1 Introduction

Algeria and neighboring regions are within the boundaries of tectonic plates. Nevertheless, seismic activity demonstrates the existence of recent geodynamic phenomena. The largest recorded earthquake in Algeria, was the Mw7.1 1980 El Asnam Earthquake which occurred near the town of Chelf in Central Northern Algeria. The Northeastern region of Algeria is a zone with moderate seismicity. Destructive earthquakes are rare, but their probability of occurrence is not nil. The strongest earthquake of the last century was the Ms 6.0 1985 Constantine Earthquake; the historical archives also record several destructive earthquakes during the last two centuries. The estimation of the seismic hazard in Algeria is therefore essential. To estimate the seismic hazard at a site is to determine the ground motion to guard structures from. The seismic hazard estimation is also a first step towards the seismic risk estimation which also integrates the vulnerability of the buildings. The probabilistic seismic hazard assessment method was first developed at the end of the 60s in the United States. Cornell (1968) proposed to calculate annual rates of exceedance of ground motion levels and to introduce these rates into a temporal process of Poisson occurrence. Probabilistic seismic hazard studies provide the level of ground motion with a probability of being exceeded over a period of time at any given site. The calculation requires the identification of the seismic source zones located within the studied region, a description of the source zones seismicity and an attenuation ground motions model. In 1976, the U.S. Geological Survey (USGS) published the first probabilistic seismic hazard maps for the United States (Algermissen and Perkins, 1976). The same year, McGuire (1976) introduced the dispersion of seismic motion into the calculus. Shortly thereafter, seismic hazard estimates for nuclear facilities also shifted to probabilistic methods (Bernreuter et al. 1989). The modifications of the method then concern essentially the modeling of the source zones and the recurrence of the earthquakes (e.g. Frankel 1995). The heart of the method to calculate a probability of exceeding a ground motion from an attenuation model remained unchanged, but the advances lie in the consideration of uncertainties. The oldest known seismic hazard map for Algeria is the macroseismic intensity map developed by Perrey (1848). In 1973, Roussel proposed a map of observed maximum intensities in which five intensity zones were defined, i.e., VI, VII, VIII, IX and X. As part of the development of the first Algerian seismic regulation, the first probabilistic seismic hazard study was conducted in 1978 (Mortgat and Shah 1978) using an earthquake catalog covering the period from 1790 to 1975. Bezzeghoud et al. (1996) updated all these maps from a catalog of Algerian seismicity compiled for the period from 1365 to 1992. In this map, seven zones were defined with the following intensity ranges: ≤ V, VI, VII, VIII, IX, X and X–XI. Several other studies have assessed seismic hazard in Algeria using deterministic and probabilistic methods. Recently a study by Hamidatou and Sbartai (2016, 2017) was proposed.

Assessment of PGA is established using many sets of ground motion prediction equations for various tectonic provinces in the study area. In the context of recent developments in seismic hazard analysis and its application to earthquake engineering, it is clear that one cannot rely completely on either probabilistic or deterministic hazard evaluation methods, as both are equally important (Bommer 2003; Bommer et al. 2005). The deterministic seismic hazard analysis (DSHA) adopts a transparent process, whereas probabilistic seismic hazard analysis (PSHA) deals with various uncertainties. PSHA gives a richer description of the expected ground motions since it provides the probability of exceeding a specific ground motion level, whereas the ground motion given by DSHA is associated with an unknown probability of exceedance. PGA estimated from a probabilistic method incorporates various uncertainties, whereas the deterministic approach generates a specific value of a ground motion parameter for a specific scenario (Sitharam et al. 2015). This study provides a probabilistic assessment of surface level ground motion using topographic gradient for site condition. Seismic hazard is based on source area and seismotectonic data. The results suggest that previous studies have underestimated the seismic hazard in the Northeast of Algeria. In the present study, an attempt was made to develop the VS30 map for the study area using a topographic slope map derived from Digital Elevation Model (DEM) data. Using appropriate site amplification factors, ground motion parameter at the surface can be estimated from that estimated at the bedrock level. Various hazard assessment studies (probabilistic methodologies as well as deterministic) have been carried out for Algeria in the past to estimate the ground motion parameter at the bedrock level. This paper presents estimation of the hazard at surface level, using appropriate site amplification factors corresponding to various site classes based on VS30 values derived from the topographic gradient (Sitharam et al. 2015). The probabilistic approach suggests that significant ground movement will occur due to seismic hazards (Cornell 1968). (McGuire 1978) presented five hazard analysis steps: (1) identification of potential earthquake sources; (2) assessment of geological, geophysical and geometric source parameters; (3) identification of the seismic motion attenuation patterns; (4) site-specific hazard calculations and (5) regional hazard mapping. This study uses the earthquake hazard evaluation procedure developed by (Kijko and Sellevoll 1992) to estimate seismic hazard parameters in Northern Algeria.

2 Tectonic-Geologic Setting and Destructive Earthquake

The tectonic regime in this part of the Alpine chain is mostly compressional since the early Cenozoic, with a late Quaternary N–S to NW–SE main shortening direction. Neogene and Quaternary post-nappes basins exhibit E–W to NE–SW striking folds and related reverse faults. The rate of motion determined from paleo-seismological data (Meghraoui 1988) and from analysis of source mechanisms is about 4–6 mm/year (DeMets et al. 1990). Since the early Cenozoic, this structural domain is under a compression regime (Fig. 1). The direction of compression is NNW–SSE. The main faults, with NE–SW strike, correspond to thrust faults dipping NW often organized in echelon systems, such as the El Asnam and Tipaza faults (Aoudia et al. 2000).

Fig. 1
figure 1

The major kinematics and tectonics features of the Nubia-Eurasia plate boundary. Deformation rates are in mm/year (Serpelloni et al. 2007)

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Northern Algeria occupies the Southern side of the Mediterranean Sea. It is known as the most active seismogenic zone in the western Mediterranean basin (Fig. 2). This activity is a result of the collision between the African and the Eurasian continental plates. As expected in a continental collision, the seismicity is distributed over a wide deformation area. From north to south, Northern Algeria is divided into four main structural domains whose formation is directly related to the multiple openings and closings of the Mediterranean Sea, during the Mesozoic and Cenozoic. The geological features, related to inter-plate processes are: The Tell Atlas, The High Plateaus, The Saharian Atlas and the Sahara Platform (Fig. 2). The Tell is the eastern part of the Rif-Tell system, an active collision area between Eurasia and Africa associated with the current convergence of African-Eurasian plates and resulting in the progressive closure of the Neogene basins and by the continuation of the construction of the Tellian Chain (Meghraoui 1988; Boudiaf 1996; Yelles-Chaouche et al. 2006). Northern Algeria has experienced many destructive earthquakes throughout its history. The largest recent events occurred in El Asnam on October 10, 1980 (Mw = 7.1), in Constantine on October 27, 1985 (Ms = 6.0), in Chenoua-Tipaza on October 29, 1989 (Ms = 5.9, USGS), and in Zemmouri–Boumerdes on May 21, 2003 (Mw = 6.8) (Fig. 3).

Fig. 2
figure 2

Superficial and medium seismicity (h < 150 km, M > 4; source NEIC) from Central Atlantic to eastern Mediterranean 1973–2008 (Belabbes 2008)

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Fig. 3
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Distribution of seismic events

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3 Earthquake Catalog

Recently Hamidatou and Sbartai (2017) prepared a comprehensive earthquake catalog for the Northeast of Algeria and adjoining areas by compiling the data from various national and international agencies. They developed correlations connecting various magnitude scales and homogenized the catalog in a unified surface magnitude scale. This declustered earthquake catalog is used to characterize seismic sources in the present study. The distribution of earthquake events in Algeria and adjoining area is given in Fig. 4. This catalog covers part of Eastern Algeria [4°E–9°E, 33°N–38°N] for the period 1365–2018.

Fig. 4
figure 4

Linear seismic sources identified in study area

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4 Linear Sources

The Structural map at 1: 5,000,000 (Vila 1977), for the Alpine chain of Eastern Algeria and the Algerian-Tunisian borders, published by the Research Center in Astronomy Astrophysics and Geophysics (CRAAG). The details of the faults, lineaments, shear zones and the geological features in Northeast Algeria and adjoining areas are presented in Meghraoui (1988). In the present study, all the sheets of Vila (1980) and Coiffait (1992) were scanned and georeferenced and the individual images were merged together to form the complete map in the study area. Georeferencing and digitization of seismotectonic maps were done using ArcGIS 10 and MapInfo Professional version 10.5. The declustered earthquake data was superimposed on the fault map and the maximum reported magnitude along each of these sources was noted. The linear sources thus selected are shown in Fig. 4.

5 Areal Sources

The seismic source areas were determined based on previous studies (Hamdache et al. 1998; Harbi et al. 1999; Aoudia et al. 2000; Yelles-Chaouche et al. 2006; Hamidatou and Sbartai 2017). The first author Hamdache et al. (1998) defined four source zones in Northern Algeria based on the observed fault mechanisms. The second one Harbi et al. (1999), correlate seismic data with the neotectonic faults in the Eastern Tellian Atlas and surrounding areas (35°N–38°N, 4°E–9.5°E) based on geological information (Vila 1980; Meghraoui 1988; Bounif et al. 1987) (Fig. 5), geophysical data (Harbi 1996) and previous studies (Hatzfeld 1978; Deschamps et al. 1991; Benouar 1993; Mokrane et al. 1994; and Bezzeghoud et al. 1996). Additional data files were also used during the analysis, including the CRAAG, the Instituto Geográfico Nacional (IGN), the International Seismological Centre (ISC) and the USGS/NEIC datasets. The third one (Aoudia et al. 2000) defined twelve source zones in the Tell Atlas based on: (1) the distribution of well identified Quaternary and active faults in Neogene basins, (2) thrust-related crustal tectonics and kinematic mechanisms at local and regional scales, (3) relationships between geological structures and earthquakes and (4) earthquake epicenter clustering patterns. In the study by Yelles-Chaouche et al. (2006), the authors used data compiled by the Algerian seismic monitoring network, as well as by the different recent field studies conducted in the aftermath of the large earthquakes that affected the country. This seismicity is expressed in various areas with seismotectonic characteristics and seismic activity. The last research (Hamidatou and Sbartai 2017) defined five source zones in the Constantine region based on seismicity, geology and tectonic. In this study, ten seismic zones are presented with their parameters and characteristics in Tables 1 and 2. Figure 6 shows regional seismic source zones in and around Northeast Algeria, based on the data and information provided in previous studies. All seismic sources are considered as area sources.

Fig. 5
figure 5

Sismotectonic map of the Eastern Tellian Atlas of Algeria (Meghraoui 1988; CRAAG, Domzig 2006)

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Table 1 Important seismogenic source zone characteristics
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Table 2 The parameters for each seismic zone
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Fig. 6
figure 6

The boundaries of the study area and the source zones and the active faults within the study area

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5.1 The Offshore EAS Zone (Z1)

The offshore EAS Zone (El-Taref, Annaba, and Skikda) is one of the coastal areas of Northern Algeria. This zone, unlike the other coastal zones of Northern Algeria, seems for the moment aseismic except at its western end where the recent seismicity of Annaba has been recorded. Except for this seismic activity, it can only be mentioned that the occurrence of the December 2nd, 1961, magnitude 5.5 and intensity VI earthquake occurred in the Gulf of Annaba. Therefore, the maximum magnitude of this zone is assumed to be 5.5. The Annaba offshore fault system determined from bathymetric and high-resolution seismic data demonstrates the compressive reactivation of the margin foot in this area (Yelles-Chaouche et al. 2006) and the existence of active structures reactivating this area. However, there is currently no seismicity associated with these accidents. In fact, very weak seismic events have been recorded in this area. This could be explained by the absence of a seismological station in the region for the historical period.

5.2 The Offshore JBT Zone (Z2)

The offshore JBT Zone (Jijel, Béjaia and Tizi Ouzou) experienced the most important historical earthquake of the region, the August 22, 1856 event which occurred off the city of Jijel. It is the strongest earthquake felt in the coastal zone of this region. It is also the most documented earthquake in the region for the pre-1900 period.

5.3 The Guelma Zone (Z3)

The Guelma Neogene basin presents a different structure. It is situated between the East–West dextral strike slip faults (Meghraoui 1988). At the ends of the pull-apart basin there is a series of N–S to NNW–SSE bounding normal fault systems that intersect the sub parallel shear faults (Aoudia et al. 2000). The seismicity map (Fig. 3) shows clusters of earthquakes in the basin. The strongest earthquake in the region is that of February 10, 1937 of maximum MSK intensity VIII and magnitude Ms5.2. (Harbi 2001). Two destructive earthquakes of MSK intensity VIII struck the same region on June 17, 1908 and December 3, 1928 (Aoudia et al. 2000). The last significant event occurred on September 20, 2003 and was of magnitude 4.8 (Yelles-Chaouche et al. 2006). The activity in this basin is located at the level of the main incident, but also at the level of the basin’s faults, which are the Bouchegouf and Hamam Nbailis Faults (Yelles-Chaouche et al. 2006). These faults affect quaternary deposits and are connected to hydrothermal vents from where they were active during this period (Vila 1980; Harbi et al. 1999).

5.4 The Constantine Zone (Z4)

In comparison with the various intermountain basins of the Tell, the Constantine basin seems perched at high altitudes. Its geomorphology shows very squeezed and deep valleys with steep slopes (Aoudia et al. 2000). The plio-quaternary deposits (conglomerates and calcarenites) are descaling on a substratum consisting of flyshs. These deposits are aligned in a NE–SW direction reminiscent of the direction of the Ain Smara Fault active during the Constantine earthquake of October 27, 1985 (Bounif et al. 1987). On the other hand, the existence of neotectonic faults affecting the plio-quaternary (Ain Smara, Sigus and Constantine respectively oriented NE–SW, EW and NS, Vila 1980) particularly related to hydrothermal vents suggests the presence of a tectonic activity. During the period before 1900, no strong earthquake in the Constantine region is known. However, it is not the case of the instrumental period where at least three earthquakes of maximum MSK intensity VIII affected the region. The first one is the Ms5.4 event of August 4, 1908, the second one is the Ms5.0 event of August 6, 1947, and finally the third one of rather recent memory is the Ms5.7 event of October 27, 1985 (Harbi 2001) or Ms6.0 (Yelles-Chaouche et al. 2006; Bounif et al. 1987). The strike-slip focal mechanism solution of the last one is in good agreement with the nature of surface ruptures and reflects well the squeezed morphology in this uplifted zone, where much of the actual deformation is more likely to be accommodated by transcurrent motions than by compressional ones. From the spatial extent of the 1985 aftershock sequence, a 30 km maximal fault length is inferred. Using Wells and Coppersmith (1994) empirical relationships for a strike slip fault, it is estimated that the Constantine fault can generate an earthquake of magnitude 6.5.

5.5 The Hodna Zone (Z5)

The Neogene Hodna Basin, which belongs to the Tellian Atlas, is located south of the Setif region. The topography of the basin is deformed or broken into a series of ridges and valleys by folds and reverse faults of E–W to NE–SW direction (Aoudia et al. 2000). The compressive structures are observed in the Hodna Basin, a series of five anticlines that affect plio-quaternary deposits northeast of Chott El Hodna (Meghraoui 1988). Historically, the region has been hit by two major earthquakes, the M’Sila earthquakes of February 12, 1946, and that of January 1, 1965 (Ms5.5) (Benouar 1993). This seismicity would be generated by E–W to NE–SW anticlines in the region (Yelles-Chaouche et al. 2006). Among these, the Chott El Hammam fault-fold formed by the Boutaleb fold which shows, on its south-east slope, a south vergence inverse fault with overlap of the ante-neogenous substratum (Meghraoui 1988). This fault, about 30 km long, is capable of generating an earthquake of about Mw = 7.0 (Aoudia et al. 2000). Moreover, the presence of pleated Pleistocene deposits on the Chott El Hammam fold is significant of its recent activity.

5.6 The Tizi Ouzou Zone (Z6)

The mountainous area of Babors is located to the east of the Soummam Valley, and is an extension of the Djurdjura Mesozoic chain (Aoudia et al. 2000). Plio-Quaternary formations, which are more developed in the south (Hodna Basin), are non-existent in this region of aquifers (Meghraoui 1988). The limestone massif of Kherrata within the Babors zone known to be the seat of a quasi-permanent seismicity (Harbi 2001). The seismic history of the region shows that the seismic activity is relatively moderate and constant (Aoudia et al. 2000). Nevertheless, on February 17, 1949 an earthquake of maximum MSK intensity VII and magnitude Ms4.7 occurred (Harbi 2001). Rothé (1950) observed surface ruptures and mapped the fault relating to an anticline trending N 070 E. This faulted fold seems to be responsible of the constant activity in the Babors zone (Meghraoui 1988; Harbi et al. 1999; Aoudia et al. 2000; Yelles-Chaouche et al. 2006).

5.7 The Bibans Zone (Z7)

In this region of the Bibans, three main zones of seismicity can be considered. The first one derives from the seismicity of the region of Sour El Ghozlane which is characterized by important topographic features in the North, such as the Jebel Dirah. This region is the site of the fourth largest earthquake in Algeria after Orleansville (1954), El Asnam (1980) and Boumerdès (2003), namely, the Aumale (formerly Sour El Ghozlane) Earthquake of June 24, 1910 with Ms6.6 and Imax = VIII on the MSK scale (Benouar 1994). This important earthquake was felt and recorded up to the eastern limits of the Bibans Mountain chain. In addition to this strong earthquake, the region was struck by the occurrence of four major earthquakes, that of September 22, 1886 (M = 5.2 and I0 = VII) which occurred at the northern limit between the Bibans and the Soummam Valley, that of August 15, 1931 (M = 5.2 and I0 = VIII) located probably on Djebel Dirah, that of December 25, 1954 (M = 5.2 and I0 = VII) and finally that of October 30, 1975 (M = 5.4 and I0 = VI). The second zone considered, would be the Beni-Ilmane region. It is a complex area that characterizes the transition between the NO-SE oriented Hodna Mountains and the E–O oriented Bibans chain. The seismicity distribution is oriented N–S south of the Béni-Ilmane village and follows the Azrou–Choukchot–Nador deformation corridor (NE–SO) of the northern part of Beni-Ilmane. The bulk of this seismic cloud is made up of the aftershocks of the seismic sequence that hit the region in 2010 (Abacha 2015). It is important to note that this sequence is the second significant event in the last 50 years after the magnitude 5.5 and maximum intensity VIII earthquake of February 21, 1960, which was mainly studied by macroseismic observations (Benouar 1994). The third considered zone is the Mansourah region (Djebel Mansourah peaks at a 920 m altitude) which is marked by the occurrence of three major earthquakes; the first, is the historical earthquake of January 8, 1887 with an Ms5.2 and a maximum MSK intensity VIII, located in Mansourah (Harbi 2001), the second is that of April 16, 1943 (M = 5.3 and I0 = VIII) which caused the loss of at least nine lives and wounded eleven others (Benouar 1994), the third event struck the region on November 24, 1973 (M = 5.2 and I0 = VII), (I0: Maximum Observed Intensity). The occurrence of February 9, 1850 earthquake, which affected the region of Zamora-Genzet (border between the wilaya of Setif and Bordj Bou Arreridj), should also be noted. Its maximum intensity was VII at Guenzet and its Ms was 4.6 (Harbi 2001).

5.8 The Saharan Atlas Zone (Z8)

The border between the Southern Algerian Atlas and the Sahara is a structural line made up of different sections that have neither the same meaning, nor the same orientation, nor the same age. In the Northeast of Algeria, this accident borders on the south the Aures and the Mountains SE of Constantine. The latter domain structured in folds and overlaps during the Mesozoic and Cenozoic times and even up to the Pleistocene. The current tectonic activity is hardly noticeable. Nevertheless, a number of studies confirm the existence of recent tectonics in this part of the Atlas. Indeed, in the Eastern zone of the Northern Saharan Atlas, using aeromagnetic studies, a large NESW fault was identified, extending from the anticline of Khenchela to the north of the Ouenza, passing south of Mesloula and that would have played from the Turonian until the Quaternary (Vila 1980). This area with more or less weak seismicity encompasses the region of Souk Ahras, Oum El Bouaghi and the Oasis of Biskra. There is also a small area at the edge of the two Atlas ranges, in the Tebessa-Ouenza axis. In this area, a relatively important event occurred in 1869 destroying the small Saharan city of Biskra (Roussel 1973b; Harbi et al. 2010).

5.9 The Batna Zone (Z9)

This zone is generally made up of neogenic lands of the Ain Regada platform and the Belezma Mountains. This area is located at the intersection of two large tectonic lineaments (Guemache 2010). The first is the Tenès-Negrine lineament, corresponding to a large dextral shear zone oriented N110°E to N120°E, which extends over nearly 700 km, from the coast of Ténès in the Northwest to the sector. A little south of Negrine to the Southeast, to the Gulf of Gabes. Further South-East, the N120°E dextral strike of Gafsa seems to join this line around Batna. The second, is the Sidi Ferdjani-El Kantra lineament (Guemache 2010) corresponding to a sinistral strike oriented N055°E, which extends for about 400 km, from the coast near the Tunisian village of Sidi Ferdjani in the Northeast to the El Kantara sector in the South West. This zone is characterized by a weak seismicity located between the Hodna Mountains and the Aures massif. Three important earthquakes on the Tellian deformation front, namely, the earthquake of the year 267 of Tazoult-Lambese which is the reference earthquake of this zone, the Ngaous Earthquake of January 17, 1885 (50 km from Batna) with maximum MSK intensity VIII and the MacMahon (Ain Touta) Earthquake of March 16, 1924 with maximum MSK intensity VIII and Ms5.3.

5.10 The Mansourah Zone (Z10)

This region is marked in its eastern part by mountains oriented N110°, with altitude of 1863 m for Jebel Mâadid, forming the Hodna Mountains. To the south of these mountains is the Neogene Hodna basin which shows similarities with the active Neogene basins of the Tellian Atlas (Cheliff, Metidja). In this region, there is a series of anticlines affecting recent deposits oriented in a NE–SW direction reminiscent of the other active structures of the Tell. The tectonic aspect studied by Vila (1980) and Meghraoui (1988) shows fold-fault geometries. As an example of these structures, the reverse fault of Chott El Hammam which limits the SE flank of the Boutaleb anticline and which is south vergence. This fault would have generated the largest earthquake in the Hodna Basin, which resulted in the loss of five lives and injury of about 25 others from the January 1, 1965 earthquake with magnitude 5.4 and maximum intensity VII (Benouar 1994). The presence of folded Pleistocene deposits on this fold of Chott El Hammam is significant of its recent activity (Harbi 2001). According to Meghraoui (1988), this fault about 60 km long is capable of generating an Mw7.0 earthquake. On the Hodna Hills, three major earthquakes occurred. The first one was located at the western end of the Boutaleb anticlinal under the Jebel Maadid on December 3, 1885 with magnitude 5.9 and Imax = IX. This earthquake killed 33 people, wounded 17 others and destroyed 3/4 of the village of M’sila (Harbi 2001). The other two earthquakes occurred in the Berhoum region in the same corridor as the 1965 M’sila Earthquake. These two events were the February 12, 1946 earthquake with magnitude 5.5 (Imax = VIII) which caused the loss of at least 277 people and injured about 118 others (Benouar 1994), and the November 24, 1973 earthquake with magnitude 5.3 and Imax = IX.

6 Ground Motion Models

Among the critical elements required in seismic hazard analysis, the PGA and peak spectral acceleration (PSA) attenuation relationships are very important. PGA ground motion attenuation relationships describe the variation of PGA as a function of earthquake magnitude and source to site distance. PSA attenuation relationships are typically developed at 0.3 s, 1.0 s and 3.0 s. Strong ground motions produced by earthquakes are influenced by the characteristics of the earthquake source, the crustal wave propagation path, and the local site geology. Accordingly, attenuation relationships typically are developed for specific tectonic environments. In this study, empirical attenuation relationships developed on the basis of statistical analysis of strong motion data recorded at locations having a similar tectonic environment were used. They are given by the following formulas (Sadigh et al. 1993):

$$ \begin{aligned} for\, M \le 6.5:ln\left( {a_{h} } \right) = - 0.624 + 1.0M - 2.10\left[ {ln\left( {R + exp\left( {1.29649 + 0.25M} \right)} \right)} \right] \hfill \\ \sigma = 1.39 - 0.14M \hfill \\ \end{aligned} $$
(1)
$$ \begin{aligned} for\, M > 6.5:ln\left( {a_{h} } \right) = - 1.274 + 1.1M - 2.10\left[ {ln\left( {R + exp\left( { - 0.48451 + 0.524M} \right)} \right)} \right] \hfill \\ \sigma = 0.38 \hfill \\ \end{aligned} $$
(2)

where R is the closest distance to the rupture area, M is moment magnitude, ah is maximum peak ground acceleration in ground surface, and σ is the standard error in ln(ah). In our study area the attenuation model chosen is that of Ambraseys et al. (2005):

$$ \begin{aligned} \log \left( {a_{h} } \right) = - 0.338 + 0.238 M_{s} - \log \left( r \right) - 0.00050 r + 0.28 P \hfill \\ h = 6.0 km , \sigma = 0.28 \hfill \\ \end{aligned} $$
(3)

where r is the closest distance to the surface projection of the rupture surface, Ms is the surface magnitude and h is the depth, P ranges from 0 (for 50% percentile) to 1 (for 84% percentile).

In the second part of our study area the attenuation model chosen is that of Ambraseys et al. (2005) which was developed from superficial zone data from Europe and the Middle East.

$$ \log y = a_{1} + a_{2} M_{w} + \left( {a_{3} + a_{4} + M_{w} } \right)log\sqrt {d^{2} + a_{5}^{2} } + a_{6} S_{s} + a_{7} S_{A} + a_{8} F_{N} + a_{9} F_{T} + a_{10} F_{O} $$
(4)

where: SS = 1 for soft soil sites and 0 otherwise, SA = 1 for stiff soil sites and 0 otherwise, FN = 1 for normal faulting earthquakes and 0 otherwise, FT = 1 for thrust faulting earthquakes and 0 otherwise and F0 = 1 for odd faulting earthquakes and 0 otherwise. a1 to a10: coefficients derived for evaluation of the horizontal peak ground acceleration and the spectral response acceleration for 5% damping. d: epicentral distance, y is the maximum surface peak ground acceleration.

7 Logic Tree Structure

Uncertainties used for seismic hazard assessment make the selection of a seismic hazard model difficult. The use of the logic tree approach allows characterization of epistemic uncertainties in various models by including alternative models in the analysis (Bommer 2003). A logic tree consists of a series of nodes and branches where the branches denote different models (hypotheses). A subjective weight, based on engineering judgment, can be given to each of these branches depending on the likelihood of being correct (Sitharam et al. 2015). The sum of the weights for all branches at a particular node should be equal to unity. The weight of the terminal branch of the logic tree can be obtained by multiplying the weightage of all the branches leading to it. The present study considers three types of source models and three different ground motion prediction equations each for various tectonic provinces in the study area. The source models employed are areal sources. Three different maximum magnitudes have been considered for areal sources; the maximum regional earthquake magnitude or maximum expected magnitude, Mmax (Kijko and Singh 2011). For the seismic sources occurring in subduction regions with high seismicity, Hellenic and Cyprian arcs, the statistical approach of (Kijko 2004) (hereinafter will be referred as statistical approach) is used to determine Mmax. For the other sources that relate to shallow-active-crust tectonic environments with low to moderate seismicity, we adopted the statistical approach in addition to an alternative approach by adding 0.5 magnitude unit to the maximum observed magnitude (\( M_{max}^{obs} ) \). It is noticed that, for some sources the calculated Mmax by the statistical approach are equal to \( M_{max}^{obs} + 0.5 \).

While estimating the seismic hazard using PSHA method, the hypocentral and magnitude uncertainties were considered. This was done by disaggregating the hypocentral distance into small intervals of 3 km and the magnitude range (between minimum and maximum magnitude) into small incremental values of 0.3 (lower values of the hypocentral incremental distance and magnitude interval did not improve the accuracy of the results significantly, but increased the computation time). For each grid point, all the area sources within a radius of 200 km were considered for evaluation of PGA values. The PGA value at each grid point was calculated using different methods (various combinations of ground motion prediction equations; source models and different approaches of Mmax estimation) and later combined to get the final value using the logic tree framework as shown in Fig. 7. The estimation of uncertainty involved in magnitude, distance and peak ground acceleration is discussed below.

Fig. 7
figure 7

Parameters and weighting factors adopted in the logic tree

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8 Estimation of Hazard

The approach used hereafter, was initially developed by Cornell (1968) and implemented in its computer form by McGuire (1976) and Algermissen and Perkins (1976). Mc-Guire developed EqRisk in 1976 and FRISK in 1978. Algermissen and Perkins (1976) developed RISK4a, presently called SeisRisk III. There are a number of commercially used PSHA models in the market such the one by Geomatrix (1993), and others with risk and financial add on modules such as those by global Catastrophe Modeling (Cat Models) companies Air Worldwide, CoreLogic, Risk Management Solutions (RMS) and others serving the insurance, the reinsurance and the capital market. It is assumed that the occurrence of earthquakes in a seismic source follows a Poisson process. Then, the probability that at a given site a ground motion parameter, Z, will exceed a specified level, z, during a specified time, T, is represented by the expression:

$$ P = \left( {Z > z} \right) = 1 - e^{ - \nu \left( z \right)T} \le \nu \left( z \right)T $$
(5)

where ν (z) is the average frequency during time period T at which the level of ground motion parameter, Z, exceed level z at a given site. The function ν (z) incorporates the uncertainty in time, size and location of future earthquakes and uncertainty in the level of ground motion they produce at the site. It is given by:

$$ \nu \left( z \right) = \mathop \sum \limits_{n = 1}^{N} N_{n} \left( {m_{0} } \right)\mathop \int \limits_{{m = m^{0} }}^{{m^{n} }} f_{n} \left( m \right)\left[ {\mathop \int \limits_{r = 0}^{\infty } f_{n} \left( {\frac{r}{m}} \right)P(Z > z/m,r)dr} \right]dm $$
(6)

where Nn (m0) is the frequency of earthquakes on seismic source n above a minimum magnitude m0 that is taken equal to 5.0 in this work. Indeed, below this value, magnitudes are considered to be without engineering significance; fn (m) is the probability density function for event size between m0 and a maximum event for the source, mu; fn (r| m) is the conditional probability density function for distance to earthquake rupture; P (Z > z| m, r) is the probability that, given a magnitude m earthquake at a distance r from the site, the ground motion exceeds level z. In practice, the integrals in Eq. (2) are replaced by summations and the density functions f (m) and f (r|m) are replaced by discrete mass functions. The resulting expression for ν (z) is given by:

$$ \nu \left( z \right) = \mathop \sum \limits_{n = 1}^{N} \cdot \mathop \sum \limits_{{m_{i} = m^{0} }}^{{m_{i} = m^{u} }} \lambda_{n} \left( {m_{i} } \right)\left[ {\mathop \sum \limits_{{r_{j} = r_{min} }}^{{r_{j} = r_{max} }} P_{n} \left( {R = r_{j} /m_{i} } \right)P(Z > z/m_{i} ,r_{j} )} \right] $$
(7)

where λn (mi) is the frequency of events of magnitude mi occurring on source n obtained by discretizing the earthquake recurrence relationship for source n. The estimation of uncertainty involved in magnitude, distance and peak ground acceleration are discussed in respective sections.

9 Site Characterization

Characteristics of local soil conditions can amplify the earthquake ground shaking to a large extent, thus aggravating damage potential of earthquakes. Hence, to evaluate the ground response and site effects, accurate knowledge about the geological, geomorphological and seismotectonic settings are necessary (Sitharam et al. 2015). Thus, the site characterization has its significance in seismic microzonation studies. The thickness of the overburden soil, its density, soil type, geometry of the subsoil structure, and the surface topography influence the amplification of earthquake ground motion. Site characterization is generally carried out either based on local geology site or on geotechnical dynamic soil properties (Fig. 8). Site characterization based on local geology can be effective for characterizing larger area such as a province or a country (Sitharam et al. 2015). Borcherdt and Gibbs (1976), Shima (1978), Evernden and Thomson (1985) and Midorikawa (1987) have proposed site characterization based on local geology and evaluated hazard intensity and amplification factors for each geological category. However, this mode of site characterization is considered as primitive and not appropriated in modern seismic microzonation practices. Hence, the shear wave velocity (Vs), which is a dynamic geotechnical property, has been accepted for seismic site characterization. Most of the codes such as the Eurocode-8 (EC8 2003), the Algerian Building Code (RPA 2003), the International Building Code (IBC 2009) etc. specify the site classification based on the average shear wave velocity values in the top 30 m soil column (VS30) as per Eq. (8) and Table 3, where 30 m is the depth corresponding to one quarter wave length of the period of interest.

$$ V_{S30} = \frac{30}{{\mathop \sum \nolimits_{i = 1}^{n} \frac{di}{Vi}}} $$
(8)

where di is the depth of each soil layer, vi is the corresponding shear wave velocity for each layer and n is the number of soil layers.

Fig. 8
figure 8

Digital elevation model (SRTM DEM) for entire Northeast of Algeria (resampled to 0.1 × 0.1 grid size)

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Table 3 Site classification as per EC8, UBC97 and Algerian Building Code (RPA 2003)
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For small sites, the average shear wave velocity for the top 30 m can be evaluated using geotechnical and geophysical field tests. Geophysical tests include seismic cross-hole, suspensions logging test, seismic uphole and downhole, Spectral Analysis of Surface Wave and Multichannel Analysis of Surface Waves while geotechnical tests include standard penetration test (SPT) in boreholes and cone penetration test (CPT) (Sitharam et al. 2015). However, for characterizing large areas, estimation VS30 based on these tests is not economically and physically viable. Hence, in the present study, site characterization for Northeast Algeria has been carried out using topographic slope map which were generated from DEM data.

9.1 Generation of Slope Map

Slope map for the study area was developed from DEM using ArcGIS 10 software. The downloaded DEM were found to be in the World Geodetic System (WGS-1984). Before proceeding to any raster analysis, the DEM was projected to the UTM system which is recommended for any terrain analysis and resampled to a 200 m × 200 m grid size (Fig. 9). Using the spatial analyst tool provided by ArcGIS, the slope at each grid point was evaluated. The slope map for the study area is presented in Fig. 9. The slope map thus obtained was converted to vector data (points) and then exported into a table form. The geographic and slope values were computed for each grid point.

Fig. 9
figure 9

Slope map of study area (gradient values)

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10 Determination of the Seismicity Parameters

10.1 Determination of λ and b Values

The relative number of generated earthquakes that occur on the seismic source is described by a magnitude distribution. In the current work, magnitude distribution is carried out in the form of the doubly-truncated exponential model. It is based on the well-known Gutenberg-Richter (GR) magnitude recurrence relation. The GR relation (Gutenberg and Richter 1954) is given by:

$$ {\text{log }}\lambda_{\text{M}} = {\text{a}} - {\text{b}} \cdot {\text{M}} $$
(9)

where \( \lambda_{\text{M}} \) is the mean annual rate of exceedance of magnitude M where a and b are constants. If earthquakes smaller than the lower magnitude threshold Mmin are eliminated and the relationship is truncated at Mmin and Mmax (Table 4), the mean annual rate of exceedance is expressed as (McGuire and Arabasz 1990):

$$ \lambda {\text{M}} = \upsilon \frac{{exp\left[ { - \beta \left( {M - M_{min} } \right)} \right] - exp[ - \beta \left( {M_{max} - M_{min} } \right)}}{{1 - exp\left[ { - \beta \left( {M_{max} - M_{min} } \right)} \right]}} $$
(10)

where \( \upsilon = \exp \left( {\alpha - \beta {\text{M}}} \right) \), \( \alpha = \ln \) a and \( \beta = ln b \)

Table 4 The seismicity parameters for each seismic zone
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10.2 Maximum Earthquake Magnitude Mmax Estimation

The maximum regional earthquake magnitude or maximum expected magnitude, Mmax, is defined as the upper limit of earthquake magnitude for a given region and is synonymous with the magnitude of the largest possible earthquake (Kijko and Singh, 2011). Due to the variation in seismicity levels for the defined seismic sources, we adopted more than one approach to define Mmax as follows:

  • For the seismic sources occurring in subduction regions with high seismicity, Hellenic and Cyprian arcs, the statistical approach is used to determine Mmax.

  • The other sources that relate to shallow-active-crust tectonic environments with low to moderate seismicity, we adopted the statistical approach in addition to an alternative approach by adding 0.5 magnitude unit to the maximum observed magnitude (\( M_{max}^{obs} ) \). It is noticed that, for some sources the calculated Mmax by the statistical approach are equal to \( M_{max}^{obs} + 0.5 \).

The maximum expected magnitude in the approach of (Kijko 2004) is equal to the maximum observed magnitude \( M_{max}^{obs} \), plus an integral term Δ \( = \mathop \int \nolimits_{{{\text{M}}_{ \hbox{min} } }}^{{{\text{M}}_{ \hbox{max} } }} [{\text{F}}_{\text{M}} \left( {\text{m}} \right)]^{\text{n}} {\text{dm}} \). Where \( \left[ {{\text{F}}_{\text{M}} \left( {\text{m}} \right)} \right] \) is the cumulative distribution function (CDF) for \( M_{max}^{obs} \). In the case of the GR relationship with magnitude upper bound Mmax, the integration Δ is given by:

$$ \Delta = \mathop \int \limits_{{{\text{M}}_{ \hbox{min} } }}^{{{\text{M}}_{ \hbox{max} } }} \left[ {\frac{{1 - exp[ - \beta \left( {M - M_{min} } \right)}}{{1 - exp\left[ { - \beta \left( {M_{max} - M_{min} } \right)} \right]}}} \right]^{\text{n}} {\text{dm}} $$
(11)

Such integration is not simple and (Kijko 2004) used Cramer’s approximation (Cramer 1961) to estimate it. Table 5 shows the maximum observed and expected magnitudes for each seismic zone.

Table 5 Maximum observed and expected magnitude
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10.3 Uncertainty Estimates of Seismic Activity Rate

Figure 10 shows the uncertainty of seismicity rate v (M) in PSHA, for each zone source. The graphs are generated using the proposed quantification method. We have chosen a small-scale area seismic source zone. This hazard analysis presents a region analyzed probabilistically to reflect the uncertainties in the seismic activity rate estimates by the GR magnitude–frequency relation and ground motion prediction inputs of seismic area source zones in a logic tree-driven probabilistic seismic analysis. This study used the new two-step approach developed by Stromeyer and Gottfried (2015). The first step makes use of the possibility that the uncertainties of the GR parameters a and b can be propagated to λM. In the second step, the resulting 1D probability distribution of seismic activity rate for any fixed magnitude M is approximated by a finite set of values and weights in a statistically optimal manner (Miller and Rice 1983). The procedure yields a set of alternative recurrence models that exhaustively approximates the epistemic uncertainties of the seismicity rate.

Fig. 10
figure 10figure 10

Observed cumulative seismicity rates (blue circles), observed noncumulative seismicity rates (red circles) and magnitude-frequency graphs for all the zones sources (Z1 to Z10)

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11 Evaluation of PSHA at Ground Surface in the Northeast of Algeria

This study integrates these new results for a better quantification of the seismic hazard of the Northeast Algerian region. The seismic hazard analysis, software CRISIS-developed by Ordaz et al. (2012) was used to produce seismic hazard curves, uniform hazard spectra (UHS) and hazard maps for PGA and PSA at periods 0.1, 0.5, 1.0, 1.5 and 2.0 s for two levels of ground shaking 10%, and 2% probability of exceedance in 50 years. These spectral periods and the different levels of ground shaking are commonly applied in Algerian building codes. For the purpose of estimating ground motion at different points as close as possible, the study area was divided into 0.1° × 0.1° small grid cells. In the computational scheme, these parameters are among the input parameters to the CRISIS program whereas the PSA are the output. Results were prepared in tabular format and used in the CRISIS software to introduce effects of the user’s attenuation model. The estimated PGA has been presented in the form of zone maps for different return periods. The seismic hazard analysis at the surface level using topographic condition, ground response estimation techniques are available for evaluating PGA at the surface level. Hence, in this paper the seismic hazard assessment at the surface is estimated using the non-linear site amplification technique proposed by Raghukanth and Iyengar (2007) using the following formula:

$$ { \ln }\left( {F_{s} } \right) = a_{1} y_{br} + a_{2} + ln\delta_{s} $$
(12)

where a1 and a2 are regression coefficients, ybr is the spectral acceleration at rock level and \( \delta_{s} \) is the error term. The values of the regression coefficients a1 and a2 vary for different site classes and for different natural periods. The amplification factor (Fs) varies as a function of the rock level PSA. The spectral acceleration can be obtained from: \( y_{s} = y_{br} F_{s} \). Where Fs is the amplification factor and is the spectral acceleration at the ground surface for a given site class (Sitharam et al. 2015). Fs varies as a function of PSA and accounts for the non-linear behavior of the soil by amplifying the seismic signals.

12 Results and Discussions

The seismic hazard assessment in the study area was established by dividing the entire region into grids of size 0.1° × 0.1° (about 200 m × 200 m). For each grid point the horizontal PGA values were evaluated at bedrock level at 10% and 2% exceedance probabilities in 50 years. These exceedance values correspond to 475- and 2475-year return periods, respectively. Note that the results obtained could be further refined to remove uncertainties due to the arbitrary choices of the attenuation laws and the zoning model as well as the hypotheses on the maximum magnitudes of the highly active sources.

A logical tree approach is needed to better understand these uncertainties and prioritize them. For the estimation of the seismic hazard parameters, Kijko and Sellevoll (1989, 1992) have developed an approach for seismic hazard evaluation consistent with the available historical and instrumental data. The importance of the method lies in its ability to estimate from incomplete data files the parameters b of the Gutenberg-Richter relationship, the mean annual activity rate λ of the events (throughout the region), the average return period and the maximum possible magnitude Mmax. The obtained PGA results at period T = 0.1 s are plotted as contour maps in Figs. 11 and 12, with 10% and 2% chance of exceedance in 50 years. The maximum values reached in Constantine and the Soummam Valley, close to the location of the Ms6 October 27, 1985 and the recent mb5.7 Beni Ourtilane Earthquake. In addition, the isolines elongates in a direction in agreement to the ENE–WSW direction of the regional stress field. PGA values at the rock level for 8 most populous cities in the study area are given in Table 6. It can be seen that the seismic hazard is high offshore along the Tell Atlas. Along the Tell Atlas region, the highest hazard is observed in the Constantine region and in the Mansourah region. For the 475-year return period, the PGA values for plate boundary regions vary from 0.02 to 0.27 g, whereas for the Sahara region the values were less than 0.02 g except for the Saharan Atlas region south of the study area. The Algerian seismic code RPA-1999 (2003) divides the country into five zones, Zone III, Zone IIa, Zone IIb, Zone I and Zone 0. The maximum expected accelerations in each of these zones are 0.10 g, 0.15 g, 0.20 g and 0.25 g, respectively. The PGA values obtained in this study for Northeast Algeria are almost similar. The present surface level PGA values match well with those obtained for various cities whose microzonation studies were carried out earlier (Table 7). The PGA obtained at ground level using this approach is a simple method and first approximation which may be used for preliminary design. It is to be noted that several factors affect the surface level acceleration depending on the soil conditions such as effect of soil layering which needs to be explored for site specific studies (Raghunandan 2012).

Fig. 11
figure 11

PGA values (g) corresponding to a return period of 475 years (10% probability of exceedance in 50 years)

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Fig. 12
figure 12

PGA values (g) corresponding to a return period of 2000 years (2% probability of exceedance in 50 years)

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Table 6 PGA values at rock level for 8 most populous cities of study area
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Table 7 Comparison of Surface level PGA values with earlier studies
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13 Conclusions

This work represents one of the first contributions to the knowledge of seismic hazard and risk reduction in the Northeastern region of Algeria. The existence of significant seismicity suggests the possibility of moderate to strong events in the region; this is why this work should be continued to better understand the different active structures of the region to better assess the seismic hazard. This work must be accompanied by a better evaluation of the seismic risk and the vulnerability of buildings in big cities. In this work, the theoretical process was presented followed by the probabilistic evaluation of the seismic hazard at a given site, according to the method proposed by Cornell (1968). This method was then applied to the study area. The results show that the cities of Constantine, Mansourah and Guelma are subject to a low seismic hazard compared to Annaba, Batna, Tizi Ouzou or other regions in Northeast Algeria, but due to the relatively high building vulnerability resulting from the large number of unreinforced buildings and non-ductile concrete buildings in this region and elsewhere in the country, the region could potentially incur damaging earthquakes. The accelerations obtained are relatively moderate because the epicenters of important earthquakes are located far from Constantine and Bibans and thus, induce a reduced seismic hazard. Further, the number of historical earthquakes taken into account in this analysis, as well as the limited period of time considered narrow the statistical representation of the data sample and contribute to a larger uncertainty in the seismic hazard in the Constantine region. Finally, even if the seismic hazard estimation methods are numerous, they all converge and contribute to the establishment of a comprehensive seismic risk reduction program as they allow a better understanding of the potential seismic threat and assist decision makers in implementing mitigation measured to safeguard lives and property.

For this study seismic hazard parameters in terms of PGA have been estimated considering: (1) estimated b-value for each seismogenic source zone, and (2) constant b-value obtained considering entire earthquake catalog (2) calculated de parameters of seismicity for each seismic zone source. The following broad conclusions could be drawn from the study. For all return periods, the estimated PGA considering constant b-value for all the source zones is on higher side as compared to those obtained using varying b-value for each source zone. For the 475-year return period, in the region enclosed by state boundary, the PGA values vary from 0.02 to 0.10 g and from 0.13 to 0.27 g considering varying b-value and constant b-value, respectively. However, considering constant b-value for most of the region in the country, the PGA varies from 0.07 to 0.26 g. For the 2475-year return period, the PGA varies between 0.08 and 0.34 g considering varying b-values.