = σ11 + σ33 ).

The Skempton’s coefficient can vary between 0 and 1 (Roeloffs 1988; Cocco et al. 2000). Commonly, it is assumed that the fault zone materials are more ductile than the surrounding materials (Rice 1992; Harris 1998). Under these conditions, \( \frac{{\Delta \sigma}_{kk}}{3}\approx {\Delta \sigma}_n \) , and Eq. (1) is frequently written as

$$ \Delta \mathrm{CFF}=\Delta \tau +\mu '{\Delta \sigma}_n $$
(3)

where ∆τ is the change in shear stress, ∆σ is the change in normal stress, μ’ = μ(1 - B) is the effective friction coefficient, and μ is the coefficient of friction. Many studies suggest that μ is (0.6–0.9) for most geological materials and the effective friction coefficient μ’ used in triggered seismicity is defined by the combination of pore pressure and friction coefficient (Byerlee 1978; Kariche et al. 2017). Previous studies suggest that one explanation for apparently low value of μ’ would be the presence of high fluid pressure (Kariche et al. 2017, Jaumé and Sykes 1992). In our study, I show that the coulomb modeling requires an effective friction coefficient of 0.1 < μ’ < 0.8 which implies a ∆CFF of 0.18 bar at the hypocenter of the receive fault2. Equation (3) is commonly used to calculate Coulomb stress changes by assuming different values for μ’ where the influence of pore pressure is included in the effective coefficient of friction (Fig. 3).

Fig. 3
figure 3

Stress loading the receiver fault 2 (256°/55°/120°) with a source fault oriented (254°/74°/175°) using different effective friction coefficient μ’. Black cross shows epicenter location

Full size image

Regional stress

The Coulomb stress modeling on optimally oriented fault planes are computed by considering both, the static stress changes \( {\sigma}_{ij}^c \) and the regional tectonic stress \( {\sigma}_{ij}^r \) (King et al. 1994)

$$ {\sigma}_{ij}^t={\sigma}_{ij}^r+{\sigma}_{ij}^c $$
(4)

In this case, the ∆CFF is computed using the total stress tensor\( {\sigma}_{ij}^t \), as shown by Eq. (4).

Many studies were conducted to calculate regional stress in many regions in North of Algeria; the general trend of the regional stress is NW-SE (Khelif et al. 2018; Soumaya et al. 2018; Beldjoudi et al. 2009, 2012, 2016). The regional stress was obtained for the region of the Beni-Ilmane by inversion of strike and dip of the focal mechanisms available in the region (Beldjoudi et al. 2016). The principal-compressive stress axis σ1 is oriented N160° and plunged 22°, the intermediate stress σ2 oriented N20° and plunged 62° and the extensive stress σ3, is oriented N77° and plunged 16°. The trend of regional stress is used in this study to calculate Coulomb stress changes on optimal planes.

Coulomb stress changes following the first shock and the second shock

On 14 May 2010 starts the seismic sequence of the Beni-Ilmane region with a first shock of Mw 5.5. The focal mechanism calculated by waveform inversion (Beldjoudi et al. 2016) shows a right lateral strike-slip fault with an azimuth of N254° for the first plane and a left lateral N345° for the second plane. The question is: Which fault plane of the focal mechanism played during this first shock? In the previous studies (Beldjoudi et al. 2016; Yelles-Chaouche et al. 2014), no one could answer this question, because the epicenter is located near two active structures and no surface trace was visible because the shock is moderate. For this, I will consider both planes as sources, and I will compute the Coulomb stress changes (∆CFF) on considering receiver faults, the second and third shocks, and then I will compare the results.

I start to calculate (∆CFF) considering first the plane oriented N345° as a seismic source. The receiver faults of the second and the third shocks were identified (Beldjoudi et al. 2016; Yelles-Chaouche et al. 2014) and are oriented N250° and N12°, respectively. I calculated the (∆CFF) at a depth of 6 km and will assume the effective coefficient of friction μ’ = 0.4 for all modeling procedure.

Fig. 4a, b show that the seismic source of the plane oriented (Strike, Dip, Rake: 345°, 85°, 16°) load the receiver fault oriented N250° of the second shock and the calculated (∆CFF) is positively equal 0.07 bar but may not be enough to trigger the second shock (less than threshold value of 0.1 bar).

Fig. 4
figure 4

a Coulomb stress change (∆CFF) associated with the plane of the first shock (345°/85°/16°) resolved on the plane of the second shock oriented (250°/55°/120°) at a depth of 6 km. (1), (2), and (3) are the faults of the seismic sequence. b Cross-section shows the variation of the (∆CFF) with depth, c (∆CFF) associated with the first and second shocks (345°/85°/16°) and (250°/55°/120°) resolved on fault plane (12°/57°/120°) of the third shock, and d cross-section shows the variation of the (∆CFF) with depth. Fault 3 is located in an area where (∆CFF < 0). Coefficient of friction (μ’ = 0.4). For all figures, the green lines are the fault trace projected up-dip. Red lines are the edge of the fault projected vertically to surface. Black line is the intersection of the target depth with the fault plane

Full size image

Figure 4c and d show the calculated (∆CFF) with the contribution of the plane oriented (Strike, Dip, Rake: 345°, 85°, 16°) of the first shock and the plane oriented (Strike, Dip, Rake: 250°, 55°, 120°) of the second shock as sources. The receiver fault corresponds to the plane oriented (Strike, Dip, Rake: 12°, 57°, 12°) which corresponds to the third shock. The computed (∆CFF) shows that this plane is located in the area where the 9(∆CFF) is negative. This means that the third shock cannot be promoted by the previous shocks because the value of (∆CFF) is negative (− 0.49 bar).

Then, I calculate (∆CFF) considering a seismic source for the second plane of the first shock oriented (Strike, Dip, and Rake: 254°, 74°, 175°) and the receiver fault as the second shock oriented N250°. This fault is located in a positive area of ∆CFF with a value of 0.18 bar, enough to promote the second shock (Fig. 5a,b), and also I compute the (∆CFF), considering as source the plane oriented N254° and the plane oriented N250° (Fig. 5c,d). The receiver fault is the third shock oriented (Strike, Dip, Rake: 12°, 57°, 12°). The fault is located in an area with positive (∆CFF) and has a value of 0.04 bar. This is less than the threshold value (Stein et al. 1992), but if I compare it to the first case, I will assume that the plane oriented N254° is the fault plane that played during the first shock.

Fig. 5
figure 5

a (∆CFF) associated with the plane of the first shock (254°/74°/175°) resolved on the plane of the second shock oriented (250°, 55°, 120°) at a depth of 6 km. b Same as Fig. 2b. c (∆CFF) associated with the first and second shocks (254°/74°/175°) and (250°/55°/120°) resolved on fault plane (12°/57°/120°) of the third shock. d Same as Fig. 2d

Full size image

Correlating the aftershock distribution with the static stress changes

In this section, I will correlate the aftershock distribution with the Coulomb stress changes obtained from the contribution of the static stress changes and the regional tectonic stress (Stein et al. 1992; King et al. 1994, Nostro et al. 1997) in the aim to find the optimally oriented planes (see section above). In the following, I will call this contribution the total Coulomb stress changes (∆CFF).

I have considered three-time windows that represent the number of periods of the seismic sequence (Fig. 6a). The first period goes from 14 to 16 May at 06:52 UTM. The second period goes from 16 May at 06:52 UTM to 23 May at13:28 UTM and the last period is from 23 May at 13:28 UTM to 31 May at 22:46 UTM. The catalog used in this study is from Yelles-Chaouche et al. (2014).

Fig. 6
figure 6

a Plot of the number of earthquakes versus time. The red arrows indicate the occurrence of the main events. b Map showing the Coulomb changes computed from the contribution of the (∆CFF) of the fault 1, and the regional tectonic stress at 6 km of depth resolved on optimal thrust faults (NE-SW). Aftershocks located during the period 1 plotted between 5.51 km and 6.50 km (± 0.5 km) of depth. c Cross-section showing the location of the same aftershocks. Black line is the fault 3

Full size image

Coulomb stress changes and aftershock distribution for period 1 (May 14–16)

In this session, I computed total Coulomb stress changes \( {\sigma}_{ij}^t \) taking into account the contribution of the static stress changes \( {\sigma}_{ij}^c \) and the regional stress \( {\sigma}_{ij}^r \)on strike-slip optimal planes and thrust optimal planes for the period 1 from May 14 to 16 (06 h 52 min) (occurrence of the second shock). Aftershocks in this period show two main directions, an ~EW and a ~NNE-SSW; the depths of aftershocks are between 1.3 and 9.78 km.

I have computed (∆CFF) on strike-slip optimal planes and on thrust optimal planes for this period. The best correlation is obtained for thrust optimal planes. I computed the (∆CFF) between 2 and 9 km with a step of 1 km, and for each step, I plotted aftershocks located in the range of depth ± 0.5 km for optimal thrust planes oriented NE-SW. For some 117 plotted aftershocks, I obtained 21% of them located in an area with a negative Coulomb stress changes, and 79% were located in a positive area. In Fig. 6b, I presented (∆CFF) computed for thrust optimal planes for a depth of 6 km. I plotted aftershocks located between 5.51 and 6.5 km. The results showed that 28 aftershocks are in the area of positive stress and only three of them are in a negative area. Generally, the results are the same for the other depth-(∆CFF) correlation, and the number of aftershocks located in a positive area is the most important. The cross-section in Fig. 6c confirms also these results.

Coulomb stress change and aftershock distribution for period 2 (May 16 to 23)

In this section, I computed the (∆CFF) for thrust optimal planes and plotted the aftershocks that occurred during period 2 (May 16 to 23). A total of 695 aftershocks were located with a depth of 0.3 to 11.08 km. Two clusters are visible with EW and NNE-SSW trends (Fig. 1). For the total number of aftershocks for this period, I located 17% of them in the negative area and 83% in the positive area of Coulomb stress changes. In Fig. 7a and b, I presented (∆CFF) computed for thrust optimal planes at a depth of 6 km oriented NE-SW. The plotted aftershocks are located between 5.51 and 6.5 km of depth and present a good correlation with Coulomb stress changes load.

Fig. 7
figure 7

Same as Fig. 6 but for period 2

Full size image

Coulomb stress change and aftershock distribution for the period 3 (May 23 to 31)

In this part, I computed (∆CFF) caused by the contribution of the three major events of the seismic sequence and the regional stress on thrust and strike-slip optimal planes. A number of 590 aftershocks were located for this period (May 23 to 31 at 22 h 46 min); the depths are between 1.22 and 9.72 km with a duration magnitude Md of 1.3 to 4.9. Two clusters are visible with EW and NNE-SSW trends (Fig. 1). First, distribution of aftershocks was correlated with (∆CFF) computed for thrust optimal faults; the results are 60% located on the negative area, and only 40% are located on the positive area. In Fig. 8a and b, I  computed (∆CFF) at a depth of 6 km and plotted aftershocks located between 5.51 and 6.5 km for this third period. It was confirmed that the major aftershocks were located in the negative area. Also, (∆CFF) were computed for strike-slip optimal planes, and the results of the correlation are less good than obtained for optimal thrust planes.

Fig. 8
figure 8

Same as Fig. 6 but for period 3

Full size image

Conclusion

The main goal of our study is the investigation of fault interaction through elastic stress transfer among the subsequent moderate size earthquakes that occurred during the 2010 seismic sequence of the Hodna basin in the transitional zone of the sub-Bibanic and the pre-Atlasic domain (Fig. 1). I investigate the spatial distribution of aftershocks, and I try to explain it in terms of Coulomb stress changes caused by a sequence of subsequent mainshocks. As presented in the previous session, the seismic sequence was divided into three periods. The period 1 started from the first shock until the occurrence of the second shock (14-16 May). The period 2 is from the second shock until the occurrence of the third shock that concern only the interaction between the main events. To correlate the distribution of aftershocks with Coulomb stress changes, I have added a period 3 which starts from the third event and stopped on 31 May of last located aftershock in the catalog of Yelles-Chaouche et al. (2014).

The results presented in this paper shows that Coulomb stress changes correlate well with the position, geometry, and slip direction of these segments. I concluded also that Coulomb interaction exists and each mainshock promoted the rupture of the following event. I identified the fault plane that played during the first shock by comparing the amount of the (∆CFF) produced by each plane of the focal mechanism of the first event. I have shown also that the fault plane oriented N254°/75°/175° is the one that ruptured during the first event. This plane (254°/75°/175°) promoted the rupture of the plane (250°/55°/120°) of the second shock. The contribution of these two first events promoted the occurrence of the third event (12°/57°/12°).

On the other hand, I have tried to explain the distribution of the aftershocks with the variation of the Coulomb stress. In this work, I have shown that the aftershocks correlated well with the (∆CFF) when this is calculated on optimal thrust faults. In period 1, 79% of aftershocks (total of 117) were located in the area of positive (∆CFF), while 21% of them were in the negative area. In period 2, 83% of aftershocks (total of 695) are in the positive area, while 17% are located in the negative area. In period 3, out of 590 aftershocks, only 40% are located in the positive area and 60% in the negative area which is contrary to our observation in the two previous periods. I computed then (∆CFF) on strike-slip optimal faults; the results obtained were less good than those obtained for thrust optimal planes; I found only 20% of aftershocks located in the positive area, and the rest are located in the negative area. This study shows that despite the fact that the faults appear unconnected, the change in the stress state around the faulted fold during the seismic sequence made them connected in terms of Coulomb stress changes, and each one played under the effect of the preceded shock. This study also reinforced the number of studies conducted in the region based on its seismic source, seismotectonic, and fault interaction.