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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B08303, doi:10.1029/2007JB005434, 2008

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Rupture velocity estimation of large deep-focus earthquakes surrounding Japan Sun-Cheon Park1,2 and Jim Mori1 Received 12 October 2007; revised 19 April 2008; accepted 6 May 2008; published 1 August 2008.

[1] Rupture velocity is an important source parameter, which is often difficult to

determine, especially for deep-focus earthquakes where there is usually limited near-source information. To help overcome this problem, we developed a new method to estimate rupture velocities of deep-focus earthquakes with better resolution. We first carry out teleseismic P waveform inversions to determine slip distributions for a range of rupture velocities on the two nodal planes. Then forward modeling of regional data is performed using the slip distributions determined in the teleseismic inversions to estimate the rupture velocity. Using this method, we attempted to determine the rupture velocities of large deep-focus earthquakes surrounding Japan, which are well recorded on teleseismic and regional networks. Empirical Green functions are used for both the teleseismic and regional analyses. Although it is difficult to determine the rupture velocity from only the teleseismic data, the analyses including regional data show clear difference which can resolve the rupture velocity and fault geometry. For three deep earthquakes, we obtained rupture velocities of about 12 km/s, which correspond to 2040% of the shear wave velocity and are much slower than typical values for shallow earthquakes. Citation: Park, S.-C., and J. Mori (2008), Rupture velocity estimation of large deep-focus earthquakes surrounding Japan, J. Geophys. Res., 113, B08303, doi:10.1029/2007JB005434.

1. Introduction [2] The rupture velocity is an important parameter in understanding the physics of the earthquake source, and many studies estimated rupture velocities of shallow and deep earthquakes. For example, Ji et al. [2002] determined a rupture model of the 1999 Hector Mine, USA earthquake (M 7.1) using a joint inversion of strong motion, teleseismic body waves, GPS displacement vectors and surface offsets. The rupture velocity obtained by their study is 1.9 km/s, which is relatively slow. Sekiguchi and Iwata [2002] used strong ground motion data obtained by regional networks to estimate the rupture velocity of the 1999 Kocaeli, Turkey earthquake. They found a ‘‘supershear’’ rupture velocity of 5.8 km/s on certain parts of the fault, with those of about 3 km/s on other parts. Yamada et al. [2005] estimated rupture velocities of very small earthquakes (0.8 < M < 1.4) in the Mponeng gold mine in South Africa using high sampling records observed very close (several hundred meters) to the sources. The rupture speeds they obtained were faster than 2.5 km/s, which is about 60% of the shear wave velocity. [3] These studies were conducted for shallow earthquakes and used not only seismic waveform data but also geodetic or surface rupture data. Furthermore good-quality data are often available close to the faults of large earthquakes, such 1 2

Disaster Prevention Research Institute, Kyoto University, Uji, Japan. Now at Korea Meteorological Administration, Seoul, South Korea.

Copyright 2008 by the American Geophysical Union. 0148-0227/08/2007JB005434$09.00

as in Japan and the United States. These different types of data can provide good constraints to estimate fault dimensions and source parameters, including rupture velocity. For deep-focus earthquakes, lack of closely observed data reduces constraints and makes it more difficult to accurately estimate earthquake source parameters. [4] Even with limited data, previous studies have estimated rupture velocities of deep-focus earthquakes, using relative locations between the hypocenter and subevents [e.g., Beck et al., 1995; Chen, 1995; Goes and Ritsema, 1995; Silver et al., 1995]. Using time differences between the initiation and later phases in the waveforms, which depend on the direction from the earthquake to stations, we can estimate the relative locations between the hypocenter and subevents and then determine the rupture velocity by dividing by the time differences. For example, the great 1994 Bolivia deep earthquake has at least four subevents [Beck et al., 1995] in about 40 s of source duration [Kanamori et al., 1998], and the waveforms showed clear onset consistent with them. So the method using the relative locations may be useful and has good resolution if clear later arrivals can be timed. However, this method has many uncertainties, especially when it is difficult to pick the arrivals of subevents in the waveforms or when the source time function is short and simple, which is common feature of deep earthquakes [e.g., Persh and Houston, 2004]. [5] Another common way to determine the rupture velocity is with seismic waveform inversions [e.g., Estabrook, 1999; Tibi et al., 1999; Tibi et al., 2003], which is also often used for shallow earthquakes. Using observed waveform data, this

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technique estimates source parameters, such as fault dimension, focal mechanism, focal depth, and rupture velocity, which produce a best fit between observed data and theoretically calculated waveforms. However, this method may not have strong constraints on the fault dimension and rupture velocity, especially for teleseismic data. It is often difficult to distinguish between larger faults having faster rupture velocity from smaller faults with slower rupture velocity, as will be mentioned in section 2.2. Other studies constrain fault dimension with other parameters, for example, geodetic data [e.g., Ji et al., 2002] or locations of subevents and termination points [Tibi et al., 2003]. To estimate the rupture velocities of deep-focus earthquakes, in this paper we develop a multistep method, including teleseismic waveform inversions and forward modeling of regional data.

2. Methodology and Data 2.1. Methodology [6] To estimate rupture velocity, we first carry out teleseismic waveform inversions, and then forward modeling of regional data assuming the slip distributions obtained by teleseismic inversions. The empirical Green function method is used for both teleseismic inversion and forward modeling of regional data. The empirical Green function method was first suggested by Hartzell [1978], and uses aftershocks or other small events near a large event, to represent the response of point sources on the fault plane, so that the complicated effects of the earth structure can be included in the inversion process. This method is frequently used to obtain source information [e.g., Antolik et al., 1996; Antolik et al., 1999; Irikura, 1986; Mori and Frankel, 1990; Velasco et al., 1994; Kamae and Kawabe, 2004; Suzuki et al., 2005]. We use smaller earthquakes as the empirical Green function event (EGF event) with the criteria that they are recorded at both teleseismic and regional stations, have appropriate size (about one of magnitude smaller than the main event), and have focal mechanisms similar to the main events. [7] For the teleseismic waveform inversions, we obtain digital P wave data for stations at distance ranges of about 30° and 90° converted to displacement and high-pass filtered at 0.005 Hz. To estimate the slip distributions, we use a multiple time window inversion [Hartzell and Heaton, 1983]. We carry out waveform inversions and obtain the slip distribution for each rupture velocity from 0.5 to 6 km/s (0.5 km/s intervals up to 4 km/s, and 5 and 6 km/s) for both nodal planes of the focal mechanism solutions. Fault dimensions are varied for the change of rupture velocities, i.e., fault dimension with faster rupture velocity becomes larger. Varying fault dimension provides a constant number of inversion parameters even though the rupture velocity is changed. If constant grid sizes are used, faster rupture velocities often produce better model fits because more grid points (more parameters) are used in the inversion. [8] Using the slip distributions obtained by the teleseismic inversions, we perform waveform modeling of the regional data using empirical Green functions. For the specific case that analyzed events surrounding Japan, we used data of the Broadband Seismic Network (F-Net) operated by the National Research Institute for Earthquake Science and Disaster Prevention (NIED). Since Japan is located within

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a very complex structure with several plates, it may be quite difficult to sufficiently include the propagation effects from a deep source to station through the slabs. Therefore we use an empirical Green function method to represent the complex structural effects. [9] Forward modeling of regional data is done to test both nodal planes and each rupture velocity, also varying the fault dimensions. The regional data that we use are displacement waveforms high-pass filtered at 0.005 Hz, similar to the teleseismic data. We determine the rupture velocity by searching a range of values to find where synthetic waveforms best match the observed regional data. We judge that the largest value (or range of value) of variance reduction between synthetics and observed data is significant when there is a maximum within a relatively smooth curve of values, as a function of rupture velocity. 2.2. Numerical Tests [10] Our method has two new aspects: (1) varying fault dimension for assumed rupture velocity changes and (2) combination of teleseismic waveform inversion and forward modeling of regional data. We performed some numerical tests to check how these methods perform on test data. We made test waveforms for teleseismic and regional stations with assumed slip distributions and rupture velocities. For the empirical Green function, we used waveforms of a Mw 6.4 on 15 September 2002. We applied random noise at the level of about 10% of the maximum amplitude. The assumed fault was at a depth of 566 km with a strike of 27° and dip of 13°. This fault geometry is similar to the shallowly dipping plane of the 28 June 2002 event (Mw 7.3), analyzed in section 3. We then used the test data as input to simulations of the teleseismic inversions and regional waveform modeling. 2.2.1. Teleseismic Inversion With Fixed Fault Dimension [11] We first fix fault dimensions to show the tradeoff between the rupture velocity and fault size. We calculated synthetic waveforms for teleseismic and regional stations using assumed slip distributions with rupture velocities of 2 and 3 km/s on a fault plane of 70  70 km2 and applying three time windows. Here three time windows mean that the input has three overlapping waveforms with a certain time offset, which is 1.0 s in this study. Multiple time windows allow a subfault to have longer slip duration in the inversion process. We here used three time windows to produce about 6 s of rupture duration, which can represent source duration for a fault length less than about 20 km. This fault length is assumed as the grid size for a rupture velocity of 4 km/s in these numerical tests. We used the test waveforms as observed data, and carried out teleseismic inversions. The procedure determined slip distributions and rupture velocity. [12] Figure 1 shows the variance reductions between the test data and model synthetics as a function of rupture velocity. This example shows that although the differences at slow rupture velocities are well resolved, it is difficult to distinguish between the faster rupture velocities. This is due to the tradeoff between rupture velocity and fault size. Even though the largest variance reductions are obtained at the input rupture velocities when time windows are appropriately applied, the differences of variance reduction between fast

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and slow rupture velocities are very small. Furthermore, in the case of fixed fault dimension, it is necessary to correctly assume the fault dimension. Usually the fault dimension is recognized by the aftershock distribution for shallow earthquakes. However, this is difficult for deep-focus earthquakes because of the small number of aftershocks. Another approach for inversions is to assume sufficiently large fault dimension and constrain the inversion process not to have large slips at the edges that might be caused by overparameterization. However, as shown in Figure 1, it may be difficult to resolve the differences for the faster rupture velocities. To address these problems, we next use a method that varies the grid size proportionally to the rupture velocity. 2.2.2. Varied Fault Dimension [13] Figure 2 shows an example of a variable fault dimension. For example, the size (grid interval) for the rupture velocity (Vr) of 2 km/s is twice that for the rupture velocity of 1 km/s. With varying fault dimension, the inversion parameters can be constant and there is no difference in terms of number of parameters for faster and slower rupture velocities for the same observed source duration. Using a constant grid spacing, faster rupture velocities usually need more fault parameters because the slip spreads out over a larger area. [14] We made test waveforms for teleseismic and regional stations using rupture velocities between 2 and 6 km/s and assumed slip distributions in the same way described in section 2.2.1. An example calculated with a rupture velocity of 2 km/s is shown in Figure 3a (teleseismic waveforms) and Figure 3b (regional data). We performed teleseismic waveform inversions for each rupture velocity from 1 to 6 km/s, at 1 km/s interval using one and three time windows. After obtaining a slip distribution using the teleseismic test data for each case, we did forward modeling of regional data to determine the best fitting rupture velocity. [15] Figure 3 shows an example of the model waveforms from the inversion results (dotted lines in Figure 3a) and forward modeled regional waveforms (dotted lines in Figure 3b), comparing to the test data produced with a

Figure 1. Test for fixed fault dimension. Variance reductions between synthetics and observed data for teleseismic inversions are plotted as a function of rupture velocity (Vr). It is difficult to resolve the differences for the faster rupture velocities. ‘‘Vr2’’ or ‘‘Vr3’’ here mean that the assumed rupture velocities are 2 or 3 km/s, respectively, and ‘‘tw’’ indicates the number of time windows used in the inversions.

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Figure 2. Setup for variable fault dimension. For faster rupture velocity, the fault dimension (grid interval) is larger. Rectangles are the fault boundaries for different rupture velocities. rupture velocity of 2 km/s. Figure 4 shows variance reductions as a function of rupture velocity for the teleseismic inversion and forward modeling. Some of the teleseismic inversion results show the largest variance reductions at rupture velocities different from the input values or increases with rupture velocity increases (see the cases for rupture velocities of 3 to 6 km/s). However, the largest variance reductions for forward modeling of regional data correspond to the input rupture velocity, except for the case of 5 km/s rupture velocity and one time window. These results indicate that our method should have proper resolution at rupture velocities slower than 4 km/s. These tests were done for several different patterns of slip distribution, unilateral propagation in several directions, circular and bilateral rupture propagation (We show the resultant slip distributions for the unilateral and circular cases in Figure S1 in the auxiliary material).1 In all cases, the inversion results well reproduce the input slip distributions in terms of the locations of large slip areas and the amount of slip. [16] We also tested the procedure for identifying the correct nodal plane. Using test data with a rupture velocity of 2 km/s and directivity effects to the northwest and southwest, the procedure was carried out assuming each nodal plane. The results are shown in Figure S2 in the auxiliary material. The slip distributions seem to recover the inputs well for the southwest directivity. However, for the northwest directivity, the correct solution does not seem to be well imaged. However, the variance reductions for forward modeling of regional data have the maximum values at the assumed rupture velocities for both cases. 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2007JB005434.

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Figure 3. Example test waveforms of (a) teleseismic and (b) regional data for an input rupture velocity of 2 km/s (solid) and inversion results for rupture velocity of 2 km/s (dotted) with focal mechanism of assumed fault plane. Waveforms are aligned on the P arrival at 5 s.

2.2.3. Why Both Teleseismic and Regional Data Are Needed [17] If we can determine the rupture velocity by modeling of regional data, why do we need the teleseismic inversion? We compare the characteristics of teleseismic and regional data in Table 1 for typical events recorded in Japan. Teleseismic data may have a good azimuthal range (360°) so

that the shape of slip distribution can be well constrained. However, since they have small range of vertical takeoff angles (2050°), they are not as sensitive to horizontal rupture propagation on the fault plane. In contrast, regional data have a larger range of takeoff angles (50135°), so they can be more sensitive to the rupture velocity. However, regional data can have limited azimuthal coverage, espe-

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Figure 4. Variance reductions as a function of rupture velocity for various combinations of search parameters. Each diagram shows the results for a different value of input rupture velocity for the test waveforms. Open symbols show the results for the teleseismic inversion. Solid symbols show the results from the forward modeling of regional data. Vr represents input rupture velocity and tw represents number of time windows. Thin and thick arrows point the maximum variance reductions for teleseismic inversions and forward modeling, respectively. Maximum variance reductions for forward modeling of regional data are obtained for the assumed rupture velocities slower than 4 km/s, while those for teleseismic waveform inversion are at various rupture velocities.

cially for deep offshore earthquake, which can cause poorer resolution of the slip distribution. [18] Figure 5 shows an example for the results of inputting a bilateral rupture with subevents relatively far from the hypocenter. The teleseismic inversion results (Figure 5b) show large slip areas at the location of the input large slip areas (circles), although there is ‘‘noise’’ obtained on other subfaults. Inversion results using regional data (Figure 5c) do not reproduce larger slip at the input locations as well. This test was done using data with an azimuthal range of about 110°. For some events we studied regional stations have an even smaller azimuthal range. Waveform inversions using only regional data will be insufficient to obtain slip distributions for these events. Another advantage of including the regional data is the higher-frequency content of the waveforms, due to less travel time and thus less attenuation.

The finer details in the waveforms allow better resolution of the rupture propagation. The combination of teleseismic and regional data provides a way to take advantage of the strengths of both data sets. First, teleseismic inversions are used to determine slip distributions for a given rupture velocities. Then, the regional data can be used to determine which rupture velocity (and thus which slip distribution) is best. Finally, once the rupture velocity is determined, Table 1. Comparison of Characteristics of Teleseismic and Regional Data Takeoff angle range Azimuthal range Number of stations

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Teleseismic Data

Regional Data

2050° 360° 20

50135° 85120° 2256 (F-net)

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Figure 5. Test examples of slip distribution for the case of a bilateral rupture. (a) Input slip distribution. Dotted circles indicate the locations of large slip. (b) Obtained slip distribution from only teleseismic inversion. (c) Obtained slip distribution from waveform inversion using only regional data. Inversion result using regional data (Figure 5c) does not reproduce large slips at the assumed locations. inversion of the regional data can be used to refine the slip distribution. 2.3. Data [19] Japan has dense high quality seismic networks, including F-Net, which consists of about 80 sites with broadband 120360 s seismometers (STS-1, 2), which is operated by NIED. Since 1997 when F-Net started, five large deep-focus earthquakes (depth >300 km) with magnitudes greater than 7 occurred in this region. Figure 6 shows the locations and focal mechanisms of two events around the China-Russia border, two near the Bonin Islands region and one near Sakhalin. Our method uses smaller earthquakes as empirical Green functions (EGF) for both the teleseismic and regional analyses, so we need well recorded nearby events. However, because of the low level of seismicity and few aftershocks, we could not find appropriate EGF events for the 8 April 1999 and 17 November 2002 events. Therefore in this paper we analyze the other three events. The earthquake source parameters from the U. S. Geological Survey (USGS) and the Harvard Centroid Moment Tensor (CMT) solutions are listed in Table 2. The smaller events listed in Table 2 were used as empirical Green functions for the analyses. [20] We carried out teleseismic waveform inversions, and then forward waveform modeling of the regional FNet data using the slip distributions. Using many regional stations improves the resolution of the rupture velocity estimate, so we used as many F-Net stations as possible with good signal-to-noise ratio. 22, 39, and 56 stations were used for the 20 August 1998, 6 August 2000 and 28 June 2002 events, respectively.

3. Event of 28 June 2002 Near the China-Russia Border [21] The 28 June 2002 event (Mw 7.3) occurred near the China-Russia border at 566 km depth within the Pacific plate. This earthquake is a reverse fault event striking in a northeast (or southwest) direction (Figure 6). Teleseismic P displacement waveforms (solid lines in Figure 7) show that source durations are less than 15 s and become shorter at

Figure 6. Locations and focal mechanisms of large deepfocus earthquakes (M > 7) since 1997. Events with solid stars are studied in this paper. Hypocenters and moment magnitudes (Mw) are from the USGS catalog and focal mechanisms are from the Harvard CMT solutions. Slab contours are plotted from 0 and 700 km depth in 50 km interval [Gudmundsson and Sambridge, 1998].

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Table 2. Earthquake Source Parameters Used in This Studya Event

Origin Time

Latitude (°)

Longitude (°)

Depth (km)

Mw

Main EGF Main Main EGF

2002. 6. 28. 17:19:30 2002. 9. 15. 08:39:32 1998. 8. 20. 06:40:55 2000. 8. 6. 07:27:12 2002. 8. 2. 23:11:39

43.752 44.833 28.932 28.856 29.280

130.666 129.923 139.329 139.556 138.970

566.0 586.0 440.5 395.0 418.0

7.3 6.4 7.1 7.3 6.3

Mo (Nm) 1.11E 4.24E 4.73E 1.20E 2.57E

+ + + + +

20 18 19 20 18

Shallowly Dipping (27, 13, (98, 19, (83, 27, (108, 27, (73, 25,

105) 163) 162) 142) 168)

Steeply Dipping (192, 77, (204, 85, (337, 82, (344, 74, (332, 85,

86) 72) 64) 68) 65)

a Origin time, hypocenter and moment magnitude (Mw) are from the USGS catalog and seismic moment (Mo) and focal mechanisms are from the Harvard CMT solutions.

southwestern stations (BTDF, PALK, HYB). Most stations have three peaks in their waveforms; however, the peaks seem to merge at stations to the southwest, suggesting rupture directivity toward the southwest. [22] We used the 15 September 2002 event (Mw 6.4) as an empirical Green function, which are shown by the dotted lines in Figure 7. Figure 8 shows velocity waveforms of the 28 June (Figure 8b) and 15 September (Figure 8c) events recorded at F-Net stations (Figure 8a) ordered as a function of azimuth and aligned on the P arrival at 5 s. The data are lowpass filtered at 1 Hz. In the velocity waveforms three relatively long pulses are recognizable for the 28 June 2002 event and the third large peak arrives earlier at the stations in southwestern Japan compared to northern stations (See dotted line in Figure 8b). This directivity is consistent with the teleseismic displacement waveforms. For the EGF event on 15 September, the waveform durations at F-Net stations become shorter to the southwest, which can be seen in comparison to the scale bars of 2 s. However, durations of teleseismic waveforms (Figure 7) at northeastern stations are

shorter than those to the southwest. The more complexity and longer duration of F-Net waveforms to the northeast for the EGF event is probably due to propagation effects. When an earthquake occurs deep in a slab, the waves may be guided and dispersed in a low velocity layer of the slab and arrive at stations with longer duration [Iidaka and Mizoue, 1991; Abers and Sarker, 1996]. Waves from the hypocenter to stations in the northeast would travel within the slab for a longer time, making longer pulse durations. Meanwhile waves to the southern stations in western Japan, travel within the slab for a shorter time, producing the shorter durations. Therefore, there may be significant structural differences for the different raypaths, emphasizing the importance of using empirical Green functions or other methods that include three-dimensional structure. 3.1. Teleseismic Waveform Inversions and Forward Modeling of Regional Data [23] For teleseismic waveform inversions, we used 18 stations with an appropriate azimuthal distribution, as

Figure 7. Station distributions used for teleseismic waveform inversions and observed displacement waveforms of the 28 June (solid) and 15 September (dotted), 2002 events. Waveforms are aligned on the P arrival at 5 s. 7 of 20

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Figure 8. (a) Station map of F-net stations and comparison of the velocity waveforms of the (b) 28 June and (c) 15 September 2002 events aligned on the P arrival at 5 s. Waveforms are low-pass filtered at 1 Hz and the amplitudes are normalized. Solid bars in Figures 8b and 8c indicate 2 s, showing duration shortening of pulses to the south. Dotted line in Figure 8b indicates the peak of the third pulse in the waveforms showing directivity to the southwest direction.

shown in Figure 7. The fault grid had 7  7 subfaults with an interval that increases from 2.5 to 30 km for rupture velocities of 0.5 to 6 km/s. Inversions were carried out for the two nodal planes determined by the Harvard CMT solutions, using one and three time windows. The shallowly dipping plane of this event has a strike of 27° and dip of 13° and the steeply dipping plane has a strike of 192° and dip of 77°. [24] As an example, Figure 9 shows slip distributions from the inversions with the source time functions for the shallowly dipping plane using three time windows. Slip mainly occurs near the hypocenter, and rupture seems to propagate in a SW to W direction. The moment magnitude (Mw) was 7.1 to 7.2 for all cases. The teleseismic waveforms of this event (Figure 7) show mainly three pulses; however, the slip distributions in Figure 9 seem to be smoothed and do not clearly show different subevents. Also the source time functions have mainly two peaks for rupture velocities faster than 1.5 km/s. We tested smaller fault sizes, i.e., subfault interval increasing from 1.5 to 18 km for rupture velocities of 0.5 to 6 km/s, and give the results in Figure S3 in the auxiliary material. Those results show large slip areas that extend to the southwest with source time functions showing three or four pulses. Even though the slip distributions in Figure 9 seem smooth, the synthetics do show clear directivity to the southwest. We show some additional examples in Figure S4 in the auxiliary material. [25] With these slip distributions obtained in the teleseismic analysis, we performed forward modeling of 56 FNet stations. Because of the favorable location of this event, the azimuthal range of the stations (Figure 8a) is about 110°, which may be sufficient to see the waveform changes due to rupture propagation.

[26] The results of the teleseismic inversion and forward modeling are shown in Figure 10. Variance reductions between synthetics and observed data of the teleseismic inversions (Figure 10a) become larger as the rupture velocity becomes faster (fault dimension also becomes larger). This means that the waveform inversion cannot constrain the fault dimension or rupture velocity. As can be expected by the similar values of variance reductions, the synthetic waveforms for the shallowly and steeply dipping planes did not show much difference. [27] However, the variance reductions for the forward modeling of F-Net (Figure 10b) data show clear maximum values at a rupture velocity of 2 km/s of the shallowly dipping plane. Furthermore, the differences of variance reductions between the shallowly and steeply dipping planes are much larger compared to the teleseismic inversion results, indicating that the shallowly dipping plane is the fault plane. We show the waveform examples in Figure 11a. Synthetics of the shallowly dipping plane (bold lines) for F-Net data (See Figure 8a for the locations) reproduce the third pulse, indicated by arrows, relatively well. But synthetics for the steeply dipping plane (thin solid lines) do not explain the third pulse well and instead the amplitudes of the second pulse become larger. [28] As mentioned in section 2.2.3, regional data are more sensitive to rupture velocity than teleseismic data because of the larger range of takeoff angles. We compare synthetic waveforms for various velocities at two F-Net stations in Figure 11b. Synthetic waveforms in the upper traces are calculated with one time window, and three time windows for the lower traces. In the upper traces, the first pulses of the synthetics for all cases arrive at the same time because this phase comes from the hypocenter. However, the second

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Figure 9. Slip distributions and the source time functions of the 28 June 2002 event obtained by teleseismic waveform inversions for the shallowly dipping plane and applying three time windows. Fault dimension and rupture velocity increase from upper left to lower right.

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dipping plane having strike of 27 degrees applying three time windows. The moment magnitude (Mw) was 7.3. The slip distribution shows slight directivity to the west, which is consistent with the results of the teleseismic waveform inversions (Figure 9). Compared to the teleseismic results, there is slightly more slip in the southeast direction. 3.3. Comparison to Other Studies [30] Tibi et al. [2003] carried out teleseismic body wave inversions for this event and found that the centroid is located at a distance of 16 km and azimuth of 246° from the hypocenter. Their favored rupture velocity is 2 km/s. Also they suggested that rupture occurred along the subhorizontal nodal plane from the estimated distance of 20 km between the initiation point and the last subevent. These results are similar to our estimates for the fault geometry and rupture velocity. [31] The Earthquake Research Institute (ERI), University of Tokyo (EIC Seismological Note 124) provides teleseismic P waveform inversions and gives a fault dimension of 50  30 km2 with a moment magnitude (Mw) of 7.3. They state that the steeply dipping fault plane has a significantly better fit. However, they used only six stations with no stations to the southwest, so the fault geometry might not be well constrained. Figure 10. Variance reductions between synthetics and observed data as a function of rupture velocity for the 28 June 2002 event. (a) Teleseismic inversions and (b) forward modeling of F-net data. Here ‘‘tw’’ is the number of applied time windows. Arrows point the maximum variance reductions, indicating the rupture velocity of the event. and third pulses are gradually delayed as the rupture velocity increases. This can be especially recognized for the third pulse by comparing its arrival with the peak in the observed data (dotted vertical line). This is because the distance of the subevent from the hypocenter becomes longer and the distance change can be seen in close stations. For teleseismic stations, relative distance changes between the hypocenter and subevents are much smaller because of the steep vertical takeoff angle. Synthetics with three time windows (lower traces) show slightly different shapes. They seem to lose the characteristic three pulses as the rupture velocity increases and have roughly one (KZK) or two (KNP) large pulses. However, synthetic waveforms for a rupture velocity of 2 km/s fit the third peak with appropriate timing, which is similar to the results using only one time window. The difference of synthetic waveforms between one and three time windows may be because a certain subfault can slip for a longer time with three time windows. When one time window is applied, a subfault is allowed to slip for a shorter time and the neighboring subfaults have to slip to fit the observed data, producing wider or more scattered slip areas. With three time windows a subfault can slip longer, so that slip areas can be more compact and time delays of phases will be shorter. 3.2. Inversion Using Regional Data [29] Using the fault geometry for a rupture velocity of 2 km/s, which had the smallest variance for the forward modeling of regional data, waveform inversions with regional data were carried out to redetermine the slip distribution (Figure 12). This is calculated for the shallowly

4. Event of 20 August 1998 in Bonin Islands Region [32] The 20 August 1998 event (Mw 7.1) occurred in the Bonin Islands region at a depth of 440 km. This earthquake is a normal fault event having a shallowly dipping plane with strike of 83° and dip of 27° and steeply dipping plane with strike of 337° and dip of 82° (Figure 6). Teleseismic displacement waveforms (solid lines in Figure 13b) have small amplitudes for the first P arrival and larger phases from about 78 s later. So subevents may be located far from the hypocenter. The source time function seems to be about 25 s. Waveforms are complicated and have relatively long duration for a deep-focus earthquake, indicating that the slip distribution may be complex. [33] For the analyses of teleseismic waveforms, a smaller event that occurred on August 2, 2002 with a similar focal mechanism (Figure 13a) was used as the EGF event. Figure 13b shows some of teleseismic displacement waveforms of the 20 August 1998 (solid) and 2 August 2002 (dotted) events. Since the stations to the south are close to a node, the ratios of signal to noise are low and we do not use these data. The waveforms of the 2 August 2002 event have a simple single pulse and duration similar to that of one pulse of the 20 August 1998 event. So this event will be appropriate as the EGF event. [34] Figure 14 shows the F-Net station map used for forward modeling and some of the displacement waveforms of the 20 August 1998 (solid) and 2 August 2002 (dotted) events. Azimuthal range of the stations is about 87°. The waveforms of the 2 August 2002 event are simpler and seem to be appropriate for the EGF event. 4.1. Teleseismic Waveform Inversions and Forward Modeling of Regional Data [35] For the teleseismic waveform inversions, we chose 13 stations, among those shown in Figure 13a considering the

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Figure 11. Comparisons of waveforms for the 28 June 2002 event. Observed waveforms are aligned on the P arrival at 10 s. (a) Comparison of synthetic waveforms for the shallowly (bold lines) and steeply (thin solid lines) dipping planes with a rupture velocity of 2 km/s. Dotted lines are observed data. The third pulse indicated with arrows is better reproduced by synthetics for the shallowly dipping plane. (b) Change of synthetic waveforms due to change of rupture velocity. Dotted lines are observed data at two F-net stations and synthetics (solid lines) are calculated for the shallowly dipping plane with rupture velocities from 1 to 6 km/s. Numbers on the left indicate rupture velocities. Dotted vertical lines in upper traces indicate the peaks of the third pulse in the observed waveforms. Later peak in the synthetic waveforms are gradually delayed as the rupture velocity increases, as shown by arrows.

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Figure 12. Slip distributions of the 28 June 2002 event resulting from waveform inversions using F-net data for a rupture velocity of 2 km/s. azimuthal distribution. The fault plane was setup as 9  9 subfaults with 2.5 to 30 km spacing for rupture velocities from 0.5 to 6 km/s. Since the source duration of this earthquake is about 10 s longer than those of the other events in this study, a larger fault size was used. Waveform inversions were performed for the two nodal planes of the Harvard CMT solutions, applying one and three time windows.

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[36] The obtained moment magnitude was 7.07.1 for all cases. Figure 15a shows the slip distributions and the source time functions obtained from the inversions for a rupture velocity of 1 to 2 km/s and three time windows on the shallowly dipping plane. As can be seen from the shapes of the waveforms, large slip areas are located relatively far from the hypocenter, with the main slip areas generally to the east. We showed in subsection 2.2.3 that inversion results for a bilateral rupture or the cases having multiple subevents far from the hypocenter may have artifact slip areas. Furthermore, we have no stations to the south, so it is difficult to constrain slip distribution and they may have corresponding uncertainties. [37] Using these slip distributions, we carried out forward waveform modeling for 22 F-Net records shown in Figure 14a, applying one and three time windows. Variance reductions between observed and synthetic waveforms for the teleseismic inversions and forward modeling are plotted in Figure 16. For both cases the variance reduction is larger for the shallowly dipping plane than for the steeply dipping plane. Teleseismic inversion results for the shallowly dipping plane have a maximum variance reduction at a rupture velocity of 3 km/s. However, the largest variance reductions for forward modeling on the shallowly dipping plane appear at rupture velocities of 1.5 (one time window) to 2 (three time windows) km/s. We think the rupture velocities for the forward modeling are reliable, following some numerical tests (section 2.2.2). The variance reductions for the shallowly dipping plane are smaller than for the steeply plane and the best fitting rupture velocities are in the

Figure 13. (a) Focal mechanisms of the 20 August 1998, 6 August 2000, and 2 August 2002 events. (b) Comparison of teleseismic displacement waveforms of the 20 August 1998 (solid) and 2 August 2002 (dotted) events at some stations shown in Figure 13a. (c) Comparison of teleseismic displacement waveforms of the 6 August 2000 (solid) and 2 August 2002 (dotted) events at some stations shown in Figure 13a. Waveforms in Figures 13b and 13c are aligned on the P arrival at 10 s. 12 of 20

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Figure 14. (a) F-net station map and (b) comparison of regional (F-net) displacement waveforms of the 20 August 1998 (solid) and 2 August 2002 (dotted) events aligned on the P arrival at 10 s. range of 1 to 2 km/s for both one and three time windows. Figure 15b shows examples of waveform fits of synthetics to the observed data from the teleseismic inversions for a rupture velocity of 2 km/s on the shallowly dipping plane. In a general sense, observed data and synthetic waveforms for the shallowly and steeply dipping planes did not show much difference. Synthetic waveforms calculated by forward modeling of F-Net stations, have clearer differences. Figure 15c shows examples of the waveform fit obtained by forward modeling for the shallowly and steeply dipping planes at three stations. These waveforms are for the case of a rupture velocity of 2 km/s and three time windows. The synthetics for the shallowly dipping plane explain well the largest pulse, which are not fit very well for the steeply dipping plane. [38] In Figure 15d, we compare the synthetic waveforms for two F-Net stations obtained by forward modeling with different rupture velocities. They were calculated for the shallowly dipping plane and three time windows. We can see slight time delays of the largest peak in the synthetics for rupture velocities faster than 4 km/s. Synthetic waveforms with rupture velocities of 1 to 2 km/s seem to fit well the large pulses, and this can be also seen in the variance reduction plot in Figure 16b. (The variance reduction

actually does not show quite large changes over the range of 1 to 2 km/s). [39] We tested for smaller subfaults using sizes from 1.5 to 18 km and from 2 to 24 km, for rupture velocities of 0.5 to 6 km/s. For the case of 1.5 to 18 km subfaults, large slips were located mainly at the fault boundaries, indicating the fault size is likely too small. For the case of 2 to 24 km subfaults, we could see large slip areas mainly in the southeast direction, similar to slip distributions in Figure 15a. We show some examples in Figure S5 in the auxiliary material to compare to Figure 15a. The variance reductions for forward modeling of regional data have maxima at a rupture velocity of 2 km/s. 4.2. Inversion Using Regional Data [40] We redetermined the slip distribution with a waveform inversion using F-Net data for the shallowly dipping plane and rupture velocities between 1 and 2 km/s, which showed the largest variance reductions for the forward modeling. Figure 17 shows the slip distributions applying three time windows. The obtained moment magnitude (Mw) is 7.0 and the variance reduction between synthetics and observed data for a rupture velocity of 2 km/s was the largest. But it is difficult to judge if the largest variance reduction is significant. Similar to the teleseismic inversion

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Figure 15

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quakes occurred between 1988 and 2000. They found the source time function of the 20 August 1998 event is about 17 s. The seismic moment mainly released from 5 s after the initiation. Our results of source time functions (Figure 15a) are about 25 s, which is longer than their source duration.

5. Event of 6 August 2000 in Bonin Islands Region

Figure 16. Variance reductions between synthetics and observed data as a function of rupture velocity for the 20 August 1998 event. (a) Teleseismic inversions and (b) forward modeling of F-net data. Arrow in Figure 16b shows the maximum variance reduction indicating likely rupture velocity of the event. in section 2.2.2, it is difficult to resolve the rupture velocity in the range of 1 to 2 km/s because of the rather limited azimuthal range of the regional data. 4.3. Comparison to Other Studies [41] For this event the teleseismic body wave inversions of Tibi et al. [2003] produce a model with three sources. The first subevent is located to the northwest relative to the initiation point and the second and third subevents are to the northeast. Their preferred fault model has dimensions of 20  20 km2 and a rupture velocity of 2 km/s. Their fault dimension is quite small compare to our estimate of about 50  60 km2. Also, our preferred fault geometry is for the shallowly dipping plane, which does not agree with their model. [42] The ERI results (EIC Seismological Note 49) show three subevents on the steeply dipping plane. This is also inconsistent with our model. We think that our results may have better resolution, because we tried to fit not only teleseismic waveforms but also regional data. [43] Persh and Houston [2004] stacked P waveforms from Global Seismographic Network (GSN) broadband seismograms to obtain source time functions of large deep earth-

[44] The 6 August 2000 event occurred close to the 20 August 1998 event as shown in Figures 6 and 13a. The moment magnitude (Mw) is 7.3 and the focal depth is 395 km according to the USGS catalog. The focal mechanism obtained by the Harvard CMT solutions has a shallowly dipping plane with a strike of 108° and dip of 27° and steeply dipping plane with a strike of 344° and dip of 74°. In Figure 13c, teleseismic displacement waveforms of this event are shown compared with those of the 2 August 2002 event, which was used as the EGF event. As mentioned in section 2.3, we analyzed events since 1997 where F-Net data are available. The 2 August 2002 event is the only that occurred close to both 1998 and 2000 Bonin Islands earthquakes since 1997, which is large enough (M > 6) to be recorded at teleseismic stations, and has a similar focal mechanism. Therefore we used the event as an EGF event for both 20 August 1998 and 6 August 2000 events. Waveform durations of the 2 August 2002 event (dotted) are about the duration of one pulse of the 6 August 2000 event (solid), indicating that this earthquake may be used as an EGF event. This may be confirmed in regional waveforms shown in Figure 18. 5.1. Teleseismic Waveform Inversions and Forward Modeling of Regional Data [45] Teleseismic waveform inversions were carried out with 11 stations from those shown in Figure 13a. The fault plane had 7  7 subfaults with 1.5 to 18 km grid spacing for rupture velocities of 0.5 to 6 km/s. As was done for the previous earthquakes, different sized grid spacing was tried before finalizing on the 1.5 to 18 km sizes. Larger grid spacing produces much larger amplitudes of synthetic waveforms and unstable variance pattern. (We show an example of slip distribution assuming larger fault size and compare the synthetics to those calculated with grid spacing of 1.5 to 18 km sizes in Figure S6 in the auxiliary material.) Waveform inversions were performed for the shallowly and steeply dipping planes applying both one and three time windows. [46] From the results of the teleseismic inversion, the obtained moment magnitude was 7.2 to 7.4. The slip distributions generally have one large slip area near the hypocenter (Figure 19a). Figure 20a shows the variance reductions between observed and synthetic data obtained by the teleseismic inversions as a function of rupture velocity. The general trend is that the variance reduction increases as

Figure 15. Slip distributions and waveforms of the 20 August 1998 event. All observed waveforms are aligned on the P arrival at 10 s. (a) Slip distributions and the source time functions from teleseismic inversions. (b) Examples of waveform fits between observed (solid) and calculated (dotted) waveforms for the shallowly dipping plane and rupture velocity of 2 km/s. (c) Synthetic waveform comparison of shallowly (bold lines) and steeply (thin solid lines) dipping planes calculated by forward modeling at three F-net stations. (d) Changes in synthetic waveforms due to increase of rupture velocity. Dotted lines are observed data at two F-net stations and synthetics (solid lines) are calculated for the shallowly dipping plane with rupture velocities from 1 to 6 km/s. Numbers on the left indicate rupture velocity. 15 of 20

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Figure 17. Slip distributions of the 20 August 1998 event from inversions using regional data for the rupture velocities of 1 to 2 km/s. rupture velocity increases, and there is not much difference between variance reductions for the shallowly and steeply dipping planes. Figure 20b shows the variance reductions of the forward modeling of 39 F-Net data, which have a good azimuthal range of about 120°, for the cases of one and three time windows. The best fit is for a rupture velocity of 1.5 km/s on the steeply dipping plane. [47] Figure 19b compares waveform fits at three F-Net stations with a rupture velocity of 1.5 km/s on the shallowly (thin solid lines) and steeply (bold lines) dipping planes. Synthetic waveforms for the steeply dipping plane explain the observed data better than for the shallowly dipping plane in producing the second large pulses (arrows in Figure 19b).

19c has a large slip area surrounding the hypocenter. The slip on subfaults in the downdip direction became smaller compared to the slip distribution from the teleseismic inversion (Figure 19a) and may be produced to fit better the amplitudes of the waveforms. We tested forward modeling of teleseismic data using the slip distribution from the F-Net inversion results (Figure 19c) and show an example of synthetics at teleseismic station CHTO in Figure 19d. The point is that the two subevents, which are difficult to see in the spatial slip distribution, can be clearly seen in the waveforms. The amplitude of the second peak (bold lines) is smaller than that of synthetics obtained by teleseismic inversion (dotted lines).

5.2. Inversion Using Regional Data [48] We carried out waveform inversions using F-Net data for a rupture velocity of 1.5 km/s on the steeply dipping plane using three time windows. The obtained moment magnitude was 7.1 and the slip distribution shown in Figure

5.3. Comparisons to Other Studies [49] For the 6 August 2000 event, Tibi et al. [2003] indicated that the centroid is located about 1 ± 2 km from the hypocenter. Assuming bilateral rupture propagation, they found that the rupture propagated along the steeply

Figure 18. (a) F-net station map and (b) comparison of regional (F-net) displacement waveforms of the 6 August 2000 (solid) and 2 August 2002 (dotted) events aligned on the P arrival at 10 s (Figure 18b). 16 of 20

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Figure 19. (a) Slip distribution for the 6 August 2000 event from teleseismic inversions. (b) Synthetic waveform comparison of shallowly (thin solid lines) and steeply (bold lines) dipping planes at three F-net stations calculated by forward modeling of regional data. Arrows indicate the second pulse of the observed waveforms that were better reproduced in the synthetics for the steeply dipping plane. (c) Slip distribution from inversions using regional data. All slip distributions are for a rupture velocity of 1.5 km/s on the steeply dipping plane. (d) Comparison of synthetics obtained by inversions using teleseismic (dotted lines) and regional (bold lines) waveforms. Waveforms in Figures 19b and 19d are aligned on the P arrival at 10 s. dipping plane in the N25°W and S25°E directions and the best fitting rupture speed is 2 km/s. The rupture velocity seems to be similar value to our estimate, 1.5 km/s. [50] The ERI results for this event (EIC Seismological Note 90) indicate that there are two subevents and the fault dimension is 30  15 km2 with a moment magnitude (Mw) of 7.3. The small fault dimension is similar to the main slip area in our inversion results for the rupture velocity of 1.5 km/s. [51] Our source time function (Figure 19a) is similar to that determined by Persh and Houston [2004], which is about 9 s. They both show a compact and simple shape.

6. Discussion 6.1. Uncertainties in Determining Rupture Velocity [52] To estimate the rupture velocities of deep-focus earthquakes we developed a method that uses teleseismic P

waveform inversions and then forward modeling of regional data, with both steps using empirical Green functions. For deep events it is often difficult to find an appropriate earthquake for the EGF, because of the small number of aftershocks and low seismicity. Indeed we were unable to find good EGF events for the 8 April 1999 and 17 November 2002 deep earthquakes. Even with good EGF events, for the case of bilateral rupture having large slips far from the hypocenter, waveform inversions using both teleseismic and regional data can produce artificial areas of slip, especially when data having limited azimuthal distribution are used. For the analysis of the 20 August 1998 event, we could not use waveforms at southern stations because of low ratio of signal to noise of the EGF event. Therefore the obtained slip distributions may have corresponding uncertainties due to the azimuthal limitation. Teleseismic waveform inversions using theoretical

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Figure 20. Variance reductions between synthetics and observed data as a function of rupture velocity for the 6 August 2000 event. (a) Teleseismic inversions and (b) forward modeling of F-net data. Here ‘‘tw’’ and ‘‘gr’’ indicate number of applied time windows and grid interval increase, respectively. Arrow in Figure 20b shows the maximum variance reduction indicating the rupture velocity of the event. Green functions with optimal azimuthal distribution may give better slip distributions for this event. [53] The 15 September 2002 event, which was used as the EGF event for the 28 June 2002 event, shows a small amount of directivity to the northeast. To see if this pattern of pulse durations affects our estimates of the rupture velocity, we carried out numerical tests using an EGF that had about 80% directivity and a rupture velocity of 2 to 3 km/s in several different directions, i.e., northeast, northwest, southeast, and southwest. The results (Figure S1 in the auxiliary material) show that variance reduction plots still have the maximum values at the assumed rupture velocities, and therefore the directivity effect of the 15 September 2002 event should not greatly affect our results. [54] For teleseismic waveform inversions, we used stations at distances between 30° and 90°. The reflected P phase at core-mantle boundary, PcP, may contaminate the direct P phase at stations farther than about 70°. We used some stations at the distance (CAN, COR, ESK, FURI, GRFO, MVSF), but we did not consider the phase during inversion process. Therefore there may be some uncertainties relating to this different phase. [55] Forward modeling of the regional data does have some limitations. Many regions have sparse stations, which is a common problem for studying deep and shallow earthquakes. Even the Japanese data, which are recorded on the densest networks in the world, may have narrow azimuthal coverage for specific earthquakes. However, regional data can provide some good information which is not resolvable in

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the teleseismic data and provide good constraints for estimating fault geometries and rupture velocities. Teleseismic data with good azimuthal coverage can constrain the shape of slip distributions well and regional data are sensitive to rupture velocity, as mentioned in section 2.2.3. We can take advantage of the strengths of both data sets in this combined method which makes it possible to determine the fault geometry and rupture velocity with better resolution. [56] Some studies use joint inversions of teleseismic and regional data to obtain source parameters as well as slip distributions [e.g., Wald et al., 1991; Yagi et al., 2004], supporting the importance of regional data. In joint inversions using both teleseismic and regional data simultaneously, there can be an issue related to the number of inversion parameters. The large number of inversion parameters is often a problem for simultaneous inversions, and tradeoffs between parameters may lead to unstable results. In our method we take a slightly different approach using a sequence of steps that tries to constrain some portions of the parameter space in each step. For example, slip distributions from the teleseismic inversion are used as constraints in modeling the regional data. For a related reason we vary the grid size in our procedure so that the inversions and forward modeling are done with constant number of parameters for all rupture velocities. A practical outcome of our procedure is that we can estimate the rupture velocities with fewer constraints on the whole inversion process. [57] Formal error estimates for the rupture velocity are difficult. Similarly there is currently no accepted way to put formal errors on slip distributions. If the error shown in the bell shaped curves were random errors, we could calculate an uncertainty based on an assumed distribution and the width of the curve. However, the errors are most likely not random and there are systematic errors and tradeoffs with other parameters. Our purpose in showing the various parameter fitting curves was to give the reader some idea about the resolution and uncertainty of our estimates. 6.2. Low Rupture Velocity and Thermal Parameter [58] Typical values of rupture velocity for shallow earthquakes are about 7090% of shear wave velocity [Abercrombie and Rice, 2005; Heaton, 1990; Kanamori and Brodsky, 2004], although some events have very slow rupture velocity (e.g., 1992 Nicaragua earthquake, 11.5 km/ s which are about 3040% of shear wave velocity [Kikuchi and Kanamori, 1995]; 2006 Java earthquake, about 1 km/s [Mori and Park, 2006]) and there are examples of local supershear rupture velocities (e.g., 1999 Kocaeli, Turkey earthquake [Sekiguchi and Iwata, 2002]; 2001 Kunlunshan earthquake [Bouchon and Valle´e, 2003]; 2002 Denali fault earthquake [Asano et al., 2005; Dunham and Archuleta, 2004]). The rupture velocities we obtained for three deep earthquakes are 12 km/s, which correspond to 2040% of the shear wave velocity (Table 3). These are quite slow compared to the typical values for shallow earthquakes. [59] It is reported that the source characteristics of deepfocus earthquakes depend on the thermal parameter (F; km) [Wiens, 1998; Estabrook, 1999; Wiens, 2001; Tibi et al., 2003], which is defined as the product of the age of the lithosphere when subduction begins (million years) and the vertical component of the subduction velocity (mm/a) at a certain depth [Frohlich, 2006]. A young plate with a slow

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subduction velocity has a small thermal parameter and is usually called a ‘‘warm slab.’’ For an old plate with fast subduction speed, the thermal parameter is large and the plate is called a ‘‘cold slab.’’ For example, the thermal parameter of the warm Nazca plate is about 2000 km and that of the cold Pacific plate near Fiji-Tonga is about 12000 km [Wiens and Gilbert, 1996]. Warm slabs with small thermal parameters (South America) tend to have high stress drop, slow rupture velocity, low seismic efficiency, and no or a small number of aftershocks. Meanwhile, cold slabs with large thermal parameters (Fiji-Tonga, Flores Sea, Mariana) seem to have lower stress drop, faster rupture velocity, higher seismic efficiency, and a relatively large number of aftershocks [Wiens, 1998; Estabrook, 1999; Wiens, 2001; Tibi et al., 2003]. [60] The thermal parameters of subducting slabs surrounding Japan are about 50007000 km, which are in the middle range [Wiens and Gilbert, 1996]. According to Tibi et al. [2003], rupture velocities of the earthquakes surrounding Japan are about 3560% of the shear wave velocity, which are similar or faster than those in warm slabs and slower than those in cold slabs. [61] The values of rupture velocity found in this study are somewhat slower than other deep-focus earthquakes in this region reported by Tibi et al. [2003]. Figure 21 shows rupture velocities (percentage of shear wave velocity) as a function of thermal parameter. Triangles indicate the values from Tibi et al. [2003], suggesting that rupture velocity in cold slab is faster and that in warm slab is slower, and circles are those obtained in this study. Here average value of estimated rupture velocities was used for the 20 August 1998 event. Our estimated rupture velocities fall at the lower end of the values of Tibi et al. [2003] for similar earthquakes in the intermediate range of thermal parameter and are more similar to their values for warm slabs. [62] Tibi et al. [2003] analyzed an earthquake, which occurred on 21 July 1994 in a region close to the 28 June 2002 event, but at a depth of 473 km. Their estimated rupture velocity of this event is 3 km/s, which is equivalent to about 60% of the shear wave velocity. Wu and Chen [2001] carried out teleseismic body wave inversions to obtain source parameters of a large deep-focus earthquake on 29 September 1973 at a depth of 575 km also in the same region. They estimated the rupture velocity as 34 km/s (5775% of the shear wave velocity), which is also faster than our values. Kuge [1994] analyzed the 12 May 1990 Sakhalin earthquake that occurred west of the 17 November 2002 event at a depth of 606 km. She looked at different features in the teleseismic waveforms (one pulse) and regional data (two pulses), and concluded that the rupture velocity is faster than the shear wave velocity. These values are added in Figure 21. If all of these estimates of rupture velocity are correct, there does not seem to be a clear Table 3. Summary of Resultsa Event

28 June 2002

20 August 1998

6 August 2000

Fault plane Vr (km/s) Vr / b (%)

shallow 2 38

shallow 12 2040

steep 1.5 31

a

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Figure 21. Rupture velocities as a function of thermal parameter. Triangles indicate the values from Tibi et al. [2003], asterisks are from Kuge [1994] and Wu and Chen [2001], and circles are for the values in this study. correlation of rupture velocity with thermal parameter, and source characteristics depending on the thermal parameter of deep-focus earthquakes may need to be reconsidered.

7. Conclusions [63] It is usually difficult to determine rupture velocity of earthquakes, especially without near-field stations. To estimate rupture velocities of deep-focus earthquakes with better resolution, we develop a procedure with new aspects that combine teleseismic waveform inversions with forward modeling of regional data, and vary the grid size of the fault plane. Combining teleseismic waveform inversions and forward modeling of regional data, we can take advantages of both data sets. Variation of grid size provides a constant number of inversion parameters so that no constraints are necessary for the change of rupture velocity. [64] Using this method, we were able to estimate reliable values of rupture velocity for deep-focus earthquakes. The regional data can constrain the fault geometries and rupture velocities, showing clear differences in the forward modeling that can resolve the rupture velocities. The rupture velocities are about 12 km/s, which are about 2040% of shear wave velocity. These values are much slower than the typical values for shallow events and slower than other estimates for deep-focus earthquakes of similar thermal parameter. [65] Acknowledgments. We appreciate Audrey Tocheport, the Assistant Editors, and anonymous reviewers for their critical and valuable comments and suggestions to improve the paper. We gratefully acknowledge the use of F-net waveform data from the National Research Institute for Earth Science and Disaster Prevention (NIED) and waveform data from the Incorporated Research Institutions for Seismology (IRIS) data center. We used the Generic Mapping Tool (GMT) for making some of the figures. This study was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan and partially supported by the project of METRI ‘‘Development of Earthquake Monitoring Environment and Tsunami Forecasting Technique in Korean Peninsula.’’

References

Shallow refers to shallowly dipping plane, steep refers to steeply dipping plane, Vr refers to rupture velocity, b refers to shear wave velocity around the focal depth (PREM model).

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