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Complex source processes and the interaction of moderate earthquakes during the earthquake swarm in the Hida-Mountains, Japan, 1998
Tectonophysics 334 (2001) 35±54
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Complex source processes and the interaction of moderate earthquakes during the earthquake swarm in the Hida-Mountains, Japan, 1998 Satoshi Ide* Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo, 113-0032, Japan Received 27 March 2000; accepted 29 January 2001
Abstract This paper presents a set of detailed source models of 18 moderate (M4-5) earthquakes that were part of the swarm activity beneath the Hida-Mountains in central Japan in 1998. To reveal the detailed rupture process, this study uses a waveform inversion procedure with the empirical Green function (EGF). Most of our models show a complicated rupture process that includes several separate rupture areas and that involves ruptures that, in some events, seem to repeat at almost the same location. In our models, we measured as characteristic values the maximums of slip, slip-rate, stress drop, and average rupture propagation velocity. In comparison with the models for larger events determined by similar methods, the maximum slip scales with the cubic squares of the seismic moment for large stress drop events only. The slip-rate has an upper limit of about 1±2 m/ s, and the stress drop is distributed widely from 1 to 50 MPa. The average stress drops, estimated using the corner frequency, are almost uniform at about 1 MPa. The ®rst event in each swarm cluster tends to have a large maximum stress drop, which re¯ects the change in the stress ®eld during swarm activity. The average rupture velocity, determined by the least squares method, is relatively slow and shows a negative relationship with the maximum stress drop. This ®nding cannot be explained by simple crack models and instead suggests a very complicated mechanism like the interactive fault system. The interaction between the slip areas of neighbor events resulted in a non-overlapping slip distribution. This ®nding indicates that previous rupture areas restrict the size and location of later events even in such complex swarm activities. q 2001 Elsevier Science B.V. All rights reserved. Keywords: source process; moderate earthquakes; scaling; interactive faulting
1. Introduction An earthquake rupture is thought to be quite a complex event composed of many small-scale ruptures such as subevents and asperities. This understanding has been con®rmed by a number of detailed * Present address: Address from 14 December 2000 to 27 November 2001: Department of Geophysics, Stanford University, Mitchell 360, Stanford, CA 94305-2215, USA. Fax: 181-3-3813-8026. E-mail address: [email protected] (S. Ide).
source models that use near-®eld strong-motion records from events with a magnitude larger than six (e.g. Hartzell and Heaton, 1983; Archuleta, 1984). Although seismic waveforms show some complexity even in smaller events, including those with a magnitude down to three or four (e.g. Ellsworth and Beroza, 1995; Singh et al., 1998), the source processes of moderate earthquakes have not been studied in detail. The empirical Green function (EGF) method (Hartzell, 1978) is useful for studies of moderate earthquakes if the waveforms from
0040-1951/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0040-195 1(01)00027-0
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S. Ide / Tectonophysics 334 (2001) 35±54
appropriate small events are available as Green functions. Utilizing this method, Mori (1996) determined the detailed rupture process of the M4.3 foreshock of the 1992 Landers earthquake and showed that the rupture propagated toward the mainshock hypocenter. Fletcher and Spudich (1998) analyzed three moderate earthquakes in Park®eld, CA, and found that the ruptures propagated to the same point where the 1966 earthquake initiated. Hellweg and Boatwright (1999) determined the source process of two of the three events studied by Fletcher and Spudich (1998) and showed that rupture behavior is different in seismic and aseismic areas. An earthquake swarm beneath the Hida-Mountain in central Japan, that began on 7 August 1998, provided good data that is suitable for the study of moderate earthquakes. The Hida-Mountains are the highest mountain range in Japan. The range extends about 150 km NNE±SSW and consists of many peaks higher than 3000 m. This region is tectonically active, as characterized by the high uplifting rate of 1±5 mm/ yr during the late Quaternary (National Research Center for Disaster Prevention, 1973). No large (M . 6) earthquake has been reported in this area; however, there are many small earthquakes, and they tend to be a part of swarm events. The 1998 swarm was the largest activity ever recorded in this region. The active period of seismicity for this swarm was in the ®rst two months after initiation, during which more than 7000 earthquakes were manually determined to have occurred. The swarm area was divided into four separate clusters (C1±C4, Fig. 1). In the present study, we determined detailed source models for moderate earthquakes in this swarm activity, extracted their characteristic parameters in order to compare them with larger earthquakes, and investigated possible interaction between events. Although many reports on earthquake complexities have been made, no suf®cient systematic studies investigating generalize features of complex ruptures yet exist. This type of general analysis is important for strong motion prediction, and in a pioneering study in this ®eld, Somerville et al. (1999) derived scaling relations among parameters including seismic moment, rupture area, average slip, and others. They used the models of 15 earthquakes from Mw 5.7 to 7.2. The smallest event they included was the 1979 Coyote Lake earthquake (Mw 5.7), which was close to the
lower limit of what can be analyzed using theoretical waveform calculation. Much more detailed studies of moderate earthquakes are needed if the general features of earthquake rupture complexity in a wide scale range are to be fruitfully discussed. The Hida swarm can provide useful examples for such a discussion. Recently, many studies have demonstrated that change in static stress (Coulomb failure stress) controls the occurrence of future earthquake events. The detailed reviews are provided by Harris (1998). Aoyama et al. (2000) used Coulomb failure stress to successfully explain the migration process of the Hida swarm. In addition to explaining seismicity change, static stress also affects rupture behavior, including slip distribution and directivity. One good example of static stress change as a precipitating factor can be seen in a sequence of large earthquakes beginning in 1939 along the North Anatolian Fault, Turkey, where nine out of ten events were explained by the change in static stress that resulted from preceding events (Stein et al., 1997). This sequence occurred along a well-developed weak zone. However, very few examples exist in the case of a complex fault system such as a swarm area. In the Hida swarm, some of the earthquakes occurred quite close to others, and it is likely that their rupture zones overlapped. The detailed rupture models in the present study provide a good example of the effects of preceding earthquakes on following events in terms of rupture propagation behavior. 2. Overall properties of moderate earthquakes in this study There were 18 moderate earthquakes whose magnitudes, as determined using maximum amplitudes of velocity seismograms by Earthquake Research Institute (ERI), University of Tokyo, MERI, ranged from 4.1 to 5.2 (Table 1). The hypocenters were determined using a master event procedure for each cluster C1± C4. The relative hypocenter location in each cluster is accurate; most standard deviations are less than 0.2 km horizontally and 0.5 km vertically. However, absolute locations, especially depth, and relative locations between clusters are questionable, and we do not discuss absolute location or differences
Fig. 1. (a) Maps showing the hypocenters in the Hida-Mountain earthquake swarm during August and September. The events with MERI of 1 or larger are shown. Arrows indexed as EV01±EV18 indicate the locations of 18 moderate earthquakes. Shaded areas C1±C4 indicate the clusters (see text). In the cross section, the surface geometry is shown along two thick gray lines in the horizontal map. The triangles denote the stations used in the routine hypocenter determination procedure. (b) The temporal distribution of the hypocenters. Beach balls represent the moment tensor solutions determined by waveform inversion.
S. Ide / Tectonophysics 334 (2001) 35±54 37
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S. Ide / Tectonophysics 334 (2001) 35±54
Table 1 Hypocenter and average properties of the moderate earthquakes ID
Date
Time
Lattidue (8)
Longitude (8)
Depth (km)
MERI
Mo (Mw) ( £ 10 15 Nm)
Fault plane (strike/dip/rake)
Ds (MPa)
EV01 EV02 EV03 EV04 EV05 EV06 EV07 EV08 EV09 EV10 EV11 EV12 EV13 EV14 EV15 EV16 EV17 EV18
08/07 08/08 08/09 08/12 08/12 08/14 08/14 08/16 08/16 08/17 08/22 08/22 09/05 09/05 09/07 09/18 09/18 09/20
14:47:14.55 19:51:57.57 12:45:23.00 09:40:34.53 15:13:03.73 14:06:53.27 19:36:14.87 03:28:18.67 03:31:07.92 10:15:05.35 03:55:45.13 04:48:23.21 10:08:00.60 12:02:01.00 16:53:25.03 17:16:10.93 17:16:47.34 06:53:03.40
36.2387 36.2389 36.2387 36.2350 36.2351 36.2969 36.3017 36.3180 36.3233 36.3512 36.2396 36.2387 36.4069 36.4243 36.2349 36.3337 36.3207 36.4400
137.6562 137.6431 137.6365 137.6503 137.6256 137.6330 137.6307 137.6410 137.6327 137.6228 137.6529 137.6692 137.6366 137.6341 137.6616 137.6577 137.6448 137.6331
4.93 5.18 4.98 5.34 3.32 3.05 3.69 2.62 3.35 3.03 2.64 3.31 3.70 3.40 6.43 1.85 3.63 3.30
4.3 4.1 4.4 4.3 4.7 4.2 4.6 4.5 5.2 4.7 4.5 4.4 4.4 4.4 4.1 4.6 4.4 4.4
1.0 (3.9) 1.2 (4.0) 2.5 (4.2) 2.5 (4.2) 7.4 (4.5) 0.7 (3.8) 4.9 (4.4) 1.6 (4.1) 51.4 (5.1) 4.9(4.4) 3.5 (4.3) 0.6 (3.8) 4.0 (4.3) 6.1 (4.5) 0.3 (3.6) 4.7 (4.4) 2.2 (4.2) 1.4 (4.0)
289/88/2163 90/87/169 279/83/2168 283/85/2171 286/77/2171 178/79/10 2175/75/10 92/63/153 98/81/178 97/90/2159 79/84/145 91/84/162 29/65/30 171/89/2 279/76/2159 85/81/2179 104/89/174 23/82/21
0.44 0.57 0.41 0.35 1.19 2.48 1.94 0.54 1.19 0.92 0.97 0.63 0.77 0.59 1.05 0.81 1.38 0.52
between clusters in this study. Moreover, the northernmost cluster, C4, has no nearby station, so the accuracy of the depth is poor and we cannot discuss the vertical hypocenter distribution for this cluster. The mechanisms of these events were determined by moment tensor inversion and are summarized in Table 1 and Fig. 1. We calculated the theoretical waveforms using the discrete wave number method of Bouchon (1981), in which the re¯ection±transmission matrices of Kennet and Kerry (1979) are used and the effect of an elasticity described by Takeo (1985) is introduced. The data in both the moment tensor inversion and the following EGF analysis are from seismograms recorded by the networks maintained by ERI, the University of Tokyo, Nagoya University, the Disaster Prevention Research Institute, Kyoto University, and the Japan Meteorological Agency (Fig. 2). These records are velocity seismograms continuously recorded on 1-Hz sensors, digitized at 100 samples per second, and telemetered to ERI. Since the AD converters have wide dynamic ranges of greater than 20 bits, P-waves, at the very least, were known to have been recorded without saturation, even for the largest event. The instrumental response was corrected to recover the long period component.
Both the theoretical Green function and the data were bandpass ®ltered in the frequency range from 0.1 to 0.2 Hz. All the events were strike-slip earthquakes whose compression axis ran almost northwest±southeast. Fukuyama et al. (1999) determined the moment tensor of these events, except for EV08 and EV17, using broadband seismograms in the frequency range from 0.02 to 0.05 Hz. In spite of the differences in analyzed frequencies and stations, their results are consistent with the mechanism solution obtained in the present study: the resemblance, measured using the correlation of the coef®cient of spherical harmonic basis function, is 0.87 on average. The seismic moments determined by Fukuyama et al. (1999) are systematically larger by 0.31 in Mw units than those in our result. However, after a correction of Mw 0.31, the standard deviation is Mw 0.08, which means that the relative ratio of seismic moments from event to event is consistently determined with the two methods. Hence we consider the error in determination of seismic moment is the order of Mw 0.1, which means a factor of 1.5 in seismic moment. The average stress drop Ds is determined by seismic moment Mo and corner frequency fc. Using the relation between stress drop and seismic moment of a
S. Ide / Tectonophysics 334 (2001) 35±54
39
Fig. 2. Station distribution used in empirical waveform analysis. Circles show the distance from the largest event, EV09.
the source depth b , as follows:
circular crack (Brune, 1970): Mo
16 Dsa 3 7
1
and assuming that the radius of the crack a is given by the corner frequency fc and the shear wave velocity at
a 0:75b=fc :
2
We calculated the average stress drops shown in Table 1. The average stress drops ranges from 0.3 to 3 MPa.
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S. Ide / Tectonophysics 334 (2001) 35±54
3. Process for determining earthquake rupture processes 3.1. Method of empirical waveform inversion The analysis method used to obtain rupture models was a simple EGF method. Although deconvolution techniques are frequently used to obtain relative source time functions for moderate earthquakes (Mori, 1996; Fletcher and Spudich, 1998), for the sake of simplicity we did not adopt these techniques in this study. For each moderate earthquake, we chose a Green function event from among the smaller events with magnitudes at least 1.5 units less than that of the event of interest. The smaller event chosen also must have taken place within 2 km in horizontal distance and 3 km in depth of the event of interest. To ®nd an event having a similar mechanism as the moderate event, we calculated the amplitude ratios of the Pand S-wave pulses between the moderate and small events for all stations. Using this method, the event having the ratio with minimum variance is identi®ed as the Green function event, and the hypocenter of each moderate event is relocated relative to that of the Green function event using the master event method. A Green function represents the velocity waveforms recorded at a station that result from a unit impulsive dislocation at a point x. The Green function is expressed using the waveforms of the Green function event gk(t) as follows: G t; x gk t 2 tt 2 tk 2 T x 1 T xk R xk =Mos R x;
3
where tt and tk are the origin times of the moderate event and the small event, respectively, and xk is the hypocenter of the small event. T(x) is the theoretical travel time of a P-wave or S-wave from x to the station. R(x) is the distance from x to the station, used to account for the geometrical spreading effect. Mos is the seismic moment of the Green function event. Although Eq. (3) is obtained under the assumption that the source time function of the Green function event is a delta function, the duration of the function is actually short but ®nite. To consider this short pulse duration, the data are convolved with an assumed source time function, which is an isoscelestriangle-shaped function whose duration is estimated
using the records from closely located stations. In the case of an M 2 event, this duration is about 0.1 s. The rupture process of an earthquake is expressed by a spatio-temporal slip distribution on an assumed fault plane. The slip-distribution was expanded by basis functions and the unknown parameters are the expansion coef®cients of the basis functions (Ide and Takeo, 1997). The spatial and temporal basis functions have triangular form, and the start time of the ®rst temporal function at each point of the fault plane is set to a time when the S-wave from the hypocenter reaches at that point. By doing this, we can maintain the causality and reduce the number of computations needed. The parameters are determined using the nonnegative least squares algorithm of Lawson and Hanson (1974). Since a rupture process progresses smoothly to some degree, we introduced constraints that minimize the difference between the coef®cients of spatio-temporally neighboring basis functions. If these constraints are considered to be prior information, the problem of determining the coef®cients becomes one of Bayesian modeling, and the weights of the constraints are determined using Akaike's Bayesian Information Criterion (ABIC, Akaike, 1980). The assumed fault plane is one of two nodal planes of the best double couple mechanism determined by moment tensor inversion (Fig. 1, Table 1). If aftershock activity followed the event, and the activity's lineation is consistent with one of these planes, that plane is chosen as the fault plane. Otherwise, the data are inverted using both planes, and the ®nal solution is chosen to minimize ABIC. Consequently, every fault plane is parallel to the local seismicity lineation: east± west in clusters C1 and C3, and north±south in clusters C2 and C4. The area of the fault plane is assumed to be wide in a preliminary inversion and then reduced to the size in which all signi®cant slip is included. The absolute values of slip and slip-rate depend on the uncertain seismic moment of the Green function event. To exclude this uncertainty, the parameter values are multiplied by a scalar number so as to equalize the total seismic moment of the model with that determined by the previous moment tensor inversion (Table 1). The uncertainty of estimated the seismic moment is approximately a factor of 1.5, and the lack of resolution may affect the parameter values. Usually the peak values are reduced by smoothing constraints. Hence even after this equalization, the
S. Ide / Tectonophysics 334 (2001) 35±54
41
Fig. 3. Parameter values (circles) and standard deviations (error bars) determined for EV02. A gray line in each box shows the temporal sequence of the parameter values and is proportional to the source time function. The number of the basis functions in length, width, and time are 11, 13, and 15, respectively. The parameters in the rectangle marked by a star correspond to the hypocenter.
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S. Ide / Tectonophysics 334 (2001) 35±54
peak values of slip and slip-rate still have ambiguity of a factor of 1.5 for their lower limit and a factor of 5 for their upper limit. 3.2. Results Fig. 3 compares the parameter values and their standard deviations for EV02 (Mw 4.0). These parameter values are proportional to the slip-rate. It should be noted that there is a spatio-temporal difference of reliability, even in one solution. Since the smoothing constraints tend to homogenize all parameters, the standard deviations are almost the same throughout the parameter space. Therefore, the reliability for a high slip-rate rupture is high, and the existence of a slow rupture is questionable. Fig. 4 shows the observed and synthetic seismograms of this event. Since these are raw data, highfrequency components are prominent in the observed waveforms and are explained well by the synthetic waveforms. Most of the data are vertical components around the onset of P-waves; some horizontal components that show clear S-wave pulses have been added. Adding horizontal components in this way is commonly used as a way of choosing data for all events. Since all the earthquakes in the Hida swarm are of the strike-slip type, impulsive SH-waves can be observed clearly for some stations as the NS component of KTJ, the EW component of KYJ, and the NS component of SAKI in Fig. 4. These records are quite useful for improving resolution. Fig. 5 shows the total slip distribution as well as the temporal change of the slip area for EV02. This event consists of three asperities that signify areas of relatively large slip-rate in the present paper; these are at the hypocenter, at 0.4±0.6 s after in a shallow area, and at 0.6±0.7 s after in a deep area 1 km east. Using this ®nal slip distribution, we can estimate the static stress drop distribution (Fig. 5) using the method of Kubota et al. (1997). We computed the summation of the stress change caused by the ®nal slips on all of small fractions of fault plane by using the analytic solution for the elastic half space of Okada (1992). We assumed the Poisson's ratio and the rigidity of the half space as 0.25 and 30 GPa, respectively. Each zone of asperity has a larger vertical extent than horizontal extent. This result is probably an artifact of the poor vertical resolution. Since this earth-
quake occurred at a shallow depth, the seismic rays from the source depart almost horizontally to the stations, and the travel time difference is small. This is a common problem for all events in this analysis, and we should be aware that the arti®cial vertical smoothing may have reduced the peak slip and sliprate values. The result shown in Fig. 5 depends on using one speci®c Green function event; however, almost the same results can be obtained using other Green function events, as demonstrated by Ide (1999) for the 1997 Yamaguchi earthquake. Fig. 6 shows the result using a different Green function event. We can see the same three asperities in slip distribution, rupture history, and stress distribution. Although the qualitative behavior is almost the same, there is some quantitative difference. The time of the maximum slip is 0.1 s later for Fig. 6, and the values of slip and stress drop of the model in Fig. 6 are about 70% as great as the values of the model shown in Fig. 5. Such difference arises from the difference of signal-to-noise ratio, mechanism, and location between two Green function events. We estimated the average rupture propagation velocity because it is a characteristic value of the inhomogeneous rupture process. A line was ®tted to the spatio-temporal locations of all of the basis functions weighted by corresponding coef®cient values (Fig. 7). Since the rupture progress was more complicated for some events, we also estimated the standard deviation. For EV02, the rupture propagation velocity was estimated as 1.64 ^ 0.47 km/s. This value does not signify the propagation velocity of the rupture front but rather the average movement of the moment centroid. Therefore, the value is smaller than that of the rupture front. Using the method just described, we determined the detailed source processes of 15 of the 18 moderate earthquakes as spatio-temporal slip-rate distributions on two-dimensional fault planes. EV14 and EV17 followed shortly after EV13 and EV16, respectively, and their waveforms have a poor signal-to-noise ratio. EV18 occurred at the northern end of the swarm activity and had a small number of aftershocks, so we could not ®nd a good Green function event. For these reasons, these three events were analyzed as horizontal line sources with a ®xed width of 1 km. Table 2 summarizes the characteristic quantities extracted from the detailed rupture models. These
S. Ide / Tectonophysics 334 (2001) 35±54
43
Fig. 4. Comparison between observed (black lines) and synthetic (gray lines) seismograms for EV02. Each set of traces is normalized by the maximum value of observed seismograms shown at the upper left corner.
quantities include the maximum total slip, the maximum slip-rate during the rupture process, the maximum static stress drop, the total rupture duration, and the average rupture propagation velocity. As a measure of the reliability of the solution, the ratio of the maximum parameter value to the maximum stan-
dard deviation value is listed in Table 2. Judging from these values, the model for EV04 was not determined well. Since the waveforms of this event are complex and have long durations, there may be some different mechanism at work that has not been considered in the present analysis method, such as the existence of a
44
S. Ide / Tectonophysics 334 (2001) 35±54
Fig. 5. Source model for EV02. Each rectangle shows the assumed fault plane whose strike and dip are N908E and 878, respectively. (a) Total slip distribution. Contour interval is 0.8 cm. (b) Time progression given as the amount of slip every 0.1 s as labeled. The contour interval is 0.6 cm. (c) Static stress change computed using the slip distribution in (a). The contour interval is 1 MPa.
non-coplanar fault plane or a diverse change of mechanism during the rupture. The rupture behaviors of many events are complex, as in EV02. Fig. 8a shows the rupture history of events that involve spatially separated asperities (EV03, EV07, EV08, EV09, EV10, EV11, and EV16). Such rupture patterns are frequently observed in large earthquakes. In some events, the ruptures occurred repeatedly in a small area around the hypocenter (EV01, EV12, EV13, and EV15, Fig. 8b). The estimated rupture propagation velocities for these events are very small. We found only two events that can each be considered a single asperity event. EV05 propagated unilaterally to the west as a single asper-
ity, and EV06 did not show any directivity of its rupture and terminated within 0.3 s (Fig. 8c). In many events, small ruptures preceded the maximum slip-rate rupture. Such small ruptures correspond to the initial part of the observed waveforms and may be identical to the initial phases of Umeda (1990) and Ellsworth and Beroza (1995).
4. Relations between characteristic quantities 4.1. Scaling relations Fig. 9 shows the scaling relations for the maximum
S. Ide / Tectonophysics 334 (2001) 35±54
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Fig. 6. Source model for EV02 estimated using a different EGF event from that for Fig. 5. (a) Total slip distribution. Contour interval is 0.7 cm. (b) Time progression given as the amount of slip every 0.1 s as labeled. The contour interval is 0.3 cm. (c) Static stress change computed using the slip distribution in (a). The contour interval is 0.7 MPa.
slip, the maximum slip-rate, and the maximum stress drop. To compare the moderate earthquakes of the Hida swarm to larger events, we have appended data from three larger earthquakes, the 1995 Kobe (Hyogoken-Nanbu) earthquake (Mw 6.8, Ide and Takeo, 1997), the 1997 Kagoshima earthquake (Mw 6.1, Wu and Takeo, 2000), and the 1997 Yamaguchi earthquake (Mw 5.9, Ide, 1999), which were analyzed by a method similar to that used for the Hida events. As expected, most of the maximum slips are distributed above the scaling relationship determined by Somerville et al. (1999) for average slip (a thick gray line in Fig. 9a). In the wide range including the Kobe, Kagoshima, and Yamaguchi events, they are
related to the seismic moment by a power of 1/2 to 1/3. If stress drop is constant and geometrical similarity holds, slip depends on the cubic root of seismic moment (Kanamori and Anderson, 1975), which is parallel to the thick gray line in Fig. 9a. Although some events (EV01, EV06, EV09, EV10, and EV13) satisfy this relationship (parallel to the thick line in Fig. 9a), most events have smaller slip than that predicted by geometrical similarity. Since the lack of resolution and smoothing constraints reduced the slip values, these values have large ambiguity to the upper bound, a factor of 5, and a smaller ambiguity with regard to the lower bound, less than a factor 1.5. We have probably underestimated the actual
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S. Ide / Tectonophysics 334 (2001) 35±54
Table 2 Characteristic parameters of the moderate earthquakes ID
Mo ( £ 10 15 Nm)
Dmax (m)
Vmax (m/s)
Ds max (MPa)
Vr (km/s)
R
EV01 EV02 EV03 EV04 EV05 EV06 EV07 EV08 EV09 EV10 EV11 EV12 EV13 EV14 EV15 EV16 EV17 EV18
1.0 1.2 2.5 2.5 7.4 0.7 4.9 1.6 51.4 4.9 3.5 0.6 4.0 6.1 0.3 4.7 2.2 1.4
0.079 0.037 0.039 0.016 0.049 0.051 0.053 0.014 0.47 0.25 0.034 0.026 0.12 (0.092) 0.0087 0.064 (0.037) (0.020)
0.51 0.38 0.27 0.094 0.27 0.97 0.16 0.077 2.16 1.51 0.16 0.19 0.79 (0.34) 0.060 0.40 (0.23) (0.16)
13.3 4.9 4.2 3.8 5.6 7.8 2.6 0.76 32.9 35.6 2.4 2.8 12.1 (9.8) 0.76 6.0 (3.4) (1.3)
0.52 ^ 0.23 1.64 ^ 0.47 1.59 ^ 0.66 1.57 ^ 0.58 2.43 ^ 0.81 2.45 ^ 1.26 1.53 ^ 0.63 2.50 ^ 1.10 0.92 ^ 0.35 1.44 ^ 0.51 1.24 ^ 0.75 1.58 ^ 0.82 1.01 ^ 0.90 (0.83 ^ 0.59) 1.63 ^ 1.08 2.12 ^ 0.86 (2.48 ^ 1.02) (1.83 ^ 0.73)
6.3 5.2 3.7 3.1 4.8 7.8 5.5 4.7 7.4 6.3 4.9 4.1 4.7 6.0 3.6 5.1 5.2 7.6
maximum slip. Nevertheless this is a common problem for all events including the larger three events and the scaling relationship among EV01, EV06, EV09, EV10, EV13, and the larger three events may still hold with such errors. Although slip-rate (Fig. 9b) seems to be proportional to the seismic moment, the deviations are large for the Hida events, and it is also possible that slip-rate has an upper limit of 1±2 m/s that is constant in the wide scale. Since slip-rate is related to the breakdown stress drop of the slip-weakening relation if a crack is propagating at a constant velocity (e.g. Ohnaka and Yamashita, 1989), the maximum slip-rate of about 1±2 m/s re¯ects a scale independent of the material properties of the crustal rock. However, uncertainty of about a factor of 5 suggests that the real limit may be larger. Fig. 9c shows the scaling relation for stress drops, with the maximum stress drop estimated using the detailed slip model and average stress drop estimated from the corner frequency and seismic moment. While average stress drops are almost constant around 1 MPa, the maximum stress drops from the detailed model have wide variation from 1 to 50 MPa. Both groups of stress drops have little size dependence. Although the average stress drop exceeds its maximum value for EV15, this is just an artifact due to
Fig. 7. The method of estimating an average rupture propagation velocity for EV02. Each circle located at the centroid of the basis function has a radius scaled by its coef®cient value. Distance is measured from the hypocenter. The black line and gray lines indicate the line of best estimate and those of the standard deviations, respectively.
S. Ide / Tectonophysics 334 (2001) 35±54
47
Fig. 8. The distributions of slip during the period labeled are shown for each of the models. (a) Earthquakes consisting of several separated asperities. (b) Events showing repeated ruptures at the same location. (c) Nearly single asperity events. Stars represent the hypocenter.
independent estimation. It is also true for maximum stress drop that the smoothing constraints and poor resolution may reduce the stress drop apparently. Of the Hida events, EV01, EV06, EV09, EV10, and EV13 all show both a large slip-rate and a large stress drop and seem to satisfy the geometrical similarity in wide scale range. Among these, EV01,
EV06, and EV13 are the ®rst moderate earthquakes of their respective clusters C1, C2, and C4 (Fig. 1). Although the ®rst event of cluster C3 is EV08, most of C3 is included in the rupture area of EV09. EV10 is also the ®rst event of a non-labeled small cluster area north of C3. These ®ndings imply that the stress drop is largest at the ®rst stage of the
48
S. Ide / Tectonophysics 334 (2001) 35±54
Fig. 8. (continued)
swarm sequence within a small area and gradually decreases as the swarm continues to release accumulated stress. The decrease of stress drop is also responsible for the breakdown of similarity in most of the Hida events. It should be noted that the average stress drop of these events is not different from that of the rest of the swarm event. This means such
a difference is not visible by examining the average stress drop alone. 4.2. Stress drop and rupture propagation velocity Fig. 10 shows the relationship between the maximum stress drops and the rupture propagation velocities in the
S. Ide / Tectonophysics 334 (2001) 35±54
Hida swarm events, the Kobe earthquake, the Kagoshima earthquake, and the Yamaguchi earthquake. Except for EV05 and EV06, which are considered to be single asperity earthquakes, propagation velocity decreases as stress drop increases. It is not easy to estimate the stress drop error; however, the errors are about a factor of 5 and the values of stress drop are distributed in two orders. Hence the observed relationship holds after taking into account the possible errors. This negative correlation is somewhat inconsistent with the previous understanding of crack rupture propagation. Das and Aki (1977) simulated the dynamic rupture of an in-plane two-dimensional crack and found that the rupture propagation velocity is determined by a nondimensional parameter S, de®ned by S
tp 2 t0 ; t0 2 tf
4
where t p, t 0, and t f are the peak, initial, and ®nal (dynamic) stress, respectively. The rupture propagates faster with smaller Svalues. These researchers used a simple maximum stress fracture criterion. A similar result was obtained when the slip-weakening friction law was used (Andrews, 1985). If strength, t p ± t f, is constant throughout the fault plane, a large stress drop, t 0 ± t f, means that S will be small, resulting in fast rupture propagation. This ®nding was con®rmed by Day (1982) in a simulation using a homogeneous strength distribution and an inhomogeneous stress drop distribution. The present results seem to contradict these ®ndings. Even in a case where strength is proportional to stress drop, S is found to be constant, and rupture propagation velocity does not show a negative relationship but is instead found to be constant. Unless strength depends more on stress drop than ®rst order, simple crack simulations cannot show a negative relationship between stress drop and propagation velocity. However, the actual faulting process likely has a very complex structure involving non-coplanar fault planes, and the interaction between these planes may produce the negative relationship. Although the Kobe, Kagoshima, and Yamaguchi earthquakes all demonstrate this negative relationship, there are many examples of events that do not. The well-studied 1992 Landers earthquake (Mw 7.2) propagated at about 2.5 km/s on average (Wald and Heaton, 1994), and the maximum stress drop was
49
larger than 10 MPa (Day et al., 1998). The 1979 Imperial Valley earthquake (Mw 6.5, e.g. Archuleta, 1984), the 1984 Morgan Hill earthquake (Mw 6.2, e.g. Beroza and Spudich 1988), and the 1989 Loma Prieta earthquake (Mw 6.9, e.g. Wald et al., 1991) propagated at about 70% of local shear wave velocity, and the stress drop was more than 20 MPa in these events (Bouchon, 1997). All these negative examples are inland strike slip events and consist of many asperities similar to most of the earthquakes analyzed in this study. A difference in the laws governing the ruptures in moderate and large earthquakes may explain such exceptions. Kame and Yamashita (1997) simulated the initial stage of an earthquake using interactive non-coplanar fault systems and found that rupture propagation is slow before a crack grows to the size where interaction between cracks becomes negligible. Most swarm event can be interpreted as occurring as being this type of interactive rupture. The time of changeover depends on the degree of interaction, and the slow rupture of the Hida events may be attributed to the strong interaction within the swarm area. 4.3. Interaction between events The area of the Hida-Mountain earthquake swarm can be divided into four clusters, C1±C4 (Fig. 1), where moderate earthquakes occurred on the fault plane parallel to the lineation of seismicity, either north±south or east±west. Cluster C1 included 8 moderate earthquakes whose slip areas were determined to lie on two-dimensional fault planes running east±west. Fig. 11 shows how the slip zone of each event extended in comparison with preceding events, using the contours of each slip distribution scaled at its maximum. Except for the ®rst event, EV01, and event EV04, the other six events started near the edge of the slip areas of the preceding event and propagated mainly outside of these areas. Event EV04 appears in the present analysis to have been the most complex and may have had complex mechanisms that cannot be resolved by our inversion scheme, as mentioned in the previous section. The fact that its starting point is surrounded by the former slipped areas may be the reason for such complex mechanisms. Fig. 11(i) shows that the overlap of the slip area is small, except in the case of EV04, whose model has
50
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S. Ide / Tectonophysics 334 (2001) 35±54
51
Fig. 10. Relations between the maximum stress drop and the average rupture velocity. Circles are the maximum stress drops of the moderate earthquake. Squares denote those of KOB, KGS, and YMG represent the 1995 Kobe earthquake, the 1997 Kagoshima earthquake, and the 1997 Yamaguchi earthquake, respectively. Error bars show standard deviations.
low reliability. If these events occurred on one common plane, a non-overlapping slip area signi®es that no given point broke twice with a large slip. This ®nding resembles the slip-area distribution of the Turkey earthquake sequence (Stein et al., 1997). However, locating all of the earthquakes in the Hida swarm in one large common fault plane is somewhat unrealistic. In fact, EV05 and EV11 are located about 500 m away from the plane that ®ts the other events. It is possible that a rupture on a parallel fault system can produce such a pattern, since a slip on one plane can suppress a slip on the adjacent parallel plane, forming
a so-called stress shadow (e.g. Harris, 1998). In any case, this pattern indicates that the stress-®eld of a previous rupture in one region strongly restricts the following rupture processes. We observed similar behavior in the other clusters. In cluster C2, the slip area of EV06 is shallower than that of EV07, and EV07 propagated to a deeper level. In cluster C3, the rupture areas of EV09, EV08, and EV16 are arranged from west to east, although the two-dimensional slip distribution of EV17 is unknown. In cluster C4, each event had aftershock activity whose location was separated clearly and
Fig. 9. Scaling relations. Solid circles show characteristic parameters of the detailed model. KOB, KGS, and YMG represent the 1995 Kobe earthquake, the 1997 Kagoshima earthquake, and the 1997 Yamaguchi earthquake, respectively. (a) Maximum slip. The thick gray line shows the scaling relation presented by Somerville (1998), log Dm 1=3log Mo Nm 2 6:8: (b) Maximum velocity. (c) The solid circles are the maximum stress drop and the open circles are the average stress drop (Table 1).
52
S. Ide / Tectonophysics 334 (2001) 35±54
Fig. 11. The slip areas of eight earthquakes that occurred in cluster C1 (Fig. 1) are projected into one vertical plane running in an east±west direction. (a)±(h) The slip area of each event compared with the slip areas of the previous events. The contour interval is scaled for each event so as to be one-fourth of the maximum slip. A star represents the hypocenter of each event. (i) Plot of all slip distributions in (a)±(h). In this ®gure, contour intervals of 1 cm are common for all events.
distinguishably even in the hypocenter map (Fig. 1). Therefore, such a pattern is the result of the interaction of events and an essential feature of such concentrated earthquake activity. 5. Discussion and conclusions The present research makes a systematic study of
the detailed source processes of moderate earthquakes. Each rupture process of these earthquakes is complex and is apparently similar to the rupture process in larger earthquakes. In most events, the maximum slip-rate rupture was preceded by small ruptures, which may correspond to the initial stage of rupture suggested by Umeda (1990) and Ellsworth and Beroza (1995). Comparing these moderate events to two relatively
S. Ide / Tectonophysics 334 (2001) 35±54
larger events, we derived scaling relations between the characteristic quantities in inhomogeneous slip models that ranged widely from M4 to M7. Among large stress drop events of the Hida swarm (EV01, EV06, EV09, EV10, and EV13) and three larger events, the maximum slip depends on the cubic root of the seismic moment, while slip-rate and stress drop are unrelated to seismic moment as geometrical similarity predicts. For other events, geometrical similarity seems not to hold. Since each large stress drop event occurs at the beginning of each cluster activity, the change of the stress-®eld during the cluster activity was responsible for the breakdown of similarity. An unexpected result of the present study is a discovery of the negative relationship between rupture propagation velocity and static stress. It is dif®cult to explain this contradiction on the basis of dynamic simulations of cracks on a single plane. Although some interaction is expected between slip areas of a large earthquake, there exist few examples of such interaction. The detailed rupture models of Hida events provide a ®ne example of the effect of a preceding earthquake on a following event in terms of rupture propagation behavior. The amount of slip overlap was small, and the following rupture was directed outside of the previously ruptured area. This pattern can be explained by a parallel-oriented fault system on which slips occur selectively on one plane, thereby suppressing slips on other planes. Such a system may be a general feature of such concentrated seismic ruptures. Further discussion is needed of the differences between swarm earthquakes and earthquakes of the mainshock-aftershock type. The Hida-Mountains contain volcanoes, and the earthquakes studied here as well as other swarm earthquakes may be related to volcanic activities. For example, in earthquakes that occurred on the Izu Peninsula, a volcanic area in Japan, the average stress drop was lower than in other areas of Japan, and Wyss et al. (1997) have found an anomalously large b-value in the Gutenberg-Richter magnitude-frequency relation. However, the Hida events show stress drops similar in size to those of larger events, and they show a b-value of almost 1.0 (Aoyama et al., 2000). Although this is not suf®cient evidence to draw a de®nitive conclusion, we have at present no reason to discriminate Hida events from other `usual' earthquakes. If, in the
53
future, systematic studies can be made of moderate earthquakes in other ®elds and of much smaller earthquakes, the differences between swarm and mainshock-aftershock activities will become much clearer. Acknowledgements I wish to thank Prof. M. Takeo and Mr H. Aoyama for their useful comments and help. This study began with the temporary observation conducted with Prof. N. Hirata, Dr S. Sakai, Mr M. Matsubara, and the staff of Shin'etsu Observatory, ERI, and I thank them for their help. The comments from two anonymous reviewers improved this paper very much. This study was supported by a Grant-in-Aid for Scienti®c Research of the Ministry of Education, Science and Culture, Japan. References Akaike, H., 1980. Likelihood and Bayes procedure. In: Bernardo, J.M., et al. (Eds.), Bayesian Statistics. University Press, Valencia, Spain, pp. 143±166. Andrews, D.J., 1985. Dynamic plane-strain shear rupture with a slip-weakening friction law calculated by a boundary integral method. Bull. Seismol. Soc. Am. 75, 1±21. Aoyama, H., Ide, S., Takeo, M, 2000. The evolution of an earthquake swarm under the Hida Mountains, Central Japan, in 1998: stress triggering and its time delay. Submitted for publication. Archuleta, R.J., 1984. A faulting model for the 1979 Imperial Valley earthquake. J. Geophys. Res. 89, 4559±4585. Beroza, G.C., Spudich, P., 1988. Linearized inversion for fault rupture behavior: application to the 1984 Morgan Hill, California earthquake. J. Geophys. Res. 93, 6275±6296. Bouchon, M., 1981. A simple method to calculate Green's functions for elastic layered media. Bull. Seismol. Soc. Am. 71, 959±971. Bouchon, M., 1997. The state of stress on some faults on the San Andreas system as inferred from near-®eld strong motion data. J. Geophys. Res. 102, 11731±11744. Brune, J.N., 1970. Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res. 75, 4997±5009. Das, S., Aki, K., 1977. A numerical study of two-dimensional spontaneous rupture propagation. Geophys. J.R. Astron. Soc. 50, 643±668. Day, S., 1982. Three-dimensional simulation of spontaneous rupture: the effect of nonuniform prestress. Bull. Seismol. Soc. Am. 72, 1881±1902. Day, S., Yu, G., Wald, D.J., 1998. Dynamic stress changes during earthquake rupture. Bull. Seismol. Soc. Am. 88, 512±522. Ellsworth, W.L., Beroza, G.C., 1995. Seismic evidence for an earthquake nucleation phase. Science 268, 851±855.
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Fletcher, J.B., Spudich, P., 1998. Tomographic inversion of three small earthquakes at Park®eld. J. Geophys. Res. 103, 835±854. Fukuyama, E., Ishida, M., Horiuchi, S., Inoue, H., Hori, S., Sekiguchi, S., Kawai, K., Murakami, H., 1999. NIED seismic moment tensor catalogue January±December 1998. Technical Note of the National Research Institute for Earth Science and Disaster Prevention 193, pp. 1±35. Harris, R.A., 1998. Introduction to special section: stress triggers, stress shadows, and implications for seismic hazard. J. Geophys. Res. 103, 24347±24358. Hartzell, S.H., 1978. Earthquake aftershocks as Green's functions. Geophys. Res. Lett. 5, 1±4. Hartzell, S.H., Heaton, T.H., 1983. Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake. Bull. Seismol. Soc. Am. 73, 1553±1583. Hellweg, M., Boatwright, J., 1999. Mapping the rupture process of moderate earthquakes by inverting accelerograms. J. Geophys. Res. 104, 7319±7328. Ide, S., 1999. Source process of the 1997 Yamaguchi, Japan, earthquake analyzed in different frequency bands. Geophys. Res. Lett. 26, 1973±1976. Ide, S., Takeo, M., 1997. Determination of constitutive relations of fault slip based on seismic wave analysis. J. Geophys. Res. 102, 27379±27391. Kame, N., Yamashita, T., 1997. Dynamic nucleation process of shallow earthquake faulting in a fault zone. Geophys. J. Int. 128, 204±216. Kanamori, H., Anderson, D.L., 1975. Theoretical basis of some empirical relations in seismology. Bull Seismol. Soc. Am. 65, 1073±1095. Kennet, L.N., Kerry, N.J., 1979. Seismic waves in a strati®ed half spaces. Geophys. J.R. Astr. Src. 57, 557±583. Kubota, T., Yamamoto, M., Mikumo, T., Miyatake, T., 1997. Static stress drop distribution of large earthquakes. Abstract of the Japan Earth and Planetary Science Joint Meeting, p. 791 (in Japanese). Lawson, C.L., Hanson, R.J., 1974. Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs, NJ. Mori, J., 1996. Rupture directivity and slip distribution of the M 4.3
foreshock to the 1992 Joshua Tree Earthquake, Southern California. Bull. Seismol. Soc. Am. 86, 805±810. National Research Center for Disaster Prevention, 1973. Explanatory text of the quaternary tectonic map of Japan. Tokyo. Ohnaka, M., Yamashita, T., 1989. A cohesive zone model for dynamic shear faulting based on experimentally inferred constitutive relation and strong motion source parameters. J. Geophys. Res. 94, 4089±4104. Okada, Y., 1992. Internal deformation due to shear and tensile faults in a half space. Bull. Seismol. Soc. Am. 82, 1018±1040. Singh, S.K., Ordaz, M., Mikumo, T., Pacheco, J., Valdes, C., Mandal, P., 1998. Implications of a composite source model and seismic-wave attenuation for the observed simplicity of small earthquakes and reported duration of earthquake initiation phase. Bull. Seismol. Soc. Am. 88, 1171±1181. Somerville, P.G., Irikura, K., Graves, R., Sawada, S., Wald, D., Abrahamson, N., Iwasaki, Y., Kagawa, T., Smith, N., Kowada, A., 1999. Characterizing crustal earthquake slip models for the prediction of strong ground motion. Seismol. Soc. Lett. 70, 59±80. Stein, R.S., Barka, A.A., Dieterich, J.H., 1997. Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering. Geophys. J. Int. 128, 594±604. Takeo, M., 1985. Near-®eld synthetic seismograms taking into account the effect of anelasticity. Meteorol. Geophys. 36, 245±257. Umeda, Y., 1990. High-amplitude seismic waves radiated from the bright spot of an earthquake. Tectonophysics 175, 81±92. Wald, D.J., Heaton, T.H., 1994. Spatial and temporal distribution of slip for the 1992 Landers, California, earthquake. Bull. Seismol. Soc. Am. 84, 668±691. Wald, D.J., Helmberger, D.V., Heaton, T.H., 1991. Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic data. Bull. Seismol. Soc. Am. 81, 1540±1572. Wu, C., Takeo, M., 2000. The role of Coulomb Failure Stress in 1997 Kagoshima earthquakes, Abstract 2000 Japan Earth and Planetary Science Joint Meeting, Sa-P005. Wyss, M., Shimazaki, K., Wiemer, S., 1997. Mapping active magma chambers by b values beneath the off-Ito volcano, Japan. J. Geophys. Res. 102, 20413±20422.
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Complex source processes and the interaction of moderate earthquakes during the earthquake swarm in the Hida-Mountains, Japan, 1998 Satoshi Ide* Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo, 113-0032, Japan Received 27 March 2000; accepted 29 January 2001
Abstract This paper presents a set of detailed source models of 18 moderate (M4-5) earthquakes that were part of the swarm activity beneath the Hida-Mountains in central Japan in 1998. To reveal the detailed rupture process, this study uses a waveform inversion procedure with the empirical Green function (EGF). Most of our models show a complicated rupture process that includes several separate rupture areas and that involves ruptures that, in some events, seem to repeat at almost the same location. In our models, we measured as characteristic values the maximums of slip, slip-rate, stress drop, and average rupture propagation velocity. In comparison with the models for larger events determined by similar methods, the maximum slip scales with the cubic squares of the seismic moment for large stress drop events only. The slip-rate has an upper limit of about 1±2 m/ s, and the stress drop is distributed widely from 1 to 50 MPa. The average stress drops, estimated using the corner frequency, are almost uniform at about 1 MPa. The ®rst event in each swarm cluster tends to have a large maximum stress drop, which re¯ects the change in the stress ®eld during swarm activity. The average rupture velocity, determined by the least squares method, is relatively slow and shows a negative relationship with the maximum stress drop. This ®nding cannot be explained by simple crack models and instead suggests a very complicated mechanism like the interactive fault system. The interaction between the slip areas of neighbor events resulted in a non-overlapping slip distribution. This ®nding indicates that previous rupture areas restrict the size and location of later events even in such complex swarm activities. q 2001 Elsevier Science B.V. All rights reserved. Keywords: source process; moderate earthquakes; scaling; interactive faulting
1. Introduction An earthquake rupture is thought to be quite a complex event composed of many small-scale ruptures such as subevents and asperities. This understanding has been con®rmed by a number of detailed * Present address: Address from 14 December 2000 to 27 November 2001: Department of Geophysics, Stanford University, Mitchell 360, Stanford, CA 94305-2215, USA. Fax: 181-3-3813-8026. E-mail address: [email protected] (S. Ide).
source models that use near-®eld strong-motion records from events with a magnitude larger than six (e.g. Hartzell and Heaton, 1983; Archuleta, 1984). Although seismic waveforms show some complexity even in smaller events, including those with a magnitude down to three or four (e.g. Ellsworth and Beroza, 1995; Singh et al., 1998), the source processes of moderate earthquakes have not been studied in detail. The empirical Green function (EGF) method (Hartzell, 1978) is useful for studies of moderate earthquakes if the waveforms from
0040-1951/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0040-195 1(01)00027-0
36
S. Ide / Tectonophysics 334 (2001) 35±54
appropriate small events are available as Green functions. Utilizing this method, Mori (1996) determined the detailed rupture process of the M4.3 foreshock of the 1992 Landers earthquake and showed that the rupture propagated toward the mainshock hypocenter. Fletcher and Spudich (1998) analyzed three moderate earthquakes in Park®eld, CA, and found that the ruptures propagated to the same point where the 1966 earthquake initiated. Hellweg and Boatwright (1999) determined the source process of two of the three events studied by Fletcher and Spudich (1998) and showed that rupture behavior is different in seismic and aseismic areas. An earthquake swarm beneath the Hida-Mountain in central Japan, that began on 7 August 1998, provided good data that is suitable for the study of moderate earthquakes. The Hida-Mountains are the highest mountain range in Japan. The range extends about 150 km NNE±SSW and consists of many peaks higher than 3000 m. This region is tectonically active, as characterized by the high uplifting rate of 1±5 mm/ yr during the late Quaternary (National Research Center for Disaster Prevention, 1973). No large (M . 6) earthquake has been reported in this area; however, there are many small earthquakes, and they tend to be a part of swarm events. The 1998 swarm was the largest activity ever recorded in this region. The active period of seismicity for this swarm was in the ®rst two months after initiation, during which more than 7000 earthquakes were manually determined to have occurred. The swarm area was divided into four separate clusters (C1±C4, Fig. 1). In the present study, we determined detailed source models for moderate earthquakes in this swarm activity, extracted their characteristic parameters in order to compare them with larger earthquakes, and investigated possible interaction between events. Although many reports on earthquake complexities have been made, no suf®cient systematic studies investigating generalize features of complex ruptures yet exist. This type of general analysis is important for strong motion prediction, and in a pioneering study in this ®eld, Somerville et al. (1999) derived scaling relations among parameters including seismic moment, rupture area, average slip, and others. They used the models of 15 earthquakes from Mw 5.7 to 7.2. The smallest event they included was the 1979 Coyote Lake earthquake (Mw 5.7), which was close to the
lower limit of what can be analyzed using theoretical waveform calculation. Much more detailed studies of moderate earthquakes are needed if the general features of earthquake rupture complexity in a wide scale range are to be fruitfully discussed. The Hida swarm can provide useful examples for such a discussion. Recently, many studies have demonstrated that change in static stress (Coulomb failure stress) controls the occurrence of future earthquake events. The detailed reviews are provided by Harris (1998). Aoyama et al. (2000) used Coulomb failure stress to successfully explain the migration process of the Hida swarm. In addition to explaining seismicity change, static stress also affects rupture behavior, including slip distribution and directivity. One good example of static stress change as a precipitating factor can be seen in a sequence of large earthquakes beginning in 1939 along the North Anatolian Fault, Turkey, where nine out of ten events were explained by the change in static stress that resulted from preceding events (Stein et al., 1997). This sequence occurred along a well-developed weak zone. However, very few examples exist in the case of a complex fault system such as a swarm area. In the Hida swarm, some of the earthquakes occurred quite close to others, and it is likely that their rupture zones overlapped. The detailed rupture models in the present study provide a good example of the effects of preceding earthquakes on following events in terms of rupture propagation behavior. 2. Overall properties of moderate earthquakes in this study There were 18 moderate earthquakes whose magnitudes, as determined using maximum amplitudes of velocity seismograms by Earthquake Research Institute (ERI), University of Tokyo, MERI, ranged from 4.1 to 5.2 (Table 1). The hypocenters were determined using a master event procedure for each cluster C1± C4. The relative hypocenter location in each cluster is accurate; most standard deviations are less than 0.2 km horizontally and 0.5 km vertically. However, absolute locations, especially depth, and relative locations between clusters are questionable, and we do not discuss absolute location or differences
Fig. 1. (a) Maps showing the hypocenters in the Hida-Mountain earthquake swarm during August and September. The events with MERI of 1 or larger are shown. Arrows indexed as EV01±EV18 indicate the locations of 18 moderate earthquakes. Shaded areas C1±C4 indicate the clusters (see text). In the cross section, the surface geometry is shown along two thick gray lines in the horizontal map. The triangles denote the stations used in the routine hypocenter determination procedure. (b) The temporal distribution of the hypocenters. Beach balls represent the moment tensor solutions determined by waveform inversion.
S. Ide / Tectonophysics 334 (2001) 35±54 37
38
S. Ide / Tectonophysics 334 (2001) 35±54
Table 1 Hypocenter and average properties of the moderate earthquakes ID
Date
Time
Lattidue (8)
Longitude (8)
Depth (km)
MERI
Mo (Mw) ( £ 10 15 Nm)
Fault plane (strike/dip/rake)
Ds (MPa)
EV01 EV02 EV03 EV04 EV05 EV06 EV07 EV08 EV09 EV10 EV11 EV12 EV13 EV14 EV15 EV16 EV17 EV18
08/07 08/08 08/09 08/12 08/12 08/14 08/14 08/16 08/16 08/17 08/22 08/22 09/05 09/05 09/07 09/18 09/18 09/20
14:47:14.55 19:51:57.57 12:45:23.00 09:40:34.53 15:13:03.73 14:06:53.27 19:36:14.87 03:28:18.67 03:31:07.92 10:15:05.35 03:55:45.13 04:48:23.21 10:08:00.60 12:02:01.00 16:53:25.03 17:16:10.93 17:16:47.34 06:53:03.40
36.2387 36.2389 36.2387 36.2350 36.2351 36.2969 36.3017 36.3180 36.3233 36.3512 36.2396 36.2387 36.4069 36.4243 36.2349 36.3337 36.3207 36.4400
137.6562 137.6431 137.6365 137.6503 137.6256 137.6330 137.6307 137.6410 137.6327 137.6228 137.6529 137.6692 137.6366 137.6341 137.6616 137.6577 137.6448 137.6331
4.93 5.18 4.98 5.34 3.32 3.05 3.69 2.62 3.35 3.03 2.64 3.31 3.70 3.40 6.43 1.85 3.63 3.30
4.3 4.1 4.4 4.3 4.7 4.2 4.6 4.5 5.2 4.7 4.5 4.4 4.4 4.4 4.1 4.6 4.4 4.4
1.0 (3.9) 1.2 (4.0) 2.5 (4.2) 2.5 (4.2) 7.4 (4.5) 0.7 (3.8) 4.9 (4.4) 1.6 (4.1) 51.4 (5.1) 4.9(4.4) 3.5 (4.3) 0.6 (3.8) 4.0 (4.3) 6.1 (4.5) 0.3 (3.6) 4.7 (4.4) 2.2 (4.2) 1.4 (4.0)
289/88/2163 90/87/169 279/83/2168 283/85/2171 286/77/2171 178/79/10 2175/75/10 92/63/153 98/81/178 97/90/2159 79/84/145 91/84/162 29/65/30 171/89/2 279/76/2159 85/81/2179 104/89/174 23/82/21
0.44 0.57 0.41 0.35 1.19 2.48 1.94 0.54 1.19 0.92 0.97 0.63 0.77 0.59 1.05 0.81 1.38 0.52
between clusters in this study. Moreover, the northernmost cluster, C4, has no nearby station, so the accuracy of the depth is poor and we cannot discuss the vertical hypocenter distribution for this cluster. The mechanisms of these events were determined by moment tensor inversion and are summarized in Table 1 and Fig. 1. We calculated the theoretical waveforms using the discrete wave number method of Bouchon (1981), in which the re¯ection±transmission matrices of Kennet and Kerry (1979) are used and the effect of an elasticity described by Takeo (1985) is introduced. The data in both the moment tensor inversion and the following EGF analysis are from seismograms recorded by the networks maintained by ERI, the University of Tokyo, Nagoya University, the Disaster Prevention Research Institute, Kyoto University, and the Japan Meteorological Agency (Fig. 2). These records are velocity seismograms continuously recorded on 1-Hz sensors, digitized at 100 samples per second, and telemetered to ERI. Since the AD converters have wide dynamic ranges of greater than 20 bits, P-waves, at the very least, were known to have been recorded without saturation, even for the largest event. The instrumental response was corrected to recover the long period component.
Both the theoretical Green function and the data were bandpass ®ltered in the frequency range from 0.1 to 0.2 Hz. All the events were strike-slip earthquakes whose compression axis ran almost northwest±southeast. Fukuyama et al. (1999) determined the moment tensor of these events, except for EV08 and EV17, using broadband seismograms in the frequency range from 0.02 to 0.05 Hz. In spite of the differences in analyzed frequencies and stations, their results are consistent with the mechanism solution obtained in the present study: the resemblance, measured using the correlation of the coef®cient of spherical harmonic basis function, is 0.87 on average. The seismic moments determined by Fukuyama et al. (1999) are systematically larger by 0.31 in Mw units than those in our result. However, after a correction of Mw 0.31, the standard deviation is Mw 0.08, which means that the relative ratio of seismic moments from event to event is consistently determined with the two methods. Hence we consider the error in determination of seismic moment is the order of Mw 0.1, which means a factor of 1.5 in seismic moment. The average stress drop Ds is determined by seismic moment Mo and corner frequency fc. Using the relation between stress drop and seismic moment of a
S. Ide / Tectonophysics 334 (2001) 35±54
39
Fig. 2. Station distribution used in empirical waveform analysis. Circles show the distance from the largest event, EV09.
the source depth b , as follows:
circular crack (Brune, 1970): Mo
16 Dsa 3 7
1
and assuming that the radius of the crack a is given by the corner frequency fc and the shear wave velocity at
a 0:75b=fc :
2
We calculated the average stress drops shown in Table 1. The average stress drops ranges from 0.3 to 3 MPa.
40
S. Ide / Tectonophysics 334 (2001) 35±54
3. Process for determining earthquake rupture processes 3.1. Method of empirical waveform inversion The analysis method used to obtain rupture models was a simple EGF method. Although deconvolution techniques are frequently used to obtain relative source time functions for moderate earthquakes (Mori, 1996; Fletcher and Spudich, 1998), for the sake of simplicity we did not adopt these techniques in this study. For each moderate earthquake, we chose a Green function event from among the smaller events with magnitudes at least 1.5 units less than that of the event of interest. The smaller event chosen also must have taken place within 2 km in horizontal distance and 3 km in depth of the event of interest. To ®nd an event having a similar mechanism as the moderate event, we calculated the amplitude ratios of the Pand S-wave pulses between the moderate and small events for all stations. Using this method, the event having the ratio with minimum variance is identi®ed as the Green function event, and the hypocenter of each moderate event is relocated relative to that of the Green function event using the master event method. A Green function represents the velocity waveforms recorded at a station that result from a unit impulsive dislocation at a point x. The Green function is expressed using the waveforms of the Green function event gk(t) as follows: G t; x gk t 2 tt 2 tk 2 T x 1 T xk R xk =Mos R x;
3
where tt and tk are the origin times of the moderate event and the small event, respectively, and xk is the hypocenter of the small event. T(x) is the theoretical travel time of a P-wave or S-wave from x to the station. R(x) is the distance from x to the station, used to account for the geometrical spreading effect. Mos is the seismic moment of the Green function event. Although Eq. (3) is obtained under the assumption that the source time function of the Green function event is a delta function, the duration of the function is actually short but ®nite. To consider this short pulse duration, the data are convolved with an assumed source time function, which is an isoscelestriangle-shaped function whose duration is estimated
using the records from closely located stations. In the case of an M 2 event, this duration is about 0.1 s. The rupture process of an earthquake is expressed by a spatio-temporal slip distribution on an assumed fault plane. The slip-distribution was expanded by basis functions and the unknown parameters are the expansion coef®cients of the basis functions (Ide and Takeo, 1997). The spatial and temporal basis functions have triangular form, and the start time of the ®rst temporal function at each point of the fault plane is set to a time when the S-wave from the hypocenter reaches at that point. By doing this, we can maintain the causality and reduce the number of computations needed. The parameters are determined using the nonnegative least squares algorithm of Lawson and Hanson (1974). Since a rupture process progresses smoothly to some degree, we introduced constraints that minimize the difference between the coef®cients of spatio-temporally neighboring basis functions. If these constraints are considered to be prior information, the problem of determining the coef®cients becomes one of Bayesian modeling, and the weights of the constraints are determined using Akaike's Bayesian Information Criterion (ABIC, Akaike, 1980). The assumed fault plane is one of two nodal planes of the best double couple mechanism determined by moment tensor inversion (Fig. 1, Table 1). If aftershock activity followed the event, and the activity's lineation is consistent with one of these planes, that plane is chosen as the fault plane. Otherwise, the data are inverted using both planes, and the ®nal solution is chosen to minimize ABIC. Consequently, every fault plane is parallel to the local seismicity lineation: east± west in clusters C1 and C3, and north±south in clusters C2 and C4. The area of the fault plane is assumed to be wide in a preliminary inversion and then reduced to the size in which all signi®cant slip is included. The absolute values of slip and slip-rate depend on the uncertain seismic moment of the Green function event. To exclude this uncertainty, the parameter values are multiplied by a scalar number so as to equalize the total seismic moment of the model with that determined by the previous moment tensor inversion (Table 1). The uncertainty of estimated the seismic moment is approximately a factor of 1.5, and the lack of resolution may affect the parameter values. Usually the peak values are reduced by smoothing constraints. Hence even after this equalization, the
S. Ide / Tectonophysics 334 (2001) 35±54
41
Fig. 3. Parameter values (circles) and standard deviations (error bars) determined for EV02. A gray line in each box shows the temporal sequence of the parameter values and is proportional to the source time function. The number of the basis functions in length, width, and time are 11, 13, and 15, respectively. The parameters in the rectangle marked by a star correspond to the hypocenter.
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peak values of slip and slip-rate still have ambiguity of a factor of 1.5 for their lower limit and a factor of 5 for their upper limit. 3.2. Results Fig. 3 compares the parameter values and their standard deviations for EV02 (Mw 4.0). These parameter values are proportional to the slip-rate. It should be noted that there is a spatio-temporal difference of reliability, even in one solution. Since the smoothing constraints tend to homogenize all parameters, the standard deviations are almost the same throughout the parameter space. Therefore, the reliability for a high slip-rate rupture is high, and the existence of a slow rupture is questionable. Fig. 4 shows the observed and synthetic seismograms of this event. Since these are raw data, highfrequency components are prominent in the observed waveforms and are explained well by the synthetic waveforms. Most of the data are vertical components around the onset of P-waves; some horizontal components that show clear S-wave pulses have been added. Adding horizontal components in this way is commonly used as a way of choosing data for all events. Since all the earthquakes in the Hida swarm are of the strike-slip type, impulsive SH-waves can be observed clearly for some stations as the NS component of KTJ, the EW component of KYJ, and the NS component of SAKI in Fig. 4. These records are quite useful for improving resolution. Fig. 5 shows the total slip distribution as well as the temporal change of the slip area for EV02. This event consists of three asperities that signify areas of relatively large slip-rate in the present paper; these are at the hypocenter, at 0.4±0.6 s after in a shallow area, and at 0.6±0.7 s after in a deep area 1 km east. Using this ®nal slip distribution, we can estimate the static stress drop distribution (Fig. 5) using the method of Kubota et al. (1997). We computed the summation of the stress change caused by the ®nal slips on all of small fractions of fault plane by using the analytic solution for the elastic half space of Okada (1992). We assumed the Poisson's ratio and the rigidity of the half space as 0.25 and 30 GPa, respectively. Each zone of asperity has a larger vertical extent than horizontal extent. This result is probably an artifact of the poor vertical resolution. Since this earth-
quake occurred at a shallow depth, the seismic rays from the source depart almost horizontally to the stations, and the travel time difference is small. This is a common problem for all events in this analysis, and we should be aware that the arti®cial vertical smoothing may have reduced the peak slip and sliprate values. The result shown in Fig. 5 depends on using one speci®c Green function event; however, almost the same results can be obtained using other Green function events, as demonstrated by Ide (1999) for the 1997 Yamaguchi earthquake. Fig. 6 shows the result using a different Green function event. We can see the same three asperities in slip distribution, rupture history, and stress distribution. Although the qualitative behavior is almost the same, there is some quantitative difference. The time of the maximum slip is 0.1 s later for Fig. 6, and the values of slip and stress drop of the model in Fig. 6 are about 70% as great as the values of the model shown in Fig. 5. Such difference arises from the difference of signal-to-noise ratio, mechanism, and location between two Green function events. We estimated the average rupture propagation velocity because it is a characteristic value of the inhomogeneous rupture process. A line was ®tted to the spatio-temporal locations of all of the basis functions weighted by corresponding coef®cient values (Fig. 7). Since the rupture progress was more complicated for some events, we also estimated the standard deviation. For EV02, the rupture propagation velocity was estimated as 1.64 ^ 0.47 km/s. This value does not signify the propagation velocity of the rupture front but rather the average movement of the moment centroid. Therefore, the value is smaller than that of the rupture front. Using the method just described, we determined the detailed source processes of 15 of the 18 moderate earthquakes as spatio-temporal slip-rate distributions on two-dimensional fault planes. EV14 and EV17 followed shortly after EV13 and EV16, respectively, and their waveforms have a poor signal-to-noise ratio. EV18 occurred at the northern end of the swarm activity and had a small number of aftershocks, so we could not ®nd a good Green function event. For these reasons, these three events were analyzed as horizontal line sources with a ®xed width of 1 km. Table 2 summarizes the characteristic quantities extracted from the detailed rupture models. These
S. Ide / Tectonophysics 334 (2001) 35±54
43
Fig. 4. Comparison between observed (black lines) and synthetic (gray lines) seismograms for EV02. Each set of traces is normalized by the maximum value of observed seismograms shown at the upper left corner.
quantities include the maximum total slip, the maximum slip-rate during the rupture process, the maximum static stress drop, the total rupture duration, and the average rupture propagation velocity. As a measure of the reliability of the solution, the ratio of the maximum parameter value to the maximum stan-
dard deviation value is listed in Table 2. Judging from these values, the model for EV04 was not determined well. Since the waveforms of this event are complex and have long durations, there may be some different mechanism at work that has not been considered in the present analysis method, such as the existence of a
44
S. Ide / Tectonophysics 334 (2001) 35±54
Fig. 5. Source model for EV02. Each rectangle shows the assumed fault plane whose strike and dip are N908E and 878, respectively. (a) Total slip distribution. Contour interval is 0.8 cm. (b) Time progression given as the amount of slip every 0.1 s as labeled. The contour interval is 0.6 cm. (c) Static stress change computed using the slip distribution in (a). The contour interval is 1 MPa.
non-coplanar fault plane or a diverse change of mechanism during the rupture. The rupture behaviors of many events are complex, as in EV02. Fig. 8a shows the rupture history of events that involve spatially separated asperities (EV03, EV07, EV08, EV09, EV10, EV11, and EV16). Such rupture patterns are frequently observed in large earthquakes. In some events, the ruptures occurred repeatedly in a small area around the hypocenter (EV01, EV12, EV13, and EV15, Fig. 8b). The estimated rupture propagation velocities for these events are very small. We found only two events that can each be considered a single asperity event. EV05 propagated unilaterally to the west as a single asper-
ity, and EV06 did not show any directivity of its rupture and terminated within 0.3 s (Fig. 8c). In many events, small ruptures preceded the maximum slip-rate rupture. Such small ruptures correspond to the initial part of the observed waveforms and may be identical to the initial phases of Umeda (1990) and Ellsworth and Beroza (1995).
4. Relations between characteristic quantities 4.1. Scaling relations Fig. 9 shows the scaling relations for the maximum
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45
Fig. 6. Source model for EV02 estimated using a different EGF event from that for Fig. 5. (a) Total slip distribution. Contour interval is 0.7 cm. (b) Time progression given as the amount of slip every 0.1 s as labeled. The contour interval is 0.3 cm. (c) Static stress change computed using the slip distribution in (a). The contour interval is 0.7 MPa.
slip, the maximum slip-rate, and the maximum stress drop. To compare the moderate earthquakes of the Hida swarm to larger events, we have appended data from three larger earthquakes, the 1995 Kobe (Hyogoken-Nanbu) earthquake (Mw 6.8, Ide and Takeo, 1997), the 1997 Kagoshima earthquake (Mw 6.1, Wu and Takeo, 2000), and the 1997 Yamaguchi earthquake (Mw 5.9, Ide, 1999), which were analyzed by a method similar to that used for the Hida events. As expected, most of the maximum slips are distributed above the scaling relationship determined by Somerville et al. (1999) for average slip (a thick gray line in Fig. 9a). In the wide range including the Kobe, Kagoshima, and Yamaguchi events, they are
related to the seismic moment by a power of 1/2 to 1/3. If stress drop is constant and geometrical similarity holds, slip depends on the cubic root of seismic moment (Kanamori and Anderson, 1975), which is parallel to the thick gray line in Fig. 9a. Although some events (EV01, EV06, EV09, EV10, and EV13) satisfy this relationship (parallel to the thick line in Fig. 9a), most events have smaller slip than that predicted by geometrical similarity. Since the lack of resolution and smoothing constraints reduced the slip values, these values have large ambiguity to the upper bound, a factor of 5, and a smaller ambiguity with regard to the lower bound, less than a factor 1.5. We have probably underestimated the actual
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Table 2 Characteristic parameters of the moderate earthquakes ID
Mo ( £ 10 15 Nm)
Dmax (m)
Vmax (m/s)
Ds max (MPa)
Vr (km/s)
R
EV01 EV02 EV03 EV04 EV05 EV06 EV07 EV08 EV09 EV10 EV11 EV12 EV13 EV14 EV15 EV16 EV17 EV18
1.0 1.2 2.5 2.5 7.4 0.7 4.9 1.6 51.4 4.9 3.5 0.6 4.0 6.1 0.3 4.7 2.2 1.4
0.079 0.037 0.039 0.016 0.049 0.051 0.053 0.014 0.47 0.25 0.034 0.026 0.12 (0.092) 0.0087 0.064 (0.037) (0.020)
0.51 0.38 0.27 0.094 0.27 0.97 0.16 0.077 2.16 1.51 0.16 0.19 0.79 (0.34) 0.060 0.40 (0.23) (0.16)
13.3 4.9 4.2 3.8 5.6 7.8 2.6 0.76 32.9 35.6 2.4 2.8 12.1 (9.8) 0.76 6.0 (3.4) (1.3)
0.52 ^ 0.23 1.64 ^ 0.47 1.59 ^ 0.66 1.57 ^ 0.58 2.43 ^ 0.81 2.45 ^ 1.26 1.53 ^ 0.63 2.50 ^ 1.10 0.92 ^ 0.35 1.44 ^ 0.51 1.24 ^ 0.75 1.58 ^ 0.82 1.01 ^ 0.90 (0.83 ^ 0.59) 1.63 ^ 1.08 2.12 ^ 0.86 (2.48 ^ 1.02) (1.83 ^ 0.73)
6.3 5.2 3.7 3.1 4.8 7.8 5.5 4.7 7.4 6.3 4.9 4.1 4.7 6.0 3.6 5.1 5.2 7.6
maximum slip. Nevertheless this is a common problem for all events including the larger three events and the scaling relationship among EV01, EV06, EV09, EV10, EV13, and the larger three events may still hold with such errors. Although slip-rate (Fig. 9b) seems to be proportional to the seismic moment, the deviations are large for the Hida events, and it is also possible that slip-rate has an upper limit of 1±2 m/s that is constant in the wide scale. Since slip-rate is related to the breakdown stress drop of the slip-weakening relation if a crack is propagating at a constant velocity (e.g. Ohnaka and Yamashita, 1989), the maximum slip-rate of about 1±2 m/s re¯ects a scale independent of the material properties of the crustal rock. However, uncertainty of about a factor of 5 suggests that the real limit may be larger. Fig. 9c shows the scaling relation for stress drops, with the maximum stress drop estimated using the detailed slip model and average stress drop estimated from the corner frequency and seismic moment. While average stress drops are almost constant around 1 MPa, the maximum stress drops from the detailed model have wide variation from 1 to 50 MPa. Both groups of stress drops have little size dependence. Although the average stress drop exceeds its maximum value for EV15, this is just an artifact due to
Fig. 7. The method of estimating an average rupture propagation velocity for EV02. Each circle located at the centroid of the basis function has a radius scaled by its coef®cient value. Distance is measured from the hypocenter. The black line and gray lines indicate the line of best estimate and those of the standard deviations, respectively.
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47
Fig. 8. The distributions of slip during the period labeled are shown for each of the models. (a) Earthquakes consisting of several separated asperities. (b) Events showing repeated ruptures at the same location. (c) Nearly single asperity events. Stars represent the hypocenter.
independent estimation. It is also true for maximum stress drop that the smoothing constraints and poor resolution may reduce the stress drop apparently. Of the Hida events, EV01, EV06, EV09, EV10, and EV13 all show both a large slip-rate and a large stress drop and seem to satisfy the geometrical similarity in wide scale range. Among these, EV01,
EV06, and EV13 are the ®rst moderate earthquakes of their respective clusters C1, C2, and C4 (Fig. 1). Although the ®rst event of cluster C3 is EV08, most of C3 is included in the rupture area of EV09. EV10 is also the ®rst event of a non-labeled small cluster area north of C3. These ®ndings imply that the stress drop is largest at the ®rst stage of the
48
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Fig. 8. (continued)
swarm sequence within a small area and gradually decreases as the swarm continues to release accumulated stress. The decrease of stress drop is also responsible for the breakdown of similarity in most of the Hida events. It should be noted that the average stress drop of these events is not different from that of the rest of the swarm event. This means such
a difference is not visible by examining the average stress drop alone. 4.2. Stress drop and rupture propagation velocity Fig. 10 shows the relationship between the maximum stress drops and the rupture propagation velocities in the
S. Ide / Tectonophysics 334 (2001) 35±54
Hida swarm events, the Kobe earthquake, the Kagoshima earthquake, and the Yamaguchi earthquake. Except for EV05 and EV06, which are considered to be single asperity earthquakes, propagation velocity decreases as stress drop increases. It is not easy to estimate the stress drop error; however, the errors are about a factor of 5 and the values of stress drop are distributed in two orders. Hence the observed relationship holds after taking into account the possible errors. This negative correlation is somewhat inconsistent with the previous understanding of crack rupture propagation. Das and Aki (1977) simulated the dynamic rupture of an in-plane two-dimensional crack and found that the rupture propagation velocity is determined by a nondimensional parameter S, de®ned by S
tp 2 t0 ; t0 2 tf
4
where t p, t 0, and t f are the peak, initial, and ®nal (dynamic) stress, respectively. The rupture propagates faster with smaller Svalues. These researchers used a simple maximum stress fracture criterion. A similar result was obtained when the slip-weakening friction law was used (Andrews, 1985). If strength, t p ± t f, is constant throughout the fault plane, a large stress drop, t 0 ± t f, means that S will be small, resulting in fast rupture propagation. This ®nding was con®rmed by Day (1982) in a simulation using a homogeneous strength distribution and an inhomogeneous stress drop distribution. The present results seem to contradict these ®ndings. Even in a case where strength is proportional to stress drop, S is found to be constant, and rupture propagation velocity does not show a negative relationship but is instead found to be constant. Unless strength depends more on stress drop than ®rst order, simple crack simulations cannot show a negative relationship between stress drop and propagation velocity. However, the actual faulting process likely has a very complex structure involving non-coplanar fault planes, and the interaction between these planes may produce the negative relationship. Although the Kobe, Kagoshima, and Yamaguchi earthquakes all demonstrate this negative relationship, there are many examples of events that do not. The well-studied 1992 Landers earthquake (Mw 7.2) propagated at about 2.5 km/s on average (Wald and Heaton, 1994), and the maximum stress drop was
49
larger than 10 MPa (Day et al., 1998). The 1979 Imperial Valley earthquake (Mw 6.5, e.g. Archuleta, 1984), the 1984 Morgan Hill earthquake (Mw 6.2, e.g. Beroza and Spudich 1988), and the 1989 Loma Prieta earthquake (Mw 6.9, e.g. Wald et al., 1991) propagated at about 70% of local shear wave velocity, and the stress drop was more than 20 MPa in these events (Bouchon, 1997). All these negative examples are inland strike slip events and consist of many asperities similar to most of the earthquakes analyzed in this study. A difference in the laws governing the ruptures in moderate and large earthquakes may explain such exceptions. Kame and Yamashita (1997) simulated the initial stage of an earthquake using interactive non-coplanar fault systems and found that rupture propagation is slow before a crack grows to the size where interaction between cracks becomes negligible. Most swarm event can be interpreted as occurring as being this type of interactive rupture. The time of changeover depends on the degree of interaction, and the slow rupture of the Hida events may be attributed to the strong interaction within the swarm area. 4.3. Interaction between events The area of the Hida-Mountain earthquake swarm can be divided into four clusters, C1±C4 (Fig. 1), where moderate earthquakes occurred on the fault plane parallel to the lineation of seismicity, either north±south or east±west. Cluster C1 included 8 moderate earthquakes whose slip areas were determined to lie on two-dimensional fault planes running east±west. Fig. 11 shows how the slip zone of each event extended in comparison with preceding events, using the contours of each slip distribution scaled at its maximum. Except for the ®rst event, EV01, and event EV04, the other six events started near the edge of the slip areas of the preceding event and propagated mainly outside of these areas. Event EV04 appears in the present analysis to have been the most complex and may have had complex mechanisms that cannot be resolved by our inversion scheme, as mentioned in the previous section. The fact that its starting point is surrounded by the former slipped areas may be the reason for such complex mechanisms. Fig. 11(i) shows that the overlap of the slip area is small, except in the case of EV04, whose model has
50
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S. Ide / Tectonophysics 334 (2001) 35±54
51
Fig. 10. Relations between the maximum stress drop and the average rupture velocity. Circles are the maximum stress drops of the moderate earthquake. Squares denote those of KOB, KGS, and YMG represent the 1995 Kobe earthquake, the 1997 Kagoshima earthquake, and the 1997 Yamaguchi earthquake, respectively. Error bars show standard deviations.
low reliability. If these events occurred on one common plane, a non-overlapping slip area signi®es that no given point broke twice with a large slip. This ®nding resembles the slip-area distribution of the Turkey earthquake sequence (Stein et al., 1997). However, locating all of the earthquakes in the Hida swarm in one large common fault plane is somewhat unrealistic. In fact, EV05 and EV11 are located about 500 m away from the plane that ®ts the other events. It is possible that a rupture on a parallel fault system can produce such a pattern, since a slip on one plane can suppress a slip on the adjacent parallel plane, forming
a so-called stress shadow (e.g. Harris, 1998). In any case, this pattern indicates that the stress-®eld of a previous rupture in one region strongly restricts the following rupture processes. We observed similar behavior in the other clusters. In cluster C2, the slip area of EV06 is shallower than that of EV07, and EV07 propagated to a deeper level. In cluster C3, the rupture areas of EV09, EV08, and EV16 are arranged from west to east, although the two-dimensional slip distribution of EV17 is unknown. In cluster C4, each event had aftershock activity whose location was separated clearly and
Fig. 9. Scaling relations. Solid circles show characteristic parameters of the detailed model. KOB, KGS, and YMG represent the 1995 Kobe earthquake, the 1997 Kagoshima earthquake, and the 1997 Yamaguchi earthquake, respectively. (a) Maximum slip. The thick gray line shows the scaling relation presented by Somerville (1998), log Dm 1=3log Mo Nm 2 6:8: (b) Maximum velocity. (c) The solid circles are the maximum stress drop and the open circles are the average stress drop (Table 1).
52
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Fig. 11. The slip areas of eight earthquakes that occurred in cluster C1 (Fig. 1) are projected into one vertical plane running in an east±west direction. (a)±(h) The slip area of each event compared with the slip areas of the previous events. The contour interval is scaled for each event so as to be one-fourth of the maximum slip. A star represents the hypocenter of each event. (i) Plot of all slip distributions in (a)±(h). In this ®gure, contour intervals of 1 cm are common for all events.
distinguishably even in the hypocenter map (Fig. 1). Therefore, such a pattern is the result of the interaction of events and an essential feature of such concentrated earthquake activity. 5. Discussion and conclusions The present research makes a systematic study of
the detailed source processes of moderate earthquakes. Each rupture process of these earthquakes is complex and is apparently similar to the rupture process in larger earthquakes. In most events, the maximum slip-rate rupture was preceded by small ruptures, which may correspond to the initial stage of rupture suggested by Umeda (1990) and Ellsworth and Beroza (1995). Comparing these moderate events to two relatively
S. Ide / Tectonophysics 334 (2001) 35±54
larger events, we derived scaling relations between the characteristic quantities in inhomogeneous slip models that ranged widely from M4 to M7. Among large stress drop events of the Hida swarm (EV01, EV06, EV09, EV10, and EV13) and three larger events, the maximum slip depends on the cubic root of the seismic moment, while slip-rate and stress drop are unrelated to seismic moment as geometrical similarity predicts. For other events, geometrical similarity seems not to hold. Since each large stress drop event occurs at the beginning of each cluster activity, the change of the stress-®eld during the cluster activity was responsible for the breakdown of similarity. An unexpected result of the present study is a discovery of the negative relationship between rupture propagation velocity and static stress. It is dif®cult to explain this contradiction on the basis of dynamic simulations of cracks on a single plane. Although some interaction is expected between slip areas of a large earthquake, there exist few examples of such interaction. The detailed rupture models of Hida events provide a ®ne example of the effect of a preceding earthquake on a following event in terms of rupture propagation behavior. The amount of slip overlap was small, and the following rupture was directed outside of the previously ruptured area. This pattern can be explained by a parallel-oriented fault system on which slips occur selectively on one plane, thereby suppressing slips on other planes. Such a system may be a general feature of such concentrated seismic ruptures. Further discussion is needed of the differences between swarm earthquakes and earthquakes of the mainshock-aftershock type. The Hida-Mountains contain volcanoes, and the earthquakes studied here as well as other swarm earthquakes may be related to volcanic activities. For example, in earthquakes that occurred on the Izu Peninsula, a volcanic area in Japan, the average stress drop was lower than in other areas of Japan, and Wyss et al. (1997) have found an anomalously large b-value in the Gutenberg-Richter magnitude-frequency relation. However, the Hida events show stress drops similar in size to those of larger events, and they show a b-value of almost 1.0 (Aoyama et al., 2000). Although this is not suf®cient evidence to draw a de®nitive conclusion, we have at present no reason to discriminate Hida events from other `usual' earthquakes. If, in the
53
future, systematic studies can be made of moderate earthquakes in other ®elds and of much smaller earthquakes, the differences between swarm and mainshock-aftershock activities will become much clearer. Acknowledgements I wish to thank Prof. M. Takeo and Mr H. Aoyama for their useful comments and help. This study began with the temporary observation conducted with Prof. N. Hirata, Dr S. Sakai, Mr M. Matsubara, and the staff of Shin'etsu Observatory, ERI, and I thank them for their help. The comments from two anonymous reviewers improved this paper very much. This study was supported by a Grant-in-Aid for Scienti®c Research of the Ministry of Education, Science and Culture, Japan. References Akaike, H., 1980. Likelihood and Bayes procedure. In: Bernardo, J.M., et al. (Eds.), Bayesian Statistics. University Press, Valencia, Spain, pp. 143±166. Andrews, D.J., 1985. Dynamic plane-strain shear rupture with a slip-weakening friction law calculated by a boundary integral method. Bull. Seismol. Soc. Am. 75, 1±21. Aoyama, H., Ide, S., Takeo, M, 2000. The evolution of an earthquake swarm under the Hida Mountains, Central Japan, in 1998: stress triggering and its time delay. Submitted for publication. Archuleta, R.J., 1984. A faulting model for the 1979 Imperial Valley earthquake. J. Geophys. Res. 89, 4559±4585. Beroza, G.C., Spudich, P., 1988. Linearized inversion for fault rupture behavior: application to the 1984 Morgan Hill, California earthquake. J. Geophys. Res. 93, 6275±6296. Bouchon, M., 1981. A simple method to calculate Green's functions for elastic layered media. Bull. Seismol. Soc. Am. 71, 959±971. Bouchon, M., 1997. The state of stress on some faults on the San Andreas system as inferred from near-®eld strong motion data. J. Geophys. Res. 102, 11731±11744. Brune, J.N., 1970. Tectonic stress and the spectra of seismic shear waves from earthquakes. J. Geophys. Res. 75, 4997±5009. Das, S., Aki, K., 1977. A numerical study of two-dimensional spontaneous rupture propagation. Geophys. J.R. Astron. Soc. 50, 643±668. Day, S., 1982. Three-dimensional simulation of spontaneous rupture: the effect of nonuniform prestress. Bull. Seismol. Soc. Am. 72, 1881±1902. Day, S., Yu, G., Wald, D.J., 1998. Dynamic stress changes during earthquake rupture. Bull. Seismol. Soc. Am. 88, 512±522. Ellsworth, W.L., Beroza, G.C., 1995. Seismic evidence for an earthquake nucleation phase. Science 268, 851±855.
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