Hasemi Akiko

Saijo Tadayasu

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Hasemi, Akiko

Saijo, Tadayasu

Tohoku University Repository (TOUR) / 東北大学機関リポジトリ

Effect of Velocity Model on HypocenterDetermination by Small Networks著者 Hasemi  Akiko, Saijo  Tadayasu雑誌名 The science reports of the Tohoku University.Fifth series, Tohoku geophysical journal巻 33号 3-4ページ 273-280発行年 1990-12URL http://hdl.handle.net/10097/45336TOhoku Geophys. Journ. (Sci. Rep.  TOhoku Univ., Ser. 5), Vol. 33, Nos. 3, 4,  pp. 273-280, 1990Effect of Velocity Model on Hypocenter   Determination by Small Networks AKIKO HASEMI          Department of Earth Sciences, Faculty of Science,               Yamagata University, Yamagata 990  TADAYASU  SAIJO Observation Center for Prediction of Earthquakes and Volcanic Eruptions,          Faculty of Science, Tohoku University, Sendai 980                  (Received August 31, 1990)   Abstract : This study investigates the effects of the velocity model on the hypocenter determination using data from a quarry explosion. Travel times were observed within about 7 km around the quarry. The shot position was determined for three different velocity  models  ; the model derived from travel time data and two arbitrary models. The results are summarized as follows. (1) Errors in determined shot position are small irrespective of velocity models if the observation points surround the shot. (2) In cases of biased distribution of observation points, an improper model causes unstable solutions. (3) A knowledge of the average velocity structure can make a considerable contribution to determining the shot position so long as the origin time is not concerned.    Deviation of the determined shot position from the true location was compared with the errors estimated by three different methods.1. Introduction    In recent years, the accuracy of hypocenter determination by small networks has been studied through numerical experiments (Peters and Crosson,  1972  ; Lilwall and Francis,  1978  ; Uhrhammer,  1980  ; Duschenes et al.,  1983  ; Pavlis and Hokanson,  1985  ; Pavlis, 1986). In these studies errors in the velocity model are not considered or assumed to be small compared with velocity uncertainties inherent in the real earth. It may be  difficult to choose a  'reasonable' extent of the modeling error in numerical experiments, because the modeling error varies greatly from region to region.    In order to investigate the effect of modeling errors on hypocenter location in the actual cases, studies by using the observation data from artificial earthquakes are useful. Asano (1954) determined locations of explosions by a small (100 m x 100 m) network and examined the hypocentral errors. Using the data from large seismic explosions, Asano (1959) and  Horiuchi et al. (1981) investigated accuracy of hypocenter determination by the networks of the Japan Meteorological Agency and the Tohoku University, respec-tively. However, studies of this kind are few.    In this study, we examine the influence of the velocity model on hypocenter determi-nation by using travel times from a quarry explosion.274 AKIKO  HASEMI AND TADAYASU  SAIJO2. Data   The locations of shot and observation points are shown in Fig. 1. We observed seismic waves using 2-Hz geophones and portable FM cassette recorders at three to five points for one shot. Recorded signals were sampled at 250 Hz and first arrivals were read on the graphic display. Reading errors were mostly within  +/-0.02  —0.02 sec. Shot Kamatusa Dam • N Hasekura •  40C^  O3 km TakadateDam 740E 742E ^ 5  km Fig. 1 Location of quarry explosion (cross) and observation points (solid circles and open    squares). Open squares indicate the observation points used for determination of shot    position, and solid circles those used for determination of the velocity model.3  km  is5--1  rrl rn  W  8  km 6 4 2  0  E  DI  STANCE  Fig. 2 Travel time curve. Open squares indicate the data used for determination of the    shot position, and solid circles those used for determination of the velocity model.    Solid lines are the travel times expected theoretically for model I given in Table 1.EFFECT OF VELOCITY MODEL ON HYPOCENTER DETERMINATION 275times were recorded by using a disposable pick-up (a small speaker) which was put on the explosive hole. We observed signals for every shot at the point (reference point) where the travel time from the shot position was accurately determined. When shot times were not recorded on the explosive hole, we calculated them from the arrival time at the reference point.    In this region a seismic refraction profile was investigated by Nishizawa et al. (1988). In this study, however, we derive a simpler velocity model from the travel time data of the quarry blasts. Travel times observed are shown in Fig. 2. Using the data shown by the solid circles, the velocity structure was approximated by a two-layer model with P-wave velocities of 3.0 and 4.8 km/sec and a layer boundary at 0.65 km depth. The standard deviation of residuals of all travel time data is 0.06 sec and is much larger than reading error (0.02 sec). 3. Determination of Shot Position    We determined the shot position for three different velocity models given in Table  I. Model I is the two-layer model obtained from observation data. Model II is a single layer model, in which the P-wave velocity is roughly equal to the average velocity ofTable  1. Velocity Models Used to Determine the Shot PositionModelVelocity (km/sec)Layer Thickness    (km) II  III3.0, 4.8  4.0   5.00.65,  co   00  coTable 2. Obtained Depth and Origin TimeDepth (km)Origin Time   (sec)Model  II  III  II  III(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) 0.1  -0 .1 -0 .1  0.1  -0 .2  0.1  -0 .5  0.1  0.1  0.1-0 .1  0.2  -0 .2 -0 .1  -0 .2 -0 .3  -0 .2  -0 .1  -0 .2  -0 .2 -0 .1  -0 .2 -0 .2  -0 .1  -0 .2  -0 .1  -0 .2 -0 .1 -0 .2  -0 .2 0.04  0.00  -0 .02  0.13 -0 .05  0.14 -0 .16  0.10  0.05  0.110.20 0.20 0.16 0.26 0.17 0.31 0.14 0.24 0.18 0.260.38 0.39 0.41 0.44, 0.34, 0.50, 0.42 0.49, 0.38, 0.47,0.48 0.42 0.550.51 0.43 0.52True depth and origin time are -0.2 km and 0.00 sec, respectively. Origin time of (d)-(f) and (h)-(j) did not converge, but oscillated for model  III.276 AKIKO  HASEMI AND TADAYASU  SAIJO(a) N Km E(b)  (C) S (d) 0 • -.5  krn.5km • 0(e)- .50 •- .5 0.5 • -5 04 (g) (h) - .50 • 0 -.5-1.0(I)- .5 0  • ,5 • 0.5 (i)1.0 - .5-1 .0  -.5 •oFig. 3 Epicenter locations determined for model I (solid circles),  II (open circles) and III    (open squares). The true location is at the origin of coordinates. Open squares    connected by a line indicate that the solution did not converge, but oscillated between    them. Location of observation points are also shown by crosses.EFFECT OF VELOCITY MODEL ON HYPOCENTER DETERMINATION 277Model I. As can be seen in Fig. 2, a line with 4.0 km/sec slope fits approximately the travel time data. Model III is also a single layer model, and its velocity is assumed to be higher than that of model II. Shot position was determined by using Geiger's method. In order to get stable solutions, the epicenter and origin time were calculated for fixed values of the shot depth. Depths were varied at 0.1 km intervals and the solution that gives the least sum of squared residuals was found.    Table 2 and Fig. 3 show the results  for various sets in configuration of observation points relative to the shot position. The deviation from the true location for model II is similar in extent to that for model I. This indicates that a knowledge of the average velocity structure like model II is very useful when only hypocenter positions are concerned. The location errors found for model III are not large compared with those for the other models when observation points are distributed uniformly around the epicenter (cases (a) and (b)). However, the solutions for model III do not converge in the cases of (d) through (f) and (h) through (j). This suggests that some knowledge of the velocity structure is necessary to get stable solutions in the case of a biased distribution of observation points. Comparing cases (c) to (f) with (g) to (j), it can be said the velocity structure is more important than the number of stations, so long as the azimuthal coverage of observation points is the same. 4. Estimated Error and Actual Error    Now we compare the deviation from the true position for model I with the errors estimated in the following three different ways. 1) The parameter standard errors obtained with the least squares solution. This may be the most conventional error estimates. 2) Errors computed through a numerical simulation. The data for the simulation were produced by computing travel times from the true shot position for model I and then adding errors which are caused by reading errors and velocity fluctua-tions. Considering quality of data and scatter of travel times in Fig. 2., we assume that the reading errors are normally distributed with the standard deviation of 0.02 sec, and that the velocity fluctuations are uniformly distributed between —10 and 10%. The travel time error resulting from a velocity fluctuation is given as  LlT=Tx4VIV (1) where T is a travel time and  4  VI V is a velocity fluctuation. The shot position was determined for 50 different data sets based on the method used in the preceding section, and then the standard deviation of 50 samples of hypocentral and origin time errors were calculated. This procedure is similar to that used by Lilwall and Francis  (1978) and Duschenes et  al. (1983) for evaluating hypocenter resolution of small seismic networks. 3) Error bounds. Pavlis (1986) has shown that the total error in hypocenter determina-tion is a combination of three  terms  ; the measurement error, modeling errors (difference between the velocity model and the true structure) and a nonlinear term (errors due to linearization of the nonlinear problem). Hypocentral errors due to the second term are bounded as278 AKIKO HASEMI AND TADAYASU  SAM 1,,A,  I  51Z1uTiir,,IS, (2) where  1h, is error of the i-th parameter,  Liu is an upper bound of slowness error  11  Vtrue  -1/  17.0det,  A  , is an element of the pseudoinverse of the matrix A with elements  37;1  3h1, and  S; is the length of ray path. If we assume the standard deviation of measure-ment error to be 0.02 sec and the upper bound of slowness error to be  +  /  -10%, the measurement error term is negligible compared with the modeling error term. Non-linear term is almost impossible to evaluate without a priori information about the size of hypocentral error, and is usually small compared with the modeling error term (Pavlis, 1986). Therefore we estimate hypocentral errors by the bounding criteria given by (2). The error in the depth cannot be obtained by the parameter standard error and the bounding criteria, because the least squares equation is solved for the fixed focal depth.    Table 3 gives the estimated errors with errors in the determined shot position for three different configurations of observation points. The standard deviation of 50 samples of errors obtained by the simulation tends to give underestimated errors. Twice the parameter standard errors is also sometimes slightly smaller than the errors in the determined shot position. Since underestimation of errors are not desirable, the errors in hypocenter determination should be estimated by the maximum error obtained through simulation or by the bounding criteria. The bounding criteria may be more preferable due to the following two reasons. Firstly the values in column 3) in Table 3Table 3. Errors of the Shot Position0) 1)  2)-1 2)-2 3) LIX  JY (b)  JZ  JOT  JX  Y (d)  JZ  JOT    LIX  JY (f)  LIZ  JOT0.19 0.15 0.10 0.00 0.51 0.40  0.30 0.13 0.49  0,06 0.30  0.140.48 ( .29) 0.68 ( .53) 0.10 ( .10) 0.50  (-  .01) 0.34  (  -  .06) 0.08  (-  .05) 0.46  (  -  .03) 0.34 ( .28) 0.10  (  -  .04)0.16  (-  .03) 0.18 ( .03) 0.18 ( .08) 0.04 ( .04) 0.34  (-  .17) 0.18  (  -.22) 0.28 ( .02) 0.09  (  -  .04) 0.40  ( -  .09) 0.16 ( .10) 0.27 ( .03) 0.10 ( .04)0.37 (.18)  0.40 (.25) 0.40 (.30) 0.09 (.09) 0.66  (.15) 0.41 (.01) 0.40 (.10) 0.19 (.06) 0.88 (.39) 0.43 (.37) 0.40 (.10) 0.18 (.04)0.57 ( .38) 0.63 ( .48) 0.08 ( .08) 0.72 ( .21) 0.38  (  -.02) 0.13 ( .00) 0.87 ( .38) 0.48 ( .42) 0.12  (  -.02) JY  , and  LIZ are the errors (in km) in the east-west, north-south and the vertical directions, respectively.  JOT is the origin time error (in sec). Column 0) is the deviation of the shot position determined for model I from the true position. Column 1) is twice the parameter standard errors. Column  2)-1 and 2)-2 are the standard deviation and the maxi-mum absolute value of 50 samples of errors calculated for 50 different data sets, respectively. Column 3) is errors calculated by using the bounding criteria given by equation (2). Numerals in parentheses are the difference from the values given in column 0). The cases (b), (d) and (f) correspond to those in Fig. 3.EFFECT OF VELOCITY MODEL ON  HYPOCEN  TER DETERMINATION 279are nearly the same as or larger than those in column 2)-2. This indicates that the bounding criteria gives fairly exact error bounds. Secondly error bounds can be calcu-lated in the process of the hypocenter determination with minor modification of the computer program. 5. Summary    The results in this study are summarized as follows. (1) Errors in determined shot position are small irrespective of velocity models if the network is developed so as to surround the shot point. (2) An improper model causes unstable solutions in cases of biased distribution of observation points. (3) A knowledge of the average velocity structure can make a considerable contribution to determining the shot position so long as the origin time is not concerned. (4) It is preferable that hypocentral errors caused by the modeling error are estimated by the bounding criteria.    In the present study, data were restricted to  P--wave arrival times. In the case of hypocenter determination of natural earthquakes, S-wave data are also used and other conditions such as velocity structure, focal depth and reading errors may be different in each case. However, studies using artificial earthquakes with known positions and origin times may be helpful to understand problems in hypocenter determination. Acknowledgment  : We thank Messrs. H. Shibuya, S. Sato and T. Nakayama for their cooperation in the observation, and Abezen Sangyo Co. who gave us permission to time the blasts at the quarry. We are grateful to Dr. T. Hirasawa for critical review of this manuscript and constructive suggestions. The present work was supported partly by the  Grant-in-Aid for Scientific Research  No.  61740211, the Ministry of Education, Science and Culture, Japan. Calculation was carried out by ACOS-630 at the Data Processing Center of the Yamagata University.                              References Asano, S.,  1954  : On the accuracy of hypocenter determination I, Bull. Earthq. Res. Inst., 32,  371-       381. Asano, S.,  1959  : On the accuracy of hypocenter determination III, Bull. Earthq. Res. Inst., 37,  337-      345 (in Japanese). Duschenes, J., R.C. Lilwall and T.J.G. Francis,  1983  : The hypocentral resolution of microearthqua-       ke surveys carried out at sea, Geophys. J. Roy. astr. Soc., 72, 435-451. Horiuchi, S., T.  Masuda, S. Asano, T. Yoshii, Y. Kaneda, H. Okada, H. Shimamura and T. Ta-      kanami,  1981  : Accuracy of hypocenter determination as revealed from observations of       seismic waves by off Tohoku explosions, Zisin, Ser. 2, 34, 521-533 (in Japanese). Lilwall,  R.C. and T.J.G. Francis,  1978  : Hypocentral resolution of small ocean bottom seismic        networks, Geophys. J. Roy.  astr. Soc., 54, 721-728. Nishizawa, A., T. Saijo, K. Suyehiro, A. Hasemi and T. Urabe,  1988  : Upper crustal structure        around Kamafusa Dam, Miyagi Prefecture, Japan, using a large airgun on land, J. Phys.        Earth, 36, 237-248. Pavlis, G.L.,  1986  : Appraising earthquake hypocenter location  errors a complete, practical        approach for single-event locations, Bull. Seism.  Soc, Am., 76, 1699-1717. Pavlis, G.L. and N.B. Hokanson,  1985  : Separated earthquake location, J. Geophys. Res., 90,  12777-      12789.280 AKIKO HASEMI AND TADAYASU SAIJOPeters, D.C. and R.S. Crosson,  1972  : Application of prediction analysis to hypocenter  determina-       tion using a local array,  Bull. Seism. Soc. Am., 62, 775-788. Uhrhammer, R.A.,  1980  : Analysis of small seismographic station networks, Bull. Seism. Soc. Am.,       70, 1369-1379.

Effect of Velocity Model on Hypocenter Determination by Small Networks

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Effect of Velocity Model on Hypocenter Determination by Small Networks

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