60 investigation of earthquake

Nat Hazards (2012) 64:311–327 DOI 10.1007/s11069-012-0240-3 ORIGINAL PAPER Investigation of earthquake tsunami sources, capable of affecting Vietnamese coast Phuong Hong Nguyen • Que Cong Bui • Xuyen Dinh Nguyen Received: 26 January 2011 / Accepted: 28 May 2012 / Published online: 23 June 2012 Ó Springer Science+Business Media B.V 2012 Abstract Based on the analysis of tectonic feature and geodynamic characteristics of regional faults systems in the southeast Asia, source zones capable of generating tsunamis affecting Vietnamese coast were delineated in the South China Sea and adjacent sea areas Statistical methods were applied to estimate the seismic hazard parameters for each source zone, which can be used for the detail tsunami hazard assessment in the future Maximum earthquake magnitude is predicted for the Manila Trench (8.3–8.7), the Sulu Sea (8.0–8.4), and the Selebes Sea source zones (8.1–8.5) Among the source zones, the Manila Trench, west of the Philippines is considered as a most potential tsunami source, affecting the Vietnamese coast The estimated Mmax values were used to develop simple scenarios (with a point source assumption) to calculate the tsunami travel time from each source zone to the Vietnamese coast The results show that for the Manila Trench source zone, tsunami can hit the Vietnamese coast in h at the earliest Keywords Tsunami source zones Á South China Sea Á Tsunami hazards Á Maximum earthquake magnitude Introduction The occurence of the Indian Ocean Tsunami on December 26, 2004 has marked a new turning point in tsunami science Many methods have been applied by scientists to assess tsunami hazards for different sea areas in the World The tsunami hazard assessment studies are implemented using two different approaches: deterministic and probabilistic Deterministic tsunami hazard studies involve hydrodynamic modeling of tsunami propagation, runup and inundation from a particular source and simulation of known destructive tsunami scenarios (Arcas and Titov 2006) Recent methodology of probabilistic assessment, developed by Thio et al (2006), allows us to display results in terms of tsunami P Hong Nguyen (&) Á Q Cong Bui Á X Dinh Nguyen Earthquake Information and Tsunami Warning Center, Institute of Geophysics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam e-mail: phuong.dongdat@gmail.com 123 312 Nat Hazards (2012) 64:311–327 hazard curves that plot tsunami annual rate of occurrence versus exceedance wave height and tsunami hazard maps that show the peak tsunami wave height that is exceeded in different periods of time along a study coast The method of probabilistic tsunami hazard analysis (PTHA) has been applied to many coastal areas of the countries bordering by the Pacific and Indian Oceans (Tadashi Anaka et al 2007; Burbridge et al 2008; Thio et al 2007 Up to now, most tsunami hazard assessment studies have been focused on the active tectonic sources at regional scale without paying attention to the tsunami sources of medium or local size When assessing tsunami hazard for the southeast Asia, Thio et al (2007) have based only on the mega subduction sources in the sea areas near Japan, the Philippines, south of Indonesia, and Malaysia, but bypassed the sources of medium and small size faults zones in the East Vietnam Sea Likewise, Burbridge et al (2008) paid attention only to the biggest source in terms of the Sumatra–Andaman mega thrust and subduction zone when assessing tsunami hazard for the west coast of Australia As the need for tsunami hazard analysis within each country is arising and becoming more and more urgent, it is necessary to carry out detail studies on the medium and small size active tectonic faults zones in the marginal sea areas, which can be the sources of the local tsunamis that sometime causing damages and losses This study aims at investigating the tsunami sources, capable of affecting the coast of Vietnam On the basis of the analysis of tectonic feature and geodynamic characteristics of regional faults systems in the southeast Asia, the tsunami source zones were delineated in the East Vietnam Sea and adjacent sea areas Statistical methods were applied to estimate the seismic hazard parameters for each source zone, which can be used for detailed tsunami hazard assessment in the future And in the end, average tsunami travel time was calculated from the source zones to the Vietnamese coast, providing some preliminary vision for tsunami warning in Vietnam in the future Main seismotectonic characteristics of the southeast Asia The southeast Asia, in particular the South China Sea has diverse tectonic structures and complicate geodynamic development history On the one hand, this is a transition zone between the Eurasian and the Australian plates; on the other hand, it plays a role of a boundary separating the Pacific Ocean from Indian Ocean The lithosphere plates in the region move relative to each other, with the tendency to converge at the East Vietnam Sea: the Pacific plate moved westward, the Indian–Australian plate moved north–northwestward In the mean time, the Indian plate moved rapidly northward and collided with the Asia plate The collision between plates have resulted in this region some main active structures as follows: • A series of mega subduction zones: the Sunda Trench stretching over 8,000 km from the northwestern boundary of southeast Asia to the eastern part of Timor island (A, Fig 2); the Philippines Trench stretching over 3,000 km along the east coast of the Philippines archipelago (F, Fig 2) Some smaller subduction zones can be listed as the Manila Trench subduction zone (1,150 km, M, Fig 2), the subduction zone in the eastern boundary of Sulu Sea (over 650 km long, SN, Fig 2) • A series of marginal seas, formed due to the back-arc spreading: the Celebes Sea (formed 54–42 Ma b.p.), the East Vietnam Sea (32–15.5 Ma b.p.), the Sulu Sea 123 Nat Hazards (2012) 64:311–327 313 Fig Seismotectonic map of the study area with the East Vietnam Sea and its adjoining seas labeled (19–17 Ma b.p.), the Molucca sea (40–35 Ma b.p.), the Banda Sea (20–15 Ma b.p.), and the Makassar Sea (23–17 Ma b.p.), (Fig 1) • Major strike-slip faults such as the Sagaing sub-longitudinal fault which is a dextral fault in the present period with average slip rate of 20 mm/year (1, Fig 2); the Red river northwest–southeast trending fault which is also a dextral fault in the present period with relatively low slip rate (5, Fig 2); the Sumatra northwest–southeast trending fault which has is a dextral fault with slip rate of from 15 mm/year to the southeast to 25 mm/year to North–northwest (2, Fig 2); the Philippine sub-longitudinal fault (on Philippines islands) which is a sinistral fault with slip rate in the middle section of 35 mm/year (20, Fig 2) Average slip rate of sub-plates inside the region relatively each to other is about 10 mm/year • Paired occurrence of subduction and strike-slip fault zones: the pair of mega subduction zones and strike-slip fault with the same name of Sumatra; the pair of subduction and strike-slip fault zones with the same name of Philippine, the pair of Timor subduction zone (the Eastern section of the Sumatra subduction zone) and Sorong strike-slip fault Figure shows principal tectonic structures in the southeast Asia As can be seen from this map, the Vietnamese coast has a specific situation as if it is ‘‘blocked’’ inside the East Vietnam Sea The ‘‘East Vietnam Sea’’ term hereafter indicates the sea area surrounded by Chinese continent from the north, by dense island systems of Thailand and Malaysia from the southwest, of Indonesia and Malaysia from the south, and by the Philippines archipelago from the east (see Fig 1) The Vietnamese coast will most probably be affected, and therefore, most considerably, by tsunamis generated from the sources inside the East 123 314 Nat Hazards (2012) 64:311–327 Fig Tectonic sketch-map of the southeast Asia (adapted from Tija 2008) Terrain boundaries: A Sunda Trench; B Banda Trench; C Jaya thrust; D Papua Trench; E Yap Trench; F Philippine Trench; G Maluku East trough; H Maluku West trough; J Gorontalo Trench; K Cotabaco Trench; SN Sulu-Negros Trench; M Manila Trench; N East Luzon trough; R Ryukyu Trench; S-NW Sabah trough; Regional Faults: Sagang; Sumatra; 2a-Bangkalis; Three Pagodas; Mae Ping; Red river; 109° meridian; Ranong; Khlong Marui; Peusangan; 10 Mentawai; 11 Axial Malay; 12 Sakala; 13 Adang/Paternoster; 14 Palu; 15 Matano; 16 Tarera-Aiduna; 17 Ransiki; 18 Sorong-Irian; 19 Gorontalo; 20 Philippine; 21 Ulugan; 22 Balabac; 23 West Baram line; 24 West Balingian line; 25 Sorol; 26-North of the East Vietnam Sea Exotic terraines/Microcontinents: AS Andaman spreading centre; Pa Paracel; Ls Luconia Shoals; Ba Bacan; Si Silembu; Na Natal; MB Macclesfield Bank; ES East Sabah; Sr Seram; Nt Timor North; SK Sikuleh; Cal Calamian block; DG Dangerous grounds; Su Sula spur; TB Tukangbesi; Sb Sumba Vietnam Sea It can hardly be affected by destructive tsunamis, originated in the central Pacific Ocean, from the Sea of Japan and East China Sea in northeast side and even from the mega subduction zones as the Sundaland and the Philippines, too In fact, the 2004 Sumatra tsunami caused no harm to the Vietnamese coast as it was blocked by the dense island arc of Indonesia and Malaysia Up to now, the only tsunami data available in the Bac Bo Gulf, East Vietnam Sea is reported by Integrated Tsunami Database for the World Ocean (ITDB 2005) This event is shown in Fig 3, recorded in January 5, 1992 and is described that it was caused by ‘‘a series of small earthquakes with the maximum being estimated at 3.7 and with a focal depth of 8–12 km occurred off the southwest coast of Hainan Island, China The tide rose abnormally beginning at 14:30 and continued until 17:00 Beijing time It was recorded by four gages around the island including at Beibu Bay with the maximum at Yulin Station near Sanya Port with a period of about 20 and a maximum amplitude of 80 cm Fishing boats in various harbors were damaged by ramming, and many had broken anchor chains’’ (Lander et al 2003 and Lin et al 1993) However, the fact that a 3.7 magnitude 123 Nat Hazards (2012) 64:311–327 315 Fig Historical Tsunamis in the southeast Asian Region 1600’s—2006 The only historical tsunami recorded in the Bac Bo Gulf, East Vietnam Sea is caused by a series of 3.7 magnitude earthquakes and caused no casualties (ITDB 2005) earthquakes can generate a tsunami causes doubts from many people and makes this event seem to be unsubstantiable In this paper, only tsunami sources capable of causing damage to the Vietnamese coast are considered In the East Vietnam Sea, the most potential tsunami sources are considered to be: (1) the Manila subduction zone; (2) the West of the East Vietnam Sea faults zone; (3) the North of the East Vietnam Sea faults zone and (4) the Northwest Borneo-Palawan fault zones (Fig 4) Detail of these sources is discussed below 2.1 The Manila subduction zone The zone consists of several trenches stretching along the west coast of the Philippines from latitude 20°N to latitude 12°N (marked as M in Fig 2) The Manila Trench forms the convergent margin between the Philippines sea plate and the Sunda plate from central Luzon to Taiwan Within this zone, many strong earthquakes have occurred, some of which has magnitude of 8.2 According to Bautista et al (2006), during period from 1589 to 2005, at least six tsunamigenic earthquakes have occurred in this zone, causing considerable losses of lives and properties These earthquakes are listed below: • West Luzon offshore earthquake in 1677 (Ms 7.3, generating a tsunami with about m run-up) • Pasig River (Manila) earthquake in 1828 (Ms 6.6, generating a tsunami with about m run-up) 123 316 Nat Hazards (2012) 64:311–327 Fig A sketch map of tsunami source zones in the South China Sea, capable of affecting the Vietnamese coast (see Sect for explanation) The numbers indicate the following sources zones: 1a Riukiu—Taiwan; 1b West Taiwan; 2a North Manila Trench; 2b Central Manila Trench; 2c South Manila Trench; The Sulu Sea; The Selebes Sea; The South Banda Sea; 6a The North Banda Sea 1; 6b The North Banda Sea 2; North of the East Vietnam Sea; Northwest Borneo-Palawan; West of the East Vietnam Sea • • • • Agno earthquake in 1872 (Ms 6.8, generating a tsunami with about m run-up) Agno earthquake in 1924 (Ms 7.0, generating a tsunami with about m run-up) San Esteban earthquake in 1934 (Ms 7.6, generating a tsunami with about m run-up) Iba—Palauig earthquake in 1999 (Ms 6.8, generating a tsunami with about 1.5 m runup) The run-up measurements given above are observed data taken from a number of existing references to historical tsunamis generated in the areas surrounding the Philippine Islands, including local chronicles, scientific reports, and partly from mareograph data Among the references, the most valuable are the bulletins of a seismological station, established as a part of the Manila Central Observatory in 1865 and operated continuously until World War II It is also known that during the interval from about 1900 until the start of World War II, the seismological station was directed by two scientists: first by Miguel Saderra Maso and then by the W C Repetti, both of whom were familiar with tsunamis and their relationship to earthquakes, and who were alert for their occurrence (Wiegel and 123 Nat Hazards (2012) 64:311–327 317 ASCE 1980) Despite of the fact that some historical events listed above, particularly those occurred in the nineteenth century are considered ‘‘probable’’ or ‘‘doubtful’’ in the chronicle catalog of local tsunami of the Philippines (Nakamura 1978), this evidence proves the existence of the tsunamis generated in the Manila subduction zone 2.2 The West of East Vietnam Sea faults zone This fault system, known under many different names, is often referred to in Vietnamese literature as ‘‘the 109° meridian deep-seated fault system’’ (numbered in Fig 2) Originated from the south Hainan island area, the major fault line goes down south, passing about 550 km along the Central Vietnam’s coast through the Tuy Hoa shear zone The less active part of the fault is extended down south in sub-longitudinal direction with a length up to 700 km The system consists of at least main fault lines, which have a submeridianal direction and sink step by step into the sea These faults slope westwards, down under the Kontum massif, with an angle of 30–40° and depth of over 100 km Besides the major faults, there are many smaller ones, breaking through the Earth crust and appearing on the surface in the form of normal faulting, while in the lower part, they have a reverse form of faulting This is a deep-seated fault zone, playing the role of boundary between the Indosinian geoblock and the East Vietnam Sea oceanic crust Geological evidence shows that its main activities have terminated in early Miocene, and during the present time, the fault becomes less active The Vung Tau earthquakes of 2005 might related with this fault zone 2.3 The North of East Vietnam Sea faults zone This is a passive continental margin zone of Atlantic type, with a series of normal faults forming grabens and depressions extending in NE–SW or ENE–WSW direction The faults have lengths ranging from some hundreds to a thousand km and can generate medium earthquakes and tsunamis The most active faults are observed in the margin of the East Vietnam Sea oceanic crust 2.4 The Northwest Borneo—Palawan faults zone This is a thrust fault zone, located in the Northwest of Sabah trough (S in Fig 2) The left part of the fault is considered to be active, while the segment along Palawan is considered to be inactive Medium earthquakes have been observed along this fault zones, with maximum magnitude of 6.0 2.5 Other potential tsunami sources Besides the mentioned tectonic elements within the East Vietnam Sea, some smaller subduction zones in the Sulu and Banda Seas can be considered as the tsunami sources, dangerous to the Vietnamese coast Among these, the Sulu-Negros Trench (SN in Fig 2) is a short convergence zone along the western margin of the central Philippines, and the Cotabato Trench (K in Fig 2) is another short trench system, located along the southwestern coast of Mindanao (Thio et al 2007) 123 318 Nat Hazards (2012) 64:311–327 Tsunami source zones, capable of affecting the Vietnamese coast The tsunami source zones are defined on the seismotectonic basis In this paper, a tsunami source zone is defined along seismically active faults by summing all the possible rupture zones caused by maximum earthquakes, which might occur within a given zone In other words, this is the projection of tectonic fault plans counting from the deepest active layer to the sea’s surface However, while delineating a seismic source zone boundary, this principle is rather flexible and sometimes extended, depending on certain observed earthquake epicenter distributions, a set of faults or related volcanic arcs, particularly in cases of scattered earthquake data The acceptable boundary for a seismic source zone has to maintain all seismotectonic characteristics of the zone as a whole, namely the azimuthal location, direction of main geological structures, and cluster of earthquake epicenters The following tsunami source zones have been delineated in the East Vietnam Sea and adjacent sea areas: The The The The The The The The The Taiwan Sea source zone; Manila Trench source zone; Sulu Sea source zone; Selebes Sea source zone; North Banda Sea source zone; South Banda Sea source zone; North of East Vietnam Sea source zone; Northwest Borneo-Palawan source zone; West of the East Vietnam Sea source zone; The source zones were divided into sub-source zones and coded by numbers as shown in Fig and Table Table Earthquake subcatalogs of the tsunami source zones in the South China Sea (after foreshocks and aftershocks removal) 123 Tsunami source zone Observation period Number of earthquakes Observed Mmax 1a Riukiu—Taiwan 1965–2008 89 1b West Taiwan 1964–2008 49 6.7 2a North Manila Trench 1958–2006 36 8.2 2b Central Manila Trench 1872–2008 193 8.0 2c South Manila Trench 1974–1993 16 6.2 7.2 The Sulu Sea 1964–2006 95 7.9 The Selebes Sea 1964–2007 139 8.0 The South Banda Sea 1998–2006 29 6.3 6a The North Banda Sea 1608–2008 156 7.6 6b The North Banda Sea 1966–2007 61 6.5 North of the East Vietnam Sea 1913–2000 34 6.5 Northwest Borneo-Palawan 1930–1995 6.0 West of the East Vietnam Sea 1919–2005 18 6.1 Nat Hazards (2012) 64:311–327 319 Statistical estimation of seismic hazard parameters for the tsunami source zones 4.1 Earthquake data analysis In this paper, the Gumbel’s Extreme Values method and the Maximum Likelihood method were used for estimating the seismic hazard parameters Detail description of the estimation methods can be found in Phuong (1991, 1997, 2001); Kijko (1984); Kijko et al (1987) The following parameters were estimated for each tsunami source zone: • Expected maximum earthquake magnitude Mmax; • Constants a, b in the Gutenberg–Richter magnitude-frequency relation and their deductive values k,b; • Mean return period T(M) of the strong earthquakes with magnitude M A catalog of 6,267 earthquakes, which consists of both historical and instrumental data up to 2007 was compiled for the study area (Fig 3) Earthquake data were grouped for each source zone and the subcatalogs were treated for completeness and homogeneity Table lists the subcatalogs of all source zones after removal of foreshocks and aftershocks As the subcatalogs were obtained from the observational data, they are different for different zones, and in some cases, it was difficult to apply statistical methods because of lack or incompleteness of data For this reason, both mentioned methods were applied in order to obtain the best choice of the sought parameters 4.2 Estimation of seismic hazard parameters by the Extreme Values method The extreme value theory was first applied to estimate the seismic hazard parameters for earthquake source zones in Vietnam in 1991 (Phuong 1991) The theory is formulated under the following assumptions (Gumbel 1958): 1) The prevailing condition must be valid in the future; 2) The observed largest values are independent of each other Let X be a random variable with a probability function of F(x): FðxÞ ¼ PfX xg The probability that x will be the largest among n independent samples from the same distribution F(x) will be: GðX Þ ¼ PfX1 x; X2 x; ; Xn xg ¼ F n ðxÞ; which is the exact distribution function of the largest value When the random character of the earthquake occurrence is taken into account, it is possible to consider the largest annual earthquake magnitudes in a given time period as a random series with distribution G(x) In most cases, the initial distribution function F(x) is not known It is then necessary to deal with the asymptotic forms of distributions introduced by Gumbel, who considered three asymptotic distributions of extreme values The first asymptotic distribution of the largest values is of the form: G1ðxÞ ¼ exp½ÀexpðÀb1 ðx À uÞފ ð1Þ where b1 and u are the distribution parameters to be determined and b1 [ If we substitute lna1 = b1u and take twice the logarithm of both sides of (IV.1), we obtain: 123 320 Nat Hazards (2012) 64:311–327 ln½ÀlnG1ð xފ ¼ lna1 À lnb1 x ð2Þ The second asymptotic distribution of the largest values is of the form: u À eb2 ! n G2ðxÞ ¼ exp À ; b2 [ 0; x ! e; un [ e ! xÀe ð3Þ where e is the lower limit of largest values, b2 is the shape parameter, and un is the characteristic largest value The third asymptotic distribution of the largest values is of the form:  x À x b ! ; b3 [ 0; x\x; u\x; ð4Þ G3ðxÞ ¼ exp À xÀu where x is the upper limit of the largest value x, and b3 and u are the distribution parameters to be determined In the first asymthotic distribution, the variate is unlimited in both directions In the second asymthotic distribution, a lower limit for the variable X exists As for assessment of seismicity of a region, only upper threshold of earthquake magnitude is interested, the second asymthotic distribution is therefore ruled out in our case In addition, as there exists an upper limit in the third asymthotic distribution of the largest values, for the occurrence of maximum earthquake magnitudes, the third asymthotic distribution naturally has a better physical meaning for a probabilistic model than either the first or the second distribution (Yegulalp and Kuo 1974) If we substitute a3 ¼ ðx À uÞb3 and take twice the logarithm of both sides of (4), we have: ln½ÀlnG3ðxފ ¼ lna3 þ b3 lnðx À xÞ ð5Þ The estimation of the parameters ai, bi, i = 1,3 is obtained by least square method using (2) and (5) The subcatalogs listed in Table were used for least squares fit procedure In this study, only the third asymptotic distribution was applied to parameter estimation, and the obtained x values correspond to the sought maximum earthquake magnitudes of the seismic source zones 4.3 Estimation of seismic hazard parameters by the maximum likelihood method 4.3.1 Extreme magnitude distribution applied to the macroseismic part of the catalog The available earthquake catalogs usually contain two types of information: macroseismic observation of major seismic events that occurred over a period of a few 100 years and complete instrumental data for relatively short periods of time Let us assume the Poisson occurence of earthquakes with the activity rate k and the doubly truncated Gutenberg– Richter distribution F(x) of earthquake magnitude x The doubly truncated exponential distribution can be represented by: F ðxÞ ¼ PðX xÞ ¼ A1 À AðxÞ ; A1 À A2 Mmin x Mmax ð6Þ where A1 ¼ expðÀbMmin Þ; A2 ¼ expðÀbMmax Þ; Ax ¼ expðÀbxÞ; Mmax is the maximum regional magnitude value, Mmin is the threshold magnitude and b is a parameter The above assumption implies that earthquakes of magnitudes greater than x can be represented by a 123 Nat Hazards (2012) 64:311–327 321 Poisson process with mean rate of occurence k½1 À F ðxފ (Benjamin and Cornell 1970) Thus, the probability that X, the largest magnitude within a period of t years will be less than some specified magnitude x is given by: & !' A2 À AðxÞ ð7Þ Gð xjtÞ ¼ PðX xÞ ¼ exp Àv0 t A2 À A10 where G is the distribution function, v0 ¼ k½1 À F ðM0 ފ; A10 ¼ expðÀbM0 Þ and M0 is the threshold magnitude for the extreme part of catalog, ðM0 ! Mmin Þ: When Mmax ! 1; M0 ¼ Mmin ¼ and t ¼ 1, we have A10 ¼ 1; A2 ¼ and Eq (7) becomes: Gð xÞ ¼ exp½Àk expðÀbxފ ð8Þ which is equivalent to the first Gumbel’s asymptote extreme In the case discussed, the data for determination of seismic parameters are the largest earthquake magnitudes X0 ¼ ðX01 ; X02 ; ; X0n Þ; selected from the first part of the catalog, from time intervals t ¼ ðt1 ; t2 ; ; tn0 Þ The seismic parameters sought are h ¼ ðb; kÞ and Mmax From Eq (7), it follows that the maximum likelihood of h is (Kijko and Dessokey 1987): L0 ðhjX0 Þ ¼ n0 Y gðX0i ; ti jhÞ ð9Þ i¼1 where g is the probability density function and ln gðx; tjhÞ ¼ A2 À AðxÞ v0 bt þ ln À bx A10 À A2 A10 À A2 ð10Þ 4.3.2 Combination of extreme and complete catalogs with different threshold magnitudes Let us assume that the second, complete part of the catalog can be divided into s subthreshold catalogs Each of those with a time span Ti is complete starting from  the known  magnitude Mi , i = 1, 2,…, s Let us also assume, that the values X ij ; X ij , j = 1,2,…, ni denote the lower and upper limits of the magnitude Intervals defined in that way contain the real unknown magnitude, ni denotes the number of earthquakes in each subcatalog, and s denotes the number of complete subcatalogs If the size of seismic events is independent of their number, the likelihood function of h for each subcatalog can be written as a product of two functions: Li ðhjXi Þ ¼ Li ðbjXi Þ:Li ðkjXi Þ ð11Þ According to the principle of combination of data (Rao 1973), the joint likelihood based on all data, that is, the likelihood function for the whole span of the catalog is given by LðhjX Þ ¼ s Y Li ðhjXi Þ ð12Þ 4.3.3 Parameter estimation   ^ ^ In order to estimate the parameters ^ h ¼ b; k , the maximum likelihood method is used ^ and ^ The sought parameters b k can be obtained by solving the system of equations: 123 322 Nat Hazards (2012) 64:311–327 ( d ln LðhjXÞ dk d ln LðhjX Þ db ¼0 ¼0 ð13Þ for k and b After cumbersome calculations, a set of two equations was obtained (Kijko and Sellevol 1990): wE1 þ wC1 ¼ 0; wE2 þ wC2 ¼ 0; where ð14Þ   no X Gðx0j tj ÞcFðxoj Þ À Gðxoj tj ÞcFðxoj Þ   ; ¼À tj Gðx0j tj Þ À Gðxoj tj Þ j¼1   n0 X Gðxoj tj ÞBðxoj Þ À Gðxoj tj ÞBðxoj Þ E   w2 ¼ À tj Gðxoj tj Þ À Gðxoj tj Þ wE1 j¼1 wC1 ¼ s gc X À Ti cFðMi Þ; k i¼1 wc2 ¼ s X D1i þ D2i ; i¼1 Bð xÞ ¼ CðMmin ; Mmax ÞF ð xÞÀEðMmin ; xÞ; Cðx; yÞ ¼ ½xAð xÞÀyAðyފ=½AðxÞÀAð yފ; D2i ¼ kTi Àni =cF ðMi ފBðMi Þ; Eðx; yÞ ¼ ½xAð xÞÀyAðyފ=½AðxÞ À Að yފ; cF(x) is a complemented cumulative probability function equal to - F(x) and nc ¼ s P ni is the number of earthquakes in the complete part of the catalog The indexes C and E in Eq (14) are introduced in order to distinguish different sources of functions w If they follow from the extreme part of the catalog, they are marked as E Otherwise, they follow from the complete parts of the catalog and are marked as C ^ and ^ k can be found by an For each determined value of Mmax, the sought parameters b iteration procedure However, as L decreases monotonically for Mmax ? ? (Cosentino et al 1977), a more realistic estimation of Mmax can be carried out by introducing some additional conditions Kijko (1984) satisfied the evaluation of Mmax by assuming that the largest observed magnitude Xmax is equal to EXPECT ðxmax jT Þ, the largest expected magnitude in the span of the catalog T: Xmax ¼ EXPECT ðxmax jT Þ ð15Þ And the largest expected magnitude in the time interval T is given by: EXPECT ðxmax jT Þ ¼ Mmax À 123 E1 ðTZ Þ À E1 ðTZ1 Þ À Mmin expðÀktÞ b expðÀTZ2 Þ ð16Þ Nat Hazards (2012) 64:311–327 323 where Zi ¼ kAi =ðA2 À A1 Þ; i ¼ 1; and E(.) denotes an exponential integral function while n0 s P P the span of the catalog consists of two parts, the extreme T0 ¼ ti and complete Ti : i¼1 i¼1 4.4 Results of the parameter estimation for the tsunami source zones Seismic parameters estimated for the tsunami source zones in the East Vietnam Sea by both the Extreme Values and the Maximum Likelihood methods are listed in Tables and Comparison of the Tables and shows that the Mmax values estimated by the maximum likelihood method are of 0.4 units higher than the values, estimated by the Extreme Value method The reasons of that difference in Mmax value can be explained by advantages of the Maximum Likelihood method over the Extreme Value method as described below A considerable implication of incompleteness of a catalog on parameter estimation was observed while applying the Extreme Value method For the First Gumbel distribution, quiescent periods in data can lead to unsubstantiable large values of Mmax (Phuong 1991) For the Maximum Likelihood method, the choice of Mmin depends on the complete part of the catalog of observational data available for the study area and the uncertainty of magnitude determination The advantage of the Maximum Likelihood procedure is that it allows incorporating as much magnitude information as possible toward the low values direction In addition, different lower threshold values of magnitude can be chosen and input from the keyboard while running the computational program As for the largest earthquake value, the Maximum Likelihood method also gives more reasonable results compared to the Extreme Value method as it allows the combination of catalog parts of different quality into a single minimally biased recurrence parameter (Kijko Sellevol 1990; Phuong 1991, 1997, 2001) The assumption that the largest earthquake is equal to EXPECT (x_max|T) has a practical meaning in the sense that in some cases it can help to avoid the divergence of iteration during computation Usually, the maximum observed magnitude of the study area was chosen for this value Maximum earthquake magnitude is predicted for the Manila Trench, the Sulu Sea and the Selebes Sea source zones In the East Vietnam Sea region, the Manila Trench source Table Seismic hazard parameters of the tsunami source zones in the South China Sea estimated by the Extreme Value method Tsunami source zone a b Mmax 1a Riukiu—Taiwan 0.170 1.89 7.3 1b West Taiwan 0.179 1.37 6.8 2a North Manila Trench 0.064 1.18 8.3 2b Central Manila Trench 0.085 1.76 8.1 2c South Manila Trench 0.410 1.09 6.3 The Sulu Sea 0.128 1.47 8.0 The Selebes Sea 0.122 1.74 8.1 The South Banda Sea 0.895 1.34 6.4 6a The North Banda Sea 0.155 1.51 7.7 6b The North Banda Sea 0.262 1.67 6.6 North of the East Vietnam Sea 0.077 1.07 6.6 Northwest Borneo-Palawan 0.027 0.38 6.4 West of the East Vietnam Sea 0.025 0.58 6.2 123 324 Nat Hazards (2012) 64:311–327 Table Seismic hazard parameters of the tsunami source zones in the South China Sea estimated by the Maximum Likelihood method Tsunami source zone b b k Mmax 1a Riukiu—Taiwan 2.34 ± 0.26 0.99 ± 0.11 18.81 ± 4.79 7.7 ± 1.60 1b West Taiwan 2.68 ± 0.43 1.14 ± 0.18 11.85 ± 4.90 7.2 ± 0.99 2a North Manila Trench 1.53 ± 0.28 0.65 ± 0.12 2.96 ± 0.90 8.7 ± 0.93 2b Central Manila Trench 2.06 ± 0.15 0.88 ± 0.06 16.50 ± 2.55 8.5 ± 0.85 2c South Manila Trench 1.33 ± 0.57 0.56 ± 0.24 3.17 ± 1.69 6.7 ± 0.28 The Sulu Sea 2.07 ± 0.22 0.88 ± 0.09 16.09 ± 3.56 8.4 ± 1.17 The Selebes Sea 2.06 ± 0.18 0.87 ± 0.08 22.77 ± 4.20 8.5 ± 1.03 The South Banda Sea 2.84 ± 0.55 1.21 ± 0.23 50.58 ± 26.12 6.8 ± 0.76 6a The North Banda Sea 2.52 ± 0.15 1.07 ± 0.06 32.95 ± 5.72 8.1 ± 0.53 6b The North Banda Sea 2.69 ± 0.37 1.14 ± 0.16 18.64 ± 0.61 7.0 ± 0.61 7.0 ± 0.23 North of the East Vietnam Sea 0.70 ± 0.23 0.30 ± 0.10 0.38 ± 0.07 Northwest Borneo-Palawan 0.94 ± 0.79 0.40 ± 0.33 0.07 ± 0.03 6.5 ± 0.42 West of the East Vietnam Sea 0.66 ± 0.58 0.28 ± 0.25 0.07 ± 0.03 6.6 ± 0.28 zone is considered to be most dangerous to the Vietnamese coast Among three subzones of the Manila Trench source zone, the two northern zones are more dangerous compare to the southern one Estimation of average tsunami travel time from the sources to the Vietnamese coast The tsunami source zones in the South China Sea were used to assess roughly the possibility of the threat to the Vietnamese coast Typical scenarios were created for each source zone, with assumption that a tsunamigenic earthquake with Mmax occurred at the centroid of a source zone Then, the average tsunami travel times from all source zones to a list of coastal cities of Vietnam were calculated using TTT software, a freeware provided by NOAA-UNESCO/IOC Partnership to the government organisations involved in providing tsunami warning and mitigation services (NOAA-UNESCO/IOC CD, May 2009) Note that the Mmax values chosen for the scenarios are of the illustration purpose only, as the travel speed of a tsunami is independent of its size The fastest tsunami propagation time from source to site are given in Table As can be seen from the table, it takes about h for a tsunami from the Manila Trench source zones (North and Central) to hit the Vietnamese coast For two source zones located closer to the coast as the West of the East Vietnam Sea and the North of the East Vietnam Sea, average travel time is about h 30 Tsunamis from the far sources, such as the Sulu Sea and West Taiwan source zones takes longer than h until they hit the Vietnamese coast An illustration of the travel time of North Manila Trench tsunami scenario is shown in Fig Table lists the travel time of tsunami generated by a scenario earthquake from the North Manila Trench source zone to the coastal cities of Vietnam (see Fig 5) It is clear from the Table that the cities of the Central Vietnam coast will be the first attacked by tsunamis The average travel time to the Central Vietnam’s coast is approximately h The northern coast segment from Dong Hoi province to the north will be hit h since the tsunami occurence The southern coast from Phan Thiet down south will be affected by 123 Nat Hazards (2012) 64:311–327 325 Table Estimated shortest tsunami travel time from some source zones in the South China Sea to the Vietnamese coast Tsunami source zone Source zone code Shortest travel time Coastal city 1b West Taiwan 1b h 21 Tuy Hoa 2a North Manila Trench 2a h 24 Tuy Hoa 2b Central Manila Trench 2b h 45 Tuy Hoa 2c South Manila Trench 2c h 04 Tuy Hoa The Sulu Sea 3 h 38 Tuy Hoa North of the East Vietnam Sea h 44 Tuy Hoa Northwest Borneo-Palawan h 53 Tuy Hoa West of the East Vietnam Sea h 30 Tuy Hoa Fig Travel time of a tsunami scenario, generated on the North Manila Trench source zone with M = 8.4 The big black circle denotes the epicenter of the scenario earthquake Solid color circles denote recorded earthquake epicenters, and the contour lines denote tsunami travel time in hours tsunami after h as the earliest An interesting results obtained as shown in the Table that for all cases, the first point to face tsunami is Tuy Hoa, a coastal city in Central Vietnam 123 326 Nat Hazards (2012) 64:311–327 Table Estimated tsunami travel time from the North Manila Trench source zone to some coastal cities of Vietnam (Epicenter: LAT 20.83, LON 120.13) No Long Lat Name of coastal cities Population Travel time 105.865 19.720 Sam Son 105.662 18.987 Dien Chau 56,000 h 04 220,000 106.553 17.528 Dong Hoi 103,000 h 51 h 43 108.229 16.122 Da Nang 777,000 h 45 109.197 15.345 Ly Son 20,000 h 41 109.302 13.772 Quy Nhon 280,000 h 39 109.370 13.091 Tuy Hoa 148,000 h 24 109.339 12.240 Nha Trang 350,000 h 48 109.074 11.560 Phan Rang 102,000 h 47 10 108.196 10.882 Phan Thiet 205,000 h 13 11 109.035 10.481 Phu Quy 24,000 h 01 12 107.140 10.346 Vung Tau 240,000 h 53 13 106.666 8.601 Con Dao 5,000 h 45 14 111.916 8.633 Truong Sa 2,000 15 105.038 10.014 Rach Gia 205,000 h 24 19 h 06 Conclusion 1) In this paper, nine source zones capable of generating tsunamis affecting Vietnamese coast were delineated in the South China Sea and adjacent sea areas on the basis of the analysis of tectonic feature and geodynamic characteristics of regional faults systems in the southeast Asia Due to its location, the Vietnamese coast will be affected mostly by tsunamis generated from the sources inside the East Vietnam Sea It can hardly be affected by destructive tsunamis, originated in the central Pacific Ocean, from the Sea of Japan and East China Sea in northeast side and even from the mega subduction zones as the Sundaland and the Philippines 2) Statistical methods were applied to estimate the seismic hazard parameters for each source zone Maximum earthquake magnitude is predicted for the Manila Trench (8.3–8.7), the Sulu Sea (8.0–8.4) and the Selebes Sea source zones (8.1–8.5) 3) In the East Vietnam Sea region, the Manila Trench source zone is consider to be most dangerous to the Vietnamese coast Calculation results show that it takes about more than h for a tsunami from the North Manila Trench and h 45 from the Central Manila Trench source zones respectively to hit the Vietnamese coast For two source zones located closer to the coast as the West of the East Vietnam Sea and the North of the East Vietnam Sea, average travel time is about h 30 Tsunamis from the far sources, such as the Sulu Sea and West Taiwan source zones takes longer than h until they hit the Vietnamese coast 4) These preliminary estimation of the tsunami threat can be used as a basis for the detail tsunami hazard and risk assessment for Vietnam in the future It is also useful in development of a standard operational procedure in tsunami warning in Vietnam Acknowledgments The authors would like to thank Prof Tjia H D from National University, Kuala Lumpur, Malaysia and Prof Phan Trong Trinh from Institute of Geological Sciences, Vietnam Academy of 123 Nat Hazards (2012) 64:311–327 327 Science and Technology for their helpful discussion and information on tectonic framework of the southeast Asia region We thank two reviewers for their helpful suggestions and comments that improve an earlier version of this manuscript References Anaka T, Satake K, Sakakiyama T, Yanagisawa K, Shuto N (2007) Logic-tree approach for probabilistic tsunami hazard analysis and its application to the Japanese coasts Pure Appl Geophys 164:577–592 Arcas D, Titov V (2006) Sumatra tsunami: lessons from 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zones and strike-slip fault with the same name of Sumatra; the pair of subduction and strike-slip fault zones with the same name of Philippine, the pair of Timor subduction... that it was caused by ‘‘a series of small earthquakes with the maximum being estimated at 3.7 and with a focal depth of 8–12 km occurred off the southwest coast of Hainan Island, China The tide