Seismic activity characteristics in the East Sea area

Vietnam Journal of Earth Sciences, 40(3), 240-252, Doi: 10.15625/0866-7187/40/3/12616 240 (VAST) Vietnam Academy of Science and Technology Vietnam Journal of Earth Sciences Seismic activity characteristics in the East Sea area Vu Thi Hoan1, Ngo Thi Lu1,2, Rodkin M. V.3, Nguyen Quang4, Phan Thien Huong5 1Institute of Geophysics, (VAST), Hanoi. Vietnam 2Graduate University of Science and Technology, (VAST), Hanoi. Vietnam 3International Institute of Earthquakes Prediction Theory and Mathermatical Geophysics, RAS, Moscow 3Vietnam Union of Geological Sciences 4Hanoi University of Mining and Geology Received 29 January 2018; Received in revised form 15 March 2018; Accepted 30 May 2018 ABSTRACT In this paper, seismic activity characteristics in the East Sea area was analyzed by authors on the base of the uni- fied earthquake catalog (1900-2017), including 131505 events with magnitude 3 ≤ Mw ≤ 8.4. The seismic intensity in the East Sea during the period 1900 - 2017 is characterized by the earthquake representative level Mw = 4.7. The strong earthquake activity in the East Sea area clearly shows the regularity in each stage. In the period from 1900 to 2017, the East Sea area has four periods of strong earthquake activity, each stage is nearly 30 years with particular characteristics. The distribution of the maximum earthquake quantities by years has a cyclicity in all four periods. In each stage there are 1-2 strong earthquakes with Mmax ≥ 8.0. The strong earthquakes with Mmax ≥ 7.5 have occurred by a repeatable rule of 3-5 years in all four stages. This allows the prediction of the maximum earthquake repeat cycle of Mmax ≥ 7.5 in the study area is 3-5 years. In other hand, the maximum magnitude values for the East Sea region has assessed by GEV method with several different predict periods (20, 40, 60, 80, 100 years), with predicted probability 80%. We concluded that it is possible that earthquake have Mmax = 8.7 will occur in next 100 years. Keywords: Seismic activity; macximum earthquake magnitude; earthquake catalog, the East Sea; Generalized Ex- treme Value distribution - GEV. ©2018 Vietnam Academy of Science and Technology 1. Introduction1 Earthquake is one of the most serious dis- asters in Asia. Study of earthquake and seis- motectonics in the mainland is interested re- cently by many workers (Duan et al, 2013; Nguyen et al., 2017). However, the study of the earthquake in the sea is limited due to lack of data and methodology. Based on the rela- tion between the seismotectonics and geody- namic, the East Sea is a part of Southeast *Corresponding author, Email: hoanvt84@gmail.com Asia. Southeast Asia is located at the bounda- ry between the two major seismic activity belts associated with the two-main tectonic- destroying belts: the Pacific Earthquakes belt and the Mediterranean-Hymalaya belt. Con- sequently, South East Asia generally and the East Sea region particularly are influenced by the tectonic activities of these belts. The East Sea area is the transition zone between the Philippine Sea Plate in the east, the Eurasian Plate in the west, and the Australian Plate in the southeast. These plates move with differ- ent velocities. The Philippine sea plate moves Vu Thi Hoan, et al./Vietnam Journal of Earth Sciences 40 (2018) 241 from east to west at the rate of 50 mm/yr (Yingchun Liu et al., 2007) or 55.6 mm/yr (Le Huy Minh et al., 2014). The Eurasian plate move north-west nearly 10 mm/yr (Bautista et al., 2001, Yingchun Liu et al., 2007, Le Huy Minh et al., 2014). And the Australian migra- tion in the north-east direction moves at the speed of 6-7 cm/yr (Phan Trong Trinh et al., 2011). These movements make the East Sea in danger of earthquakes and tsunamis. There- fore, the study about the characteristics of earthquake activities and assessing the maxi- mum earthquake magnitude for this area are significantly important; it plays a critical role in forecasting earthquakes and tsunamis in the East Sea. There are various studies about these topics. We can mention to the earth- quake zonation studies, recent basalts and fea- tures of the East Sea tsunami (Pham Van Thuc, 2001) or Pham Van Thuc and Nguyen Thi Kim Thanh (Pham Van Thuc and Nguyen Thi Kim Thanh, 2004, Le et al. 2017). In the research in 2004, Pham Van Thuc and Ngu- yen Thi Kim Thanh built a zoning evaluation map with scale 1: 1 000 000 for the East Sea and coastal. It is said to be the first project which divides the East Sea into different tec- tonic-dynamic regions. The authors divided the study area which contains the earthquakes catalog collected from 1524 to 2002 into nine sub-regions with corresponding Mmax values. In this paper, the strongest earthquake zone is the North East Coast of the East Sea with Mmax = 7.5 and the weakest one is the western part of the East Sea with Mmax = 3 (Pham Van Thuc and Nguyen Thi Kim Thanh, 2004). Moreover, the tectonic stress field in the East Sea was studied by Nguyen Van Luong, 2002, Nguyen Van Luong et al., 2003, 2008 (a, b). It shows the suitability of geodynamic mechanisms on seismic fault systems. Specif- ically, there are the oblique reverses on the Manila subduction zone. Meanwhile, on the fault systems North East North and East Sea East, the most popular type of focal mecha- nism is strike-slip. In other works, the authors have concentrated on the assessment of earth- quake risk like Pham Van Thuc et al., 2004; Nguyen Van Luong et al., 2003; Nguyen Hong Phuong, 2001; Nguyen Hong Phuong et al., 2012, 2015. There are more studies about the causes of earthquake-tsunami after the Sumatra tsunami in December 2004, (Bui Cong Que et al., 2010; Cao Dinh Trieu et al., 2008; Phan Trong Trinh, 2006; Phan Trong Trinh et al., 2010; Nguyen Dinh Xuyen et al., 2007; Cao Dinh Trieu et al., 2009; Vu Thanh Ca et al., 2008). Vietnam and East Sea earthquake risk map was established in 2004 by Nguyen Hong Phuong (Nguyen Hong Phuong, 2004). In this study, the author used the software to filter the foreshocks and aftershocks, and adjusted the boundaries of the source regions according to the seismic data in the period of 114-2002. In the following years, Nguyen Hong Phuong and his co-authors have continued to study about the seismic source of this area. In these studies, the data included historical seismic data and machine seismic data. Tsunami source zones in the East Sea have been identi- fied, within the Northern Manila Trench is the highest seismic risk with Mmax = 8.7 ± 0.93 for 2658 years (Nguyen Hong Phuong et al., 2012, 2015). This result is the same with re- sult of another Chinese author using earth- quake data from NEIC in the period 1900- 2013 and Global CMT’s catalog in the period 1963-2013 with M> 5.0 (Zhiguo Xu, 2015). Meanwhile, a group of authors from the Nan- yang Technological University in Singapore shown that the tsunami earthquake in this area could reach 9.0 (Megawati al., 2009). It is no- ticeable that these studies didn’t show a speci- fied duration for predicting Mmax. The meth- odology of the Generalized Extreme Value Distribution (GEV) can solve this problem. This probabilistic method has been developed by Pisarenko and his colleagues to evaluate the maximum earthquake magnitude for many catalogs such as the Harvard earthquake list (Pisarenko et al., 2008, 2014), the Japanese earthquake catalog (Pisarenko et al., 2010), Thus, in general, it has been shown that the East Sea area has the potentially high seismic Vietnam Journal of Earth Sciences, 40(3), 240-252 242 risk. However, historical earthquake data and machine data were used and the magnitudes have not been unified. In addition, predicting Mmax does not have a specified duration. In this paper, the characteristics of earthquake activity in the East Sea area will be studied on the basis of the unified earthquake catalog for the period 1900-2017, and Mmax will be esti- mated by GEV method. 2. Data and Methodology 2.1. Data The study area is limited by the coordi- nates φ = 5°S÷30°N; λ = 100°÷127°E. How- ever, some foreshocks and aftershocks in the East Sea region can belong to main shocks which are not in this region. Therefore, to en- sure the independence of events in the study area, it needs to extend the area for collecting seismic data. The area extended is limited by the coordinates ϕ=11.2°S-35.5°N; λ = 92.5°E- 132°E. Earthquake data were collected and adjust- ed from various sources: International Seis- mological Center (ISC), U.S. Geological Sur- vey (USGS), Regional Integrated Multi- Hazard Early Warning System for Africa and Asia (RIMES). The earthquake catalog of the East Sea and neighboring for the period 1900 -2017 has 316516 earthquakes with magni- tude M ≥ 3.0. It should be noted that there is some kind of magnitude scales: local magni- tude (ML), surface-wave magnitude (MS), body-wave magnitude (mb), moment magni- tude (Mw). Therefore, it is necessary to unify magnitude scale. On the other hand, ML, MS, mb have saturated value which is almost the same value of strong earthquakes. In addition, the moment magnitude is used the most com- mon to estimate the seismic hazard and warn tsunami. Therefore, in this paper, the Mw is only scale used. The others will be converted to Mw by practical functions. In the extensive region, period 1900 - 2017, we collected 377784 events with Mw in the range from 3 to 9.1. The spacetime win- dow method which proposed in (Ngo and Tran, 2013) was used to separate the groups of foreshocks and aftershock from the above- mentioned earthquake. The independence cat- alog of the East Sea region and neighboring area includes 202544 events with magnitude Mw (3 ≤ Mw ≤ 9.1) in which has 131505 events with magnitude 3 ≤ Mw ≤ 8.4 belong to the East Sea region. This is a list of earth- quakes that will be used in the calculations below. 2.2. Methodology The distribution function generalized ex- treme value is defined as follows (Pisarenko, 2007, 2008, 2010): GEV(x |σ,µ, ζ) = �exp ( −[1 + ζσ ⋅(x –µ)]–1ζ , ζ 0; 𝑥𝑥 ≤ µ − σ/ζ , ζ ≠ 0 exp � – exp �− x –µ σ �� , ζ = 0 (1) Where x is variable representing the mag- nitude earthquake value, σ is the scale param- eter, µ is the location parameter, ζ is the form parameter. To determine the GEV function, we need to identify 3 parameters ζ, σ, µ in formula (1). These parameters ζ, σ, µ are determined in each period T, solving by the equations below: 1 𝑛𝑛 ∑ 𝑥𝑥𝑘𝑘 𝑛𝑛𝑘𝑘=1 = 𝜇𝜇 - 𝜎𝜎𝜁𝜁 + 𝜎𝜎𝜁𝜁 𝛤𝛤(1 - 𝜁𝜁) = M1 (2) 1 𝑛𝑛 ∑ (𝑥𝑥𝑘𝑘 𝑛𝑛𝑘𝑘=1 - 𝑀𝑀1)2 = (𝜎𝜎𝜁𝜁)2[𝛤𝛤(1 − 2𝜁𝜁) − (𝛤𝛤(1 − 𝜁𝜁))2] = M2 (3) 1 𝑛𝑛 ∑ (𝑥𝑥𝑘𝑘 𝑛𝑛𝑘𝑘=1 - 𝑀𝑀1)3 = (𝜎𝜎)3 �−2(𝛤𝛤(−𝜁𝜁))3 − 6𝜁𝜁 𝛤𝛤(−𝜁𝜁)𝛤𝛤(−2𝜁𝜁) − 3𝜁𝜁2 𝛤𝛤(−3𝜁𝜁)� = M3 (4) Vu Thi Hoan, et al./Vietnam Journal of Earth Sciences 40 (2018) 243 With Γ (x) is the Gamma function: Γ (t) = ∫ 𝑥𝑥𝑡𝑡−1 ∞ 0 𝑒𝑒 −𝑥𝑥𝑑𝑑𝑥𝑥, n is the number of earth- quakes in each T-intervals, xk is magnitude of kth earthquake. It is important to determine T-intervals fit with each catalog because T-intervals influ- ence the values of the three parameters ζ, σ, µ of the GEV function. To find T-intervals, we determine the density Poisson distribution (λ) of the magnitude values: λ = 𝑁𝑁 𝑡𝑡′ , where N is the number of inde- pendent earthquakes, t is the time between the first event and the last event. The T- intervals value (days) must satisfy three conditions: (a) All T-intervals is non-empty. (b) Value 1 / λT → 0 (with λ is the fre- quency earthquakes with magnitude M ≥ m). (c) Value of parameter ζ is enough stable to determine the GEV function. Choose an interval of values (TL; TH) for time interval durations T, for which the cata- log still contains a sufficient number of T- intervals; Choose in this interval (TL;TH) a finite set of u time-interval durations T(TL ≤ T1 < T2 << Tu ≤ TH); The GEV parameters are estimated by the equations (2-4) for each of the u time - inter- val durations T, which yields the following set of parameters: ζ(T1), ζ(T2),..., ζ(Tu); σ(T1), σ(T2), ...,σ(Tu); µ(T1), µ(T2),..., µ(Tu); To estimate the average values , , of the GEV parameters ζ, σ, µ The τ is the predict period (from the time of the earthquake event was chosen as sup- porting event). The parameters ζ, σ, µ are rep- resented as the functions of τ by the formulas (5-7) below: ζ(τ) = ζ(T); (5) σ(τ) = σ(T)⋅(τ/T)ξ; (6) µ(τ) = µ(T) + (σ(T) /ξ)⋅((τ/T)ξ - 1); (7) The quantile in this period is: Qq(τ) = h + (s/ξ)⋅(a⋅(λτ)ξ - 1) (8) Inside: a = (log(1/q))-ξ , h = µ + (σ/ξ)⋅((λT)-ξ -1; s = σ. (λT)-ξ. When τ → ∞ then Qq(τ) = Mmax(τ)→Mmax: 𝑀𝑀𝑚𝑚𝑚𝑚𝑥𝑥 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡 = lim τ → ∞ 𝑄𝑄𝑞𝑞 (𝜏𝜏) (9) Thus, after finding the appropriate T- intervals, in each time period T-intervals the parameters ζ, σ, µ would be determined. From that we will determine the GEV function, dec- ile point value of Qq(τ), and assess the value Mmax. In order to estimate the Mean Square Error (MSE) of these estimates, we use formulas (Gumbel, 1958): 3. Characteristic of earthquake activity in the East Sea Based on the earthquake catalog with 131505 independent events, this study focused on the seismic activity in the East Sea. The Gutenberg - Richter magnitude- frequency relationship. Base on Table 1, the Gutenberg-Richter re- lation between the number of earthquakes with magnitudes written for the natural loga- rithm is: LgN = 8.89 - 0.91Mw (10) With correlation coefficient R = 0.99 Where N is number of earthquakes of magnitude Mw in certain range (Table 1). ζ σ µ 2/1 )( )/1( 1 2 j         −= ∑ = n j nMES ζζζ 2/1 )( )/1( 1 2 j         −= ∑ = n j nMES σσσ 2/1 )( )/1( 1 2 j         −= ∑ = n j nMES µµµ Vietnam Journal of Earth Sciences, 40(3), 240-252 244 Table 1. The number of earthquakes depened on magnitude value Mw N Log(N) Mw N Log(N) 3-3.4 11297 4.05296313 6-6.4 909 2.95856 3.5-3.9 24373 4.38690899 6.5-6,9 327 2.51455 4-4.4 60435 4.78128853 7-7.4 139 2.14301 4.5-4.9 23336 4.36802642 7.5-7.9 61 1.78533 5-5.4 8357 3.9220504 8-8.4 10 1 5.5-5.9 2261 3.35430056 Table 1 and Figure 1 show that the East Sea has threshold earthquake magnitude M = 4.7. Figure 1. The Gutenberg-Richter frequency-magnitude diagrams (1900 - 2017) Distribution of earthquake number with the depth Base on the collected database, we analyze the distribution of earthquake number with the depth. The results are performed in Figure 2 and Table 2. Figure 2. Distribution of earthquake number depended on depth Table 2. Distribution of earthquake number with the depth H(Km) 50 100 150 200 250 300 350 400 N 90650 21055 9512 4574 2358 858 451 296 % 59.1 59.1 13.7 6.2 3 1.5 0.6 0.3 H(Km) 450 500 550 600 650 700 750 800 N 292 242 410 435 322 46 1 3 % 0.2 0.2 0.3 0.3 0.2 0 0 0 Table 2 and Figure 2 show that the majori- ty of earthquakes in the East Sea area occur in the depth of 0-75 km (79.27%) equivalent to the crust of the Earth. This result is nearly similar to the previous study on the Northern Luzon subduction model where the authors used shorter period data 1619-1997 (Bautista et al., 2001). This proves the objectivity and reliability of this work. Distribution of earthquake epicenters in the period 1900-2017 Based on the earthquake catalog and a re- gional geodynamic scheme in accordance with the structure, we have established an earth- quake epicenter distribution map of the East Sea with Mw ≥ 5.0 (Figure 3). Figure 3 shows that the majority of earthquake epicenters in East Sea region are distributed around Philip- Vu Thi Hoan, et al./Vietnam Journal of Earth Sciences 40 (2018) 245 pine. Noticeably, throughout the study period (1900-2017), there were eight the strongest earthquakes with the magnitude Mw ≥ 8.0, of which the strongest with M = 8.4 occurred on the 12th September 2007 at coordinates φ = - 4.4°N, λ = 101.4°E (Table 3). Most of them located in the eastern and southeastern part of the study area (Figure 3). These results are quite similar to the results obtained by Zhiguo Xu using earthquake catalog’s NEIC from 1900 to 2013, and the earthquake catalog’s Global CMT from 1963 to 2013 (Zhiguo Xu, 2015) or by Hsu using the data period 1973- 2010 with Mw 4.6-7.7 (Hsu et al., 2012). Table 3. The strongest earthquakes catalog (Mw ≥ 8.0) in the East Sea from 1900 to 2017 No. Year Month Day Hour Minute Second Latitude Longitude Depth Mw 1 1910 4 12 0 22 24 25.9 124 235 8.1 2 1918 8 15 12 18 21 6 124.4 20 8.3 3 1920 6 5 4 21 35 23.7 122 20 8.1 4 1924 4 14 16 20 36 6.7 126 15 8 5 1939 12 21 21 0 31 -0.1 122.5 35 8.1 6 1965 1 24 0 11 17 -2.6 126 20 8.2 7 1972 12 2 0 19 52 6.4 126.6 60 8 8 2007 9 12 11 10 26 -4.4 101.4 34 8.4 Figure 3. Earthquake distribution in East Sea and its adjacent regions 1900-2017 (M≥5.0) ←Note: 1, 2 - major faults, active in Late Cenozoic: 1- transverse (a - determine and assume, b - fault the planet); 2 - Large subsidence zone (a - Benhiop zone, b- Other subsidence zone); 3- Expansion structures: a - Deep coastal trenches, b - Sediment tanks within the continental limits and continental shelf; 4 - Deep-water seabed belt; 5, 6 - Moving vectors: 5 - of the main litho- sphere, 6 - of the eastern part of the European - Asian plate. Main arrays are marked by the letters: EU - Eu- rope - Asia, P - Pacific, PH - Philippine Plates. The Ro- man numerals denote the blocks: I - Tibet - Hymalaya, II - Southeast China, III - Indochina, VI - East Sea, V - Middle East, VI - Kalimantan - Iava The time - magnitude distribution of the catalog is presented in Table 4 and in Figure 4. It illustrated that before 1964, the number of earthquakes was not recorded much (few dozen times/year). Later in the year of 1964 - 1983, the number of earthquakes raised to hundreds and since 1984 reached thousands; it reached the peak of 8748 earthquakes in 2012. A part of the phenomenon comes from the seismic network that was sparse and the sensi- tivity of the seismograph which was not high enough to record weak and distant earth- quakes. Hence, considering the rule of strong earthquake activity, we need to pay special attention to the earthquake threshold. Vietnam Journal of Earth Sciences, 40(3), 240-252 246 Earthquake procedure time line in the East Sea period 1900-2017 With N is the number of earthquakes an- nually. The distribution of maximum earth- quake magnitude by year The annual maximum earthquake mag- nitude is shown in Table 5 and Figure 5. Table 4. The time - magnitude distribution of the East Sea’s catalog (3 ≤ Mw ≤ 8.4) from 1900 to 2017 Year N Year N Year N Year N Year N 1900 2 1924 9 1948 7 1972 377 1996 4133 1901 3 1925 14 1949 3 1973 405 1997 3715 1902 2 1926 16 1950 18 1974 358 1998 4567 1903 1 1927 9 1951 45 1975 565 1999 5941 1904 1 1928 8 1952 14 1976 618 2000 5421 1905 1 1929 15 1953 9 1977 604 2001 5421 1906 5 1930 8 1954 17 1978 648 2002 6058 1907 5 1931 18 1955 27 1979 668 2003 5399 1908 4 1932 30 1956 19 1980 956 2004 5461 1909 5 1933 17 1957 25 1981 691 2005 5834 1910 7 1934 21 1958 28 1982 912 2006 6533 1911 2 1935 22 1959 22 1983 911 2007 8188 1912 3 1936 20 1960 17 1984 1125 2008 7402 1913 3 1937 10 1961 20 1985 2059 2009 8307 1914 2 1938 16 1962 26 1986 2800 2010 6990 1915 5 1939 7 1963 29 1987 960 2011 6749 1916 1 1940 10 1964 228 1988 914 2012 8748 1917 1 1941 22 1965 247 1989 1044 2013 7713 1918 8 1942 7 1966 289 1990 1597 2014 8360 1919 8 1943 7 1967 244 1991 1639 2015 8093 1920 3 1944 3 1968 349 1992 1750 2016 3684 1921 4 1945 4 1969 303 1993 2303 2017 3388 1922 5 1946 4 1970 442 1994 2114 1923 8 1947 3 1971 199 1995 3173 Figure 4. Earthquake procedure time line in the East Sea period 1900-2017 Vu Thi Hoan, et al./Vietnam Journal of Earth Sciences 40 (2018) 247 Table 5. The annual maximum earthquake magnitude Year Mmax Year Mmax Year Mmax 1900 7 1940 6.9 1980 6.8 1901 7.5 1941 7.5 1981 6.6 1902 7 1942 7.5 1982 7.1 1903 7 1943 7.8 1983 6.9 1904 7.8 1944 6.8 1984 7.5 1905 7.8 1945 6.8 1985 7 1906 7.3 1946 6.8 1986 7.5 1907 7.6 1947 7.4 1987 6.9 1908 7.2 1948 7.8 1988 7.3 1909 7.6 1949 7.4 1989 7.6 1910 8.1 1950 7.3 1990 7.8 1911 8.2 1951 7.8 1991 7.5 1912 7.5 1952 7.4 1992 7.3 1913 7.8 1953 6.9 1993 7 1914 7.6 1954 6.7 1994 7.9 1915 7.4 1955 7.5 1995 7.2 1916 7.2 1956 6.7 1996 7.9 1917 7 1957 7.3 1997 7 1918 8.3 1958 7.2 1998 7.7 1919 7.1 1959 7.5 1999 7.7 1920 8.2 1960 6.6 2000 7.9 1921 7.5 1961 6.9 2001 7.5 1922 7.5 1962 6.5 2002 7.5 1923 7.4 1963 7.2 2003 7 1924 8 1964 7.4 2004 7.3 1925 7.3 1965 8.2 2005 7.1 1926 6.8 1966 7.7 2006 7.1 1927 7 1967 6.8 2007 8.4 1928 7.5 1968 7.6 2008 7.4 1929 7.3 1969 7.6 2009 7.2 1930 6.9 1970 7.4 2010 7.8 1931 6.8 1971 7 2011 7.4 1932 7.8 1972 8 2012 7.6 1933 6.8 1973 7 2013 7.3 1934 7.6 1974 6.8 2014 7.7 1935 7 1975 7.2 2015 8 1936 7.8 1976 7.9 2016 7.9 1937 7.6 1977 7 2017 7.3 1938 7.7 1978 7.4 1939 8.1 1979 7.1 With Mmax as the maximum earthquake magnitude in the year, Figure 5 shows the cy- clical nature of the strong earthquake activity at each stage. It is possible to divide the study period into 4 stages, each stage lasting nearly 30 years (from 1900 to 2017). Each stage has particular characteristics shown below: Stage 1: From 1900 to 1927, it was charac- terized by the majority of Mmax ≥ 8.0 and the minimum were above 7.0. Stage 2: From 1927 to 1960 with the ma- jority of Mmax ≥ 7.5, while the minimum are 6.7 to 7.0. Stage 3: From 1960 to 1987 was character- ized by the majority of Mmax ≥ 7.5, with some points below 7.5, the minimum points are 6.5 -7.0. Stage 4: From 1987 to 2013 with most of the Mmax in the range of 7.0-7.8. At the end of this period, there was 8.4 in the year 2007. Figure 5 shows that the maximum number of earthquakes is seasonal in all four stages (Figure 5). In each phase, there are 1 to 2 max with Mmax ≥ 8.0. Each 3-5 years, there is one earthquake with magnitude 7.5. This allows forecasting the maximum earthquake repeat cycle of Mmax ≥ 7.5 in the study area of 3-5 years. From the increasing trend of the graph, we can see a new cycle with a maximum earth- quake magnitude. Figure 5. The distribution of maximum earthquake magnitude by year 4. Results of estimating Mmax by the gev method for the East Sea region To assess the maximum earthquake magni- tude in the East Sea region, the used of magni- tude values must be greater than or equal to the selected threshold value. This threshold value must greater than the earthquake magni- tude which represent for catalog of the study Vietnam Journal of Earth Sciences, 40(3), 240-252 248 area and it is sufficiently reliable in calculat- ing parameters of GEV function. Accordingly, the threshold magnitude value was chosen M* = 5.0. In order to ensure the reliability of results, the used data should be continuous. Analysis shows that it is continuous since 1917, so we chose the period from 1917 to 2017 for esti- mating Mmax. There are 12006 earthquakes with M ≥ 5.0 in this period. In next section, we present the calculation results for the given data. Step 1: Calculate the density Poisson dis- tribution (λ) The period from 30/7/1917 (t1) to 8/12/2017 (tn) is used with the daily unit. The total is 36655 days. Density Poisson distribution is calculated as follows: λ = N/t = 12006 /36655 = 0,33 Step 2: Select the jump (T) The longest time of two events in the cata- log is 291 days (from 11/11/1921 to 29/8/1922). Therefore, to satisfy the condition (a) above, the greater value of T-intervals is 291 days. The T-intervals in the correspond- ing product λT are the following: In principle above, the closer values to the value "0" (1/λT) are, the better T-intervals are. From Table 6, the greater T-intervals are, the smaller values of 1/ λT are. However, to satis- fy the condition (c), Figure 6 shows an ap- proximate “stabilization” of the ζ- estimates with T in range 300-350 days. Therefore, the value of T-interval is 350 days. Table 6. Table of T, λT, 1/ λT T(days) 290 295 300 305 310 315 320 325 λT 95 97 98 100 102 103 105 106 1/ λT 0.0105 0.0103 0.0102 0.0100 0.0098 0.0097 0.0095 0.0094 T(days) 330 335 340 345 350 355 360 365 λT 108 110 111 113 115 116 118 120 1/ λT 0.0093 0.0091 0.0090 0.0088 0.0087 0.0086 0.0085 0.0083 Figure 6. Graph the function ζ (T) Step 3: Determine the parameters ζ, σ, µ With T = 350 days, then the number of T- intervals is: n= interger 𝑡𝑡𝑛𝑛−𝑡𝑡1 𝑇𝑇 = interger = 104 We need to solve 104 systems of equations (2-4) to receive 104 sets of the three parame- ters ζ, s, m. Taking the average of these three parameters in turn gives us the value of the parameters: = -0.23; = 0.46; = 6.23. There are results: MSE(ζ) = 0.05; MSE(s) = 0.06; MSE(m) = 0.21. Therefore, the parameters are: ζ = -0.23±0.05; s = 0.46±0.06; m = 6.23± 0.21. Step 4: Determine predicted Mmax In use of earthquake catalog, the last strongest earthquake, which has occurred on January 10th 2017 with magnitude M = 7.3 at latitude ϕ = 4.5°N and longitude λ = 122.6°E. 350 36655 ζ σ µ Vu Thi Hoan, et al./Vietnam Journal of Earth Sciences 40 (2018) 249 So we have chosen this event as supporting event. 𝑀𝑀𝑚𝑚𝑚𝑚𝑥𝑥 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡 = lim τ → ∞ 𝑄𝑄𝑞𝑞 (𝜏𝜏) Using the results of the previous sections, we get the graph of the function Qq(τ) in Fig- ure 7 and its value in Table 7, with probability of 80%. Table 7. The values of Q0,8(𝜏𝜏) at the different 𝜏𝜏 τ (year) 20 40 60 80 100 Period 2017- 2037 2017- 2057 2017- 2077 2017- 2097 2017- 2117 Q0,8(τ) 8.25 8.50 8.6 8.65 8.7 According to the Figure 7 and Table 7 above, we have Q0,8(20) = 8.25. It means the prediction of Mmax is Mmax = 8,25 in the next 20 years from the supporting event. When τ proceeds to infinity (since the value of 100 years), graph of the function Q0,8(τ) is almost unchanged (Figure 7). It means that the Mmax predicted the value for the East Sea region is Mmax = 8.7 with proba- bility 80%. Figure 7. Graph of the function Qq(τ) with q = 0.8 for the East Sea region (M ≥ 5,0) period 1917-2017 5. Discussions Comparing the results obtained in this work with a series of previous research results of different authors in the East Sea region (Pham Van Thuc, 2001, Pham Van Thuc et al., 2004; Nguyen Van Luong et al., 2012; Zhiguo Xu, 2015), the East Sea is considered to be a high risk area for earthquakes, espe- cially the possibility of strong earthquakes from the east of the study area along the Ma- nila Trench. The maximum earthquake magni- tude in the area is estimated at Mmax ≥ 7.5. From the results of calculating the maxi- mum earthquake magnitude Mmax above, we see that when using the universal value distri- bution function GEV, the result will depend on the factors such as the completeness and uniformity of the set: How to select the T jump, and how to select the magnitude earth- quake threshold value. Because of the method of using the GEV predictive function, Mmax is one of the probability methods, so its results are consistent with the predicted results by other probabilistic methods such as the maxi- mum rational method by Nguyen. Hong Phu- ong used Mmax = 8.7 ± 0.93 for a repeat cycle of 2658 years for the northern part of Manila submergence zone (Nguyen Hong Phuong, 2015). Meanwhile, the results in this work are slightly higher than the results of the tectonic geological methods have been ap- plied by other authors such as author Phan Trong Trinh results Mmax = 8.6 (according to the author) fault or Mmax = 8.3 (by fault length) (Phan Trong Trinh et al., 2011); Bui Cong Que evaluated Mmax = 8.5 (in terms of fault length) (Bui Cong Que, 2010); Or, ac- cording to a regular meeting held by the USGS in 2005, this confirmed that the poten- tial for strong earthquakes exceeded 8.5 (Kir- by et al., 2005). This difference may be due to the fact that the tectonic geological methods have evaluated Mmax through intermediate var- iables such as faults. Fault lengths based on fixed assumptions for all source areas fracture is a rectangle that is twice the width of the width; it is also possible that the field results do not fully reflect these parameters. In addi- 0 20 40 60 80 100 120 140 160 180 200 220 240 6 6.5 7 7.5 8 8.5 9 Qq(τ) τ(years) Vietnam Journal of Earth Sciences, 40(3), 240-252 250 tion, the probability result depends on the probability of expectation (the larger the probability, the smaller the Mmax result). Therefore, when evaluating Mmax for any giv- en region, reference should be made to the re- sults of both probabilistic and geological methods. In spite of the similarity of these assess- ments, the results obtained in this work are more reliable because the calculations made using seismic data are purely logarithmic. Re- ceived by machine, the earthquake list was es- tablished on the basis of calibration and unifi- cation of data from different sources for a sin- gle magnitude torque. In addition, other prob- abilistic methods for evaluating Mmax over a very long period, several hundred years or several thousand years, but the results of the Mmax evaluation in this work are limited to pe- riods. It should be noted, however, that during the data period of the study, although the highest density of earthquakes was observed in the eastern part of the East Sea, some of the strongest earthquakes with Mw ≥ 8.0 occurred out in the southeast of the study area. There- fore, in order to confirm that the maximum earthquake magnitude Mmax = 8.7 is predicted for a specific part of the East Sea, it is still necessary to evaluate the maximum magni- tude of the earthquake for the particular re- gion of the zone. That is the direction that re- search should continue in the East Sea. 6. Conclusions Based on seismic data collected from dif- ferent sources, we have the following conclu- sion: The seismic region of the East Sea be- tween 1900 and 2017 is characterized by the magnitude 4.7. The earthquakes are mainly distributed in the earth’s crust at the eastern and southeastern part of the study area. Strong earthquake activity in the East Sea area shows that the cyclicality through each period. From 1900 to 2017, it has four stages of strong earthquake activity, each stage lasts nearly 30 years with particular characteristics. In each phase, there are 1-2 strong earth- quakes with Mmax ≥ 8.0. The strong earth- quakes with Mmax ≥ 7.5 occur according to the rule of repeatability of 3-5 years. On the basis of the unified earthquake catalog in period 1917-2017 with Mw ≥5.0, maximum magnitude values for the East Sea region has assessed by GEV method with sev- eral different predict periods (20, 40, 60, 80, 100 years). With predict period 100 years, we have 𝑀𝑀𝑚𝑚𝑚𝑚𝑥𝑥 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡 = lim τ → ∞ 𝑄𝑄𝑞𝑞 (𝜏𝜏) = 8.7. This result is quite similar to previous re- search results. It proves that the results of pre- vious studies are objective and the application of the GEV method to evaluating Mmax is fea- sible. 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