An intermediate deep earthquake rupturing on a dip-bending fault: Waveform analysis of the 2003 Miyagi-ken Oki earthquake

Abstract

[1] Using waveform analysis, we propose a dip-bending fault model for the 2003 Miyagi-ken Oki earthquake. Dip angle of the upper fault plane is estimated as 87° on the basis of focal mechanism from P-wave first motions. S-wave polarization analysis leads to a dip angle of 60° for the lower portion of the fault plane. Inversion results show that the rupture started on the southern fault plane. In the beginning 5 seconds, slip was mainly confined in the hypocenter area on the southern fault. From 5 seconds on rupture propagated to the northern part, where the largest slip (3 m) occurred in the northern deep part. The complex stress field in the slab and compositional difference in the upper and the other portion of the slab account for such a bending fault even at intermediate depth.

1. Introduction

[2] Large crustal earthquakes usually are associated with complexity of fault geometries. During an earthquake rupture, the fault may be segmented, branched or bent. Lindh and Boore [1981] proposed that the rupture was controlled by fault geometry during the 1966 Parkfield earthquake. Detailed maps of the surface rupture trace of the 1992 Landers earthquake also showed complexity of the fault geometry [Lazarte et al., 1994]. However, there remain doubts whether the complex fault geometry is merely confined to shallow earthquakes.

[3] A large in-slab earthquake occurred off the Pacific coast of Miyagi Prefecture, northeastern Japan on May 26, 2003. According to Japanese Meteorological Agency (JMA), hypocenter of the earthquake was located at N38.81°, E141.65°, and 71 km deep. It was an intermediate deep earthquake occurring on a high-dipping reverse fault in the slab of the Pacific plate subducting to the overriding continental plate. This shock supplies us a chance to identify the complexity of fault geometry of an intermediate deep earthquake.

[4] Usually fault geometry is inferred from aftershock distribution, surface rupture trace, or the focal mechanism/centroid moment tensor (CMT) solutions. If no surface trace is observed, the mechanism solutions are the only applicable information for earthquakes occurring far from a regional seismic network. With the improvement of seismic network density and earthquake location resolution, the aftershock distribution is useful information, especially for those inland strike-slip earthquakes. In the case of a reverse-faulting earthquake like the 2003 Miyagi-ken Oki earthquake, unfortunately, due to resolution limitation in depth direction, the aftershock distribution poorly constrains the estimate of the dipping angle of the fault plane.

[5] Since the foresaid traditional methods are not applicable to this earthquake, we estimate the fault geometry from waveform inversion. To infer the fault geometry on the basis of waveform analysis, there are two conditions for deployment of seismic stations. Stations first should be close to the faulting area; second, stations should encircle the faulting area. Fortunately, we have enough stations to satisfy these two conditions for this earthquake. Therefore we can estimate fault geometries from waveform inversion. It is noteworthy that such a kind of fault information cannot be obtained by the traditional methods.

2. Data

[6] Strong motion data from 20 Kik-net stations are used in this study (Figure 1). We use those underground channels deployed in the boreholes. All the three components with duration of 25 seconds are included. The observation waveforms are corrected into north-south (NS) and east-west (EW) components for those components that do not correspond to due NS or EW directions. The acceleration seismograms are then integrated into velocity seismogram. We apply a 0.05 Hz∼1.0 Hz bandpass filter to the velocity waveforms and re-sample the waveforms at 10 Hz. The number of total waveform data points is 15,000.

Figure 1

Tectonic settings and station map for the Miyagi-ken Oki earthquake. Circles and squares mean the strong motion stations. The asterisk is the epicenter. E.A. Plate means Eurasian Plate, N.A. Plate, North America Plate, P. Plate Pacific Plate, and Ph. Plate Philippine Sea Plate.

[7] Velocity structures are constructed from studies by Iwasaki et al. [2001] and Nakajima et al. [2001, 2002]. According to the borehole logs supplied by the National Research Institute for Earth Science and Disaster Prevention (NIED), we take the average value (Table 1) of those log-recorded P- or S-wave velocities as the surface layer for those stations deployed on the base of rock (marked by circles in Figure 1), and two additional lower velocity layers for those on the sedimentary layer (marked by squares in Figure 1).

Table 1. Velocity Structure

Vp (km/s)	Vs (km/s)	density (g/cm^3)	depth (km)	Qp	Qs
1.93	0.69	2.05	0.0	100.0	70.0
2.75	1.59	2.50	0.4	200.0	100.0
6.08	3.50	2.60	0.7	340.0	170.0
(5.18	2.68	2.50	0.0	250.0	100.0)^a
6.23	3.60	2.65	5.0	360.0	180.0
6.35	3.64	2.70	13.0	400.0	250.0
6.55	3.68	2.75	21.0	450.0	350.0
6.95	3.96	2.90	27.0	600.0	350.0
7.60	4.29	3.10	32.0(30)	700.0	400.0
7.69	4.31	3.15	40.0	1000.0	500.0
7.73	4.34	3.20	65.0	1000.0	500.0
8.27	4.56	3.30	90.0	1000.0	500.0
8.37	4.61	3.35	120.0	1000.0	500.0
8.37	4.61	3.35	150.0	1000.0	500.0

• a Those inside the parentheses is for stations near the coastal line.

3. Inversion Method

[8] We use the non-negative least square linear waveform inversion method developed by Ide et al. [1996]. The fault plane is represented by I × J equally spaced grid points. Source time functions are expressed by K time-windows which are denoted by half overlapped isosceles triangles and among which starting time of the first time window is controlled by an assumed rupture velocity (here about 70% of the shear wave velocity). Hence the n-th component of the synthetic wave is given by

where D_l(i, j, k) means the slip rate vector in the l-th direction at the i-th grid in the strike direction, the j-th grid in the dip direction, and the k-th time window; G_nl(t:i, j, k) is the n-the component of Green's function corresponding to the above mentioned source D_l(i, j, k). The Green's function is computed by the discrete wave-number method [Bouchon, 1981] and the reflection-transmission method [Kennett and Kerry, 1979], with a horizontally layered velocity structure assumed. The effects of anelasticity are taken into account by introducing complex velocities [Takeo, 1985]. Calculations show that in this study the difference of the Green's function of a surface receiver with that of an underground receiver is negligible.

[9] We introduce the following fourth-order difference formula

for spatial and temporal smoothing constraints, respectively. The weights of these two smoothing constraints are objectively determined by Akaike's Bayesian information criterion [see Ide et al., 1996].

4. Result

[10] We first simply assume one of the nodal planes (strike 194°, dip 72°) from Harvard CMT as the fault plane, which is consistent with the local strike of the subducting Pacific plate. The rake is allowed to vary between 45° and 135°. We assume 68 km as depth of the hypocenter, with which the synthetic travel times calculated from the velocity structures and the observed arrival times are consistent. The fault plane used here has dimensions of 24 km along the strike direction and 20 km along dip direction. It is further divided into 2 km-spaced grids. Such a simple fault model gives very good waveform fittings except the horizontal components at some stations (e.g. the east-west component of Station iwth04 and iwth05, the north-south component of Station iwth21, Figure 2). Since we have a generally good fitting, it is unreasonable to attribute the misfits of some components to problems of the velocity structures.

Figure 2

a) Comparison of waveform fittings for the single fault model. b) Those for the dip-bending fault model. The grey lines mean the observation data, the black the synthetic waveforms. The unit of the maximum amplitude shown over each component is cm/s.

[11] Noticing the misfits of waveforms at some stations, we adjust the fault model on the basis of waveform information. One of the nodal planes of focal mechanism obtained from P- wave first motions shows a similar strike with the CMT solution but a different dip angle (87°). It suggests that the first sub-event occurring in the hypocentral area has a dip angle of 87°. Hence we introduce a new fault model, the dip-bending fault model: the fault plane in the upper part (8 km long in the dip direction) has a dip angle of 87°, the lower fault plane (12 km) remains to be determined. We shall point out that the exact depth of the bending remains a choice and is not a parameter well defined here.

[12] One can clearly identify two peak S-wave phases from the seismograms. S-wave polarization information of the second S peak is used to estimate the dip angle of the lower part. Amplitudes of the second S peak at three components are measured from the observation waveforms to calculate the observation S-wave polarization. Then the synthetic S wave polarization at each station can be computed assuming a shear faulting of a certain strike, rake, and dip angle [Aki and Richards, 1980]. By search the minimum misfit between the observation and synthetic polarization, a value of 60° is estimated as the dip angle of the lower part. Now we carry out the waveform inversion using this new model. With the same arrangement of grid mesh and time windows, and the same assumed rupture velocity as the foresaid simple fault model, this new fault model yields excellent waveform fittings. Waveform fittings have been significantly improved for those phases that are poorly fitted in the case of a simple fault model (Figure 2). Besides this obvious improvement, waveform fittings at some stations are slightly improved too, and keep excellence at the other stations. Figure 3 shows the synthetic and observation waveforms for all 20 stations.

Figure 3

Waveform fittings for all 20 stations. Symbols are the same as Figure 2.

[13] Inversion results from this model show that rupture started in the hypocentral area and continued for about five seconds in the southern part. From about five seconds on the rupture propagated to the northern fault plane and finally stopped in 10 seconds. Rupture on the northern fault plane was confined in the deep portion, whereas rupture on the southern fault plane was confined in hypocentral area. Figure 4 shows a three-dimensional view of the slip distribution. A total moment is calculated as 4.0 × 10¹⁹Nm, the same as Harvard CMT value. The best double couple solution of the total moment tensor, which is obtained by summation from each grid, gives a nodal plane (strike 194°, dip 72°, rake 92°) similar to that of the Harvard CMT solution (strike 194°, dip 72°, rake 96°).

Figure 4

3-dimensional view of slip distribution for the Miyagi-ken Oki earthquake. The hypocenter is marked by a red circle. Grey circles mean background seismicity in this area.

5. Discussion

[14] It should be pointed out that distribution of dense and close stations is of great importance to estimate the fault geometry. Had we not included those stations where the waveforms cannot be explained by the simple fault model, we would have lost information of the real fault geometry. The generally excellent fitting mainly results from the following reasons. First, all the waveform data used for the Miyagi-ken Oki earthquake are recorded by underground seismographs deployed in boreholes. Most seismometers are deployed on rock basis according to NIED boring logs. Most contamination from surface soil layer has hence been excluded. The other advantage of this study is that velocity structures in this area have been well studied by Japanese seismologists. With the excellent waveform fittings, we are confident of the proposed dip-bending fault model. Our final model is consistent with the distribution of aftershock hypocenters [Sekine et al., 2003]. It suggests that fault bending is not merely a surface effect.

[15] The Pacific slab in northeastern Japan is featured with double-zone seismicity, with a distance about 30 to 40 km between these two zones [Hasegawa et al., 1977]. According to Hasegawa et al., earthquakes in the upper zone are characterized by reverse faulting with down-dip compressional stresses, and those in the lower zone by down-dip extensional stresses. The 2003 Miyagi-ken Oki earthquake occurred close to the upper zone. The down-dip-compression-dominant stress field in the upper zone is consistent with the high-dipping reverse faulting.

[16] To explain PS-P time data observed in this area, Matsuzawa et al. [1986] proposed a two-layered oceanic plate model composed of a thin low-velocity layer (less than 10 km) and a thick high-velocity lower layer. They maintained that the fact of the high descending rate of this old and cold plate might probably lead to a relatively low velocity within the descending crust without occurrence of phase changes. Our dip-bending fault model for this earthquake supports the proposal of distinguishing compositional difference between the upper thin layer and the lower portion. The upper part of this bending fault is in the supposed original oceanic crust, and it hence keeps somewhat crustal characteristics. Five-second delay of the second event properly suggests that the original oceanic crust is more brittle than the lower mantle portion. The complex stress field in the slab and compositional difference in the upper portion (oceanic crust) and the lower portion (oceanic mantle) of the slab lead to such a bending fault even at the intermediate depth. Note that the rupture started in the slab oceanic crust and propagated to the slab oceanic mantle, though it is well known that rupture of crust earthquakes is confined in the crust. It is interesting to compare this rupture pattern with the 2001 Geiyo, Japan, earthquake, a slightly shallower in-slab normal-faulting earthquake (46 km). Kakehi [2004] proposed a curved fault model with the dip changing from 60° to 70° when the strike varies from 170° to 190° for the Geiyo earthquake. He further showed that rupture of the Geiyo earthquake started near the slab oceanic crust-mantle boundary and the rupture area extended over both of the oceanic crust and the oceanic mantle. These two in-slab earthquakes indicate that unlike the continental mantle the slab oceanic mantle is relatively brittle and prone to earthquake rupturing.

[17] Some figures addressing our detailed results can be found in the supplemental material.

6. Conclusion

[18] According to the waveform inversion, we propose a dip-bending fault model for the 2003 Miyagi-ken Oki earthquake. Dip angle of the southern fault plane is estimated as 87° on the basis of the focal mechanism from P-wave first motions. S-wave polarization analysis leads to a dip angle of 60° for the northern fault plane. Besides a generally excellent fitting, waveform fittings using this fault model are significantly improved at those stations where some phases cannot be explained using a single fault model. Inversion results show that rupture started on the southern fault plane. In the beginning 5 seconds, slip was mainly confined in the hypocenter area on the southern fault. From 5 seconds on rupture propagated to the northern part, where the large slip is mainly concentrated in the deep part. The total moment was about 4.0 × 10¹⁹Nm. The total moment tensor obtained by summation from each grid is similar to the Harvard CMT. The complex stress field in the slab and compositional difference in the upper and the other portion of the slab account for such a bending fault occurring at the intermediate depth.

Acknowledgments

[19] This study is supported by the Special Project for Earthquake Disaster Mitigation in Urban Areas from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Strong motion data of the Miyagi-oki earthquake are supplied by NIED. We would like to express our gratitude to the reviewers for their helpful comments.