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Research Center for Prediction of Earthquakes and Volcanic Eruptions, Graduate School of Science, Tohoku University, Sendai, Japan
Corresponding author: Y. Ohta, Research Center for Prediction of Earthquakes and Volcanic Eruptions, Graduate School of Science, Tohoku University, 6-6 Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan. (firstname.lastname@example.org)
 A magnitude 7.3 foreshock occurred at the subducting Pacific plate interface on March 9, 2011, 51 h before the magnitude 9.0 Tohoku earthquake off the Pacific coast of Japan. We propose a coseismic and postseismic afterslip model of the magnitude 7.3 event based on a global positioning system network and ocean bottom pressure gauge sites. The estimated coseismic slip and afterslip areas show complementary spatial distributions; the afterslip distribution is located up-dip of the coseismic slip for the foreshock and northward of hypocenter of the Tohoku earthquake. The slip amount for the afterslip is roughly consistent with that determined by repeating earthquake analysis carried out in a previous study. The estimated moment release for the afterslip reached magnitude 6.8, even within a short time period of 51h. A volumetric strainmeter time series also suggests that this event advanced with a rapid decay time constant compared with other typical large earthquakes.
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 The March 11, 2011, moment magnitude (Mw) 9.0 Tohoku earthquake (hereafter referred to as the mainshock) generated a large tsunami, which caused devastating damage and the loss of more than 15,800 lives. On March 9, 2011 at 2:45 (UTC), an M7.3 interplate earthquake (hereafter referred to as the foreshock) occurred ∼45 km northeast of the epicenter of the Mw9.0 mainshock. The focal mechanism estimated by the National Research Institute for Earth Science and Disaster Prevention (NIED) incorporates reverse fault motion with a west-northwest to east-southeast compression axis (http://fnet.bosai.go.jp) (Figure 1). This foreshock preceded the 2011 Tohoku earthquake by 51 h. Shao et al.  investigated coseismic slip distribution by jointly inverting the waveforms of seismic and GPS data. They found that the rupture of the foreshock was dominated by the failure of an elliptical asperity. Miyazaki et al. investigated the co- and postseismic slip distribution on the basis of onshore GPS data, but found it difficult to delineate exactly the spatial extent of the slip distribution using only inland GPS data.Miyazaki et al.  also pointed out that it is presently unclear whether there was more extensive slip than usual leading up to the Mw9.0 Tohoku earthquake. It is extremely important to understand the nucleation process of the Tohoku earthquake.
 In this paper, we explore the relationship between the foreshock and the nucleation of the 2011 Tohoku earthquake. We derive a co- and postseismic slip model for the foreshock based not only on the inland GPS data but also on data from ocean bottom pressure gauges (OBPs). We also discuss decay time characteristics of the afterslip for the foreshock on the basis of inland geodetic data.
2. Onshore and Offshore Geodetic Data
 The Geospatial Information Authority of Japan (GSI) established GEONET, a nationwide GPS network composed of more than 1,300 stations [Hatanaka, 2003]. This network is sparse near the coast and on some small offshore islands. Since 1994, Tohoku University (TU) has been establishing continuous GPS stations in the Tohoku region to complement GEONET and to improve the sampling resolution of the interplate slip expected during the predicted Miyagi-oki earthquake [Miura et al., 2006].
 We have compiled the data from the continuous GPS stations from four different institutions—TU, GSI, JNES (Japan Nuclear Energy Safety Organization), and NAO (the National Astronomical Observatory of Japan)—and collaborative research sites of TU and GSI (Figure 1). We estimated daily site coordinates before and after the foreshock (March 9, 2011) using the Bernese GPS software version 5.0 [Dach et al., 2007]. In this analysis, we used precise ephemerides and earth rotation parameters distributed by the International GNSS Service (IGS). Coordinates are based on the ITRF2008 [Altamimi et al., 2011] by constraining the daily coordinates of four IGS sites around Japan (AIRA, DAEJ, KHAJ, and YSSK). For the day of the foreshock, we adopted the period of the raw GPS data after the foreshock to avoid contamination of the displacement before and after the earthquake. Coseismic displacements at each site are calculated from coordinate differences before and after the M7.3 foreshock. The estimated displacement vectors are indicated in Figure 2a (black vectors). As a reference site for GPS sites, we fixed 0154, located ∼380 km NW of the epicenter (not shown in Figure 1). It was difficult to assess the vertical component because it was subject to more noise than the horizontal component. Thus, for the GPS data we only used the horizontal component displacement field for estimation of the co- and postseismic slip distribution. To extract the postseismic deformation after the foreshock, we divided the raw GPS data into 3 h periods and processed the sub-daily coordinates using the same procedure as described above. Postseismic displacements at each site were calculated from coordinate differences between the first 3 h after the foreshock and last 3 h of March 10, which ended approximately 5.7 h before theMw9.0 mainshock. It was not possible to use coordinates acquired just before the Mw9.0 mainshock because several of TU's GPS sites lost data as a result of the occurrence of the Mw9.0 mainshock. The estimated postseismic displacement vectors are shown in Figure 2b (black vectors) and indicate relatively small displacements, many less than 20 mm. The displacement direction may, however, indicate a coherent pattern, especially along the coastline.
 We used ocean bottom pressure (OBP) data at nine sites near the foreshock focal area (Figure 1). The OBP observations were based on autonomous gauges with pop-up recovery (P02, P06, P07, P08 P09, GJT3, and TJT1) [Hino et al., 2009; Ito et al., Episodic slow slip events in the Japan subduction zone before the 2011 Tohoku-Oki earthquake, submitted to Tectonophysics, 2012] and real-time seafloor cabled system (TM1 and TM2) [Kanazawa and Hasegawa, 1997]. The OBP time series with 1 min sampling was prepared by stacking raw data with 1 min duration. The OBP data obtained by the autonomous gauges were de-tided, de-drifted and corrected by an ocean model for detecting seafloor vertical deformation [Inazu et al., 2012]. Inazu et al.  showed longer residual OBP time series at three sites (P02, GJT3, and TJT1). They pointed to an evident slow seafloor movement from the foreshock to the Mw9.0 mainshock [see Inazu et al., 2012, Figure 11]. We assumed the OBP records at station P08, located in the middle of the OBP array, as a common reference for obtaining the OBP time series of P02, P06, P07, P09, GJT3, and TJT1. The OBP data recorded at this station is relatively stable until the occurrence of the Mw9.0 mainshock. Thus, we assumed that the fluctuations at station P08 were representative of the noise of all stations. In addition, the coseismic offset due to the Mw6.5 aftershock on March 9, 2011, at 21:24 (UTC) appeared at P09 was corrected. After these corrections, we fitted a linear function to the OBP time series to estimate the coseismic steps and the rate of postseismic deformation. The amount of postseismic deformation was obtained as the product of the rate of deformation and its duration. See Text S1 in the auxiliary material for more detailed description of the above analysis of the OBP data. The OBP data from the seafloor cabled system needs an additional temperature compensation [Inazu and Hino, 2012] to detect vertical seafloor displacements (Figure S1). There seems no apparent coseismic offset for the foreshock in the corrected OBP records. Even in the corrected records, it was difficult to detect the postseismic displacement, as indicated by Inazu and Hino . Thus we assume the zero displacement at TM1 and TM2 for the co- and postseismic displacement in this study.
3. Coseismic and Afterslip Distribution for the Foreshock
 We estimated the co- and postseismic slip distribution on the plate interface by applying a geodetic inversion method devised byYabuki and Matsu'ura  to our GPS and OBP displacements. We assumed the geometry of the subducting slab used by Kita et al. , and defined a curving model fault with dimensions of 120 km by 160 km in the strike- and dip- directions, respectively. We estimated the co- and postseismic slip distributions as superpositions of bi-cubic B splines, with a smoothness constraint for regularization. The smoothness weighting hyperparameter was estimated using Akaike's Bayesian Information Criterion; specifying that this hyperparameter determine the optimal slip distribution. The inversion method estimates the variable slip vector on the plate interface, subject to smoothness constraints in an elastic half space [Okada, 1992]. We weighted OBPs vertical displacements 3 times heavier than GPS horizontal one for inversion analysis because the OBPs were located just in and around the focal area of the foreshock. Figure 2ashows the estimated coseismic slip distribution, which is mainly concentrated down-dip of the hypocenter. Maximum slip reaches 1.8 m, and the calculated moment magnitude was 7.2 (assumed rigidity was 30 GPa). The spatial extent of the coseismic slip was clearly smaller than that ofMiyazaki et al. . The OBPs provide a strongly constraint the spatial extension, especially for the dip-direction. The sites P02 and P06 subsided, while the sites P09 and GJT3 uplifted (Figure 2a). This vertical displacement pattern constrains the spatial extension in the dip-direction. Because of the limitation of the OBPs coverage in the strike direction, the onshore GPS horizontal vectors provide additional and useful information. The coseismic slip model explains the data well and reproduces the vertical displacement pattern around the focal area (Figure S2). Figure 2a also shows the aftershock distribution following the foreshock until the Mw9.0 mainshock determined by Suzuki et al. on the basis of the ocean bottom seismometer data. The aftershocks were mainly concentrated in the up-dip extension of the coseismic slip distribution.Figure 2b shows the afterslip distribution following the mainshock. The estimated maximum slip amount was approximately 0.4 m, and the calculated moment magnitude was 6.8. Figure S3 shows the residual distribution between the observed displacement and the calculated one from our model. The afterslip model also explains the data well, even for the small displacements at inland GPS stations.
Figure 2cshows a comparison of the distribution of co- and postseismic slip of the foreshock and coseismic slip of theMw9.0 mainshock [Iinuma et al., 2012]. Our results clearly show that the areas of maximum afterslip and coseismic slip distribution do not overlap. The afterslip distribution was mainly concentrated in the up-dip extension of the coseismic slip. The coseismic slip and afterslip distribution of the foreshock were also located in the slip deficit region (between 20–40 m slip) of the coseismic slip of theMw9.0 mainshock. The spatiotemporal relationship between the foreshock and its afterslip will be discussed further in the following section.
4. Discussion and Conclusion
Kato et al.  pointed out aftershock migration after the foreshock along the trench axis toward the epicenter of the Mw9.0 mainshock on the basis of an earthquake catalog, which was created using a waveform correlation technique. They also estimated aseismic slip amount by the repeating earthquake analysis conducted for each rectangular region, denoted in Figure 2c. From the repeating earthquake analysis, regions (b) and (c) were found to show large slips, reaching approximately 200 mm. In contrast, region (d) showed less slip (∼100 mm). This spatial pattern is roughly consistent with our results based on geodetic data. For regions (b) and (c), our results show slip of 300–400 mm. For region (d), the estimated slip amount is smaller than that for region (c) (∼200–300 mm) (Figure 2c). On the basis of our geodetic evidence and by repeating earthquake analysis of Kato et al. , we conclude that the aseismic slip after the foreshock occurred in the up-dip extension of the coseismic slip region for the foreshock, which might have later migrated along the trench axis toward the epicenter of theMw9.0 mainshock. We speculate that aftershocks occurring after the foreshock may have been triggered by strain concentrations at the edges of areas experiencing afterslip. These aftershocks may have nucleated the huge Mw9.0 Tohoku earthquake off the Pacific coast.
Figure 3shows the volumetric strainmeter time series and norm of sub-daily horizontal components GPS time series for the Kinka-san Island and NATR stations, respectively (seeFigure 1for locations). We removed tidal effects using the program BAYTAP-G [Tamura et al., 1991] to extract the postseismic deformation. We also corrected coseismic offset for the Mw6.5 aftershock on March 9, 2011, at 21:24 (UTC) in the time series. To extract the characteristics of the afterslip, we fitted the logarithmic function y(t) = a log(1 + t/τ) to the observed time series, where t is the elapsed time since the mainshock, τ is the decay time constant, and a is the magnification factor. This is a logarithmic law very commonly used for postseismic deformation study [Freed, 2007]. We estimated a and τby employing a non-linear least-squares method. The estimated decay time constant was 4.8 ± 0.09 h (0.2 ± 0.004 d) for the strainmeter time series. For the sub-daily GPS data, we only estimated parameteraafter the decay time constant was fixed to the value estimated from the strainmeter data. The fitted logarithmic function explains well both the strainmeter and sub-daily GPS time series data. We also fitted the same function to the OBP time series with fixed decay time (0.2 d) (Figure S4). The OBP time series clearly contains more noise than the strainmeter and sub-daily GPS time series. The fitted function, however, is able to explain the postseismic deformation pattern suggested by the OBP time series. The obtained logarithmic decay time is shorter than that for other large interplate or inland earthquakes (e.g., theM8.0 2003 Tokachi-oki earthquake [Takahashi et al., 2004] (τ = 4.5–11.4 d), the Mw8.7 2005 Nias earthquake [Kreemer et al., 2006] (τ = 6.2 d), the M6.0 2004 Parkfield earthquake [Freed, 2007] (τ = 14.6 d), and the Mw6.7 2007 Chuetsu-oki earthquake [Ohta et al., 2008] (τ = 0.35–2.83 d). The exact reason of short decay time for this foreshock afterslip is unclear at present, but it was possibly controlled by the frictional property on the plate interface. The estimated afterslip was just located at down-dip end of the largest slip area ofMw9.0 mainshock (∼more than 40 m, see Figure 2c). This relationship suggests some kind of frictional difference between the afterslip region of the foreshock and the Mw9.0 coseismic slip region, although further investigation is required to confirm this speculation. Ide et al.  proposed a scaling law relating the released seismic moment and characteristic duration. In this study, the moment magnitude of the afterslip was approximately 6.8, and the duration was 2 d. However, it was difficult to define the exact duration time for the afterslip because of the subsequent occurrence of the Mw9.0 mainshock. From the scaling law of Ide et al. , the duration of aseismic slip with Mw6.8 should be more than 1 month. Nevertheless, the postseismic signal shows a rapid decay time constant of less than 1 d. Thus, we suggest that this afterslip following the foreshock may be difficult to describe using the scaling law, although further investigation is required to confirm this exception.
 In conclusion, geodetically observed co- and postseismic displacements in inland and offshore regions following theM7.3 foreshock provide detailed information regarding the distribution of coseismic and postseismic slip. It is suggested that afterslip is distributed in the up-dip extension of the coseismic slip. Postseismic displacements suggest the possibility of afterslip occurrence within a short period of time. A more detailed investigation of the entire process of theM7.3 foreshock is required for a better understanding of the subsequent huge earthquake.
 GPS data were obtained from GSI, JNES and NAO. We also thank M. Shinohara and S. Sakai for permitting us to use the cabled OBP data from off Kamaishi. The paper benefited from careful reviews by S. Miyazaki and an anonymous reviewer. This study was supported by MEXT project, Japan, titled “Observation and Research Program for the Prediction of Earthquakes and Volcanic Eruptions” and “Research Concerning Interaction between the Tokai, Tonankai and Nankai Earthquakes.” The study was also supported by JSPS KAKENHI (20244070). We used Generic Mapping Tools [Wessel and Smith, 1998] to produce the figures.
 The Editor thanks two anonymous reviewers for assisting in the evaluation of this paper.