Estimation of errors in determination of main parameters of earthquake hypocenter, recorded by the national seismic network of Vietnam

Vietnam Journal of Earth Sciences, 40(1), 1-16, Doi: 10.15625/0866-7187/40/1/10875 1 (VAST) Vietnam Academy of Science and Technology Vietnam Journal of Earth Sciences Estimation of errors in determination of main parameters of earthquake hypocenter, recorded by the national seismic network of Vietnam Ngo Thi Lu1,2*, Burmin V. Y.3, Phung Thi Thu Hang1,2, Vu Thi Hoan1, Ha Thi Giang1 1Institute of Geophysics, Vietnam Academy of Science and Technology, Hanoi, Vietnam 2Graduate University of Science and Technology, Hanoi, Vietnam 3Institute of Physics of the Earth, Russian Academy of Sciences. 10, B. Gruzinskaya st., 123995, Moscow, Russia Received 8 June 2017; Received in revised form 27 October 2017; Accepted 10 November 2017 ABSTRACT In this paper the authors present the error estimation in determining main parameters of earthquake hypocenter based on solving the system of linear equations, expressing the relationship between earthquake coordinates and the coordinates of the seismic stations. The results of the error estimation in determining the epicenter coordinates and the focus depth of the earthquakes recorded by the system of 30 seismic stations in Vietnam are presented, interpreted and compared with the results of the previous studies. The results show that the operation of the seismic network of Vietnam is not really optimal, particularly when de- termining the epicenter coordinates and the focus depth of the earthquakes in the East Vietnam Sea region. The national seismic network of Vietnam allows determination of the epicenter coordinates and the focal depth of earthquakes for most of the Vietnam territory with the errors ∆h ≤ 20 km, ∆φ ≤ 4 km, ∆ ≤ 5 km. The errors of the de- termination of the epicenter coordinates and the focal depth of the earthquakes are increasing to the south and south- west areas of the territory of Vietnam and reach the maximum in these areas. Particularly, errors of the determination of the epicenter coordinates (∆φ, ∆λ) and the focal depth (∆h) of earthquakes increase very rapidly toward the East Sea of Vietnam and reach the maximum in the region between the longitudes of 116-118°E. The Vietnam seismic network allows determining the epicenter coordinates and the focal depth of earthquakes in the Northern Vietnam with the smaller errors than in Central and Southern Vietnam, and this fact proves that the dis- tribution of seismic network in the Northern Vietnam is more optimal than the station networks in the Central and Southern Vietnam. Therefore, in order to improve the effectiveness of the Vietnam seismic network, more seismic stations need to be added to the Central and Southern Vietnam. Keywords: Error; estimation of errors; parameter; earthquake hypocenter; seismic network. ©2018 Vietnam Academy of Science and Technology 1. Introduction1 Earthquakes in Vietnam are related mainly *Corresponding author, Email: ngothiluigp@gmail.com with principal active fault zones like Dien Bien Phu fault, Son La fault, Red river fault, Ca River fault. Active fault segmentations are determined from geological, geophysical or Ngo Thi Lu, et al./Vietnam Journal of Earth Sciences 40 (2018) 2 geomorphological data (Nguyen Van Hung et al., 2016). The main parameters (coordinates, the focal depth and magnitude) of earthquakes are important characteristics for the estimation of the maximum earthquake in the studied re- gion (Bui Van Duan et al., 2013). The project entitled “Enhancing the seismic network for earthquake prediction and tsunami warning in Vietnam” was started in 2008 and finished at the end of 2016 with a total of 30 seismic sta- tions in the whole territory of Vietnam. Up to now, the network of 30 national seismic sta- tions of Vietnam is in operation. However, there have been no studies on the evaluation of the effectiveness of the above seismic sta- tions; as a result, the accuracy of the earth- quake hypocenter parameters recorded by this network has not yet been clarified. Therefore, the error estimation in determining the main parameters of earthquake hypocenter (epicen- ter coordinates (Δφ, Δλ), focal depth (Δh)) recorded by the seismic network of Vietnam is not only a very important and necessary task in the seismology of Vietnam but also the basis for the verification and examination of the results and outputs of the project “En- hancing the seismic network for earthquake prediction and tsunami warning in Vietnam”. Thus, the calculations in this study will be ap- plied to the network of 30 seismic stations ac- cording to the station list of this project and this network will be called the national seis- mic network of Vietnam. The objective of this study is to estimate the errors in determining main parameters of earthquake hypocenter, recorded by the seis- mic station network in the whole territory of Vietnam, for the purpose of evaluating the ef- fectiveness of this network. It means that it is necessary to carry out the above task in order to answer the question: Can the main parame- ters of earthquake hypocenter be accurately determined from the seismograms recorded by the national seismic network of Vietnam and what is the minimum error? The evaluation of effectiveness and opti- mal planning of seismic network have been considered and conducted by different authors in a variety of studies (Aranovich Z.I., 1977; 1980; Burmin V. Yu., 1976; 1986; 1992; 1994; Ngo, 1990, 1999; Nguyen Quy Hy et al., 1979; Savarenski E. F. et al., 1979; Iosif T. et al., 1972; 1974; Kijko A., 1975;, 1978; 1980; Marshall A. W. et al., 1965; 1969; Sato and Skoko, 1965; Sato and Ochi 1967; Skoko D. et al., 1966; 1968; Uhrhammer R. A., 1980; 1982; Burmin V. Yu. et al., 2001; 2009). For the territory of Vietnam, the same task has been carried out in several works (Burmin V. Yu., Ngo et al., 1992; Ngo, 1990; Nguyen Quy Hy, Pham Van Thuc et al., 1979; Burmin V. Yu. et al., 2009). In the works done by Burmin V. Yu., Ngo et al., 1992; Ngo, 1990, the authors conducted the geometric analysis of seismic network and determined the opti- mal locations for adding seismic stations in Northern Vietnam according to the approach proposed in Burmin V. Yu., 1976; 1986. In the work by Nguyen Quy Hy et al., 1979, the task of optimizing the seismic network in Vi- etnam territory was solved by the method of experimental seismic planning. The authors of work (Burmin V. Yu. et al., 2009) evaluated the effectiveness of seismic network in Northern Vietnam at that time by calculating errors in the determination of main parameters of earthquake hypocenter. Conse- quently, the authors proposed the optimal seismic network in Northern Vietnam includ- ing 14 stations. In this study, we calculate the errors in the determination of earthquake hypocenter pa- rameters, recorded by the seismic network of Vietnam Journal of Earth Sciences, 40(1), 1-16 3 Vietnam, for the purpose of evaluating the ef- fectiveness of this network. We apply the ap- proach that was proposed in Burmin V. Yu., 1986); Burmin V. Yu., Akhmechiev V. M., 1994) and implemented for the Northern Vietnam in Burmin V. Yu. et al., 2009. 2. Theoretical basis of research methodology It is well known that the basis for the de- tailed and comprehensive study on seismicity in a territory is the collection of sufficiently reliable information on the main parameters of earthquake hypocenter in that territory. Then, the accuracy of solving seismological tasks is directly or indirectly related to the accuracy of determining main parameters of earthquake hypocenter. The accuracy of determining main parame- ters of earthquake hypocenter in the heteroge- neous environment is an extremely important problem, especially for the areas with com- plex geological and tectonic structures as the territory of Vietnam. Practical experience and numerical calcu- lations show that the accuracy of determining earthquake hypocenter parameters significant- ly depends on the positions of seismic stations relative to the earthquake hypocenters. From the viewpoint of minimizing errors in the determination of earthquake hypocenter parameters, the seismic network with a given number of stations is considered to be optimal when errors in the determination of earth- quake hypocenter parameters are minimal. Accordingly, the basis for effectiveness eval- uation or optimal planning of seismic station network in a certain territory is the system of equations, representing the relationship be- tween the earthquake hypocenter coordinates and the coordinates of seismic stations as fol- lows: ( ) ( ) ( )Χ Υ− + − + = −xi yi H Vi ti to 2 2 2 2 2 (1) where i = 1, 2, ..., n - the ordinal number of seismic stations; xi, yi - the coordinates of seismic stations; X, Y, H - the coordinates of earthquake epicenter and focal depth; to - time of earthquake occurrence; ti - travel time of seismic wave to the ith station. Vi - seismic wave velocity (apparent velocity), calculated by the ratio between straight line distance from the ith station to earthquake hypocenter and travel time of seismic wave along the dis- tance. In case Vi is the function of variables X, Y, H, xi, yi, the determination of earthquake hy- pocenter coordinates is very complicated. However, if considering the homogeneous en- vironments or environments with constant ve- locity, the task of determining earthquake hy- pocenter coordinates is considerably simpler. Therefore, when solving the task of evaluating the effectiveness of seismic network and choosing the optimal locations of stations, the environment can be considered in a first ap- proximation to be nearly the homogeneous one, it means Vi = V = Const. When adding the parameter η = X2 +Y2 + H2 -V2 t02, the system of equations (1) can be easily converted into the system of linear equations by grouping the unknowns as fol- lows (Burmin V. Yu. et al., 2009): Xxi + Yyi + t0Vi 2ti + 0.5η = f i (2) where i = 1, 2,, n; with n ≥ 3; f i = 0.5 (xi2 + yi2 + V2 ti2); The focal depth is determined by the fol- lowing equation: H2 = η - X2 -Y2 + V2 t02 (3) Equations (2) and (3) determine the coor- dinates X, Y, H and t0 on the condition that the seismic wave velocity is constant. To cal- culate the actual velocity distribution, we con- sider the iteration procedure. With the given values of Vi, the system of linear equations (1) can be converted into the form: Ngo Thi Lu, et al./Vietnam Journal of Earth Sciences 40 (2018) 4 Xxi + Yyi - t0V2ti + 0.5 ξ= f i (4) where i = 1, 2,..., n; ξ = X2 +Y2 + H2; f i = 0.5 [(xi2 + yi2 - Vi2(ti2 + t02)]. To solve the system of equations (4), we need to give the value of t0 in the right-hand side of (4). The first value of t0 can be ob- tained when solving the system of equations (2). The obtained value of t0 is added to the right-hand side of equation (4) in order to solve the system of equations. The obtained value of t0 in the solution of the system of equations (4) is again added to the right-hand side of formula (4) and this equation is repeat- edly solved. If the iteration process is conver- gent, it will provide the solution to the prob- lem of determining earthquake hypocenter coordinates for the heterogeneous environ- ment. Then, the errors of the required parame- ters (of the unknowns) will be determined on- ly by the properties of system matrix and will be the errors of input data. It is easy to see that the matrices of systems of equations (2) and (4) differ only by the multipliers V and Vi. Then, we will write the systems of linear equations, which represent the relationships between earthquake hypocenter coordinates, the seismic wave velocity, and the time at hy- pocenter, in a matrix form as follows: КР = f (5) where K = {kij} - is the matrix of the system, representing the mathematical model of the studied dependence. PT = {pj} = {X, Y, t0, ξ} - is the column vector of sought parameters; f T = {fi} - is the column vector of observed quantities; i = 1, 2,..., n; j = 1, 2,, m; n ≥ m. The solution of equation (5) is found by the least squares method and given by the fol- lowing formula: P = K+f Where K+ is the generalized inverse ma- trix, in this case K+ = (K+K)-1KT. The estimation (3) is true for the error of total vector of unknown parameters in the sys- tem of equations: ∆ ∆ ∆p p K Rv ti i n =       ≤ = +∑ 2 1 1 2/ ~ . .ρ (6) Where Rv R vi i i i n iρ ρ ρ=      = ∑ 2 1 1 2/ ; - is the weight, characterizing the quality of recording in the ith station; R - is the vector whose com- ponents are the corresponding epicenter dis- tances; |∆t| - is the absolute value of the error in determining the travel time of seismic wave to the station. The characteristics of the errors can be different. The errors can be random or systematic, estimated by the deviation be- tween the value of the apparent velocity of seismic wave Vi used in the calculation and the actual value. The objective function J K Rv0 = +~ . ρ determines the accuracy of earthquake hypo- center parameters; essentially, it characterizes the quality of seismic station network. The quantity J0 is the objective function corre- sponding to earthquake hypocenter parameters (J0(Δφ, Δ, Δh)) and is the error of total devia- tion vector when |Δt| = 1 second. When changing the locations of different seismic stations and calculating the corresponding values of the function J0, it is possible to indi- cate the seismic network that ensures the highest accuracy in earthquake positioning. More details on the theoretical basis of the method can be found in (Burmin V. Yu., 1986; Burmin V. Yu. et al., 1994; 2009). Thus, the evaluation of the effectiveness of seismic network is essentially the task of min- imizing the error values in the determination of unknown quantities (earthquake epicenter coordinates and focal depth) from equation (6) or minimizing the values of objective function J0. The specific task in this study is to esti- mate the errors in determining main parame- Vietnam Journal of Earth Sciences, 40(1), 1-16 5 ters of earthquake hypocenter, recorded by the seismic network of Vietnam. Therefore, the coordinates of all seismic stations in the net- work are known. The main parameters and the sketch map of the seismic network of Vietnam are presented in Table 1 and Figure 1. Figure 1. Plan of the existing national seismic network of Vietnam (∆φ)(km) ( - Seismic station) Ngo Thi Lu, et al./Vietnam Journal of Earth Sciences 40 (2018) 6 Table 1. Main parameters of seismic network of Vietnam No. Station code Station coordinates Station name Elevation (m) Longitude Latitude 1 SPVO* 103.83000 22.33300 Sa Pa 1550 2 DBVB 103.01800 21.39000 Dien Bien 480 3 SLV 103.90500 21.33400 Son La 607 4 HBVB 105.3277 20.8422 Hoa Binh 54 5 BGVB 106.22700 21.29000 Bac Giang 13 6 PLVO* 106.63000 20.80600 Phu Lien 5 7 VIVO* 105.70000 18.54800 Vinh -6 8 DLV 108.48300 11.90000 Da Lat 1530 9 HGVB 104.99238 22.83507 Ha Giang 119 10 BCVB 105.85632 22.14992 Bac Kan 112 11 CBVB 106.27118 22.65752 Cao Bang 239 12 MCVB 104.67170 20.83468 Moc Chau 13 LSVB 106.76225 21.82510 Lang Son 285 14 TYVB 107.38933 21.33467 Tien Yen 37 15 LAVB 105.24765 20.13587 Lang Chanh 53 16 THVB 105.78355 19.84475 Thanh Hoa 1 17 CCVB 104.85583 19.05707 Con Cuong 30 18 HUVB 107.56890 16.41553 Hue 8 19 BMVB 107.89300 12.81900 Buon Me Thuot 20 NHAV 109.09236 12.30376 Nha Trang 5 21 BTVB 108.31845 11.05338 Binh Thuan 22 PQVB 108.93737 10.53500 Phu Quy 23 CĐVB 106.60147 8.69512 Con Dao 24 MLAV 103.15500 22.03900 Muong Lay 270 25 VTVB 104.89850 22.25260 Vinh Tuy 71 26 VCVB 104.49433 21.56901 Van Chan 274 27 QBVB 106.32775 17.60315 Quang Binh 28 QNVB 108.74210 15.34753 Quang Ngai 29 GLVB 107.99212 14.23255 Gia Lai 30 BĐVB 109.11109 13.86446 Binh Dinh 10 3. Result: Error estimation in determining main parameters of earthquake hypocenter recorded by the seismic network of Vietnam 3.1. Input data for the calculation When estimating the errors in the deter- mination of main parameters of earthquake hypocenter recorded by the existing seismic network in the whole territory of Vietnam, we have used the following input data: - The coordinates and parameters of 30 seismic stations presented in Table 1. - The model of seismic wave velocity in the Earth’s crust, appropriate for the real envi- ronment in Vietnam, obtained from Ngo et al., 2014. It should be noted that the model of seis- mic wave velocity in the Earth’s crust pro- posed by Ngo et al., 2014 is applied to the depth of Moho boundary. However, according to the requirement of the project “Enhancing the seismic network for earthquake prediction and tsunami warning in Vietnam”, the station network should be able to detect the earth- quakes with magnitude M ≥ 3.5 in the whole territory of Vietnam and with M ≥ 6.5 in the whole area of the East Vietnam Sea. There- fore, we need to calculate and establish the distribution sketch maps of error values in de- termining main parameters of earthquake hy- pocenter, which can be recorded by the exist- Vietnam Journal of Earth Sciences, 40(1), 1-16 7 ing seismic network in the Vietnam territory, for the East Vietnam Sea area. The model of seismic wave velocity obtained from Ngo et al., 2014 only meets this requirement at close distance (800-1000 km from seismic station). Accordingly, based on the combination of three velocity models obtained in the studies by Ngo et al., 2014; Burmin et al., 2001; 2009), we have presented the model in Table 2 that ensures both the characteristics of local velocity model and the characteristics of re- gional velocity model (Table 2). Table 2. Velocity model used in the calculation Accor ing to Ngo et al., 2014; Burmin et al., 2001; 2009 Layer Depth of lay- er boundary (km) Velocity on the surface of boundary (km/s) Velocity at the bottom of boundary (km/s) 1 2.0 2.80 2.85 2 3.0 4.00 4.05 3 21.0 6.20 6.30 4 24.0 6.90 7.20 5 80.0 8.00 8.30 6 130.0 8.30 8.50 7 160 8.50 9.10 8 220 9.30 9.95 3.2. Error estimation in determining main parameters of earthquakes hypocenters, rec- orded by the existing national seismic net- work in the whole territory of Vietnam Error in determining the focal depth (∆h) With the above input data, after many ex- perimental calculations, we have established the sketch map of the distribution of error val- ues in determining focus depth (Δh, km) which can be recorded by the existing national seismic network in the whole territory of Vietnam. The calculated results are presented in Figure 2. The analysis of the results in Fig- ure 2 shows that: The seismic network of Vietnam allows the determination of focal depth in most of Vietnam territory with the error Δh ≤ 20 km and the maximum error Δh max up to 130 km in the East Vietnam Sea area ( within the area between the longitudes of 116-118°E). The error in determining focal depth grad- ually increases toward the south of Vietnam and reaches the maximum in the Southern re- gion with Δh = 30~40km. In the Northern and Central regions, the er- ror in determining focal depth seems to be smaller (Δh ≤ 10 km); however, in the South- ern region and especially in the southwest of this region, the error in determining focal depth is higher; at some locations, the value of Δh is 40 km or greater. The values of the isolines of errors in de- termining focal depth Δh increase rapidly to- ward the East Vietnam Sea and reach Δh = 130-150 km in the region within longitudes of 116-118°E. It means that from the viewpoint of evaluating the effectiveness of station net- work based on the error estimation in deter- mining focal depth, the network of 30 stations of Vietnam is not really optimal, especially when determining the focal depth of earth- quakes outside the Vietnam territory in the East Sea area. Errors in determining the epicenter coor- dinates in latitude (∆φ) and in longitude (∆λ) After many experimental calculations, we have established the sketch map of the distri- bution of error values in determining epicenter coordinates in latitude (Δφ) and in longitude (∆λ) which can be recorded by the existing national seismic network in the whole territo- ry of Vietnam. The results are presented in Figures 3, 4. The analysis of the results in Figures 3 and 4 shows that: With the existing seismic network, it is possible to record and determine the epicenter coordinates in latitude (Δφ) and in longitude (∆λ) in most of Vietnam territory with the er- rors Δφ ≤ 4 km, ∆λ≤ 5 km. The largest errors Ngo Thi Lu, et al./Vietnam Journal of Earth Sciences 40 (2018) 8 for latitude (Δφmax) reaches 14-16 km and for longitude (∆λmax) reaches 35-40 km in the East Vietnam Sea (within the area be- tween the longitudes of 116-118°E). Figure 2. Error distribution in determination of the depth of earthquake hypocenter for the existing seismic network of Vietnam (∆h); - Seismic station; - Isoline of errors in determination of the depth of earthquake hypocenter for the existing seismic network of Vietnam (∆h) (km) Vietnam Journal of Earth Sciences, 39(4), 1-16 9 Figure 3. Error distribution in determination of Y coordinate of hypocenter for the existing seismic network of Vietnam; - Seismic station; - Isoline of errors in determination of Y coordinate of hypocenter for the existing seismic network of Vietnam (∆φ)(km) The errors in determining epicenter coor- dinates in latitude (Δφ) and in longitude (∆λ) increase toward the south and southeast of Vietnam, reaching the maximum in the Southern region with Δφmax = 4 km, ∆λmax = 5 km. In the Northern and Central regions, the er- rors in determining epicenter coordinates are smaller (Δφ ≤ 2 km, ∆λ ≤ 2.5 km); however, in the Southern region and especially in the southwest of this region, the errors in deter- mining epicenter coordinates in latitude and in longitude are higher; at some locations, Δφ Ngo Thi Lu, et al./Vietnam Journal of Earth Sciences 40 (2018) 10 reaches 3 km or greater, and ∆λ reaches 5 km or greater. The values of the isolines of errors in determining epicenter coordinates in latitude Δφ and in longitude ∆λ increase rapidly to- ward the East Vietnam Sea, and reach Δφ = 14-16 km and ∆λ = 35-40 km in the region within the longitudes of 116-118°E. Figure 4. Error distribution in determination of X coordinate of hypocenter for the existing seismic network of Vietnam (∆λ)(km); - Seismic station; - Isoline of errors in determination of X coordinate of hy- pocenter for the existing seismic network of Vietnam (∆λ)(km). Thus, the results of the estimation of errors Δh, Δφ, Δλ show that from the viewpoint of evaluating the effectiveness of seismic net- work based on the error estimation in deter- mining main parameters of earthquake hypo- center (epicenter coordinates (Δφ, Δλ), focal depth (Δh)), recorded by the existing seismic network in the whole territory of Vietnam, the Vietnam Journal of Earth Sciences, 39(4), 1-16 11 network of 30 stations of Vietnam is not really optimal, especially when determining epicen- ter coordinates and focus depth of the earth- quakes in the East Vietnam Sea area. The ex- isting seismic network allows determining ep- icenter coordinates and hypocenter depth in the Northern and Central regions with the smaller errors than in the Southern region. To verify the accuracy of the above remark, we have divided the studied territory into three regions including the Northern, Central and Southern regions of Vietnam and estimated the error in determining focal depth (Δh) for each region. The results are presented in Figures 5- 7, respectively. The captions of Figures 6, 7 are similar to the caption of Figure 5. Figure 5. Error distribution in determination of the depth of earthquake hypocenter for the existing seismic network in the North of Vietnam (∆h); - Seismic station; - Isoline of errors in determination of the depth of earthquake hypocenter for the existing seismic network in the North of Vietnam (∆h) (km) Ngo Thi Lu, et al./Vietnam Journal of Earth Sciences 40 (2018) 12 Figure 6. Error distribution in determination of the depth of earthquake hypocenter for the existing seismic network in the Central region of Vietnam (∆h) The analysis of the calculated results in Figures 5-7 shows that the seismic network in the Northern Vietnam is relatively dense, the stations are evenly distributed in distance; therefore, the result of error estimation in de- termining focus depth (Δh) is not significantly high and acceptable (Δh ≤ 25 km). However, the calculated results for the seismic network in the Central and Southern regions of Vietnam show that the seismic stations in these two re- gions are inappropriately distributed, the num- ber of stations is smaller than in the Northern region and uneven in distance. In the Central region, the stations are distributed in a nearly straight line in the north-south direction, so the error values in determining focus depth (Δh) are significantly higher than the corresponding results in the Northern region. In the Southern region, there are no seismic stations in the south and southwest of this region, so the error values in determining focus depth (Δh) in- crease quite rapidly toward these directions, reaching Δh = 50 km in some locations. In ad- dition, the isolines of errors obtained in Figure 5 are distributed relatively evenly while those obtained in Figures 6 and 7 are distributed with the more tortuous shape and closer to each oth- er than the results in Figure 5. Vietnam Journal of Earth Sciences, 39(4), 1-16 13 The error estimation in determining epicen- ter coordinates (Δφ, Δλ) has been conducted for the Northern, Central and Southern regions and the same results have been obtained. Figure 7. Error distribution in determination of the depth of earthquake hypocenter for the existing seismic network in the South of Vietnam (∆h) 4. Discussions The above results show that the seismic network in the Northern region allows record- ing and determining earthquake hypocenter parameters with the smaller errors than in the Central and Southern regions. It means that the seismic network in the Northern region is more optimal than in the Central and Southern regions. However, it should be noted that in com- parison with the optimal seismic network (in- cluding 14 stations) proposed for Northern Vietnam in Burmin V. Yu. et al., 2009, the existing seismic network in Northern Vietnam (including 18 stations) allows recording and determining earthquake hypocenter parame- ters in most of this region with the same val- ues of errors of epicenter coordinates (Δφ ≤ 4 km; Δλ ≤ 5 km), but the error of focal depth is higher (Δhmax = 25km) compared to the optimal seismic network proposed in Burmin V. Yu. et al., 2009 (Δhmax = 14km). It means that from the viewpoint of evaluating the ef- fectiveness of seismic network, the existing seismic network in the Northern region is denser than the optimal seismic network (only Ngo Thi Lu, et al./Vietnam Journal of Earth Sciences 40 (2018) 14 including 14 stations) proposed in Burmin V. Yu. et al., 2009. Thus, the existing seismic network in the Northern region is not really economically effective compared to the opti- mal seismic network proposed in Burmin V. Yu. et al., 2009 due to the extra cost of equipment purchase, installation and opera- tion for 4 additional seismic stations. Therefore, in order to improve the effec- tiveness of the seismic network of Vietnam, a number of stations should be added to the Central and Southern regions of Vietnam. In addition, in order to economize, it is possible to reduce 4 stations out of 18 existing stations in the Northern region (if necessary). 5. Conclusions The results of error estimation of epicenter coordinates and focal depth, recorded by the national network of 30 seismic stations of Vietnam allow drawing the following conclu- sions: The existing national seismic station net- work of Vietnam allows determining epicen- ter coordinates and focus depth in most of Vietnam territory with the errors Δh ≤ 20 km, Δφ ≤ 4 km, Δλ ≤ 5 km; Δhmax reaches 130 km, Δφmax reaches 14-16 km, and Δλmax reaches 35-40 km in the East Vietnam Sea area (in the area between the longitudes of 116-118°E). The values of errors in determining epicen- ter coordinates and focus depth increase to- ward the south and southwest of Vietnam and reach the maximum in the Southern region with Δhmax = 40~50 km, Δφmax = 4 km, Δλmax = 5 km. The values of the isolines of errors in de- termining epicenter coordinates (Δφ, Δλ) and focus depth (Δh) increase rapidly toward the East Vietnam Sea, and reach the maximum in the region within the longitudes of 116-118°E. From the viewpoint of evaluating the ef- fectiveness of seismic network based on the error estimation in determining main parame- ters of earthquake hypocenter (epicenter coor- dinates (Δφ, Δλ), focal depth (Δh)), recorded by the existing national seismic network of Vietnam, this network is not really optimal, especially when determining epicenter coor- dinates and focal depth of the earthquakes in the East Vietnam Sea area. The national seismic network of Vietnam allows determining epicenter coordinates and focus depth in the Northern region with the smaller errors than in the Central and South- ern regions. It means that the seismic network in the Northern region is more optimal than in the Central and Southern regions. Therefore, in order to improve the effectiveness of the national seismic network of Vietnam, a num- ber of stations should be added to the Central and Southern regions of Vietnam. 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