TOhoku Geophys. Journ. (Sci. Rep. TOhoku Univ., Ser. 5), Vol. 32, Nos. 3, 4, pp. 77-89, 1990 77 Scaling Relations for Source Parameters Magnitude of Earthquakes in the zu Peninsula Region, Japan and MASAYUK TAKEMURA Kobori Research Complex, Kajima Corporation Akasaka 6-5-30, Minato-ku, Tokyo 107 TOMONOR KEURA Kajima nstitute of Construction Technology, Kajima Corporation Tobitakyu 2-19-1, Chofu-shi, Tokyo 182 RYOSUKE SATO Association for the Development of Earthquake Prediction Mitoshiro-cho 3, Chiyoda-ku, Tokyo 101 (Recieved November 18, 1989) Abstract : Relations among source parameters and magnitude are examined for the earthquakes in the zu peninsula region. Seismic moment M, and fault area S are newly evaluated from S-waves of strong motion records for the 1980 and 1983 earthquake swarm activities. t is found that Mo and S of the events satisfy the similarity relation in the Mo range from 1022 to 1026 dyne cm, which gives us the stress drops as being consistent with the world-wide average of shallow earthquakes. On the other hand, the relation between seismic moment Mo and JMA magnitude M is obtained as follows : log Mo=1.17M +17.72, which is not coincident with the average formula derived from the data for the events in and around Japan. JMA magnitude M of large events in the zu peninsula region shows larger value, when compared with M of the ordinary events with the same seismic moment. The same tendency is also found for inland shallow events in other regions. Judging from the results of the M,--S relation, it is difficult to conclude that the large value of M is due to anything unusual of source parameters. JMA magnitude M is usually determined from maximum amplitudes of seismic-waves at the period of several seconds observed in a local network. One of the possible reasons for the large value of M is in the difference of the excitation of the medium-period surface-waves. 1. ntroduction The zu peninsula, located about 100 km southwest of Tokyo, separates the two troughs of Sagami and Suruga, which are the tectonic boundaries between two plates of the Philippine Sea and the Honshu island (Sugimura, 1972 ; Nakamura, 1984). Moderate large earthquakes have occurred frequently in and around the zu peninsula since 1930. The hypocenters of these events are located at depths of 0 to 20 km in the shallower part of the Philippine Sea plate (shida, 1987). The major destructive events are the 1930
78 MASAYUK TAKEMURA, TOMONOR KEURA AND RYOSUKE SATO North-zu (M = 7.3), the 1974 zu-oki (M =6.9), the 1978 zu-oshima (M =7.0), and the 1980 zu-toho-oki (M =6.7) earthquakes. 11 earthquake swarm activities occurred east off the zu peninsula from 1978 to 1986 and the magnitude of the largest event of each swarm is 2.2 to 6.7 (shida, 1987). Many strong motion records have been obtained in the zu peninsula and in and around the Tokyo metoropolitan area of the recent large events and the earthquake swarm activities. Through the analyses of these records, it has been indicated that the short-period components of the seismic waves are small when compared with those of the events of the same magnitude occurring in other regions of Japan (e.g., Tanaka, 1979 : Nagahashi, 1983 ; Takemura and Ohta, 1983). According to these results, a question arises as to whether or not the scaling relations for source parameters arid magnitude are different in the zu peninsula region from other regions. Source parameters of the events in the zu peninsula region have been evaluated by using various kinds of observation records, and the relations among source parameters and magnitude have been investigated. Abe (1978), Shimazaki and Somerville (1979), and Takeo (1988), respectively, evaluated source parameters for the destructive large events from far-field long-period seismograms, near-field displacement type strongmotion records and the static displacement in the vicinity of the fault. Sasaki et al. (1981) analyzed accelerograms in near field for the aftershocks of the 1978 zu-oshima event, of which magnitude ranges from 1.2 to 2.5, and indicated that the stress drop ranges from 40 to 100 bar for most events. Tsujiura (1983) estimated source spectra for the foreshocks and aftershocks with magnitude of 3.2 to 5.8 of the 1978 zu-oshima event from the seismic-wave records at Dodaira which is about 100 km distance from the source region. t was concluded in spite of large scattering of data that the stress drop of foreshocks takes a low value when compared with that of the aftershocks. The stress drops of the aftershocks are almost consistent with the values estimated by Sasaki et al., (1981). Yoshida et al. (1988) analyzed P wave records obtained by the microearthquake observation and evaluated source parameters for events with magnitude from 1.6 to 4.1 of the 1985 earthquake swarm activity east off the zu peninsula. Some empirical relations among seismic moment, corner frequency of P-wave source spectrum, and magnitude were obtained for the micro-earthquakes. n the present study, we will newly evaluate source parameters for the 1980 and 1983 earthquake swarm activities and elucidate the scaling law of earthquakes in the zu peninsula region. For these purposes, strong motion records in near field are available. 2. Data and Method of Analysis Epicenters of analyzed earthquakes and locations of observation stations are shown in Fig. 1. Each station comprises a vertical array of accelerometers. The underground accelerometers in each station are located in a fairly hard stratum in the period of Miocene of the Tertiary, hence the amplification effects of the seismic waves due to the soft surface-layers are avoided. We analyzed the records by the underground accelerometers installed at GL-36 m in Shuzenji (SZJ) and at GL-38 m in Tateyama (TTY). Figure 2 shows the examples of accelerograms analyzed in this study. Cosine-type
SCALNG RELATONS FOR ZU PENNSULA EARTHQUAKES 79 okyo TTY Fig. 1 Locations of epicenters of analyzed events and of stations. the Shuzenji and Tateyama stations, respectively. 20.] -20 8 2 SZJ NS.0 io 20 SZJ and TTY 5C indicate 60 h.0 B02 TTY NS MAX,3.379 Gai 4-404 --. A -4.D 5EC/ 2^ 60 E10 100 120 3.0-004 NS Q- -3. 0 20 30 to 50 60 5 0 - El NS - 5. 0 10 30 50 60.SEC 813 SZJ MS ti 0 D15 20 25 30 35 A LSEC/ 40 Fig. 2 Examples of accelerograms for analyzed events. 1 8 1 10 io io to Fig. 3 Data window adopted for analysis of accelerograms. The length of the window to is 20 s for the 1980 main shock (M=-6.7) and 7 s for the other events.
80 MASAYUK TAKEMURA, TOMONOR KEURA AND RYOSUKE SATO tapered data-window in Fig. 3 is applied for the S-waves in the spectral analysis. The length of the window is to= 7s. Seismic-moment density M(f) is obtained from S-wave spectra to evaluate seismic moment Mo and fault area S for each event. The far-field spectral amplitude of S-waves Uo(f) in an infinite homogenious elastic medium can be written by the seismic-moment density M(f) as follows (e.g. Kanamori, 1972) : U0(f)=R00111(f)1 (47.60Vs3X) (1) where Roo is the point-source radiation coefficient, X the distance from the center of the fault to the observer, and Vs and p are S-wave velocity and density of the medium. Amplitude spectrum Us (f)obtained from the observed records is related to the spectral amplitude Uo(f) as follows : Us(f)---U0(.1)111(f)Hg(i) exp { 711X1 (Qs Vs )}, (2) where 1-1,(f) and Hg(f) are the absolute values of transfer functions due to instrumental response and ground response for incident seismic waves. The exponential term is for Table 1 Source Parameters of Analyzed Events No. Date and Time (JST) M X(km) (SZJ) Mo x 10" (dyne cm) S (km') 233 4 6 266 269 271 272 302 329 346 355 360 372 374 378 391 771 792 802 804 808 813 1980 JUN 25 18 1980 JUN 27 5 1980 JUN 27 6 1980 JUN 28 11 1980 JUN 28 11 1980 JUN 28 12 1980 JUN 28 12 1980 JUN 29 0 1980 JUN 29 16 1980 JUN 29 19 1980 JUN 30 2 1980 JUN 30 2 1980 JUL 6 14 1980 JUL 6 15 1980 JUL 7 19 1980 JUL 22 5 1983 JAN 16 16 1983 JAN 18 3 1983 JAN 20 0 1983 JAN 20 0 1983 JAN 25 6 1983 JAN 25 7 3.4 4.6 4.9 3.1 3.6 4.9 3.8 3.6 4.1 3.9 4.9 4.6 4.1 4.0 4.5 3.5 4.3 3.9 4.5 3.7 4.0 3.9 23 23 22 25 20 29 32 25 22 29 32 29 29 28 27 7.2 53 120t 31 9.5 280t 27 10 31 46 330t 73t 33 8.3 77t 6.4 25 19 88t 7.9 23 7.7 0.71 1.3 4.1 0.84 1.8 4.1 2.1 0.71 1.81 4.1 5.9 2.1 2.1 1.3 2.4 1.1 1.3 1.1 1.8 0.65 0.40 1.8 t Average of the values at SZJ and at TTY
SCALNG RELATONS FOR ZU PENNSULA EARTHQUAKES 81 the effect of seismic energy attenuation along the propagation path from the source to the station. Qs is a quality factor for S-waves. Table 1 shows the list of analyzed earthquakes. M and X are earthquake magnitude in the JMA (Japan Meteorological Agency) scale and hypocentral distance for the SZJ station. While observed records at SZJ are analyzed for all the events, those at TTY are analyzed only for the Nos. 6, 271, 355, 360, 378, and 802 events, bacause observation records cannot be obtained for the other events at TTY. Results by moto et al. (1981) and moto (1984) indicated that almost all the analyzed events in this study show the strike slip on a vertical fault plane with the N-S strike, which is located in the shallower part of the crust. The TTY and SZJ stations are located respectively in the directions of west and east close to the focal regions. Therefore, SH-waves are dominant in NS-component at each station, hence it is pertinent that the radiation pattern coefficient R0 for the NS-components is taken as 1.0. The transfer function Hg(T) of ground response is assumed to be 2.0, in consideration of the SH-wave incidence to the ground with the outcrop of the hard stratum. This assumption is exactly valid at least in the frequency range lower than the natural frequency fo of the surface layers over the location of the underground accelerometers. ( a ) 1 0 ----\ 1 0 2 O2 i i \ /- \L' iliv\ 111\1 1, UL Z; V r; a~~ i 1,7, 1 4. 1 0, " -- = \ ti-. - -,,, n C Li JAN. 20. 1983 (M=4. 5) SJ NS 1 4 _5 10 - X 106 0' 0 6 JAN. 20, 1983 (M=4.5) S/J NS ( -t - 4 - a91 1! 1 0. 0.2 01.'3 2 5 (.) 2(1 FREQUENCY (Hz) Fig. 4 (a) An example of S-wave di: displacement-spectrum at SZJ corrected for the instrumental response 1W). (b) An example of S-wave displacement-spectrum at SZJ corrected for the instrumental response H1(f) and the effect of seismic energy attenuation along the propagation path. Quality factor Qs is assumed to be 200. Solid line indicates the envelope of the spectrum and fc is the corner frequency. :gl 0.1 0.2 0.5 1 2 5 FREQUENCY (Hz) 1 10 20
82 MASAYUK TAKEMURA, TOMONOR KEURA AND RYOSUKE SATO Table 2. Source Parameters of Large Events Year M Mo (dyne cm) S (km2) References 1930 1934 1974 1974 1976 1978 1980 7.3 5.5 6.9 4.9 5.4 7.0 6.7 2.7 X 1026 9.5 x 1023 5.9 X 1025 3.2 X 1023 2.2 x 10" 1.3 X 1026 5.0 X 1025 5.0 x 1025 264 28 144 10.5 31.5 210 113 71 Abe (1978) Abe (1978) Abe (1978) Abe (1978) Abe (1978) Shimazaki and Somerville (1979) Fukuyama and rikura (1989) This study 10 ill 1 fc '\r\ o" 1, 4, aw >7.!t ar, J JUN 29 1980 (M =6 7) : C SZJ NS 11 1) 1_ riv, (1. 11 1 FREQUENCY (Hz) Fig. 5 S-wave spectrum at SZJ for the 1980 main shock (M=6.7) corrected for the instrumental reponse H1(f) and for the effect of seismic energy attenuation along the propagation path. Quality factor Q., is assumed to be 200. Solid line and f show the envelope of the spectrum and the corner frequency. The natural frequency of surface layers is about 3 Hz at both the SZJ and TTY stations. The accelerometers are force balance type with natural frequency of 450 Hz and damping constant of 0.7. The instrumental response can be approximately written as 1-11(f)---(2zf)Z in the frequency range from 0.1 to 50 Hz. Figure 4(a) shows an example of spectral amplitude of observed S-waves at SZJ for the Jan. 20, 1983 (No. 802) event. The spectrum is corrected for the instrumental response 111(f). The corner frequency can be identified at about 1.5 Hz. The spectrum is also corrected for inelastic attenuation using the Q, values of 200 for SZJ and of 500 for TTY. The Q, values are determined on the assumption that the high-frequency
SCALNG RELATONS FOR ZU PENNSULA EARTHQUAKES 83 27 26 a (._., a., = >, 9:=, -_, o 323 25 22 41141 0/ //0 4./log mo 21( / i 1 3 4 5 6 7 8 M Fig. 6 Relation between seismic moment Mo and JMA magnitude M for the events in the zu peninsula region. Solid circles indicate Mo's determined in this study and Open circles those obtained by other authors. The line (4) is the relation for the events in and around Japan by Sato (1979, 1989), and thick line (5) is that for the events in the zu peninsula region by the method of least squares. decay of source spectrum is proportional to f-2 (Aki, 1967). The determined values are consistent with (2,-value of the crust in northeastern Honshu, Japan by Umino and Hasegawa (1984). Figure 4(b) shows the corrected spectrum Us(f )/H(f)/exp { R-fX1 (Qs VS )}. The seismic moment Mo is evaluated from the spectral amplitude in the frequency range lower than the corner frequency ff. The numeral values of S-wave velocity and density are assumed to be Vs =3.8 km/ s and p =2.5 g/ cm. The source radius r is determined from fc on the basis of a circular crack model by Sato and Hirasawa (1973). On the assumption that the ratio of the rupture velocity Vr to the S- wave velocity V, is 0.8, the relation between r and fc may be written as follows : r =0.3 VS/ (3) The fault area S can be easily calculated from the source radius r. The seismic moment Mo and the fault area S are also shown for each event in Table 1. While the seismic moment Mo with a cross f in Table 1 is evaluated as the average of the values from observed spectra at SZJ and TTY, the fault area S is obtained from the corner frequency fc of the spectrum only at the SZJ station, in consideration of uncertainty of the attenuation correction for the distant station. 3. Results The magnitude range of the earthquakes listed in Table 1 is 3.1 to 4.9. To examine the relations among magnitude and source parameters, we also summarize in Table 2 as a reference the seismic moment M, and the fault area S of large events in the zu
84 MASAYUK TAKEMURA, TOMONOR KEURA AND RYOSUKE SATO 27 26 o, 0 3 (6) 25 r0 0-23 0 r 22 21 _ 0 1 2 3 log S ( k rn2 ) Fig. 7 Relation between seismic moment Mo and fault area S for the events in the zu peninsula region. Solid and open circles indicate the data obtained in this study and by other authors, respectively. Solid line (6) is the relation determined for the events in and around Japan by Sato (1979, 1989) on the assumption of the similarity relations among source parameters. peninsula region by other authors. The seismic moment M. and the fault area S are redetermined by the method in the present study for the 1980 zu-toho-oki earthquake (M =6.7), which is the largest event in the 1980 earthquake swarm. Figure 5 shows the corrected spectrum at SZJ for the 1980 event. The data window of t0 = 20s is used for this event. The corrected spectrum shows that the co-2 fall-off in the frequency range higher than the corner frequency fc. M. and S obtained from the corrected spectrum are also listed in Table 2. The seismic moment M. obtained here is identical with the result by Fukuyama and rikura (1989), while the fault area S is a little smaller than the result as indicated by them. Fukuyama and rikura (1989) determined the fault area from the distribution of aftershocks of the 1980 event. Meanwhile, the fault area S in the present study is evaluated from the corner frequency of S-wave spectrum based on the circular crack model. t may be understood that the fault area estimated in this study corresponds to the area of large displacement on the fault plane (Fukuyama and rikura, 1989). To examine the relation between M. and S, we will adopt the value of fault area obtained from aftershock distribution, since the fault area for the other large earthquakes is estimated from aftershock region of each event. The relation between seismic moment M. and magnitude M is shown in Fig. 6. Sato
c SCALNG RELATONS FOR ZU PENNSULA EARTHQUAKES 85 (1979, 1989) determined the Mo-M relation from the data of earthquakes with M from 4 to 8 in and around Japan as follows : log Mo =1.5M +16.2. (4) This relation is also shown in Fig. 6. We find that the relationship (4) cannot explain the data of large earthquakes in the zu peninsula region. The seismic moments of these events are meaningfully smaller than those calculated from M by the formula (4). A different relation is determined by the method of least squares as follows : proposed log Mo =1.17M +17.72. (5) On the other hand, the relation between seismic moment Mo and fault area S by Sato (1979, 1989) explains the data of events in the zu peninsula region (Fig. 29 28 1. 5 M+ 16. 2 (4) 0..80 O 0/ 8 gc q) /(3... c.) 27 ca.) = 4,' 26 OPetle i./ iz.0 ch 0 25 23 / /O0 41/ log m / o-----1.17m+17.72 (5) 22 4 5 6 7 8 M Fig. 8 Relation between seismic moment Mo and JMA magnitude M for the events of the focal depth shallower than 80 km in and around Japan. The data are summarized by Sato (1989). Solid circles show the data for the inland events in the upper crust, and open circles those for the events in the subduction region along the Pacific coast of Japan and in the region along the eastern margin of the Japan sea. The relation (4) and (5) are explained in Fig. 6.
86 MASAYUK TAKEMURA, TOMONOR KEURA AND RYOSUKE SATO 7), though the Mo-S relation is obtained from the data of almost the same events for the determination of the Ma-M relation by Sato (1989). The relation by Sato (1979, 1989) is as follows : log Mo= 1.5 log S+ 22.3. (6) This relation shows the condition of similarity of earthquake fault (Kanamori and Anderson, 1975). According to Aki (1967), the stress drop Zia on the fault plane is constant irrespectively of seismic moment under the similarity condition. Sato (1979, 1989) indicated that the equation (6) is derived under the assumption of lid= 50 bar. 4. Discussions Masuda (1988) indicated that the seismic moment Mo and corner frequency fc generally show the relation of Mocc fc-3 for the events of Mo from 1022 to 103 dyne cm occurring in various regions all over the world. The same result was obtained by Takemura and Koyama (1983) for the events of Mo from 1022 to 1029 dyne cm in the subduction region along the Japan trench. The relation between Mo and fc for the local earthquakes were examined by io (1986). According to the result by io (1986), the data of events of Mo from 10" to 1021 dyne cm does not support the relation of Moccf3 but the relation of M0ccfc4. Chouet et al. (1978) determined the scaling laws of earthquake source spectra in some regions, and indicated that the corner frequency fc is frequently constant irrespectively of seismic moment Mo for the events of M, smaller than 1022 dyne cm, while larger events show the relation of Mockfc-3. These results suggest that the earthquakes of seismic moment Mo larger than about 1022 dyne cm usually occur under the similarity condition of earthquake fault. The range of seismic moment of the events analyzed in the present study is about 1022 to 1026 dyne cm and the relation between seismic moment Mo and fault area S is explained by the formula (6), which shows the similarity condition of earthquake fault. The stress drop JO is estimated to be about 50 bar from the relation between Mo and S, which is consistent with the values for the 1978 zu-oshima event and its aftershocks by Sasaki et al. (1980), Shimazaki and Somerville (1979), and Tsujiura (1983). According to Geller (1976) and Kanamori and Anderson (1975), a good average of the stress drop is about 50 bar for shallow large events all over the world. it should be concluded from these facts that the earthquakes in the zu peninsula region have the same similarity condition of earthquake fault as ordinary shallow earthquakes. On the other hand, the data of seismic moment Mo and magnitude M for the events in the zu peninsula region cannot be explained by the relationship (4), which is obtained from the data of almost the same events used for determining the relationship (6). Figure 8 shows the comparison of the relationships (4) and (5) to the data of Mo and M for the earthquakes with focal depth shallower than 80 km in and around Japan, which were summarized by Sato (1989). Solid circles indicate the data of inland events occurring in the upper crust, which include the data of the events in the zu peninsula region. Their focal depths are shallower than 20 km. The earthquakes along the
SCALNG RELATONS FOR ZU PENNSULA EARTHQUAKES 87 eastern margin of the Japan sea are indicated by open circles. We can find that the solid circles are better explained by the formula (5). This indicates that the Mo-M relation obtained for the events in the zu peninsula region applies to the inland shallow earthquakes of other regions. Takemura and Ohta (1983) newly defined the magnitude scale Ma determined from peak accelerations of strong ground motions, and examined the difference between M and Ma for about 70 events in and around Japan from 1963 to 1980. The value of M. corresponds with the amplitude of source spectrum in the short period range, because peak acceleration is usually given by short period S-waves. Takemura and Ohta (1983) found four earthquakes showing significantly larger values of M than those expected from the average M-Ma relation. They all occurred inland, of which magnitude M is larger than 6.4 and the focal depth is shallower than 20 km. Three of them are the events in the zu peninsula region. These results suggest that inland shallow large events show larger M value when compared with the expected value not only from the seismic moment but also from the short-period amplitude of source spectrum. JMA magnitude is determined from the maximum amplitudes of seismic waves observed by the displacement-type seismographs with natural periods of about 5 s at many stations. The maximum amplitudes of the displacement records by JMA are usually given by surface-waves at the period of several seconds for shallow earthquakes (e.g. Mamula et al., 1985). Taking into account the shallow focal depth of the inland events, one of the possible reasons for the different relation between Mo and M is the large excitation of medium-period surface-waves near the source regions. The corrected S-wave spectrum in Fig. 5 of the 1980 zu-toho-oki event (M=6.7) can be explained by the co-square model (Aki, 1967) and does not show the anomalous large amplitude at the period of several seconds. This fact also supports the foregoing reason. 5. Conclusion The relations between seismic moment Mo and fault area S and between seismic moment Mo and JMA magnitude M are examined for the earthquakes in the zu peninsula region in the range of Mo from 1022 to 1026 dyne cm. be summarized as follows : The results obtained can (1) The seismic moment Mo and fault area S of these events are explained by the similarity relation by Sato (1979, 1989) as follows : log M0=1.5 log S+ 22.3. (6) The stress drop Zic of these events is about 50 bar, which is consistent value of shallow earthquakes in various regions all over the world. (2) The M0-M relation of these events is obtained as follows : This is different with the average log Mo 1.17M +17.72. (5) from the average formula derived from the data of events in and around Japan by Sato (1979, 1989). The JMA magnitude M of large events in the zu peninsula
88 MASAYUK TAKEMURA, TOMONOR KEURA AND RYOSUKE SATO region shows larger values, when compared with M of the ordinary events with the same seismic moment. These characteristics are also shown for inland shallow events in other regions. Meanwhile, JMA magnitude M shows the same tendency in its relation to peak accelerations of strong ground motions, which are usually given by short-period S-waves. Judging from the definition of the JMA magnitude M, one of the possible reasons for the large value of M is the difference of excitation of the medium-period surface-waves near the source regions. References Abe, K., 1978 : Dislocation, source dimensions and stresses associated with earthquakes in the zu Peninsula, Japan, J. Phys. Earth, 26, 253-274. Aki, K., 1967 : Scaling law of seismic spectrum, J. Geophys. Res., 72, 1217-1231. Chouet, B., K. Aki, and M. Tsujiura, 1978 : Regional variation of the scaling law of earthquake source spectra, Bull. Seism. Soc. Am., 68, 49-79. Fukuyama, E, and K. rikura, 1989: Heterogeneity of the 1980 lzu-hanto-toho-oki earthquake rupture process, Geophys. J. nt., 99, 711-722. Geller, R. J., 1976 : Scaling relations for earthquake source parameters and magnitude, Bull. Seism. Soc. Am., 66,1501-1523. io, Y., 1986: Scaling relation between earthquake size and duration of faulting for shallow earthquakes in seismic moment between 10" and 1025 dyne cm, J. Phys. Earth, 34, 127-169. moto, M.,. Karakama, R.S. Matsu'ura, F. Yamazaki, and K. shibashi, 1981 : Focal mechanisms of the 1980 earthquake swarm off the east coast of the zu Peninsula, Japan, Zisin Ser., 34, 481-493 (in Japanese with English abstract). moto, M., 1984 : Temporal change in the magnitude-frequency relation for the January 1983 zu earthquake swarm, Japan, Zisin Ser. 37, 13-22 (in Japanese with English abstract) shida, M., 1987 : Recent activity in and around the zu peninsula, Proc. Earthq. Predict. Svmpo., 51-60 (in Japanese with English abstract). Kanamori, H., 1972 : Mechanism of tsunami earthquakes, Phys. Earth Planet. nter., 5, 426-434. Kanamori, H., and D.L. Anderson, 1975 : Theoretical basis of some empirical relations in seismology, Bull. Seism. Soc. Am., 65, 1073-1095. Mamula, L., K. Kudo, and E. Shima, 1985 : Distribution of ground-motion amplification factors as a function of period (3-15 sec), in Japan, Bull. Earthq. Res. nst., 59, 467-500. Masuda, T., 1988: Scaling law peculiar to micro-earthquakes, Mathematical Seismology (Suri- Jishin-gaku), 3, 194-203 (in Japanese). Nakamura, K., 1984 : On a hypothesis of the Japan sea-fossa Magna plate boundary, The Earth Monthly, 6, 25-28 (in Japanese). Nagahashi, S., 1983: A study on the effects of earthquake focal depth on the attenuation characteristics of ground motion amplitude against hypocentral distance, Summaries of Technical Papers of Alf, 631-632 (in Japanese). Sasaki, S., H. Sawada, H. Yajima, and A. Sakurai, 1981 : On the characteristics of accelerograms recorded on bedrock near origins-part (2) Peak acceleration and source parameters, Rep. of Central Res. nst. of Electric Power nd., 380032, 1-22 (in Japanese with English abstract). Sato, R., 1979: Theoretical basis on relationships between focal parameters and earthquake magnitude, J. Phys. Earth, 27, 353-372. Sato, R., 1989 : Handbook of fault parameters for Japanese earthquakes, Kajima nstitute Publishing Co. LTD., 1-390 (in Japanese). Sato, T., and T. Hirasawa, 1973 : Body wave spectra from propagating shear cracks, J. Phys. Earth, 21, 415-431. Shimazaki, K. and P. Somerville, 1979 : Static and dynamic parameters of the zu-oshima-kinkai earthquake of January 14,1978, Bull. Seism. Soc. Am., 69, 1343-1378. Sugimura, A., 1972 : Plate boundaries near Japan, KAGAKU, 42, 192-202 (in Japanese). Takemura, M., and J. Koyama, 1983 : A scaling model of low-frequency earthquakes-relation of
SCALNG RELATONS FOR ZU PENNSULA EARTHQUAKES 89 source spectra between tsunami earthquakes and small low-frequency earthquakes, Zisin Ser. //, 36, 323-336 (in Japanese). Takemura, M., and T. Ohta, 1983 : A new scale of earthquake magnitude based on observed acceleration amplitudes, Annual Rep. Kajima nst. Const. Tech., 31, 113-118 (in Japanese with English abstract). Takeo, M., 1988: Rupture process of the 1980 zu-hanto-toho-oki earthquake deduced from strong motion seismograms, Bull. Seism. Soc. Am., 78, 1074-1091. Tanaka, T., 1979 : A study on peak accelerations of recent destructive earthquakes, The 7 -th Sympo. on Ground Vibrations 3-8 (in Japanese). Tsujiura, M., 1983 : Waveform and spectral features of earthquake swarms and foreshoks in special reference to earthquake prediction, Bull. Earthq. Res. nst., 58, 65-134. Umino, N., and A. Hasegawa, 1984 : Three-dimensional Qs structure in the northeastern Japan Arc, Zisin Ser., 37, 217-228 (in Japanese with English abstract). Yoshida, M., M. Mizoue, H. Chiba, and H. Hagiwara, 1988 : P-wave source spectra and source parameters of small earthquakes near east coast of zu Peninsula, central Japan, Bull. Earthq. Res. nst., 63, 99-113 (in Japanese with English abstract).