Detection of a slow slip event from small signal in GPS data

Abstract

[1] By correcting for seasonal noise contained in GPS data, we are able to detect small but compelling post-seismic deformation following a medium-sized interplate earthquake (2001 August 14, M_W 6.4) that occurred off the Pacific coast of northern Honshu, Japan. Its decaying-time constants are similar among the stations with an average of 2.2 months. We inverted for the slip distribution, assuming that post-seismic deformation was due to a slow slip near the main shock fault. Slow slip spreads mainly over the northern periphery of the northern asperity of the 1968 Tokachi-Oki earthquake (M_W 8.2) that has been considered a seismic gap since 1994. The seismic moment of the slow slip is about three times greater (M_W 6.7) than that of the co-seismic slip. The present case suggests that the post-seismic slow-slip is common not only for the large earthquakes but also for relatively small interplate earthquakes in this region.

1. Introduction

[2] Off the Pacific coast of Aomori, northern Honshu, Japan, large interplate earthquakes have occurred repeatedly. Two such types of earthquakes in the last forty years are the 1968 Tokachi-Oki earthquake (Mw 8.2) and the 1994 Sanriku-Haruka-Oki earthquake (Mw 7.6) (Figure 1). While the 1968 earthquake ruptured two segments that were about 80 km apart along the strike of the Japan Trench, the 1994 earthquake ruptured only the southern segment, leaving the northern segment unbroken [Sato et al., 1996; Nagai et al., 2001]. The fact that nearly the same segment slipped during the two consecutive earthquakes suggests that the asperities are characteristic of space and time-invariant. This leads further to the inference that the northern segment of the 1968 earthquake retains large strain energy sufficient for causing a large earthquake (Mw 7.6) since it was not broken during the 1994 earthquake.

Figure 1

Horizontal displacements predicted from the main-shock fault. The open arrow indicates the co-seismic slip vector. Triangles indicate GPS stations used in this study. The square denotes the reference station. In the inset, the ellipses indicate the source areas of the 1968 Tokachi-Oki earthquake and 1994 Sanriku-Haruka-Oki earthquake. J.T. denotes Japan Trench.

[3] On August 14, 2001, an M_w 6.4 interplate earthquake occurred at the eastern end of the northern asperity. This was a rare event given that six years had passed since the last M > 6 earthquake occurred in this area. In view of the possibility that this earthquake might represent a precursory seismic activity, we investigated the rupture process of the earthquake and scrutinized its post-seismic deformation.

2. Post-Seismic Deformation

[4] The rupture process of the 2001 earthquake was inverted using waveform data recorded by the strong-motion seismograph network, K-NET [Sato et al., 2003]. The inversion revealed that the rupture propagated symmetrically outward along the fault for about 8 seconds, resulting in a total faulting area of about 35 by 25 km² with an average slip of 11 cm. The seismic moment is estimated at 5.0 × 10¹⁸ Nm (Mw = 6.4). Following the Harvard CMT catalog, we assumed strike = N188°E, westward dip = 20° and rake = 73°. Figure 1 shows the surface displacements due to the co-seismic slip model in a uniform, half-space Poisson solid [Okada, 1985]. The predicted horizontal displacements on land are about 2 mm at most.

[5] In order to investigate crustal deformation associated with the earthquake, we analyzed data of daily site positions provided by the Japanese permanent Global Positioning System network, called GEONET [Hatanaka et al., 2003]. The stations we used are shown in Figure 1. Station 950157 is chosen as the reference point. Figure 2 shows the three-components of daily site positions observed at one of the stations. The solid curves indicate the theoretical models fit to the data for the period 1999.1.1–2002.10.12. The theoretical model consists of a linear trend and a seasonal variation that in turn consists of yearly, half-yearly, 1/3-yearly,…, and 1/N-yearly periodic sine and cosine functions [Sagiya, 2002]. The order N was determined using the Akaike Bayesian information criteria (ABIC). It was two or three for most cases. We introduced as an additional unknown parameter – the step of displacement between the periods before and after the main-shock, while eliminating the period of two-months and a half after the main-shock (2001.8.15–2001.10.31) from the fit. It is noted that the theoretical curves shown in Figure 2 do not include the fitted step terms and that the curves for the period eliminated from the fitting are interpolated with the stationary trend fit for the rest. Thus the residuals of the observed minus the theoretical values ideally reveal the post-seismic deformation, if any, after being corrected for the stationary trend that includes seasonal variations.

Figure 2

Three-component daily coordinates at Station 940024. The solid curves show the theoretical curves consisting of a linear trend and seasonal terms. The vertical dashed lines indicate the time when the main-shock occurred (2001.08.14).

[6] Figure 3 shows the east-west component residuals for six stations nearest to the main-shock fault. While it is hard to identify the co-seismic displacements, we find clear post-seismic displacements with a decaying-time constant of nearly two months though their amplitudes are small and less than 6 mm. We fitted the theoretical function

to the post-seismic displacements for the five stations in Figure 3. Here γ corresponds to the co-seismic displacement and β the decaying-time constant. The estimated values of β are stable, yielding an average of 0.18 ± 0.03(year). The β of 0.18 year corresponds to 2.2 months. The standard deviation of β is 15% of the average value, suggesting a common source for the post-seismic displacements. The values of γ did not agree with the displacements calculated for the co-seismic slip model (Figure 1). It suggests that the amplitudes of the real co-seismic displacements are close to or significantly smaller than the predicted ones that are comparable to the noise level of GPS data. The horizontal bars in Figure 3 denote the steps described earlier in the modeling of the stationary trend. Later we adopt these steps as the estimates of the total post-seismic displacements. The post-seismic displacements for the north-south components are less obvious because of their smaller amplitudes. It was impossible to retrieve any vertical post-seismic displacements because S/N ratio for the vertical components is much poorer than that for the horizontal components.

Figure 3

Residuals of EW components for the six stations that are shown with station codes in Figure 1. The solid curves show the least-squares fits of exponential function given by equation (1). Horizontal bars indicate the steps determined during the fitting of the stationary trend.

[7] We fitted the theoretical curves to the observed data at other stations though the post-seismic displacements for those stations are less clear. The distribution of steps thus obtained is shown in Figure 4. The calculated errors of the steps are less than 0.1 mm. Since they are too small to be indicated by error ellipses for the displacement scale in Figure 4, we showed the relative magnitudes of the inverses of estimated errors by the widths of arrows. If we neglect the contribution of co-seismic displacements, the steps shown in Figure 4 can be regarded as representing the displacements totally due to the post-seismic deformation. Regardless of the difference in the level of amplitude, the spatial variation of the post-seismic displacements is similar to that predicted for the co-seismic slip model, indicating that the post-seismic deformation was caused by a slow slip event occurring close to the co-seismic slip. A viscoelastic mechanism seems to be inappropriate since numerical simulation [Pollitz et al., 2001] shows that the decaying-time constant of two months requires a mantle viscosity less than 10¹⁸ Pa s. This viscosity differs significantly from the mantle viscosity of 10¹⁹ Pa s that was estimated to explain the correlated earthquakes and surface deformations in Tohoku, northern Honshu, Japan [Rydelek and Sacks, 1990].

Figure 4

Comparison of the observed (solid arrows) and calculated (open arrows) post-seismic displacements. The rectangles indicate the configuration of subfaults assumed for the source of slow slip. The dotted ellipse indicates the northern asperity of the 1968 Tokachi-Oki earthquake [Nagai et al., 2001].

3. Slow Slip

[8] We determined the fault parameters of the slow slip event by minimizing the residuals of the observed minus calculated displacements. We first performed the inversion for four different faults that are shown in Figure 4. F1 is the same as the fault of the co-seismic slip model. F2 lies on the down-dip of F1. F3 is placed on the north along the strike of F1. F4 is located on the down-dip of F3. Each fault has the same fault size. The fault tops of F1 and F3 are located at a depth of 41 km. The rakes and slips were chosen as unknown parameters whereas the strikes and dips of these faults were fixed and taken to be the same as those of the co-seismic slip model. The results of the inversions are listed in Table 1. Judging from the standard deviation of residuals and ABIC value, F3 is considered the best fit model and F4 the second best. The fit of F2 is the worst, suggesting that the down-dip extension of the co-seismic fault is not likely the main source of the slow slip. It is thus inferred that the main source of the slow slip does not overlap the central part of the northern asperity. The seismic moments for the four fault models range between 1.3–1.6 × 10¹⁹ Nm, which corresponds to a M_W 6.7 event.

Table 1. Inverted Fault Parameters^a

Fault	Fault Top Depth (km)	Rake (deg)	Slip Amount (cm)	S.D. of Residuals (mm)	ABIC	ΔCFF (MPa)
F1	41	65 ± 5	30 ± 2 (7 ± 3)	0.39	133	0.16
F2	53	79 ± 5	26 ± 2 (4 ± 2)	0.47	146	−0.73
F3	41	97 ± 5	33 ± 2 (12 ± 3)	0.36	127	0.11
F4	53	106 ± 4	32 ± 2 (10 ± 3)	0.37	130	0.3

• a For multi-subfault model, slips are shown in the parentheses and S.D. of residuals = 0.37 mm, ABIC = 131, ΔCFF = −0.15MPa.

[9] In the next step we assumed a larger fault consisting of the previous four faults as subfaults (multi-subfault model). Since the solutions were unstable when the slip and rake are both considered unknowns, we fixed the rake of each subfault at the value obtained from the previous inversions and imposed a loose constraint on slip (±3cm) to determine the slips on the four subfaults simultaneously. The initial values of slips were all set as 10 cm. The inverted slips for each subfault are listed in Table 1. The slip vectors and the horizontal displacements predicted from the multi-subfault model are shown in Figure 4. The slip of subfault 3 is the largest, being followed by the slip of subfault 4. The sum of slips for subfaults 3 and 4 is about twice the sum of slips for subfaults 1 and 2. This result also indicates that the main segment of the slow slip deviates from the central part of the northern asperity of the 1968 Tokachi-Oki earthquake. The seismic moment of the total slip equals 1.6 × 10¹⁹ Nm (M_W 6.7). It is three times larger than that of the co-seismic slip 5.0 × 10¹⁸ Nm (Mw = 6.4) obtained from the seismic waveform data. We performed a similar inversion for Poisson's ratio equal to 0.3. The inverted slips are about 5% smaller than those for the case of Poisson solid. The relative magnitude of slips on the subfaults is almost the same as shown in Figure 4. In view of the standard deviation of the residuals and ABIC value, the multi-subfault model and the single fault models F3 and F4 are equally well fit to the observations. In either case, however, we can state that the main slip does not overlap the central part of the northern asperity.

4. Discussion and Concluding Remarks

[10] The 1994 Sanriku-Haruka-Oki earthquake is famous for its large slow slip that lasted for about a year after the main shock [Heki et al., 1997]. Slow slips following the main shocks were also detected using strainmeters for the 1989 Sanriku-Haruka-Oki earthquake (M_W 7.4) and 1992 Sanriku-Oki earthquake (M_W 6.9) [Kawasaki et al., 1995, 2001]. The source areas of these earthquakes lie just on the south of the 1994 earthquake. Further south along the Japan Trench, there is the 1978 Miyagiken-Oki earthquake (M_W 7.6) that was followed by a slow slip found using tide-gauge and leveling data [Ueda et al., 2001]. All these cases suggested that large interplate earthquakes occurring off the Pacific coast of northern Honshu, Japan, are usually accompanied by slow slips. Here we have shown that a medium-sized earthquake (M_W 6.4) is followed by a slow slip with the seismic moment about three times larger than that of the main-shock slip. This finding suggests that the post-seismic slow-slip is a common phenomenon even for relatively small interplate earthquakes in this region. Most likely we have not been able to detect post-seismic deformations following smaller earthquakes because of their small signals.

[11] The decaying-time constant of 2.2 months is shorter than that (half a year) of the 1994 Sanriku-Haruka-Oki earthquake [Heki et al., 1997] and larger than those (1–10 days) of 1989 Sanriku-Haruka-Oki earthquake [Kawasaki et al., 2001] and 1992 Sanriku-Oki earthquake [Kawasaki et al., 1995]. There is a possibility that the short-term slow slip determined from the strainmeter data merely reflects a transient process that would gradually shift to a year-long slow slip [Heki and Tamura, 1997].

[12] It is reported that the segment of the afterslip is shifted toward the down-dip direction away from the segment of the main-shock slip for the 1994 Sanriku-Haruka-Oki earthquake [Yagi et al., 2003] and the 1996 October and November earthquakes (M_W 6.8 and 6.7) off the Hyuga-nada of Kyushu, Japan [Yagi et al., 2001]. Moreover, in the case of the 1996 Hyuga-nada earthquakes, the afterslip area extended in time in such a way that it surrounded the asperity of the 1968 M_W 7.3 Hyuga-nada earthquake [Yagi and Kikuchi, 2003]. The present case is consistent with these previous cases in that the central segment of slow slip lies on the periphery of the known asperity.

[13] In order to evaluate the triggering effect of the slow slip against the northern asperity of the 1968 Tokachi-Oki earthquake, we calculated the increase of the Coulomb Failure Function (ΔCFF) at the center of the northern asperity for each fault model (Table 1). We assumed the internal friction coefficient to be 0.4. The fault parameters of the target earthquake are the same as those of the 2001 August 14 earthquake. Since ΔCFF at a point is critically dependent on the slip distribution nearby, a higher spatial resolution of slip distribution is required for more reliable estimation of ΔCFF. The 1994 Sanriku-Haruka-Oki earthquake yields a ΔCFF increase of 0.32 MPa at the same target, which is comparable to the increase due to the single fault model F4.

[14] In addition to the post-seismic deformation signal, the residuals in Figure 3 show other long-period (a few months to a year) fluctuations superposed on the short-period scatter. These fluctuations represent the deviations from the stationary trend fit to the four years of data. Since the technology of the geodetic measurements at the sea bottom close to the causative faults is still challenging, developing a method of reducing the seasonal noise in the GPS data is critical for detecting smaller slow slip events that might play an important role during the preparatory stage prior to the high-speed rupture of the northern asperity of the 1968 Tokachi-Oki earthquake.

Acknowledgments

[15] We express our thanks to the Geographical Survey Institute (GSI) of Japan for providing us with the GPS data. We thank T. Nishimura of GSI for his comment on the GPS data reduction. We are grateful to K. Heki, K. Larson and an anonymous reviewer for their critical comments that were helpful in revising the manuscript.