Sensitivity analysis on relations between earthquake source rupture parameters and far field tsunami waves: Case studies in the Eastern Mediterranean region

We present several sensitivity tests, that were applied to exhibit the effects of earthquake source rupture characteristics on amplitudes, frequency contents and arrival times of earthquake generated tsunami waves in the far field, as case studies in the eastern Mediterranean.

Turkish Journal of Earth Sciences (Turkish J Earth Sci.), Vol 19, 2010, pp 313–349 Copyright ©TÜBİTAK doi:10.3906/yer-0902-8 First published online 24 August 2009 Sensitivity Analysis on Relations Between Earthquake Source Rupture Parameters and Far-Field Tsunami Waves: Case Studies in the Eastern Mediterranean Region SEDA YOLSAL & TUNCAY TAYMAZ Department of Geophysical Engineering, Seismology Section, the Faculty of Mines, İstanbul Technical University, Maslak, TR−34469 İstanbul, Turkey (E-mail: yolsalse@itu.edu.tr) Received 22 January 2009; revised typescript receipt 23 August 2009; accepted 24 August 2009 Abstract: We present several sensitivity tests, that were applied to exhibit the effects of earthquake source rupture characteristics on amplitudes, frequency contents and arrival times of earthquake generated tsunami waves in the far field, as case studies in the eastern Mediterranean The investigated earthquake parameters are principally epicentral location, focal mechanism parameters (strike, dip and rake angles), faulting area dimensions, maximum displacement and focal (centroid) depth We have implemented a numerical method of TUNAMI-N2 based on non-linear shallowwater theory to obtain synthetic water surface fluctuations at selected pseudo tide gauge locations in the eastern Mediterranean It has been observed that the most important source parameters that effect tsunami wave characteristics in the far field are: [1] magnitude and seismic moment (Mo= μ × A × D) of earthquake that is a measure of the energy release radiated at the centroid depth We have observed that wave amplitudes and shapes change considerably with variation of magnitude and seismic moment since tsunami waves develop in direct proportional relation to them; [2] another parameter is the accurate estimation of tsunamigenic earthquake epicentre Variation of the earthquake location does not significantly affect the initial tsunami wave heights, but final tsunami wave characteristics and their arrival times have been slightly changed due to the variation of distance between the epicentre and coastal plains along the path Especially, wave spreading causes tsunami waves to decrease in amplitude as they move away from earthquake source; [3] variation in focal mechanism solutions modify the tsunami wave propagation directions, wave amplitudes, shapes and arrival times of tsunami waves observed at the coastal plains; [4] in addition, due to the linearity between the amount of vertical co-seismic displacement and initial tsunami wave, very different tsunami amplitudes were obtained at each pseudo tide gauge stations in case of the variation in maximum displacement; [5] details of local bathymetry (e.g., extended sedimentary shelf area) and the sea bottom irregularities (e.g., sea-mounts, volcanoes, accretionary prisms, trenches, pressure ridges) clearly have crucial effects on tsunami wave characteristics in the far field Historical records confirm that the eastern Mediterranean region is at risk from tsunamigenic sources located on the Hellenic-Cyprus arcs Thus, higher resolution near-shore bathymetry data as well as a detailed study of potential tsunami sources in segments of subduction zones are necessary to verify our simulation results Key Words: bathymetry, Dalaman-Fethiye-Rhodes trough, earthquake source parameters, eastern Mediterranean, sensitivity, tsunami, Turkey Deprem Kaynak Parametreleri, Kırılma (Yırtılma) Özellikleri ve Uzak Alan Tsunami Dalgaları Arasındaki likiler iỗin Duyarllk Analizleri: Dou Akdeniz Bửlgesinden ệrnek ầalmalar ệzet: Bu ỗalmada, deprem kaynak (yrtlma) parametrelerinin uzak alandaki tsunami dalga genlik, frekans iỗerii ve kylara olan var zamanlarna olan etkilerini gửstermek iỗin uygulanan duyarllk analizlerinin sonuỗlar gửsterilmitir ncelenen deprem parametreleri, deprem lokasyonu, kaynak mekanizmas (dorultu, dalm ve kayma aỗlar), faylanan alanın boyutları, maksimum yerdeğiştirme miktarı ve odak derinliğidir Doğu Akdeniz bửlgesi kylarnda seỗilen hayali ak ửlỗỹm (tide-gauge) noktalarnda oluacak yapay su yỹzeyi yỹksekliklerini elde edebilmek iỗin, dorusal olmayan s su teorisine dayal olan TUNAMI-N2 matematiksel simỹlasyon program kullanlmtr Sonuỗ olarak, 313 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES uzak alanda tsunami dalga özelliklerini etkileyen en önemli kaynak parametrelerinin; [1] kaynakta boşalan enerjinin miktarını gưsteren sismik moment (Mo= μ × A × D) ile depremin büklüğü olduğu gưrülmüştür Tsunami dalgalarının genlik ve şekilleri bu parametrelere bağlı olarak belirgin şekilde değişim göstermektedir; [2] bir diğer parametre deprem merkezüstünün (episantırının) doğru olarak belirlenebilmesidir Duyarllk analizi sonuỗlarna gửre, deprem merkezỹstỹnỹn deimesi her ne kadar balangỗ tsunami dalga yỹksekliini deitirmese de, sonuỗ tsunami dalga özelliklerini ve bu dalgaların kıyılara varış zamanlarını etkilemektedir Özellikle dalganın deniz iỗerisinde deprem kaynandan uzaa doru ilerlemesi ile dalga genliklerinde azalma meydana gelmektedir; [3] odak mekanizmas ỗửzỹmỹnỹn deimesi tsunami dalgalarnn yayılma doğrultularını, şekil, genlik ve dalgaların kıyılara ulaşma sürelerini değiştirmektedir; [4] dỹey kosismik yerdeitirme ve balangỗ tsunami dalgas arasndaki dorusal ilikiden dolay, seỗilen ửlỗỹm noktalarnda hesaplanan yapay tsunami dalgalarnn ửzellikleri bu parametrenin değişmesinden etkilenmektedir; [5] ayrıca, deprem kaynağı ile kıyılar arasında yer alan adalar, deniz dağları, yığışım prizması ve hendekler gibi sỹreksizlik yaplarnn varl, ky batimetrisi (ửrn; deniz iỗerisine yaylm sedimanter kıta alanı) ve kıyı şeklinin de tsunami dalga genliklerini etkiledikleri dalga simỹlasyonlarnda aỗkỗa gửrỹlmektedir Tarihsel kaytlar dou Akdeniz bửlgesinde Hellenik-Kıbrıs yayları boyunca tsunami riskini vurgulamaktadır Bu yüzden dalma-batma zonlarındaki potansiyel tsunami kaynaklarnn yỹksek ỗửzỹnỹrlỹklỹ ky batimetri verisi ile detayl olarak ỗallmas simỹlasyon sonuỗlarmz dorulamak iỗin gereklidir Anahtar Sửzcỹkler: batimetri, Dalaman-Fethiye ỗukurluu, Dou Akdeniz, duyarllk, odak parametreleri, tsunami, Tỹrkiye Introduction It has been widely observed that tsunamis can lead to significant loss to coastal populations both near the earthquake source and at distant locations (Ammon et al 2005; Bilham 2008; Lay et al 2005; Liu et al 2005; Gica et al 2007) Tsunami waves known as shallow water waves with long wave-lengths and periods are generally produced by earthquakes, underwater slumps or volcanic activities Their generation and propagation in oceanic areas are described by the linearized theory of long-period gravity waves (Shuto et al 1990; Pelinovsky et al 2001; Todorovska & Trifunac 2001; Yalỗner et al 2003, 2004; Zahibo et al 2003; Salamon et al 2007; Yalỗner & Pelinovsky 2007; Yolsal et al 2007a, b; Lorito et al 2008; Shaw et al 2008; Yolsal 2008) Many nations have been severely affected by tectonic activities world-wide in the past For example, 1755 Lisbon, 1946 Aleutian, 1960 Chilean, 1998 Papua New Guinea and 2004 Sumatra-Andaman are the most illustrative examples of catastrophic earthquake induced tsunamis of the world (Okal 1999; Heinrich et al 2000; Lay et al 2005; Ni et al 2005; Stein & Okal 2005; Taymaz et al 2005; Bilham 2008; Konca et al 2008; Barkan et al 2009) These earthquakes are named tsunamigenic earthquakes, and are characterized by shallow focal depths with fault dislocations greater than several metres, fault surfaces smaller than that of normal earthquakes, long source time functions and slow-smooth 314 ruptures (Kanamori 1972; Fukao 1979; Kikuchi & Kanamori 1995; Polet & Kanamori 2000; Ammon et al 2006) Many destructive tsunamis also originate from submarine landslides and volcanic eruptions which generally have more complex natures and physical descriptions than those of tectonic earthquakes In particular, submarine landslides affecting weak sediments can create destructive tsunamis with very large wave amplitudes at coastal plains, and they typically can cause significant tsunami run-up heights in areas proximal to the source while the earthquake induced tsunamis are more widely distributed (Matsuyama et al 1999) Volcanic eruptions of 3500 yr BP Santorini and 1883 Krakatoa can be given as manifested examples depicting high amplitude tsunami waves in historical times (see Bond & Sparks 1976; Okal 1988; Cita & Aloisi 2000; Minoura et al 2000 for details) Many alternative stochastic numerical methods such as the Cornell COMCOT model (Liu et al 1994, 1995; Wang & Liu 2005, 2006), the MOST model (Titov & Synolakis 1998), and TUNAMI-N2 model (Imamura 1995; Imamura et al 2006) have been developed to simulate tsunami wave propagations and to predict tsunami wave heights and travel-times at selected pseudo tide gauge locations These methods require reliable bathymetry and source mechanism parameters as input data for tsunami simulations Accordingly, the geometry and evolution of potential source regions S YOLSAL & T TAYMAZ and source rupture processes along main active fault zones should be better known and defined in detail Moreover, the importance of high resolution bathymetry, dispersion, non-linearity, bottom friction, tsunami wave directivity and tsunami impacts have been highlighted by several studies (Heinrich et al 1998; Fujima 2001; Ortiz et al 2001; Horillo et al 2006; Chatenoux & Peduzzi 2007; Ioualalen et al 2007; Yolsal et al 2007a; Bilham 2008; Shaw et al 2008; Yolsal 2008) However, one of the most significant uncertainties in tsunami wave height prediction comes from the difficulty of accurate estimation of source parameters (e.g., Synolakis et al 1997; Gica et al 2007) Thus, sensitivity analyses of earthquake source parameters become essential to check the variation of tsunami wave characteristics in the near and far fields (Okal 1988; Satake & Tanioka 1995; Geist 1999, 2005; Titov et al 1999; Piatanesi & Tinti 2002; Pires & Miranda 2003; Yalỗner et al 2003, 2004; Weisz & Winter 2005; Dao & Tkalich 2007; Gica et al 2007, 2008; Ioualalen 2007; Lorito et al 2008; Okal & Synolakis 2008; Shaw et al 2008; Yolsal 2008; Yolsal et al 2008a, b) In this study, we present the effects of the variation in earthquake location, focal mechanism parameters (strike (φ), dip (δ) and rake (λ) angles), focal depth (h), fault area (A) and amount of the maximum displacement (Dmax) on tsunami propagation, synthetic tsunami wave amplitudes and theoretical arrival times of initial tsunami waves at the coastal plains in the far field We choose the eastern Mediterranean Sea region as a target area since several studies of historical documents revealed repeated tsunami impact on the region and its environs, together with geomorphological, sedimentological, geochemical, geological and geophysical analyses (Fokaefs & Papadopoulos 2006; Scheffers & Scheffers 2007) Due to active tectonic motions between the Arabian, African and Eurasian plates, this region has a very complex tectonic regime manifested by intense seismic activity and destructive earthquakes (Figures & 2) Especially, subduction-related shallow tsunamigenic earthquakes (h < ~40 km) concentrate along the Hellenic arc system and a few historic, subductiontype earthquakes occurred at various segments of the subduction zone (Taymaz 1990; Taymaz et al 1990, 1991, 2004, 2007a, b; Yolsal & Taymaz 2004, 2005, 2006; Bohnhoff et al 2005; Yolsal et al 2007a, b; Shaw et al 2008; Yolsal 2008; Reilinger et al 2009) Yolsal et al (2007a, b) and Yolsal (2008) classified the historical earthquakes and associated tsunamis identified from verified catalogues (e.g., Ambraseys et al 1994; Guidoboni et al 1994; Ambraseys & Melville 1995; Papadopoulos 2001; Guidoboni & Comastri 2005a, b; Papadopoulos & Fokaefs 2005; Sbeinati et al 2005; Papadopoulos et al 2007), and synthesized the historical tsunamis and tsunamiwave propagations in the eastern Mediterranean region, with particular attention to the Hellenic and Cyprus arcs and the Levantine basin Historical catalogues reflect that the most destructive earthquakes occurred in the eastern Hellenic arc (e.g., 365, 1303, 1481, 1494) threatening the coastal plains of Crete, Rhodes, Cyprus, Levantine Sea and Alexandria-Nile Delta (Egypt) environs in agreement with the obtained numerical tsunami simulations In this study, we have applied numerical sensitivity tests in order to check the effects of earthquake source parameters on tsunami generation and wave characteristics resembling the historical 1222 Cyprus (M ~7.0–7.5) and 1303 Crete (M ~8.0) earthquakes studied by Yolsal et al (2007a, b) and Yolsal (2008) Earthquake source parameters have been constrained by using historical documents, empirical scaling equations, GPS data, by analogy of current plate boundaries, reported field observations and earthquake source mechanisms obtained by teleseismic P- and SHbody waveform inversions (Yolsal 2008; Table 1) Here, we present sensitivity test results by illustrating examples of synthetic mareogram calculations at each selected coastal locations in the eastern Mediterranean region to compare tsunami wave characteristics in the far field Wave heights presented at each pseudo tide gauge stations are calculated by adding maximum positive and negative wave amplitudes Method Numerical Tsunami Simulations Simulations and sensitivity tests were performed by using the numerical code TUNAMI-N2 developed 315 316 Figure Map of epicentre distribution of the M ≥ earthquakes in the Mediterranean and surrounding regions reported by USGS-NEIC from1973 to 2009 Bathymetry and topography data are derived from GEBCO/97–BODC (Smith & Sandwell 1997a, b) and USGS-SRTM30, respectively Rectangular box indicates the current study area in the Eastern Mediterranean region USGS-NEIC 1973-2009 M>4 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES ic S Arc Pliny Crete A n ea eg Africa Mediterranean Sea HB SuF ESM s pru Cy TGF Sinai Sub-plate P KFZ EcF ErF Anatolia Cyprus Arc PTF BGF BuF TF RB ASM BMG G bo St a Se Ge Si EPF NAF EF alm y ol e dB lt Arabia BF F EA OF SF F MF e rid DF KF KB PS F Thr ust -Z ag ro F Tu F M T AF Bit lis NE asu sM ain Sa F Be Mediterranean Ridge c ni lle He Gr ee ce Black Sea Cau c s ld Fo lt Z a g Te F ro s u tu rz re Al bo AS strike - slip collision zone normal fault thrust fault plate motion S Kura Caspian Sea Figure Active tectonic structures and bathymetry in the Eastern Mediterranean Sea region compiled from our observations and those of Le Pichon et al (1984), Philip et al (1989), Mascle & Martin (1990), Kempler & Garfunkel (1991), Taymaz et al (1990, 1991, 2004, 2007a, b, 2008), Şaroğlu et al (1992), Taymaz & Price (1992), Taymaz (1993, 1996), Kurt et al (1999), Woodside et al (2000, 2002), Bozkurt (2001), Zanchi et al (2002), Poisson et al (2003), Guidoboni & Comastri (2005a, b), Tan & Taymaz (2006), Yolsal et al (2007a, b, 2008a, b), Yolsal (2008) and thereafter Abbreviations: NAF– North Anatolian Fault, NEAF– North East Anatolian Fault, EAF– East Anatolian Fault, DSF– Dead Sea Transform Fault, AS– Apşeron Sill, ASM– Anaximander seamounts, BF– Bozova Fault, BGF– Beyşehir Gölü Fault, BMG– Büyük Menderes Graben, BuF– Burdur Fault, CTF– Cephalonia Transform Fault, DF– Deliler Fault, EcF– Ecemiş Fault, EF– Elbistan Fault, EPF– Ezine Pazarı Fault, ErF– Erciyes Fault, ESM– Eratosthenes Seamount, G– Gökova, Ge– Gediz Graben, GF– Garni Fault, IF– Iğdır Fault, KBF– Kavakbaşı Fault, KF– Kağızman Fault, KFZ– Karataş-Osmaniye Fault Zone, MF– Malatya Fault, MRF– Main Recent Fault, MT– Muş Thrust, OF– Ovacık Fault, PSF– Pampak-Savan Fault, PTF– Paphos Transform Fault, RB– Rhodes Basin, SaF– Salmas Fault, Si– Simav Graben, SuF– Sultandağı Fault, TeF– Tebriz Fault, TF– Tatarlı Fault, TGF– Tuz Gölü Fault Large black arrows exhibit relative plate motions with respect to Eurasia (McClusky et al 2000, 2003; Reilinger et al 2009) Bathymetric contours are shown at 500 m, 1000 m, 1500 m and 2000 m, and were obtained from GEBCO-BODC (1997) Ionian Sea CTF ea ine IF RF ant M Lev iat Adr F G DSF Eurasia S YOLSAL & T TAYMAZ 317 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES Table Approximate earthquake source parameters of the historical 1222 Cyprus and 1303 Crete tsunamigenic earthquakes compiled after Ergin et al (1967), Ambraseys et al (1994), Guidoboni & Comastri (2005a, b), Yolsal et al (2007a, b) and Yolsal (2008) Earthquake Parameters 11 May 1222 - Cyprus 08 August 1303 - Crete Origin Time (to) 06:15 UT 03:30 UT Latitude - Longitude 34°42´N × 32°48´E 35°11´N × 25°38´E Estimated Intensity Io ~ IX Io ~ X Estimated Magnitude M ~ 7.0-7.5 M ~ 8.0 Strike / Dip / Rake 305° / 35° / 110° 115° / 45° / 110° h (focal depth) 15 km 20 km D (Displacement) 3m 8m L (Fault length) ~ 50 km ~ 100 km W (Fault width ) ~ 25 km ~ 30 km by Imamura (1995) to simulate tsunami wave generation, propagation and coastal amplification of non-linear long waves in a given arbitrarily shaped bathymetry Full details can be found in Imamura (1995), Pelinovsky et al (2001), Yalỗner et al (2003, 2007), Zahibo et al (2003); Imamura et al (2006) Additionally, we have used global bathymetric data provided by GEBCO-BODC (1997) and Smith & Sandwell (1997a, b) with a 1000 m grid size and a time step of Δx/Δt= (2ghmax)1/2, where hmax and g are the maximum still water depth and gravitational acceleration, respectively, providing stable and meaningful simulation results and satisfying in all cases the Courant-Friedrichs-Lewy (CFL) stability criterion (Imamura & Imteaz 1995; Yalỗner et al 2003, 2004; Yolsal et al 2007a, b; Yolsal 2008) Theory Wave propagation is computed by means of a finite difference model solving the non-linear shallow water equations on a staggered leap-frog scheme demonstrated by Aida (1974), Satake (1995), Imamura (1995) and Imamura et al (2006) The governing equations of mass conservation and momentum in three dimensions (Imamura 1995; Imamura et al 2006; Equations 1–4) are expressed by the following theory, 2o 2o 2o 2o 2p +u +o +w + + 2t 2x 2y 2z t 2y (2) 2τ 2τ 2τ c m t 2x + 2y + 2z = xy yy yz 2o 2o 2o 2o 2p +u +o +w + + 2t 2x 2y 2z t 2y (3) 2τ 2τ 2τ c m=0 + + t 2x 2y 2z xy yy yz 2p g + t 2z = (4) With dynamic and kinetic conditions, we obtained two dimensional equations named the shallow water theory (Imamura 1995; Imamura et al 2006; Equations 5–7) 2h 2M 2N + + =0 2t 2x 2y (5) 2M b M l b MN l + 2y D + + 2t 2x D (6) 2η 2u 2o 2w + + + =0 2t 2x 2y 2z 318 (1) + n gD 2x + tx = A d 2x 2y 2h x 2 M 2 M S YOLSAL & T TAYMAZ 2N b MN l b N l + 2y D + + 2t 2x D (7) 2h xy N N n + gD 2y + t = A d 2x 2y 2 where x, y: horizontal axes; z: vertical axis; t: time; D: total water depth (h+η) ; h: still water depth; η: the vertical displacement of water surface above the still water surface; u, v and w are water particle velocities in the x, y and z directions, g: the gravitational acceleration τx and τy : the bottom frictions in the xand y- directions, r: the liquid density, A: the horizontal eddy viscosity which is assumed to be constant in space (Figures & 4) M and N are the discharge fluxes in the x- and y- directions (Imamura 1995; Imamura et al 2006; Equations & 9) and they are given by, h M= # udz = u (h + η) = UD (8) odz = o (h + η) = oD (9) -h h N= # -h Synthetic tsunami waveforms are computed as an integration of initial and boundary conditions (Abe & Okada 1995) Once source parameters have been determined by using all available seismological information (e.g., source mechanism solutions of earthquakes, seismic moment estimations and a general understanding of active tectonics of the region; Figure 3), then the co-seismic displacement resulting from the earthquakes can be calculated by Okada’s (1985) equations The Okada (1985) elastic dislocation theory assumes that an earthquake can be modelled as a rupture of a single rectangular fault plane characterized by parameters describing the epicentre location, strike, dip and rake angles, displacement, rupture length and width, and focal depth (Figure 3) By assuming that the rupture speed of the fault plane is much larger than the phase speed of the tsunami wave and that the water is incompressible, initial water elevation is expected to be equal to the co-seismic vertical displacement of the sea bottom and the initial velocity field to be identically zero (Imamura & Goto 1988; Shuto 1991, 1993; Imamura 1995; Yalỗner et al 2004; Imamura et al 2006; Gica et al 2007) Then, it is used as an initial condition for the propagation and run-up phases (Legg & Borrero 2001) We further assumed that the vertical acceleration of water particles is neglected compared to the gravitational acceleration, that is, the water mass from the ocean bottom to the surface moves uniformly in horizontal direction In addition, wave theory supposing that a wave travels as a package of energy through the water column is dealt with by the tsunami wavelength (λ), wave height (amplitude) and water depth (h) Because the wavelength of the tsunami wave (λ) is much greater than the water depth (h), tsunami waves are called shallow water waves Basically, tsunami wave speeds depend upon the water depth, and consequently the waves undergo accelerations or decelerations in passing respectively over an ocean bottom of increasing or decreasing depth (Bryant 1991, 2001) It is reported that non-linear convection terms of shallow water wave equations can be neglected when water depths are greater than approximately h= 50 m (Shuto 1991; Satake 1995; Geist 2002) However, non-linear and dispersion effects become important and may not be neglected, and thus, if so, Boussinesq type equations and improved grids of bathymetry will be necessary in tsunami wave simulations Figure summarizes the details of tsunami wave simulation steps that we have followed in this study Empirical Seismological Scaling Several empirical self-similarity scaling equations are commonly used for constructing a finite fault source model (e.g., Romanowicz & Rundle 1993; Wells & Coppersmith 1994; Pegler & Das 1996; Fuji & Matsu’ura 2000; Mai & Beroza 2000; Konstantinou et al 2005; Tan & Taymaz 2005) and for a quick evaluation of real-time tsunami assessment (Geist 2002; Gica et al 2007, 2008; Yolsal et al 2007a, b; Yolsal 2008) However, it is also possible to determine the faulting area (A= L × W) and coseismic displacement from spatio-temporal slip distribution studies on the fault plane Several inversion algorithms have been developed based on teleseismic broad-band and near-field strong motion 319 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES Strike N W L( m ) (a) (m Rupture Area ) f di p Hypocenter d l Mo= mAD Mo = seismic moment (Nm) m = rigidity (N/m2) A = fault area (L x W)(m ) D = displacement (m) d Fault Line Epicenter (Hypocenter) Fault Plane Figure (a) Sketch diagram of slip distribution on a fault plane and schematic view of fault orientation parameters (φ: strike, δ: dip and λ: rake angles), (b) the ray paths of teleseismic waves (upper left corner) and a schematic rupture area (see c–e) as represented by dip at angle δ Angle δ= δo or δ= 180–δo depending on the strike angle and on the position to the vertical (normal or reverse fault) The strike direction is perpendicular to the fault and is oriented at strike angle φ counted clockwise from North The slip operates at rake angle λ counted counterclockwise from strike (facing the dipping section), compiled from Aki & Richards (1980, 2002), Okada (1985), Taymaz (1990), Tan (2004), Tan & Taymaz (2006), Ioualalen (2007), Yolsal (2008) and Yolsal et al (2008a, b) earthquake data (e.g., Kikuchi & Kanamori 1991; Yagi & Kikuchi 2000) Inversion results provide direct information about total moment rate function, stress drop and slip distribution of earthquakes These studies have important impacts on mitigating earthquake hazard as well as providing crucial information such as the seismic moment tensor, Mij, that can be used to better determine the tsunamigenic potential of an earthquake (Pasyanos et al 1996; Geist 2002) Seismic moment, measure of rupture size and earthquake magnitude (see Figure 320 Focal 3a), can be calculated by using the Aki (1966) and Aki & Richards (1980, 2002) equations: Mo = μ × A × D (10) where μ is rigidity (N/m ), A is the faulting area (L (length) × W (width), m ), and D is the maximum displacement (m) Kanamori (1972), Abe (1973) and Ward (1980) pointed out linear relationships between tsunami wave amplitudes and seismic moment (Mo) values Although empirical scaling equations help us to estimate the relation between source parameters and earthquake seismic moment nta lS ec tio n S YOLSAL & T TAYMAZ Ho riz o North Sl ip f No l 180-d0 Strike al ers e Dipping Section d0 (b) (a) Inv rm (c) (b) Strike North Strike Horizontal Section t f l0 f ip l0 es W g in e) pp rs Di nve (I Sl Di (N ppin or g ma W l) est Horizontal Section North Sli p 360-l0 d0 (d) (c) Di (In ppin ve g rs Ea e) st 180-d0 d0 (e) (d) 360-l0 Di (N ppin or g ma Ea st l) 180-d0 Figure Continued (Kanamori & Anderson 1975; Bonilla et al 1984; Wells & Coppersmith 1994; Mai & Beroza 2000; Tan 2004; Tan & Taymaz 2005, 2006; Konstantinou et al 2005; Yolsal 2008), it is worth noting that the accuracy of these methods depends on the spatial and azimuthal coverage of seismic stations and the number of earthquakes analyzed Sensitivity Analyses of Earthquake Source Parameters Tsunami wave characteristics in both near and far fields are affected by various factors that can be grouped as the source, propagation and local near- shore bathymetry (Satake 1988) As explained above, numerical tsunami simulations require earthquake source geometry as a starting model to calculate the initial waves; hence source rupture parameters should be chosen as precisely as possible Besides, the wavelength and period of tsunami waves will depend on the generating source mechanisms and faulting dimensions Kajiura (1970), Ben-Menahem & Rosenman (1972) and Yamashita & Sato (1974) suggested that the source effect includes the directivity due to fault orientation and fault parameters such as strike, dip angles and amount of slip The propagation path also comprises the effects of Earth's sphericity (Miyoshi 1955; Hatori 1963), 321 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES (a) Obtaining bathymetry data Choosing dx and dt parameters GEBCO / 97 - BODC bathymetry data dx: Spatial grid size dt: Time step Determining the gauge points Calculating start and end point locations of the fault Determining fault parameters Fault area (length and width) Tectonic maps, recent and historical seismic activity catalogs etc Source mechanism solutions (strike/dip/rake angles, focal depth, seismic moment and Dmax displacement etc.) Slip distributions and / or empirical equations Calculating the displacement on the fault plane Choosing the total time of wave simulation TUNAMI N2 wave simulation program (b) Obtaining grid files and converting them to BMP, JPG and AVI Inundation line or limit Tsunami waves i am n Tsu Tsunami u h Shoreline D Water level at shoreline Maximum water level Run-up Datum h Horizontal inundation Basement Figure 322 (a) Flow chart of numerical tsunami simulation steps (for details see Okada 1985; Shuto 1993; Imamura 1995 and Yalỗner et al 2003, 2004) and (b) a simple illustration of common tsunami parameters D– total water depth (h+η); η– vertical displacement of water surface above the still water surface (h); u– water particle velocities in the x direction (Imamura 1995; Imamura et al 2006) S YOLSAL & T TAYMAZ 115°/45°/110°/20 km Dmax = m W = 30 km L = 100 km Model 220°/40°/140°/20 km Dmax = m W = 30 km L = 100 km Model 150°/40°/95°/20 km Dmax = m W = 30 km L = 100 km Model Figure 12 Snapshots of the initial tsunami wave heights generated with the parameters summarized above and locations of pseudotide gauge stations by varying source mechanisms Initial wave heights with maximum positive and negative amplitudes are shown in the boxes located at the lower left corners Above the map, source parameters used in the study are given in order of strike, dip, rake angles, focal depth, maximum displacement, fault width and length Red squares show the earthquake epicentres A vertical colour scale indicates the water surface height given on the right-hand side in metres 335 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES Figure 13 Comparison of synthetic tsunami records at selected pseudo-tide gauge locations in case of variation in earthquake focal mechanism solution for models of M1, M2 and M3 336 S YOLSAL & T TAYMAZ 115°/45°/110°/20 km Dmax = m W = 30 km L = 100 km D=5m 115°/45°/110°/20 km Dmax = m W = 30 km L = 100 km D=8m 115°/45°/110°/20 km Dmax = 10 m W = 30 km L = 100 km D = 10 m Figure 14 Snapshots of the initial tsunami wave heights generated with the parameters summarized above and locations of pseudotide gauge stations by varying maximum displacement (Dmax) Initial wave heights with maximum positive and negative amplitudes are shown in the boxes located at the lower left corners Above the map, source parameters used in the study are given in order of strike, dip, rake angles, focal depth, maximum displacement, fault width and length Red squares show the earthquake epicentres A vertical colour scale indicates the water surface height given on the right-hand side in metres 337 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES Figure 15 Comparison of synthetic tsunami records at selected pseudo-tide gauge locations in case of variation in vertical displacement values of Dmax m, m and 10 m 338 S YOLSAL & T TAYMAZ 115°/45°/110°/5 km Dmax = m W = 30 km L = 100 km H = km 115°/45°/110°/10 km Dmax = m W = 30 km L = 100 km H = 10 km 115°/45°/110°/20 km Dmax = m W = 30 km L = 100 km H = 20 km Figure 16 Snapshots of the initial tsunami wave heights generated with the parameters summarized above and locations of pseudotide gauge stations by varying focal depth (H) Initial wave heights with maximum positive and negative amplitudes are shown in the boxes located at the lower left corners Above the map, source parameters used in the study are given in order of strike, dip, rake angles, focal depth, maximum displacement, fault width and length Red squares show the earthquake epicentres A vertical colour scale indicates the water surface height given on the right-hand side in metres 339 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES Figure 17 Comparison of synthetic tsunami records at selected pseudotide gauge locations in case of variation of focal depth values at km, 10 km and 20 km 340 Tobruk AFRICA Sallum Herodotus Basin ? Anaximander ? FR ? AB ANATOLIA MH Eratosthenes Latakia Ridge Cyprus Anamur AK PTF Egypt (Nile) Delta ? Alexandria Mediterranean Matruh y in Pl bo St Rh ? FZ FB IA Sinai Sub-plate Gaza ? RF AK F ? EAF Palmyra Fold Belt ARABIA DSF Beirut BTB EF Z Figure 18 Summary sketch map of coastal plains that are at tsunamigenic earthquake risk marked with red wave-curves, and plots of representative fault plane solutions of historical Eastern Mediterranean earthquakes shown in lower hemisphere projection estimated from current earthquake source mechanisms and by analogy of plate boundaries Active faults are compiled from Garfunkel et al (1981), Le Pichon et al (1984), Philip et al (1989), Mascle & Martin (1990), Taymaz et al (1990, 1991, 2004, 2007), Kempler & Garfunkel (1991), Şaroğlu et al (1992), Taymaz (1993, 1996), Guidoboni et al (1994), Salamon et al (1996, 2003), Woodside et al (2000, 2002), Bozkurt (2001), Zanchi et al (2002), Poisson et al (2003), Guidoboni & Comastri (2005a, b), Alỗiỗek et al (2006), Gardosh & Druckman (2006), Schattner et al (2006a, b), Tan & Taymaz (2006), Schattner & Ben-Avraham (2007), Yolsal et al (2007a, b, 2008a, b), Aksu et al (2008), Ben-Avraham et al (2008), Hall et al (2008), Yolsal (2008) and thereafter Abbreviations: AB– Aksu Thrust, AKF– Akkar Fault, AKMH– Aksu, Köprü, Manavgat Basins, BMG– Büyük Menderes Graben, BTB– Beirut-Tripoli Thrust, CaFZ– Carmel Fault Zone, DSF– Dead Sea Fault, EAF– East Anatolian Fault, EF– Ecemiş Fault, FBFZ– FethiyeBurdur Fault Zone, FR– Florence Rise, IA– Isparta Angle, KFZ– Karataş Fault Zone, PTF– Paphos Transform Fault, RF– Roum Fault, RTF– Rhodes Transform Fault, YF– Yammouneh Fault Libya Pitolemy Crete od es Gökova F RT Aegean Sea CaFZ BMG L ev a nt i ne KF YF Greece S YOLSAL & T TAYMAZ 341 EARTHQUAKE SOURCE RUPTURE PARAMETERS AND FAR-FIELD TSUNAMI WAVES Conclusions The far field tsunami wave characteristics are closely related to the nature of associated tsunamigenic earthquakes, the source rupture properties and the bathymetrical features of the region at risk Historical earthquakes and associated tsunamis in the eastern Mediterranean Sea offer a unique opportunity to improve our understanding of tsunami wave simulations in relation to earthquake source and tsunami wave characteristics Reliable historical sources greatly helped us to get a better understanding the tectonic processes in active convergent zones of the eastern Mediterranean, the mode and nature of seismic, volcanic and geomorphological events and their effect on humanity and civilizations In this paper, numerical sensitivity tests were used to exhibit the relationship between tsunami waves and their source parameters These results help us to get more accurate assessments of tsunami hazard Figure 18 displays a summary sketch map of coastal plains at tsunamigenic earthquake risk and plots of representative fault plane solutions of historical eastern Mediterranean earthquakes obtained from current earthquake source mechanisms shown in a lower hemisphere projection Details of numerical simulations of other historical tsunamigenic earthquakes in the region are discussed elsewhere by Yolsal et al (2008a,b) We summarize our findings and the results of sensitivity tests indicating major parameters below: [1] We have observed that the most critical parameter effecting tsunami wave characteristics is seismic moment (Mo) because amplitudes and shapes of tsunami waves develop in direct proportion to the variation of magnitude and seismic moment of tsunamigenic earthquake [2] Bathymetry and local topography have crucial effects on tsunami wave propagation in both near and far fields As observed in this study, an extended continental shelf with thick sedimentary basins protects coasts from destructive tsunami waves due to its defocusing effect that widely flattens tsunami waves If the continental shelf is small and narrow, tsunami waves may not develop because of defocusing 342 processes in a short time In addition, a series of seamounts and other structural features shown in bathymetric profiles also affect tsunami wave propagation by behaving as natural barriers and/or asperities [3] The accurate estimate of tsunamigenic earthquake epicentres is important, especially for near field tide gauge stations Gica et al (2007, 2008) observed that a far-field tsunami time series is clearly sensitive to the earthquake epicentre and magnitude We suggest that the variations in other source parameters not significantly change the tsunami signal as much as earthquake location in the near field Similarly, according to our sensitivity tests variations in the earthquake location did not affect the initial tsunami wave heights, but the final tsunami wave characteristics and their arrival times were changed in the near and far fields Especially, cylindrical spreading causes tsunami waves to decrease in amplitude with increasing distance from the earthquake source However, it is sometimes hard to calculate the earthquake location accurately due to the lack of valuable and definitive historical earthquake catalogues Therefore, the compilation of reliable earthquake catalogues and verified records is of great importance for future earthquake sources, tsunami modelling studies and early warning operations [4] Focal mechanism solutions influence amplitudes, frequency contents and arrival times of tsunami waves in the far field Especially, the dip and rake angles are key parameters that control the subsidence/uplift dipole (i.e: the crest/depression for the tsunami waves) The focal depth of the epicentre also controls the nature of the leading tsunami wave [5] Due to linearity between the amount of vertical co-seismic displacement and coastal deformation, initial and final tsunami wave amplitudes are calculated as significantly related to the earthquake source With variation in maximum displacement, focal depth and faulting area, tsunami wave amplitudes evidently changed, but their theoretical arrival times were almost the same S YOLSAL & T TAYMAZ Despite the simplified nature of the estimated earthquake source and the lack of high resolution bathymetry data, we have adequately simulated the principal characteristics of tsunami waves in the far field, particularly the directivity of the wave towards the Alexandria (Egypt) coastal plain Furthermore, dip-directed variations in slip will have a major effect on co-seismic vertical displacements, but uniform slip in the dip direction will cause an underestimation of wave amplitudes and the leading wave steepness of the local tsunami In summary, accurate tsunami risk estimates in the near and far fields depend on reliable determination of earthquake source parameters, specifically earthquake location, focal mechanism, seismic moment and higher resolution of the bathymetry data However, in addition to these parameters, other important source factors affecting wave characteristics, such as slip distribution models, number of sub-events, are not discussed in the current article These and other relevant issues will be addressed in another study by the same authors We suggest that the idea is worth additional enhancement since it may help in some circumstances to qualify earthquake source parameters, and ultimately a tectonic setting if the latter is simple enough to predict As a consequence, future seismological, oceanographic and marine geophysical observations should aim to improve the accuracy of numerical tsunami simulations and details of bathymetry in order to get improved results Acknowledgements The authors thank İstanbul Technical University Research Fund (İTÜ-FBE-BAP), the Turkish National Scientific and Technological Research Foundation (TÜBİTAK), the Turkish Academy of Sciences (TÜBA) in the framework for Young Scientist Award Program (TT–TÜBA–GEBİP 20012-17) for their support Generic Mapping Tools (GMT; Wessel & Smith 1998) and SAC2000 (Goldstein et al 1999, 2003) softwares were used to generate some of the figures and to process conventional earthquake data, respectively The authors also thank Ahmet C Yalỗner, Nobuo Shuto, Fumihiko Imamura, Efim Pelinovsky and 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(2002) demonstrated the importance of rupture complexity in combination with other tsunami parameters such as distribution of water depth in the source region, reductions in shear modulus near the