Mustapha Meghraoui
email: m.meghraoui@unistra.fr

Paleoseismic History of the Dead Sea Fault Zone

Keywords: Active faulting, Earthquake rupture, Seismicity, Seismic slip deficit, Slip rate, Trench investigations

Introduction

Major continental faults often constitute plate boundaries with transtensional and transpressional styles of active deformation. The repetition of large earthquakes with Mw > 7 along these faults is closely associated to the rate of activity between the plates and to the rupture segmentation over the late Quaternary [START_REF] Sieh | The repetition of large-earthquake ruptures[END_REF]. In the last century, large earthquakes with surface ruptures have been documented on the San Andreas fault in California, the North Anatolian fault and East Anatolian fault in Turkey, the Alpine fault in New Zealand, and the northern Tibet transcurrent faults in China. The observation, description, and measurements of coseismic surface faulting constitute the basis for the development of earthquake geology and paleoseismic investigations [START_REF] Yeats | The geology of earthquakes[END_REF]). Nevertheless, among all continental transform systems, the Dead Sea fault (DSF, Fig. 1) is an exception because of its apparent last-century seismic quiescence and, therefore, variability of earthquake activity and faulting behavior (Fig. 2).

The existence of a dense population with small and large urban areas throughout the successive civilizations is the source for a continuous record of seismic events that favors a completed seismicity catalogue for major earthquakes along the DSF [START_REF] Ambraseys | The 1759 earthquake in the Bekaa valley: implications for earthquake hazard assessment in the eastern Mediterranean region[END_REF][START_REF] Amiran | Earthquakes in Israel and adjacent areas: macroseismic observations since 100 BCE[END_REF][START_REF] Sbeinati | The historical earthquakes of Syria: an analysis of large seismic events from 1365 B.C. to1900 A.D[END_REF][START_REF] Ambraseys | Earthquakes in the Mediterranean and Middle East: a multidisciplinary study of seismicity up to 1900[END_REF]). The instrumental seismicity (younger than 1900 A.D.) of the continental Dead Sea fault is of a relatively low level compared to other faults, such as the nearby East Anatolian fault or North Anatolian fault. Indeed, the largest earthquake that took place in the last century is the 13 July 1927 with a local magnitude M L = 6.2 that caused severe damage in Jericho and Jerusalem. More recently, the Mw 7.3 Nuweiba earthquake that took place offshore and further south in the Gulf of Aqaba and northern Red Sea occurred as a reminder that large seismic events may be generated further north along the DSF. The apparent quiescence and the lack of major seismic events with Mw > 6.0 on most fault segments in the last centuries are in contradiction with the historical catalogue and related report of faulting events over the last 3,000 years or so along the continental DSF [START_REF] Guidoboni | Catalogue of ancient earthquakes in the Mediterranean area up to the 10th century[END_REF][START_REF] Ambraseys | Faulting associated with historical and recent earthquakes in the Eastern Mediterranean region[END_REF][START_REF] Sbeinati | The historical earthquakes of Syria: an analysis of large seismic events from 1365 B.C. to1900 A.D[END_REF].

The understanding of earthquake rupture parameters and pattern of surface deformation is a critical aspect for the identification of recurrent surface faulting and building of a paleoseismic history (McCalpin 1996). Models of earthquake faulting were first based on the fault segmentation with persistent structural boundaries and characteristic earthquake behavior that suggest the repetition of same size events with similar coseismic slip along strike [START_REF] Sieh | The repetition of large-earthquake ruptures[END_REF][START_REF] Wesnousky | Predicting the endpoints of earthquake ruptures[END_REF]. Field investigations on pre-instrumental earthquakes using tectonic geomorphology, paleoseismology and archeoseismology along the DSF benefit from the richness of the historical archives and seismicity catalogue [START_REF] Agnon | Pre-instrumental earthquakes along the Dead Sea Rift[END_REF]. These field approaches tracing the past surface ruptures with related coseismic slip and other fault parameters provide an estimate of seismic moment of past large earthquakes with the constraint of interseismic periods and level of seismic coupling along the DSF.

The aim of this entry is to describe the DSF as a transform plate boundary pointing out the rate of active deformation, fault segmentation, and geometrical complexities as a control of earthquake ruptures. The distribution of large historical earthquakes from a revisited seismicity catalogue using detailed macroseismic maps allows the correlation between the location of past earthquakes and fault segments. The recent results of paleoearthquake investigations (paleoseismic and archeoseismic) with a recurrence interval of large events and long-term slip rate are presented and discussed along with the identification of seismic gaps along the fault. Finally, the implications for the seismic hazard assessment are also discussed. [START_REF] Wdowinski | GPS measurements of current crustal movements along the Dead Sea Fault[END_REF][START_REF] Reilinger | GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions[END_REF][START_REF] Gomez | Global positioning system measurements of strain accumulation and slip transfer through the restraining bend along the Dead Sea fault system in Lebanon[END_REF][START_REF] Béon | Slip rate and locking depth from GPS profiles across the southern Dead Sea Transform[END_REF][START_REF] Alchalbi | Crustal deformation in northwestern Arabia from GPS measurements in Syria: slow slip rate along the northern Dead Sea fault[END_REF][START_REF] Tarazi | GPS measurements of nearfield deformation along the southern Dead Sea fault system, G-cubed 12[END_REF][START_REF] Mahmoud | Kinematic study at the junction of the East Anatolian fault and the Dead Sea fault from GPS measurements[END_REF][START_REF] Masson | Variable behavior of the Dead Sea Fault along the southern Araba segment from GPS measurements[END_REF]. The DSF is a boundary between Arabia plate to the east and the Sinai (Africa) plate to the west. GPS velocities are given with Arabia-fixed frame; fault segments and offsets are in Fig. 3. Topography and bathymetry data is from SRTM 3-second-arc and GEBCO_08 grid

The Dead Sea Transform: A Continental Plate Boundary

The DSF is a north-south trending continental plate boundary and transform crustal structure that separates the Arabian plate to the east from the African-Sinai plate to the west (Fig. 1). The left-lateral 1,000-km-long fault exhibits a southern transtensional section that includes the Dead Sea until the Gulf of Aqaba, a central section characterized by the Lebanese restraining bend, and the northern section that limits to the west the Syrian coastal ranges [START_REF] Garfunkel | Active faulting in the Dead Sea rift[END_REF]. The DSF results from the differential northward movement of Arabia and Africa relative to Eurasia and connects the seafloor spreading of the Gulf of Aqaba -Red Sea in the south to Anatolia in the north. Indeed, both plates drift north at a rate of 18 mm/year for Arabia and at about 6 mm/year for Africa-Nubia [START_REF] Reilinger | GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions[END_REF]. GPS campaigns from 1991 to 2011 on about 35 stations along all the DSF (computed for Arabia or Eurasia fixed) provide an average geodetic velocity field of $5 mm/year, $ 4.7 mm/year, and $2 mm/year for the south, central, and north segments, respectively (Fig. 2). It is worth to mention that GPS measurements and late Quaternary tectonic investigations across the NE trending Palmyride fold belt, a branch of the DSF in Syria, show less than 1 mm/year of active regional shortening along the NNW-SSE direction [START_REF] Chaimov | Crustal shortening in the Palmyride fold belt, Syria, and implications for movement along the Dead Sea fault system[END_REF][START_REF] Abou Romieh | Active crustal shortening in NE Syria revealed by deformed terraces of the River Euphrates[END_REF][START_REF] Alchalbi | Crustal deformation in northwestern Arabia from GPS measurements in Syria: slow slip rate along the northern Dead Sea fault[END_REF]. Dislocation models based on GPS profiles across the fault reveal an average 11-km locking depth for the elastic crustal thickness along the fault zone [START_REF] Wdowinski | GPS measurements of current crustal movements along the Dead Sea Fault[END_REF][START_REF] Reilinger | GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions[END_REF][START_REF] Gomez | Global positioning system measurements of strain accumulation and slip transfer through the restraining bend along the Dead Sea fault system in Lebanon[END_REF][START_REF] Béon | Slip rate and locking depth from GPS profiles across the southern Dead Sea Transform[END_REF][START_REF] Alchalbi | Crustal deformation in northwestern Arabia from GPS measurements in Syria: slow slip rate along the northern Dead Sea fault[END_REF][START_REF] Tarazi | GPS measurements of nearfield deformation along the southern Dead Sea fault system, G-cubed 12[END_REF][START_REF] Mahmoud | Kinematic study at the junction of the East Anatolian fault and the Dead Sea fault from GPS measurements[END_REF][START_REF] Masson | Variable behavior of the Dead Sea Fault along the southern Araba segment from GPS measurements[END_REF]. The crustal structure depicted from deep seismic and gravity profiles, combined with the outcropping geology across the Dead Sea basin and Araba valley, reaches from west to east from 26 to 39 km, indicating a small asymmetric topography of the Moho discontinuity [START_REF] Weber | Anatomy of the Dead Sea transform from lithospheric to microscopic scale[END_REF]. Focal mechanisms of earthquakes and geodetic and tectonic observations characterize the stress and strain field which is in agreement with the left-lateral strike-slip mechanism, even if locally main principal stress directions may rotate and show normal (Dead Sea) or thrust mechanisms [START_REF] Hofstetter | Stress tensor and focal mechanisms along the Dead Sea fault and related structural elements based on seismological data[END_REF][START_REF] Palano | Current stress and strain-rate fields across the Dead Sea fault system: constraints from seismological data and GPS observations[END_REF]). In the northern sector of the DSF, the stress field results from the complex tectonic interaction between the Arabian, Anatolian-Eurasian, and African-Sinai plates which occurs along the Hatay triple junction [START_REF] Mahmoud | Kinematic study at the junction of the East Anatolian fault and the Dead Sea fault from GPS measurements[END_REF].

The onset of the fault activity is not well constrained, but the largest recorded slip on the fault and size of the Dead Sea basin (>100 km in length when including the Jordan valley) provide some evidence. Leftlateral strike-slip motions are visible on all three sections, thanks to geologic and geomorphic offsets along the DSF (Fig. 3). Initially, [START_REF] Dubertret | Les formes structurales de la Syrie et de la Palestine[END_REF], who adopted the continental drift theory as a possible mode for structuring the Red Sea and the surrounding areas, proposed a model whereby the "Sinai block" drifted southward for 160 km along the DSF. Later on, a total of 107-km slip is estimated from the offset of a Jurassic stratigraphic sequence and offset dikes dated to 20 Ma that result in a 4-7-mm/year slip rate during 15-20 Myr along the southern section of the fault [START_REF] Quennell | The structural and geomorphic evolution of the Dead Sea rift[END_REF][START_REF] Bartov | Sinistral movement along the Gulf of Aqabaits age and relation to the opening of the Red Sea[END_REF][START_REF] Garfunkel | Active faulting in the Dead Sea rift[END_REF]. Different authors suggest that the fault structure and left-lateral motion result from two main tectonic episodes with 65-km slip accumulating during the Miocene and 42-km post-Miocene slip. The southern section of the plate boundary also probably functioned independently accumulating about 60 km of pre-Pliocene slip, and offset basalts in the northern section document the post-Miocene-early Pliocene (5-6 Ma) displacement [START_REF] Chaimov | Crustal shortening in the Palmyride fold belt, Syria, and implications for movement along the Dead Sea fault system[END_REF][START_REF] Brew | Tectonic and geological evolution of Syria[END_REF]. The complex structure of the Lebanese restraining bend and adjacent Palmyride fold belt may be responsible for the discrepancy in the fault offset between the northern and southern sections of the DSF. Hence, the total southern offset becomes partitioned further north into fault-parallel slip and fold-perpendicular compression (e.g., [START_REF] Chaimov | Crustal shortening in the Palmyride fold belt, Syria, and implications for movement along the Dead Sea fault system[END_REF]). The fault geometry and left-lateral behavior govern the kinematics of all segments, with auxiliary tectonic regimes such as pull-apart basins (Dead Sea, Hula and Ghab depressions) and shortening within the LRB.

A Tectonic Fault Trace with Geometrical Complexities

The marks of Quaternary deformation are observable at all scale and on all sections along the DSF. Using the geological and geomorphological maps, the linear shape of the fault affecting late Pleistocene and Holocene deposits can be identified on Landsat, SPOT, and QuickBird satellite photographs as well as on aerial photographs.

The southernmost DSF zone crosses the western edge of the Gulf of Aqaba and extends further north for about 40 km crossing fluvial and alluvial terraces of Avrona Playa and the Wadi Araba Valley. Several fault branches may outcrop showing normal geometry in this area, but they may result from the slip partitioning on branches of the main DSF [START_REF] Zilberman | Surface ruptures induced by the devastating 1068 A.D. earthquake in the southern Arava valley, Dead Sea Rift, Israel[END_REF]. To the north, except for the Encyclopedia of Earthquake Engineering DOI 10.1007/978-3-642-36197-5_40-1 # Springer-Verlag Berlin Heidelberg 2015 accumulation of sand dunes that conceals the fault zone around latitude 30 N, the fault can be seen to affect successive stream channels and terraces. The northern half of the Wadi Araba fault exposes outstanding tectonic geomorphology with linear fault scarps showing offset alluvial fans and channels visible until the southeastern edge of the Dead Sea [START_REF] Barjous | Tectonic evolution of the Gulf of Aqaba -Dead Sea transform fault system[END_REF]. The southern end of the DSF meets the Gulf of Aqaba that shows NNE-SSW trending relay fault system with large pull-apart basins in the sea bottom that may act as a geometrical barrier that limits the Wadi Araba fault zone to the south. Indeed, the Wadi Araba fault section is about 200-km long if we include the eastern edge of the Dead Sea area (Fig. 4), it may constitute a single fault segment or two distinct segments if a major geometrical complexity (relay zone) is hidden below the mid-distance sand dunes.

The Dead Sea area has the characteristics of a large pull-apart basin (100-km long, 17-km wide) limited by two north striking segments, the southern Wadi Araba fault zone and the northern Jordan valley fault segment. The latter segment follows the Jordan River, extends from the Dead Sea (right bank of the Jordan River) to the Tiberiade Lake and is made of a suite of 10-20-km-long subsegments (mostly on the left bank of the Jordan River) for a total length of $110 km. In the valley, small pull-apart basins and restraining bends limit the subsegments and show left-lateral slip of stream channels (Fig. 5; Ferry Fig. 4 The $200-km-long Wadi Araba fault section from the eastern edge of the Dead Sea area to the Aqaba Gulf. The fault zone is linear exposing offset alluvial fans (west of Petra) and archeological features (Qasr Tilah); although the central part (about 30 km) is concealed by sand dunes and may hide a main geometrical complexity, the fault section can be considered as a single fault segment and may be at the origin of a characteristic earthquake with Mw !7.5. Topography data is from SRTM (3-arc-second) Encyclopedia of Earthquake Engineering DOI 10.1007/978-3-642-36197-5_40-1 # Springer-Verlag Berlin Heidelberg 2015 et al. 2007). Although the Tiberiade Lake shows no pull-apart structure, it is located west of the fault and can be correlated further north to the Hula pull-apart [START_REF] Heimann | Young faults in the Hula pull-apart basin, central Dead Sea transform[END_REF].

The Lebanese restraining bend (LRB) is about 200-km-long positive flower structure, striking NE-SW, almost midway and on a right-stepping structure of the DSF (Fig. 3). Although the structure is made of four active fault branches, only the central Yammouneh fault is throughgoing and represents the main continuation of the DSF across the bend (Fig. 6; [START_REF] Gomez | Holocene faulting and earthquake recurrence along the Serghaya branch of the Dead Sea fault system in Syria and Lebanon[END_REF][START_REF] Nemer | Coseismic growth of sedimentary basins along the Yammouneh strike-slip fault (Lebanon)[END_REF]. From the southern end of LRB, the westernmost Roum fault shows left-lateral strike-slip and vertical movements and is associated with fresh fault scarps and pressure ridges which attest for recent coseismic ruptures. To the northwest and from the northernmost end of the LRB, other southwest trending fault branches with reverse geometry seem to extend offshore [START_REF] Elias | Active thrusting offshore Mount Lebanon: source of the tsunamigenic A.D. 551 Beirut-Tripoli earthquake[END_REF]). The Rachaya and Serghaya faults are the easternmost fault branches showing left-lateral strike-slip movements associated with different geomorphic expressions of young surface ruptures (fault scarps, mole tracks, pressure ridges) and cumulative leftlateral slip on stream channels, alluvial fans, and small pull-apart basins. The LRB constitutes a large geometrical complexity as a result of the left-lateral block movements on the plate boundary.

The DSF northern section is made of two main north trending and linear segments that include the impressive Ghab pull-apart depression. From the LRB, the section begins with the Al Boqueia pull-apart structure (15-km long and 6-km wide) and extends with the $90-km-long and linear Missyaf segment until the Ghab pull-apart (Fig. 7; [START_REF] Brew | Tectonic and geological evolution of Syria[END_REF][START_REF] Meghraoui | Evidence for 830 years of seismic quiescence from palaeoseismology, archaeoseismology and historical seismicity along the Dead Sea fault in Syria, Earth Planet[END_REF]. The Ghab depression is 15 km wide and is limited to the west by a $100-km-long fault segment that ends in the Amik basin and to the east by the continuation of the Missyaf segment. The northern area of the Ghab depression shows a partition between strike-slip faults and normal faulting, where the NE trending Antakya and Latakia strike-slip faults affect the western block and the Afrin fault "en echelon" system limits the eastern edge (Fig. 8; [START_REF] Gomez | Global positioning system measurements of strain accumulation and slip transfer through the restraining bend along the Dead Sea fault system in Lebanon[END_REF][START_REF] Trifonov | Neotectonics, recent geodynamics and seismic hazard of Syria[END_REF][START_REF] Mahmoud | Kinematic study at the junction of the East Anatolian fault and the Dead Sea fault from GPS measurements[END_REF]. The northern end of the DSF and Ghab fault segments also shows left-lateral stream offsets, but the fault trace enters the Amik basin and becomes concealed below the young Quaternary sedimentation [START_REF] Aky€ Uz | Historical earthquake activity of the northern part of the Dead Sea fault zone, southern Turkey[END_REF]). The $200-km-long Missyaf and Ghab fault segments show different sizes of left-lateral stream offsets with shutter ridges and are probably responsible of the 2,000-m-high topographic offset of the western coastal range.

The occurrence of large earthquakes along the DSF closely depends on the extent of fault segments and the control of coseismic ruptures by the geometrical complexities. Large step overs and pull-apart basins (with width >5 km) and restraining bends may contribute to the arrest of earthquake ruptures and limit the Fig. 7 Missyaf fault segment (yellow arrows) limited by the El Boquea and Ghab pull-apart basins, to the south and north, respectively [START_REF] Meghraoui | Evidence for 830 years of seismic quiescence from palaeoseismology, archaeoseismology and historical seismicity along the Dead Sea fault in Syria, Earth Planet[END_REF]. Topography data is from SRTM (3-arc-second) Encyclopedia of Earthquake Engineering DOI 10.1007/978-3-642-36197-5_40-1 # Springer-Verlag Berlin Heidelberg 2015 length of coseismic faults and, hence, the size of earthquakes [START_REF] Wesnousky | Predicting the endpoints of earthquake ruptures[END_REF]. Main tectonic structures of the DSF such as the "en echelon" faults and basins of the Aqaba Gulf, the Dead Sea pull-apart basin, the Hula pull-apart basin, the LRB (although coseismic fault ruptures may occur with the restraining bend), the Ghab depression, and the Amik basin may act as major geometrical complexities and end points of large earthquakes (Mw > 7).

Large Earthquakes and Episodic Seismicity

A unified parametric earthquake catalogue was compiled for the whole DSF and covering the period before 2000 [START_REF] Apame ; Mustapha | Archeoseismology and paleoseismology for the protection of cultural heritage and archeological sites in the Middle East: the impact of large earthquakes on the archaeological sites Encyclopedia of Earthquake Engineering[END_REF]. The parametric catalogue is accompanied by a descriptive document which provides the macroseismic historical information and references which have been used for the compilation of the former [START_REF] Sbeinati | The historical earthquakes of Syria: an analysis of large seismic events from 1365 B.C. to1900 A.D[END_REF][START_REF] Ambraseys | Earthquakes in the Mediterranean and Middle East: a multidisciplinary study of seismicity up to 1900[END_REF]). For the pre-instrumental period, macroseismic data and a kriging technique were used to estimate macroseismic locations. In all, 1,000 earthquakes were identified and processed, to estimate position and uncertainty (Fig. 2). The catalogue shows that during the last century, seismic strain release of the DSF is curiously low with respect to that expected for a plate boundary. The instrumental seismicity shows the localized occurrence of shallow earthquakes (with a seismogenic layer 15-km depth) with most local magnitude M L between 1 and 5.5 [START_REF] Hofstetter | Stress tensor and focal mechanisms along the Dead Sea fault and related structural elements based on seismological data[END_REF][START_REF] Apame ; Mustapha | Archeoseismology and paleoseismology for the protection of cultural heritage and archeological sites in the Middle East: the impact of large earthquakes on the archaeological sites Encyclopedia of Earthquake Engineering[END_REF]) and the largest event being the 11 July 1927, Ms 6.3 in the Dead Sea area. Focal mechanism solutions show mostly strike-slip faulting, but normal faulting mechanisms occur also in regions of pull-apart basins, while some thrust mechanisms appear in the LRB. The seismicity is not equally distributed along strike, and some fault segments such as the Missyaf and Jordan valley have seismic gaps (Fig. 2). Although taking place offshore in the Gulf of Aqaba, the 22 November 1995 seismic event reached Mw 7.3 and illustrates the north-south trending, left-lateral strike-slip mechanism with typical size of plate boundary earthquakes. [START_REF] Elnashai | Earthquake hazard in Lebanon[END_REF] combined the available instrumental and historical seismicity data of the continental DSF region to estimate the annual GR frequency-magnitude distribution. They found that for the instrumental seismicity, the frequency-magnitude distribution follows the relationship log N = 3.02-0.73 M, while the historical distribution follows log N = 14.8-2.73 M (Fig. 9). They noted that the seismicity of the last 100 years has been lower than expected to accommodate the Arabia-Africa relative motion.

The pre-instrumental seismicity and in particular large earthquakes of the prehistorical (archeological and antiquities) and historical period in the DSF region are well described. Earthquakes and their related severity of damage are reported by the different civilizations in wall inscriptions, manuscripts, poems, volumes of geographers, and mailed letters [START_REF] Sbeinati | The historical earthquakes of Syria: an analysis of large seismic events from 1365 B.C. to1900 A.D[END_REF][START_REF] Finkbeiner | Catalogue of damage distribution due to historical earthquakes in the Middle East, APAME EC project -ICA-CT-2002-10024 -DG XII Brussels Galli P[END_REF][START_REF] Ambraseys | Earthquakes in the Mediterranean and Middle East: a multidisciplinary study of seismicity up to 1900[END_REF]. The oldest earthquake is reported in $1365 B.C. from the description of the destruction of Ugarit city in a letter sent by the governor Abilmiki of Tyre to the Pharaoh Amenophis IV (Akhenaton). The earthquakes of 31 B.C., 115 A.D., 363 A.D., and 526 A.D. are among the well reported during the Roman and Byzantine era; the latter is revealed by the monks following the destruction of the Saint Simeon monastery and nearby villages of northern Syria (also reported as the "legend of 1,000 lost villages" by historians). Large earthquakes reported in the medieval time (from eighth to sixteenth century) are among the well described, thanks to the Arab-Muslim civilization corroborated by the Crusader chroniclers. The earthquake of 1,202 estimated to be Ms 7.5 affected Lebanon where several km-long surface faulting is reported as crossing villages in mountains [START_REF] Ambraseys | Earthquakes in the Mediterranean and Middle East: a multidisciplinary study of seismicity up to 1900[END_REF] segments without large uncertainties and ultimately to faulting events in paleoseismic and archeoseismic investigations.

Paleo-archeo-earthquakes and the Rate of Slip

First accounts of seismic structures in geological deposits reported in the Lisan lacustrine deposits of the Dead Sea describe continuous large earthquake sequences in the last 50 ka [START_REF] El-Isa | Earthquake deformations in the Lisan deposits and seismotectonic implications[END_REF][START_REF] Marco | Long-term earthquake clustering: a 50,000-year paleoseismic record in the Dead Sea Graben[END_REF]. Recent studies describing obvious faulting outcrops and clear accounts of historical earthquakes with surface ruptures generated a strong interest in the development of paleoseismic excavations along fault strike.

The richness of archeological sites along the DSF constitutes an exceptional advantage for dating prehistorical earthquakes. Field investigations revealed left-lateral faulting of the following archeological sites: a total of 2.1-m offset walls of a Crusader castle during the 20 May 1,202 and 30 October 1,759 earthquakes [START_REF] Ellenblum | Crusader castle torn apart by earthquake at dawn, 20 May 1202[END_REF]; the cumulative 13.6-m offset of the Al Harif aqueduct since the Roman time, the most recent event being the 29 June 1,170 earthquake [START_REF] Meghraoui | Evidence for 830 years of seismic quiescence from palaeoseismology, archaeoseismology and historical seismicity along the Dead Sea fault in Syria, Earth Planet[END_REF]; the 2.2-m offset wall of Qasr Tilah that can be related to an earthquake event in 608-826 A.D. (Klinger et al. 2000a); the offset Galei Kinneret city walls during the 18 January 749 earthquake [START_REF] Marco | Archaeology, history, and geology of the A.-D. 749 earthquake, Dead Sea transform[END_REF]; the minimum 1-m vertical slip of a qanat during the 1,068 earthquake on the southern DSF near Eilat [START_REF] Zilberman | Surface ruptures induced by the devastating 1068 A.D. earthquake in the southern Arava valley, Dead Sea Rift, Israel[END_REF]; the cumulative offset of the Roman-Byzantine-Islamic Qasr Tilah site of the northern Araba valley during the 634 or 659/660, 873, 1,068, and 1,546 earthquakes (APAME 2007); a total of $25 m of the $2000 B.C. Tell Sicantarla, Hittite road, and Roman walls, with $9-m offset during the 1,408 and 1,872 earthquakes [START_REF] Altunel | Archaeological sites (Tell and Road) offset by the Dead Sea fault in the Amik Basin, Southern Turkey[END_REF]), and Tell Saidiyeh in $759 B.C., $1150B.C., $2300B.C., and $2900B.C. (Jordan Valley, Ferry et al. 2011). These archeo-seismological studies of the DSF are complemented with tectonic geomorphology and paleoseismic investigations that constrain paleoearthquake faulting episodes and slip rates.

In trenches, radiocarbon dating brackets the 1,759 earthquake on the northern Jordan valley fault segment and the Serghaya fault branch through 3D trenching with 0.5 and 2.5-m left-lateral slip, respectively [START_REF] Gomez | Holocene faulting and earthquake recurrence along the Serghaya branch of the Dead Sea fault system in Syria and Lebanon[END_REF][START_REF] Marco | Late Holocene activity of the Dead Sea transform revealed in 3D paleoseismic trenches on the Jordan Gorge segment[END_REF]. The major 1,202 earthquake (Mw 7.6, Ambraseys and Jackson 1998) is bracketed in the northern Jordan valley at Beyt Zayda with 1.6-m left-lateral slip [START_REF] Marco | Late Holocene activity of the Dead Sea transform revealed in 3D paleoseismic trenches on the Jordan Gorge segment[END_REF] and in the Lebanese segment of the DSF at the Yammouneh pull-apart basin (Fig. 7; [START_REF] Daëron | 12,000-year-long record of 10 to 13 paleo-earthquakes on the Yammouneh fault (Levant fault system, Lebanon)[END_REF][START_REF] Nemer | Coseismic growth of sedimentary basins along the Yammouneh strike-slip fault (Lebanon)[END_REF]. Faulting of the 749 earthquake of the Jordan valley segment is resolved at Beyt Zayda (north of Tiberiade Lake) and Tell Saidiyeh (south Jordan valley) paleoseismic sites [START_REF] Marco | Late Holocene activity of the Dead Sea transform revealed in 3D paleoseismic trenches on the Jordan Gorge segment[END_REF][START_REF] Ferry | Episodic behavior of the Jordan Valley section of the Dead Sea fault from a 14-kyr-long integrated catalogue of large earthquakes[END_REF]. Paleoseismic trenches near the Al Harif aqueduct resolve three faulting events in 160-510 A.D., 625-690 A.D., and 1010-1210 A.D., the latter being correlated with the 1,170 large earthquake [START_REF] Sbeinati | Timing of earthquake ruptures at the Al Harif Roman Aqueduct (Dead Sea fault, Syria) from archeoseismology and paleoseismology, Special volume "Archaeoseismology and paleoseismology[END_REF]. At the northern end of the DSF, faulting in trenches provides evidence for three historical earthquakes in 859, 1408859, , and 1872859, A.D. (Aky€ uz et al. 2006)). The longest paleoseismic records on the DSF are determined in the Jordan valley with a sequence of 12 coseismic surface ruptures over the last 14 ka [START_REF] Ferry | Episodic behavior of the Jordan Valley section of the Dead Sea fault from a 14-kyr-long integrated catalogue of large earthquakes[END_REF]) and 10-13 faulting events over the last 12 ka on the Yammouneh fault of the DSF restraining bend in Lebanon [START_REF] Daëron | 12,000-year-long record of 10 to 13 paleo-earthquakes on the Yammouneh fault (Levant fault system, Lebanon)[END_REF]). Although the correlation with individual fault segments is problematic, another source of earthquake records in the Dead Sea lake sediments and speleothems indicates a succession of seismites synchronous to historical earthquakes in 1927, 1293, 1202/1212, 749, 551, 419, 33 A.D. and 31 B.C. and mid-second century B.C. [START_REF] Marco | Long-term earthquake clustering: a 50,000-year paleoseismic record in the Dead Sea Graben[END_REF][START_REF] Kagan | Intrabasin paleoearthquake and quiescence correlation of the late Holocene Dead Sea[END_REF]. From recent paleoseismic trenching, [START_REF] Klinger | 5000 yr of paleoseismicity along the southern Dead Sea fault[END_REF] identified faulting events along the southern DSF in the Wadi Araba, which can be correlated with past earthquakes in 1458, 1212, 1068, and 363 A.D., in addition of one faulting event bracketed between 806 A.D. and 1044 A.D., which can be correlated with the 972 earthquake.

Encyclopedia of Earthquake Engineering DOI 10.1007/978-3-642-36197-5_40-1 # Springer-Verlag Berlin Heidelberg 2015 Slip rate: The succession of large earthquakes is totally dependent on the rate of deformation and slip along the fault. Geologic and geomorphologic slip-rate estimates are mainly based on offset geomorphologic markers (e.g., stream channels, drainage basin, alluvial fans, terraces) and offset archeologic piercing points during an estimated time span that is usually determined using cosmogenic -isotopic dating. The characteristics of successive earthquake ruptures and coseismic displacement obtained from the geological and geomorphological offsets and paleoseismic studies on different fault segments provide access to the long-term seismogenic clock and average timing for the recurrence of large seismic events.

From earlier studies, the 107-km offset of 20 Myr dikes of Sinai and Jordan and 40-45-km offset upper Miocene formations provide 5.35-6.4-mm/year slip rate [START_REF] Bartov | Sinistral movement along the Gulf of Aqabaits age and relation to the opening of the Red Sea[END_REF][START_REF] Garfunkel | Active faulting in the Dead Sea rift[END_REF]. [START_REF] Garfunkel | Active faulting in the Dead Sea rift[END_REF] also estimate 5-10-mm/year seismic slip rate of the DSF based on the 8-km-offset Homs basalt north of the LRB during the Pleistocene and along the Yammouneh fault. Later on, [START_REF] Ginat | Translocated Plio-Pleistocene drainage systems along the Arava fault of the Dead Sea transform[END_REF] proposed a slip-rate range of 3-7.5 mm/year since late Pliocene/early Pleistocene. Using offset stream channels and alluvial fans along the Wadi Araba segment, Galli (1999) estimated 10-mm/ year slip rate of for the southern Wadi Araba and the southern Jordan valley for the last 50 and 18 kyr, respectively. Subsequent and more recent studies using more precise offset measurements (by means of total station and DGPS) and isotopic dating provide a better estimate of the long-term slip rate (Fig. 10; Table 1). Klinger et al. (2000b) suggested 2-6-mm/year slip rate over the late Pleistocene (77-140 kyr), and [START_REF] Niemi | Late Pleistocene and Holocene slip rate of the Northern Wadi Araba fault, Dead Sea Transform, Jordan[END_REF] proposed a slip-rate range of 3.4-6 mm/year for the last 15 kyr. This slip rate is in agreement with the 5.4 AE 2.7 mm/year obtained from cosmogenic dating of paleosurfaces offset by the fault over the last $11 ka in the southern Wadi Araba (Le [START_REF] Beon | Early Holocene and Late Pleistocene slip rates of the southern Dead Sea fault determined from Be-10 cosmogenic dating of offset alluvial deposits[END_REF]). In the Jordan valley, offset stream channels affecting the Lisan lacustrine deposits and archeological features yield $5 mm/year for the last 47.5 kyr and 25 ka, respectively [START_REF] Ferry | A 48-kyr-long slip rate history for the Jordan Valley segment of the Dead Sea fault, Earth Planet[END_REF][START_REF] Ferry | Episodic behavior of the Jordan Valley section of the Dead Sea fault from a 14-kyr-long integrated catalogue of large earthquakes[END_REF]. North of the Sea of Galilee, at [START_REF] Meghraoui | Evidence for 830 years of seismic quiescence from palaeoseismology, archaeoseismology and historical seismicity along the Dead Sea fault in Syria, Earth Planet[END_REF][START_REF] Sbeinati | Timing of earthquake ruptures at the Al Harif Roman Aqueduct (Dead Sea fault, Syria) from archeoseismology and paleoseismology, Special volume "Archaeoseismology and paleoseismology[END_REF], Yammouneh [START_REF] Daeron | Constraints on the post-25-ka slip rate of the Yammouneh fault (Lebanon) using in situ cosmogenic Cl-36 dating of offset limestone-clast fans[END_REF][START_REF] Nemer | Coseismic growth of sedimentary basins along the Yammouneh strike-slip fault (Lebanon)[END_REF], Serghaya [START_REF] Gomez | Holocene faulting and earthquake recurrence along the Serghaya branch of the Dead Sea fault system in Syria and Lebanon[END_REF], Roum [START_REF] Nemer | Evidence of coseismic ruptures along the Roum fault (Lebanon): a possible source for the AD 1837 earthquake[END_REF], Jordan Gorge [START_REF] Marco | Late Holocene activity of the Dead Sea transform revealed in 3D paleoseismic trenches on the Jordan Gorge segment[END_REF], Jordan valley [START_REF] Ferry | A 48-kyr-long slip rate history for the Jordan Valley segment of the Dead Sea fault, Earth Planet[END_REF], and Wadi Araba (Klinger et al. 2000b;[START_REF] Niemi | Late Pleistocene and Holocene slip rate of the Northern Wadi Araba fault, Dead Sea Transform, Jordan[END_REF][START_REF] Beon | Early Holocene and Late Pleistocene slip rates of the southern Dead Sea fault determined from Be-10 cosmogenic dating of offset alluvial deposits[END_REF] Encyclopedia of Earthquake Engineering DOI 10.1007/978-3-642-36197-5_40-1 # Springer-Verlag Berlin Heidelberg 2015

Beyt Zayda, [START_REF] Marco | Late Holocene activity of the Dead Sea transform revealed in 3D paleoseismic trenches on the Jordan Gorge segment[END_REF] estimate a minimum 3-mm/year slip rate from a paleoseismic study and 15-m-left-lateral offset stream channel during the last 5,000 years. Further north, the fault splays formed by the Yammouneh, Roum, Rachaya, and Serghaya faults revealed consistent slip rates across the LRB. The correlation of two $50-km-apart alluvial fan offsets along the Yammouneh fault by [START_REF] Daeron | Constraints on the post-25-ka slip rate of the Yammouneh fault (Lebanon) using in situ cosmogenic Cl-36 dating of offset limestone-clast fans[END_REF] yields 5.1 AE 1.3-mm/year slip rate during the late Pleistocene-Holocene. From stream offsets and paleoseismic trenching across the Roum fault, [START_REF] Nemer | Evidence of coseismic ruptures along the Roum fault (Lebanon): a possible source for the AD 1837 earthquake[END_REF] estimate 0.86-1.05-mm/ year slip rate during the last 10,510 years. With the Rachaya and Serghaya faults being considered as pertaining to the same fault system, a 1.4 AE 0.2-mm/year slip rate during the Holocene is obtained from offset stream channels and paleoseismic studies [START_REF] Gomez | Holocene faulting and earthquake recurrence along the Serghaya branch of the Dead Sea fault system in Syria and Lebanon[END_REF][START_REF] Nemer | Coseismic growth of sedimentary basins along the Yammouneh strike-slip fault (Lebanon)[END_REF]. Further north, on the Missyaf fault segment, the $13.6-m offset Al Harif Roman aqueduct analyzed using paleoseismic and archeoseismic approach provides 4.9-6.3-mm/year slip rate during the last 4,300 years [START_REF] Meghraoui | Evidence for 830 years of seismic quiescence from palaeoseismology, archaeoseismology and historical seismicity along the Dead Sea fault in Syria, Earth Planet[END_REF][START_REF] Sbeinati | Timing of earthquake ruptures at the Al Harif Roman Aqueduct (Dead Sea fault, Syria) from archeoseismology and paleoseismology, Special volume "Archaeoseismology and paleoseismology[END_REF]. Along with paleoseismic evidence of coseismic fault ruptures, the northern end of the DSF displays cumulative left-lateral offset stream channels and tells archeological feature, and yields an average 6.07-mm/year slip rate during the last 7 kyr [START_REF] Aky€ Uz | Historical earthquake activity of the northern part of the Dead Sea fault zone, southern Turkey[END_REF][START_REF] Altunel | Archaeological sites (Tell and Road) offset by the Dead Sea fault in the Amik Basin, Southern Turkey[END_REF][START_REF] Karabacak | Field evidences from northern Dead Sea Fault Zone (South Turkey): new findings for the initiation age and slip rate[END_REF].

The Worrying Silence of a Major Continental Transform Fault

In a recent past, the low-level instrumental seismicity and temporal seismic quiescence of the DSF erroneously suggested inactive faulting implying serious underestimation of the earthquake hazard in the Middle East. In contrast, large historical earthquakes (Mw > 7) equally distributed along the entire fault length indicate the zones with seismic quiescence during the last centuries (Fig. 2). This distribution appears as not random, and the accuracy of historical seismicity catalogue (APAME 2007) combined with the fault-related geometrical complexities (see section "A Tectonic Fault Trace with Geometrical Complexities") and paleoseismic results (see also section "Paleo-archeo-earthquakes and the Rate of Slip") suggests long periods of quiescence primarily on individual fault segments (Fig. 11). In fact, the long-term rate of active faulting and long record of past earthquakes, compared to the geodetic rate of active deformation (GPS velocity rate), point toward the level of a significant seismic coupling on the Jordan valley and Missyaf rupture segments of the DSF [START_REF] Meghraoui | Slip deficit and location of seismic gaps along the Dead Sea fault[END_REF].

A seismic slip deficit can be estimated from the comparison between the geodetic rate (deep off-fault deformation) and fault slip rate taking into account the DSF segmentation, fault segment length, maximum size of historical earthquakes, and inferred coseismic slip distribution (from paleoseismology and archeoseismology). The left-lateral slip obtained from the geodetic rate or tectonic rate of deformation [START_REF] Meghraoui | Evidence for 830 years of seismic quiescence from palaeoseismology, archaeoseismology and historical seismicity along the Dead Sea fault in Syria, Earth Planet[END_REF][START_REF] Marco | Late Holocene activity of the Dead Sea transform revealed in 3D paleoseismic trenches on the Jordan Gorge segment[END_REF][START_REF] Ferry | A 48-kyr-long slip rate history for the Jordan Valley segment of the Dead Sea fault, Earth Planet[END_REF][START_REF] Alchalbi | Crustal deformation in northwestern Arabia from GPS measurements in Syria: slow slip rate along the northern Dead Sea fault[END_REF][START_REF] Tarazi | GPS measurements of nearfield deformation along the southern Dead Sea fault system, G-cubed 12[END_REF]), compared to the seismic quiescence for large earthquakes in the last 1,000 years or so, implies $4.5-m slip deficit which corresponds to the occurrence of a Mw 7.4-7.5 along the fault. The interseismic time reaches 952 AE 115 years and 761 AE 150 years for Mw 7.5-7.4 on the Jordan valley and Missyaf fault segments, respectively (Table 2; [START_REF] Meghraoui | Slip deficit and location of seismic gaps along the Dead Sea fault[END_REF].

The identification of seismic gaps with temporal quiescence reaching 982 and 845 years (as per the year 2015) on the Jordan valley and Missyaf fault segments, respectively, calls for an urgent earthquake hazard evaluation and related risk mitigation, especially in major urban areas. If the interevent times proposed by [START_REF] Meghraoui | Slip deficit and location of seismic gaps along the Dead Sea fault[END_REF] are valid for other DSF segments as the Ghab and LRB, the occurrence of large seismic events with M > 7 in 1,408 and1759-1837 (Fig. 11;[START_REF] Apame ; Mustapha | Archeoseismology and paleoseismology for the protection of cultural heritage and archeological sites in the Middle East: the impact of large earthquakes on the archaeological sites Encyclopedia of Earthquake Engineering[END_REF][START_REF] Ambraseys | Earthquakes in the Mediterranean and Middle East: a multidisciplinary study of seismicity up to 1900[END_REF]) suggests a relatively low seismic risk for these regions. An uncertainty remains, however, for the Wadi Araba fault segments where the location and size of past earthquakes are poorly known. Although archeoseismic and geomorphic studies of paleoearthquake markers document faulting events (Galli 1999; Klinger et al. 2000a;[START_REF] Zilberman | Surface ruptures induced by the devastating 1068 A.D. earthquake in the southern Arava valley, Dead Sea Rift, Israel[END_REF][START_REF] Beon | Early Holocene and Late Pleistocene slip rates of the southern Dead Sea fault determined from Be-10 cosmogenic dating of offset alluvial deposits[END_REF][START_REF] Klinger | 5000 yr of paleoseismicity along the southern Dead Sea fault[END_REF], the 200-km-long and linear fault zone in the desert still needs more paleoseismic studies, especially because historical seismicity data is very limited and the correlation between past large earthquakes from catalogue (e.g., the 365 earthquake that destroyed Petra; Ambraseys 2009) and faulting events is not straightforward.

Encyclopedia of Earthquake Engineering DOI 10.1007/978-3-642-36197-5_40-1 # Springer-Verlag Berlin Heidelberg 2015 An attempt at seismic hazard evaluations including earthquake geology and paleoseismic data is provided for the northern DSF in Syria and Lebanon and in northern Araba valley and the Jordan valley segment [START_REF] Al-Tarazi | Alternative models of seismic hazard evaluation along the Jordan Dead Sea transform[END_REF]. Preliminary results that include earthquake faulting parameters and paleoseismic data suggest a high level of hazard and risk along the DSF and on the Jordan valley and Missyaf fault segments in particular, where the peak ground acceleration (PGA) may reach 0.8 g. For the long-term, 2,000-year-long period of observations, it is found that the frequency-magnitude distribution Fig. 11 Historical large earthquakes (M > 6.4) correlated with each fault segment according to the detailed study of earthquake damage area along the Dead Sea fault [START_REF] Guidoboni | Catalogue of ancient earthquakes in the Mediterranean area up to the 10th century[END_REF][START_REF] Ambraseys | Faulting associated with historical and recent earthquakes in the Eastern Mediterranean region[END_REF][START_REF] Sbeinati | The historical earthquakes of Syria: an analysis of large seismic events from 1365 B.C. to1900 A.D[END_REF][START_REF] Zilberman | Surface ruptures induced by the devastating 1068 A.D. earthquake in the southern Arava valley, Dead Sea Rift, Israel[END_REF][START_REF] Apame ; Mustapha | Archeoseismology and paleoseismology for the protection of cultural heritage and archeological sites in the Middle East: the impact of large earthquakes on the archaeological sites Encyclopedia of Earthquake Engineering[END_REF][START_REF] Finkbeiner | Catalogue of damage distribution due to historical earthquakes in the Middle East, APAME EC project -ICA-CT-2002-10024 -DG XII Brussels Galli P[END_REF][START_REF] Ambraseys | Earthquakes in the Mediterranean and Middle East: a multidisciplinary study of seismicity up to 1900[END_REF]. Gray segments belong to a Middle Age earthquake sequence and southward migration along the fault. GPS velocities are obtained with Eurasia-fixed reference frame [START_REF] Reilinger | GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions[END_REF], and background topography/bathymetry is from GEBCO

Fig. 1

 1 Fig.1Plate boundaries (thick black lines) in the eastern Mediterranean pointing out the Dead Sea fault (DSF), East Anatolian fault (EAF), North Anatolian fault (NAF), and GPS data[START_REF] Wdowinski | GPS measurements of current crustal movements along the Dead Sea Fault[END_REF][START_REF] Reilinger | GPS constraints on continental deformation in the Africa-Arabia-Eurasia continental collision zone and implications for the dynamics of plate interactions[END_REF][START_REF] Gomez | Global positioning system measurements of strain accumulation and slip transfer through the restraining bend along the Dead Sea fault system in Lebanon[END_REF][START_REF] Béon | Slip rate and locking depth from GPS profiles across the southern Dead Sea Transform[END_REF][START_REF] Alchalbi | Crustal deformation in northwestern Arabia from GPS measurements in Syria: slow slip rate along the northern Dead Sea fault[END_REF][START_REF] Tarazi | GPS measurements of nearfield deformation along the southern Dead Sea fault system, G-cubed 12[END_REF][START_REF] Mahmoud | Kinematic study at the junction of the East Anatolian fault and the Dead Sea fault from GPS measurements[END_REF][START_REF] Masson | Variable behavior of the Dead Sea Fault along the southern Araba segment from GPS measurements[END_REF]. The DSF is a boundary between Arabia plate to the east and the Sinai (Africa) plate to the west. GPS velocities are given with Arabia-fixed frame; fault segments and offsets are in Fig.3. Topography and bathymetry data is from SRTM 3-second-arc and GEBCO_08 grid

Fig. 2

 2 Fig. 2 Last-century instrumental seismicity (1900-2012, yellow circle) and historical seismicity (1365 B.C.-1900, red box) along the Dead Sea fault (see text for references therein). Focal mechanisms are from Harvard CMT. Note the last-century low-level background seismicity with respect to the significantly large historical earthquakes that illustrate the variability of earthquake activity and faulting behavior. Topography and bathymetry data is from GEBCO_08 grid

Fig. 3

 3 Fig. 3 Dead Sea fault trace from the detailed mapping of individual segments using aerial and satellite photographs combined with field investigations. The fault detailed mapping is from the results of the APAME Project (APAME 2007). Various late Holocene offsets from published works are indicated along with geological offsets (e.g., 107-km left-lateral offset of the erosion surface of late Jurassic units; see text for references). Topography data is from SRTM (3-arc-second)

Fig. 5

 5 Fig. 5 (a) Aerial photograph of the Jordan valley fault (red lines) exposing small pull-apart basins with left-lateral en echelon fault structures and stream channel offsets (at Ghor Katar), (b) detail of the Ghor Kabed pull-apart basin with high-resolution topography and fault branches affecting the Lisan lacustrine deposits (see also trench sites TK1 and TK2 in Ferry et al. 2007)

Fig. 6

 6 Fig. 6 Lebanon restraining bend with related fault branches and major earthquakes (stars) with M > 6.5 (Nemer et al. 2008). YF Yammouneh fault, SF Serghaya fault, RF Roum fault, RcF Rachaya fault, MY Missyaf fault, HB Hesbaya fault, HB Hula basin, CM Chouf mountains, and CF Chouf fault. Main large historical earthquakes are indicated (star). Topography data is from SRTM (3-arc-second)

Fig. 8

 8 Fig. 8 Northern Dead Sea fault (DSF) and its connection with the East Anatolian fault (EAF) with the LRB and Missyaf-El Ghab segments, Afrin fault branch, Karasu fault (KF), Karasu block (KB), Karatas-Osmaniye fault (KOF), and Cyprus Arc (CA). Large historical earthquakes and their extent along fault segments are marked by colored areas (Sbeinati et al., 2005). The Arabian, Anatolian, and African plates mark the triple junction. Large arrows are plate velocities from GPS results, and focal mechanisms are from Harvard CMT solutions. Topography data is from SRTM (3-arc-second)

Fig. 9

 9 Fig.9Magnitude/frequency relation for the instrumental period (A) log N = 3.02-0.73 M, and the historical distribution (B) follows log N = 14.8-2.73 M (N is the number of earthquakes of a given magnitude M or greater) for the Dead Sea fault area[START_REF] Elnashai | Earthquake hazard in Lebanon[END_REF]

Fig. 10

 10 Fig. 10 Late Pleistocene-Holocene slip rate along the Dead Sea fault from different fault segments (compiled by Matthieu Ferry; see alsoTable 1): Hacipasa (Aky€ uz et al. 2006; Altunel et al. 2009), Missyaf[START_REF] Meghraoui | Evidence for 830 years of seismic quiescence from palaeoseismology, archaeoseismology and historical seismicity along the Dead Sea fault in Syria, Earth Planet[END_REF][START_REF] Sbeinati | Timing of earthquake ruptures at the Al Harif Roman Aqueduct (Dead Sea fault, Syria) from archeoseismology and paleoseismology, Special volume "Archaeoseismology and paleoseismology[END_REF], Yammouneh[START_REF] Daeron | Constraints on the post-25-ka slip rate of the Yammouneh fault (Lebanon) using in situ cosmogenic Cl-36 dating of offset limestone-clast fans[END_REF][START_REF] Nemer | Coseismic growth of sedimentary basins along the Yammouneh strike-slip fault (Lebanon)[END_REF], Serghaya[START_REF] Gomez | Holocene faulting and earthquake recurrence along the Serghaya branch of the Dead Sea fault system in Syria and Lebanon[END_REF], Roum[START_REF] Nemer | Evidence of coseismic ruptures along the Roum fault (Lebanon): a possible source for the AD 1837 earthquake[END_REF], Jordan Gorge[START_REF] Marco | Late Holocene activity of the Dead Sea transform revealed in 3D paleoseismic trenches on the Jordan Gorge segment[END_REF], Jordan valley[START_REF] Ferry | A 48-kyr-long slip rate history for the Jordan Valley segment of the Dead Sea fault, Earth Planet[END_REF], and Wadi Araba(Klinger et al. 2000b;[START_REF] Niemi | Late Pleistocene and Holocene slip rate of the Northern Wadi Araba fault, Dead Sea Transform, Jordan[END_REF][START_REF] Beon | Early Holocene and Late Pleistocene slip rates of the southern Dead Sea fault determined from Be-10 cosmogenic dating of offset alluvial deposits[END_REF]

Table 1 )

 1 : Hacipasa (Aky€ uz et al. 2006; Altunel et al. 2009), Missyaf

Table 1

 1 Late Quaternary slip rate along the DSF

	Encyclopedia of Earthquake Engineering
	DOI 10.1007/978-3-642-36197-5_40-1
	# Springer-Verlag Berlin Heidelberg 2015
				Slip rate
	Fault segment	Method	Time frame	(mm/year)	References
	DSF	Geology	15-20 Myr	4-7	Quennell (1958)
	Wadi Araba	Geomorphology	Late Pliocene/early	3-7.5	Ginat et al. (1998)
			Pleistocene
	Wadi Araba	Geomorphology	141 kyr	5.4 AE 2.7	Le Beon et al. (2010)
				4.5 AE 0.9
				8.1 AE 2.9
	Northern Wadi Araba	Geomorphology	77-140 kyr	2-6	Klinger et al. (2000b)
	Northern Wadi Araba	Geomorphology	15 kyr	3.4-6	Niemi et al. (2001)
	Wadi Araba, Jordan	Geomorphology	50 kyr	10	Galli (1999)
	valley		18 kyr	10
	LRB (Yammouneh	Geomorphology	Pleistocene	5-10	Garfunkel et al. (1981)
	fault)
	LRB (Yammouneh	Geomorphology	25 kyr	3.8-6.4	Daeron et al. (2004)
	fault)
	Roum fault	Paleoseismic	Holocene	0.86-1.05	Nemer and Meghraoui
					(2006)
	DSTF	Seismicity	1,000-1,500 year	1.5-3.5	Garfunkel et al. (1981)
	Wadi Araba	Geomorphology	Pleistocene	4.7 AE 1.3	Niemi et al. (2001)
	Wadi Araba	Geomorphology	Pleistocene	2-6	Klinger et al. (2000b)
	Hula basin	Archeoseismic	2,000 year	>2.8 AE 0.2	Agnon (2014)
	Jordan valley	Paleoseismic	Holocene	2.5	Marco et al. (2005)
	Jordan valley	Paleoseismic	5,000 year	!3	Marco et al. (2005)
	Jordan valley	Geomorphology	47.5 kyr	4.7-5.1	Ferry et al. (2007)
	Amik basin	Geomorphology	Pleistocene	4.94 AE 0.13	Karabacak et al. (2010)
		Paleoseismic
	Amik basin	Archeoseismic	7 kyr	6	Altunel et al. (2009)
	Missyaf	Paleoseismic	2,000 year	6.9	Meghraoui et al. (2003)
		Archeoseismic
	Missyaf	Paleo-	3,500 year	4.9-6.3	Sbeinati et al. (2010)
		archeoseismic
	LRB (Serghaya fault)	Paleoseismic	Holocene	1.4 AE 0.2	Gomez et al. (2003)
	LRB	GPS	4 year	4.5	Gomez et al. (2007)
	Northern DSF	GPS	8 year	1.8-3.3	Alchalbi et al. (2010)
	DSF triple junction	GPS	3 year	1-2	Mahmoud et al. (2013)
	DSF	GPS	10 year	4.4 AE 0.3	Reilinger et al. (2006)
	Southern DSF	GPS		4.3-5.3	Al Tarazi et al. (2011)
	Southern DSF	GPS	6 year	4.9 AE 1.4	Le Béon et al. (2008)
	Araba valley	GPS	12 year	4.7 AE 0.7	Masson et al. (2015)
	Southern DSF	GPS	7 year	3.3 AE 0.4	Wdowinski et al. (2004)

Table 2

 2 Fault parameters of the Jordan valley and Missyaf fault segments with slip rate and time interval T i Encyclopedia of Earthquake Engineering along the DSFZ is not only strongly nonlinear but also that seismicity is clustered in time[START_REF] Apame ; Mustapha | Archeoseismology and paleoseismology for the protection of cultural heritage and archeological sites in the Middle East: the impact of large earthquakes on the archaeological sites Encyclopedia of Earthquake Engineering[END_REF][START_REF] Salamon | Patterns of seismic sequences in the Levantinterpretation of historical seismicity[END_REF][START_REF] Sbeinati | Timing of earthquake ruptures at the Al Harif Roman Aqueduct (Dead Sea fault, Syria) from archeoseismology and paleoseismology, Special volume "Archaeoseismology and paleoseismology[END_REF]).

		Length	Width		Seismic moment	Geodetic rate	Slip rate
	Fault	(km)	(km)	Slip (m)	(N.m.)	(mm/year)	(mm/year)	T i (year)
	Jordan	110	12	4.5 AE 1.5 2.0 10 20	5	4.9	T = 952 AE
	valley							115
	Missyaf	90	12	4.5 AE 0.3 1.6 10 20	3	5.9	T = 761 AE
	segment							150


Thurston's Compactification of Techmüller Space

Seddik Gmira

Introduction

In this paper, we give a construction of a notable compactification of the Teichmüller space. Using hyperbolic geometry, we define a system of coordinates called the Fenchel-Nilson coordinates on Teichmüller space of a closed Riemann surface. Moreover an embedding of the Teichmüller space will be given by means of geodesic lengths, which has its origin in a classical investigation of Fricke and Klein. At the last section we give a (useful) ideal boundary for the Teichmüller space of genus , which is due to W.Thurston.

Poincaré Metric and Hyperbolic Geometry

The Poincaré metric is an important natural metric on the unit disk For any , ∊ , we set = where is a rectifiable curve in connecting and . Using Schwarz lemma, every holomorphic mapping f : satisfies

Geodisics

For any two points , ∊ , a rectifiable closed arc , connecting these points is a geodesic, if

= =

1.1.1 Proposition For ∊ there exists a unique geodesic connecting these points. Morever it is a subarc of the cercle or the line segment which passes through and orthogonal to the boundary .

Proof

Since the Poincaré metric is invariant under the action by Aut( ), we may assume that = 0 and >0, via a transformation by an element ∊ ,

=

. Then for every closed arc connecting 0 and , we have Hence = (0, ) if and only if is coincident with the line segment .

Recall that, when ∊ Aut( ) is hyperbolic, has two distinct fixed points. The part in of the circle or the line segment which passes through theses points and is orthogonal to the boundary is called the axis of . The axis is invariant under the action by . So by the last proposition, every geodesic connecting any two points on the axis is a subarc on .

Remark

The Poincaré metric on the upper-half plane H, is defined by setting = (the pull-back of the Poincaré metric on the disk by the Möbus transformation ).

Hyperbolic Metric on a Riemann Surface

Let ℛ be a Riemann surface whose universal covering surface is biholomorphically equivalent to the unit disk . Consider a Fuchsian model of ℛ acting on with the projection : ℛ . Since the Poincaré metric is invariant under the action by , then we have a Riemannian metric on ℛ, ℛ .

For a given universal covering surface (ℛ , ℛ) of a Riemann surface ℛ, there is a universal group isomorphic to the fundamental group ℛ of ℛ: for any element ℛ , the action on ℛ is defined by:

ℛ =
In particular, determines the free homotopy class of . We say that covers the closed curve .

Proposition

Let ℛ be a Riemann surface with universal covering surface H, and be a Fuchsian model of ℛ acting on H. If the transformation is the subgroup of Γ consisting of all elements ∊ such that = . Then is a free group generated by two hyperbolic transformations, and / Now, let see the relationship between the complex structure of a triply domain ῼ and the hyperbolic structure of , the unique paints of ῼ, induced by the hyperbolic metric on ῼ.

Let , , be the boundary components which are simple closed geodesics of the pair of pants P. Let be a Fuchsian model of the domain ῼ acting on . Then is a free group generated by two hyperbolic transformations and . We assume that and cover , respectively.

Theorem

For any arbitrarily given triple of positive numbers, there exists a triply connected planar Riemann surface such that = , j = 1, 2, 3 Proof

Teichmüller'sTheorem

The Fricke space is a domain in ℝ and homeomorphic to ℝ , we denote by ℛ the point in corresponding to . Let : ℛ ℛ be a markingpreserving homeomorphism. For every ∊ , let be the unique closed geodesic in homotopy class of on ℛ , we can show that = is a system of decomposing curves on ℛ .

Proposition

Let be the Fuchsian model of ℛ represented by . Note that is the projection of the axis of an element of which covers for every i. Now, for every , and every let be the hyperbolic length as a function on the Fricke space . Proposition 2.1 implies that every geodesic length function is real analytic on .

We have a real analytic mapping : ℝ t Teichmüller's theorem stats that, the Fricke space is a simply connected domain.

Then, every has a single valued continuation branch on by the monodromy theorem, for every j.

For a fixed single-valued continuous branch of , the mapping : is a homeomorphism of onto ℝ ℝ . We call these coordinates Fenchel-Nilson coordinates. In fact the mapping is a diffeomorphism . And . Now we consider the problem of finding a set of simple closed geodesics on a Riemann surface of genus g , whose hyperbolic lengths determine the surface. In fact by constructing a set of simple closed geodesic whose length functions separate points of , we replace each in Fenchel-Nilson coordinates with geodesic length functions.

Consider a fixed Riemann surface ℛ of genus g , a decomposing curves on ℛ. Let be the path decompositions of ℛ corresponding to . For every ∊ denote by and the elements of having as boundary component of ( ). For every we set = .

Fix a simple closed geodesic in which intersects and let be the unique simple closed geodesic which is freely homotopic to the simple curve obtained from by applying the Dhen twist with respect to .

For every t ∊ , let ℛ be the corresponding point of . For every closed geodesic L on ℛ, we express as L the corresponding closed geodesic on ℛ , and denote by the hyperbolic length of L . Set

= , = , =
for every and set =

Theorem

The mapping is a proper embedding of into ℝ

To prove this theorem, fix a point of arbitrarily, and write

ℝ ℝ

Fix j, and for every s ℝ, define a point

We can show that the function is strictly convex and proper on ℛ. In particular, there is a unique value of at which satisfies the minimum .

Thurston's Compactification

Denote by the set consisting of all free homotopy classes of simples closed curves on a closed surface ℛ of genus g For any t in the Fricke space , let ℛ be the Riemann surface represented by an element t, and for every ∊ , let (t)( ) be the hyperbolic length ( ) of the unique geodesic in the homotopy class on ℛ corresponding to . Then we have a mapping : ℝ for every t ∊ , or equivently we have a mapping : ℝ . We regard ℝ as a topological space with the product topology.

Theorem(4.1) implies the following corollary

Now if is the isotopy class of in ℛ, then i( ) , the map extends to a map defined by the same symbol: ℝ ℝ , given by the formula ℝ into ℝ by setting

(λ )( )=
For every ∊ ℝ ∊ . It is clear that

ℝ

We know the following result .

Theorem

The subset of ℝ is homeomorphic to = ∊ ℝ

The set ℝ can be identified with the set ℳ of all equivalence classes under isotopy and Whitehead's operations of measured foliations . Hence we can write as ℳ = ℳ .

Measured Foliations

Let F be a foliation of ℛ, with isolated singularities. A transverse invariant measure is a measure that is defined on each arc transverse to the foliation and that satisfies the following invariant property:

If ℛ are two arcs that are transverse to the foliation F and that are isotopic through transverse arcs whose endpoints remain in the same leaf, then .

Let be a closed curve. We set , where are arcs of the curve mutually disjoint and transverse to F, and where the supermum is taken over all sums of this type. In other words, is the total variation of the y coordinate along the curve in an atlas, that defines the measured foliation. This quantity is also denoted by Thurston as .

A measured foliation is, by definition, a pair of foliation F on ℛ with such isolated singularities and a transversal measure for F.

When

ℝ is defined with a measured foliation , we have , where

. From here on is written as even for a general ℳ

Let be an element of , and I ∊ , which is an invariant isotopy.

Thus we have a function

ℳ ℝ such that
The following diagram is commutative

ℝ ℳ ℝ When ∊ ℝ ∊
is defined with a measured foliation , we have

∊ Where ∊ .
From here on, is written as ∊ even for a general p= ∊ ℳ . As the mapping ℝ ℝ is injective, ℝ ℳ is also an injection.

A typical example of a measured foliation on ℛ, when ℛ is equipped with a complex structure along every leaf of which a prescribed non-zero holomorphic quadratic differential is positive, equipped with the canonical transversal measure .

On the other hand, Hubbard and Masur showed that, for any given complex structure on ℛ, ℳ can be identified with the space of holomorphic quadratic differential on ℛ (with respect to the given complex structure) which in turn is known to be homeomorphic to ℝ .

Proposition

The image is disjoint from ℳ in ℝ

Proof

For every t ∊ , the image ∊ is bounded from below by a constant, depending on t. In fact, for every , take a transversal arc such that By Poincaré's recurrence theorem, there is a sub-arc of a leaf which stars and ends at . Hence we have a simple closed curve L such that which implies the assertion.

Theorem

For every system = of decomposing curves of ℛ, there is a natural homeomorphism U ℳ

Where U = ∊ ℳ ∊ .

Proof

For every ∊ we can construct a measured foliation such that is transversal to , for every and that = , , or equivalently = , , where is the geodesic on the marked Riemann surface represented by t. We set .

It is known that the mapping is a homeomorphism onto U .

Theorem

The subset ℳ of ℝ with the relative topology is a compact manifold with boundary. Moreover ℳ is homeomorphic to the real -dimensional closed ball ∊ ℝ and the boundary is coincident with ℳ , which is homeomorphic to .

Proof

Fix ℳ such that ∊ arbitrarily. Then there is a system = of decomposing curves of ℛ such that , j=1,….3g-3

As in §4,the system allows to construct a family of simple closed curves , which gives an embedding of into ℝ .

For every let = ∊ , and W= .

Clearly, is open in , and . As the mapping is injective on , we define a mapping of W into W as follows.

We set = ,

For every , we put = By using a fundamental inequality:

x , ,

We can show that this mapping is a homeomorphism onto its image, and hence it gives local coordinates in a neighborhood of .

The importance of this compactification may be shown by the following result

  , a, b, c, d ∊ ℝ, ad -bc = 1 is hyperbolic, and is the closed geodesic on ℛ corresponding to , surface ℛ which admits the hyperbolic metric, cutted by a family of mutually disjoint simple closed geodesics. Let Р be a relatively compact connected component of the resulting union of subsurfaces. If contains no more simple closed geodesic of ℛ, then should be triply connected: homeomorphic to a planar region: Р Such a surface can be considered as one of the smallest pieces for rebuilding ℛWe call a relatively compact subsurface Р of ℛ a pair of pants of ℛ if Р is triply connected and if every connected component of the relative boundary of Р in ℛ is a simple closed geodesic.Fix a pair of pants arbitrarily. Let Γ be a Fuchsian model of ℛ acting on the disk , and ℛ = ℛ be the projection. Let be a connected component of . If

  Let = be an arbitrary system of decomposing curves on a closed Riemann surface ℛ of genus , and let Ƥ = be the pants decomposition of ℛ corresponding to . Then and satisfy and Proof Cut ℛ along an element ∊ . If is the number of connected components of ℛ -, and is the sum of genera of all connected components of ℛ -. Then -= and ℛhas two boundary components. We can see by induction, with an added cut along a new element of , the number of boundary components incre ases by two, and the sum of genera of all connected components minus the number of connected components decreases by one. Hence and 4 Geodesic length functions Fix a point ℛ in the Teichmüller space: ℛ ∊ , and let = be a decomposing curves on ℛ. For every point in the Frike space:

Corollary

The mapping ℝ is a proper embedding Moreover, this mapping remains an embedding, even we take the associated projective space, the quotient ℝ = ℝ ℝ with a projection

ℝ ℝ

where P ℝ is given the quotient topology. In fact, letting P be the composed mapping of with the projection of ℝ into the projective space ℝ , we have the following theorem

Theorem

The mapping : ℝ is an embedding

There is a natural mapping of into ℝ , which is defined by using the geometric intersection number of curves.

For any , ∊ , the geometric intersection number i( ) of and is by definition the infimum of the number of intersection points of and , where moves in the free homotopy class of for each k. In particular i( )= i( ) and i( )=0 for every ∊ S.

Define a mapping : ℝby setting ( )(.) = i( ), ∊ , where we denote simply by 0.

Proposition

The mapping ℝ is injective

Proof

If i( ) 0, it suffices to take .

If i( )=0, there exist simples closed curves ∊ ' ∊ such that '= . By cutting the surface ℛ along , we obtain a surface N containing ' in its interior.

As ' is not isotopic to , there exists in N a curve ' that cannot be separated from ' in N. we take with card( )=1.

If ' separate N into and , we take = , where is an arc representing a nontrivial element of ( ); this is possible because the genus of ℛ is .

If is the isotopy class of in ℛ, then by the following proposition 5.4, we have

Corollary

Every orientation-preserving homeomorphism of ℛ onto itself induces a homeomorphism of = ℳ onto itself.

Proof

Every orientation-preserving homeomorphism of ℛ onto itself induces a natural action of onto itself, and hence induces a continuous self-mapping Ф of ℝ .

Here, and ℳ are clearly invariant under the self mapping. The inverse of is obtained from .


Camille Cany

Christine Mansilla
email: christine.mansilla@cea.fr

Gilles Mathonnière

Pascal Da Costa

Nuclear power: what optimal contribution to the French electric power mix?

Keywords: Nuclear Power generation, Power System Economics, Power System Reliability, Renewable Energy Sources I

In the French context of increasing renewable penetration and significant nuclear power, the optimal contribution of this energy source is discussed from two viewpoints. On the one hand, from the social planner viewpoint, the nuclear optimum contribution is the one that minimizes the overall electric price, whatever the resulting load factor. The use of screening curves, often implemented to design the optimal power mix is questioned, being highly sensitive to the assumptions. On the other hand, from the plant operator viewpoint, the nuclear power plants need to amortize the capital expenses, hence achieve the longest operating time. With a view to make the two viewpoints meet, we propose to operate nuclear power plants as baseloads and consider modulation through the power use, i.e. supply electricity to the electric system when requested and use the remaining power to produce other valuable products, such as heat or hydrogen.

INTRODUCTION

The general 3X20 European directive proposes renewable penetration goals [1]. In France, 27% of the electricity is to be produced by renewable resources by 2020 [START_REF]de l'Energie, du Développement Durable et de la Mer[END_REF] and this share will be continuously growing up to 2050. In 2013, the share of renewable power already reached 18% of the domestic production, namely approximately 100 TWh [START_REF] Rte | Bilan prévisionnel de l'équilibre offre-demande d'électricité en France -édition 2014[END_REF]. Among these resources, some are not dispatchable, which triggers challenges to maintain the reliability target level of the power system, both in the short and long term [START_REF] Gross | The costs and impacts of intermittency: an assessment of the evidence on the costs and impacts of intermittent generation on the British electricity network[END_REF], [START_REF] Hart | The potential of intermittent renewables to meet electric power demand: current methods and emerging analytical techniques[END_REF]. Wind and solar are expected to contribute to about 10% of the French electricity production in 2020 [START_REF] Rte | Bilan prévisionnel de l'équilibre offre-demande d'électricité en France -édition 2014[END_REF], [START_REF] Ancre | Scénarios de l'ANCRE pour la transition énergétique[END_REF], and according to voluntaristic scenarios they could contribute to over 50% of the total electricity production by 2050 [START_REF] Ademe | L'exercice de prospective de l'ADEME : Vision 2030-2050[END_REF]. The recent European agreement appears voluntaristic, by announcing a binding target of at least 27% of renewable energy used at the European level by 2030, and will promote such a development [START_REF]Energy and climate goals for 2030[END_REF]. The French power system is currently characterized by a high nuclear penetration: it supplied 82% of the French domestic consumption and 73% of the total demand (including exportations) in 2013 [START_REF] Rte | Bilan prévisionnel de l'équilibre offre-demande d'électricité en France -édition 2014[END_REF]. As a matter of fact, nuclear power is meant to remain a significant contributor to the French power system in the medium term, as a low-carbon power source (the current French government projects aim at reducing the nuclear share to 50% from 2025) [START_REF] Nationale | Projet de loi relatif à la transition énergétique pour la croissance verte[END_REF].

In such a context, one may wonder what would be the optimal contribution of nuclear power to the electric power mix. This paper proposes to provide some insights about this issue.

Two viewpoints are discussed hereafter. On the one hand, from the electric power mix viewpoint, the optimum contribution of nuclear power is the one that minimizes the overall power price for the consumer, whatever the resulting load factor. On the other hand, from the plant operator viewpoint, the nuclear power plants need to amortize the capital expenses, hence achieve the longest operating time. The consequences of these approaches are discussed in what follows and a proposal is done to target making both views meet.

II. THE ELECTRIC SYSTEM VIEWPOINT

A. Designing the optimal power mix: The screening curve methodology

The screening curve methodology is a usual methodology to design prospective optimal mix from the social welfare viewpoint. Indeed, the aim is to target the lowest power production cost for the consumer. This methodology consists in plotting the annual cost of the installed capacity according to the utilization time of the considered technology (cf. Fig. 1). By plotting the curves for each of the available technologies, the optimal annual operating time is obtained for each resource type. On the example given by Fig. 1, nuclear would be operated as a base load: it would supply the demand occurring for durations longer than 7900 hours per year. On the contrary, gas would be used for peak demand (durations shorter than 2750 hours per year). The second step is to copy the obtained operating time on residual load duration curves, to assess the corresponding optimal installed power, for each power plant type.

A load duration curve represents the sorted hourly load of one year, starting with the highest load hour. The residual load duration curve (cf. Fig. 2) is obtained by withdrawing wind and solar production to the total production on an hourly time step, thus considering that they have a dispatch priority, and then ordering the residual demand from the highest to the lowest value. Besides the screening curves by themselves, residual load duration curves are also used to provide insights about existing power mix management, i.e. how installed capacity operation factor may be affected by the introduction of additional capacity with a dispatch priority. Residual load duration curves that were constructed for this study (cf. Fig. 2) are based on historical wind and solar production hourly profiles (between 2010 and 2013), from RTE data (the French Transmission System Operator) [START_REF]RTE database[END_REF]. Assuming similar hourly variation shapes, wind and solar production profiles were extrapolated for three renewable penetration rates, as represented in Fig. 2. These rates correspond to scenarios developed by the ANCRE (Alliance Nationale de Coordination de la Recherche pour l'Energie, the French National Alliance for Energy Research Cooperation) for 2030 (16.5%) and 2050 (30%) [START_REF] Ancre | Scénarios de l'ANCRE pour la transition énergétique[END_REF], and by the ADEME (Agence de l'Environnement et de la Maîtrise de l'Energie, the French Environment and Energy Management Agency) for 2050 (50%) [START_REF] Ademe | L'exercice de prospective de l'ADEME : Vision 2030-2050[END_REF]. Even if wind and solar penetrations are aggregated in the displayed rates, separate assumptions were considered and the corresponding production profiles were treated separately in the calculations.

It should also be noted that the considered demand, to which wind and solar production are withdrawn, actually includes the exportations. Thus, exportations are assumed exogenous. Additional exportations in case of excess capacities for certain hours may be of interest, if the interconnection capacities allow it.

B. Sensitivity analysis of the optimal mix to the selected assumptions Thus, the screening curve methodology seems to be a very straightforward way to design an optimal power mix from the electric system, or social planner, viewpoint. However, we will see in what follows that this method is questionable due to its very high sensitivity to the retained assumptions.

We chose to illustrate this sensitivity through the nuclear share, focus of this paper, and two parameters:

• The discount rate: indeed, this assumption proves critical for very capex-intensive technologies, such as nuclear; • The carbon price: it is obviously a key parameter to increase the economic competitiveness of low-carbon technologies. As a matter of fact, the European Commission is considering introducing a market stability reserve for Phase 4 of the EU ETS in 2021 [START_REF] Gregorin | Reform of the EU emissions trading system[END_REF].

The number of hours for which nuclear becomes the lowest-cost technology compared to coal and gas (e.g. 7900 hours for the case presented in Fig. 1) is provided in Table 1, according to the discount rate and the carbon price assumptions. Cost assumptions were taken from [START_REF] Salvadores | Projected costs of generating electricity[END_REF]. As a result, the nuclear power that would be installed from the electric system viewpoint would be much contrasted according to the retained assumptions. To illustrate this statement, we calculated the sensitivity of the requested nuclear power for the ANCRE scenario for 2030, corresponding to a 16.5% renewable penetration in France (wind plus solar). The reference case is chosen to be 8% discount rate and no carbon price. The results are presented in Table 2. Besides the high sensitivity of the methodology we presented, this approach limits the nuclear use to supplying power to the electric system. As we will see in section IV, other operating modes may widen the scope.

III. THE PLANT OPERATOR VIEWPOINT

The plant operator viewpoint is somewhat different. The operating time is actually a target. The nuclear power plants need to amortize the capital expenses, hence achieve the longest operating time. This statement may appear straightforward, but it is all the more important that nuclear power plants are capex-intensive.

Giving dispatch priority to variable renewable energy results in lowering the operating time of already existing nuclear reactors, in the short term. We assessed this impact according to the nuclear power capacity and the renewable installed capacity, through the use of residual load curves. The renewable penetration assumptions were derived from the scenarios presented in section II.A [6]- [START_REF] Ademe | L'exercice de prospective de l'ADEME : Vision 2030-2050[END_REF]. Two nuclear installed capacity values have been considered: i/ the installed capacity needed to supply 50% of the annual electricity production, in line with the French Government policy, and ii/ an in-between value of 65% (as a compromise between the current contribution of nuclear power in the French electricity mix and the prospective 50% value). Results in terms of nuclear load factors are presented in Table 3. By considering the French current unit capability factor: 78% [START_REF] Elecnuc | Nuclear power plants in the world[END_REF], and the French regulated tariff for nuclear energy: €42/MWh (i.e. tariff for power suppliers that want to buy nuclear power in order to sell it to consumers; this tariff was implemented in 2010 to smooth the advantage of the historical utility, and make it possible for the other utilities to compete), the annual revenue losses can be estimated. Using the above assumptions, they are calculated as the energy losses (i.e. energy production difference between the resulting load factor from Table III and the unit capability factor), multiplied by the power price. The figures are presented in Table 4. In Table 5, the revenue losses are estimated as a share of the maximum foreseeable revenue, according to the unit capability factor. These figures highlight that reduced load factors are not economically viable in the long-run. However, significant renewable power penetration does not necessarily mean reducing the nuclear share. As a matter of fact, to achieve a low-carbon power mix, low-carbon power sources should be complementarily promoted. Thus, a possible way would be not reducing the nuclear load factor but finding new outlets. This is what is discussed in next section.

IV. NUCLEAR MODULATION: TOWARDS A VIEWPOINT

MERGING

As a matter of fact, a gap can result from the difference between the installed nuclear capacity and what is considered optimal: either from the electric system viewpoint (with all the attached uncertainties that were pointed out in section II), or from the operator viewpoint, to reach the maximum load factor. Figure 3 provides an illustration. Nuclear power could participate to system balancing thanks to characteristics compatible with power modulation [START_REF] Bruynooghe | Load following operating mode at nuclear power plants and incidence on operation and maintenance costs. Compatibility with wind power variability[END_REF]- [START_REF] Choho | Major innovation in PWR load follow operations by AREVA[END_REF]. Indeed, nuclear modulation seems to be achievable, especially in the case of France, since a large production variation could be reached only by small increments in each power plant. This would remain true as long as installed nuclear power is large enough, in terms of contribution to the total electricity mix. Further R&D works are still needed though, to check if implementing higher modulation needs appears technically and economically feasible. However, instead of charging power modulation, which would mean charging energy losses, it would be worth considering taking advantage from the available energy to produce valuable services and products [START_REF] Ruth | Nuclear-renewable hybrid energy systems: opportunities, interconnections and needs[END_REF]. Indeed, when the load factor becomes too low, the nuclear economic equation remains unsolved in the case of a new plant to be built. The share of capital is too large to allow an efficient use with such low load factors. The question appears more complex if we examine the case of already existing reactors. This load factor is in the range for which the competitiveness of nuclear begins to decline when facing gas combined cycles and possibly wind power. In fact, the decision of maintaining nuclear power plants with low load factors would be highly linked with payments for grid services (i.e. reduction of system costs). Future research should address this question in details. Thus, we propose to consider nuclear power modulation through the power use. In this case, the nuclear power plant would be operated as a baseload and electricity would be supplied to the electric system when requested. For the remaining time, instead of reducing the plant load, the output could be used to produce other vectors, such as heat or hydrogen. Hydrogen is also a chemical product that has very numerous outlets: ammonia production, refining activities, synthetic fuel production, and is a means to enhance connections between energy networks (e.g. power and gas, through power-to-gas). Finally, hydrogen also makes it possible to integrate high shares of low-carbon energy into a given mix by avoiding both to reduce baseload power such as nuclear and to curtail non-dispatchable renewable energy [START_REF] Caumon | Flexible hydrogen production implementation in the French power system: expected impacts at the French and European levels[END_REF].

Detailed business models remain to be developed in this field though. Indeed, systems comprising nuclear power plant together with a hydrogen process may propose new energy services such as hydrogen and power supply. What is more, implementing high temperature steam electrolysis (HTSE) process [START_REF] Mougin | Stack performances in High temperature steam electrolysis and co-electrolysis[END_REF] in the longer term can make it possible to supply power as a baseload (thanks to the nuclear plant) and for peak demand (thanks to reversible HTSE operation). During high demand peaks, such a new concept would allow to use the power from the nuclear power plant, but also from the reversible electrolyser (thus acting as an energy storage), doubling the instantaneous power of the nuclear plant. This will be the topic of future works.

By promoting new concepts, potentially more economical, R&D is needed to improve the business cases. First studies demonstrated that, to reach a low-carbon power mix, both nuclear and renewables are needed, in a stronglyinterconnected energy system perspective [START_REF] Caumon | Flexible hydrogen production implementation in the French power system: expected impacts at the French and European levels[END_REF].

V. CONCLUSION AND PERSPECTIVES

In the French current electricity mix which is characterized by a high share of nuclear power, and in the context of current design of energy transition policies, the optimal nuclear share is a central issue.

This paper investigated the screening curve methodology, which is usually implemented to calculate prospective optimal power mixes. We highlighted that defining the optimal nuclear installed capacity following this methodology entails uncertainties. Following the electric system viewpoint, the target is the lowest electricity production cost, not the plant amortization. Thus, it may lead to reduced load factors.

From the operator viewpoint, the capital expenses must be amortized, hence the maximum load factor should be aimed at. We assessed that, according to installed renewable and nuclear power in the mix, significant revenue losses may result from both high penetration rates of renewable and nuclear.

Nevertheless, what should be aimed at is the lowest carbon-content. There should not be harsh competition between low-carbon power sources. On the contrary, complementarities, and even synergies, should be sought for.

Despite the fact that nuclear modulation seems to be achievable, especially in the case of France since a large production variation could be reached only by small increments in each power plant, using the available energy seems more profitable at first sight. Conversely, even if excess renewable energy could be curtailed, taking advantage of the excess power seems more fruitful. Thus, we proposed to consider nuclear power use modulation rather than nuclear power production modulation. In this case, available power is converted into valuable services to the electric system and can also be converted into valuable industrial products. In this respect, hydrogen seems especially worthwhile, given its multiple outlets and future specific position within the energy system.

To reach a low-carbon power mix, both nuclear and renewables are needed, in a strongly-interconnected energy system perspective. In such a synergistic power system, both nuclear power plant flexibility and nuclear plant operation time extension should be examined, also by considering novel uses.

New economic tools have to be built to address these important questions. However, first of all, the physical and safety constraints limiting nuclear plants power ramps needs to be investigated. In this paper, it is supposed that a perfect load follow would be achievable. This is yet to be verified and a first task is to improve our knowledge in this field. Works are underway in the research organizations.

Figure 1 .

 1 Figure 1. Screening curve example (cost data from [10], 8% discount rate, no carbon price), own calculus

Figure 2 .

 2 Figure 2. Residual load duration curves, own calculus

Figure 3 .

 3 Figure 3. Example of assessment of the nuclear power modulation capacity (P opt is assessed to reach a 78% load factor), own calculus

TABLE I

 I

	.	MINIMUM OPERATING TIME FOR NUCLEAR TO BE THE
		CHEAPEST TECHNOLOGY
			Carbon price
			$0 /tonCO2	$30 /tonCO2
		5%	5000 h	3000 h
	Discount rate	8%	8000 h	5000 h
		10%	Never competitive	6000 h

TABLE II

 II

	.	OPTIMAL REQUESTED NUCLEAR POWER (% VARIATION
	COMPARED TO REF) FROM THE ELECTRIC SYSTEM VIEWPOINT -16.5% WIND
		AND SOLAR PENETRATION
			Carbon price
			$0 /tonCO2	$30 /tonCO2
		5%	+ 19%	+ 42%
	Discount rate	8%	Reference	+ 19%
		10%	-100%	+ 13%

TABLE III

 III

	.	RESULTING NUCLEAR LOAD FACTOR ACCORDING TO THE
	RENEWABLE AND NUCLEAR INSTALLED CAPACITIES IN THE FRENCH
		ELECTRICITY MIX
			% Nuclear
			50	65
		16.5	74%	70%
	% Renewable	30	69%	61%
		50	51%	43%

TABLE IV

 IV

	.	ANNUAL REVENUE LOSSES ACCORDING TO THE RENEWABLE
	AND NUCLEAR INSTALLED CAPACITIES IN THE FRENCH ELECTRICITY MIX
		(M€)
			% Nuclear
			50	65
		16.5	660	1550
	% Renewable	30	1430	3390
		50	4150	6960
	TABLE V.	ANNUAL REVENUE LOSSES ACCORDING TO THE RENEWABLE
	AND NUCLEAR INSTALLED CAPACITIES IN THE FRENCH ELECTRICITY MIX:
	SHARE OF THE MAXIMUM FORESEEABLE REVENUE (%)
			% Nuclear
			50	65
		16.5	5	10
	% Renewable	30	12	22
		50	34	45

ACKNOWLEDGMENT

This work was carried out in the framework of a PhD thesis. The authors want to thank J. C. Bocquet, Head of the Laboratoire de Génie Industriel, and J. G. Devezeaux, Head of the Institute for techno-economics of energy systems (I-tésé) for the fruitful discussions.