Modeling of the post-seismic slip of the 2003 Tokachi-oki earthquake M 8 off Hokkaido: Constraints from volumetric strain
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A Sacks-Evertson borehole volumetric strainmeter (SE strainmeter) at a site located 105 km from the epicenter of the mainshock recorded a clear slow strain event following the 2003 M w 8.0 Tokachi-oki earthquake (September 25, 2003, 19:50:06 UTC). This consisted of an episode of contraction for 4 days followed by expansion for 23 days. GPS sites in southeastern Hokkaido also recorded displacement changes during the same time interval. We use quasi-static calculations to generate synthetic waveforms for the measured quantities. All the data are satisfied by a propagating line source 2-stage model of slow reverse slip, uniform amplitude of 50 cm, with rupture propagation velocities of constant 9 cm/s (first stage) and exponentially decreasing from 3 to 0.7 cm/s (second stage). This post-seismic slip event is taken to be coplanar with the main shock rupture on the upper plane of the double Wadati-Benioff seismic zone (DSZ), and largely overlaps the seismic rupture. Regular earthquakes release only about 30% of the plate motion in this section of the subduction zone; post-seismic slip appears to account for at least some of the deficit.
Key wordsPost-seismic slip event volumetric strainmeter 2003 Tokachi-oki earthquake aftershock activity state space approach
In a study of GPS data of GEONET sites in Hokkaido, for the period between September 4, 2003, and March 6, 2004, the time evolution of its post-seismic slip, together with the coseismic slip distribution were estimated (Ozawa et al., 2004). Miyazaki et al. (2004) estimated the spatial and temporal evolution of post-seismic slip in the 30 days following the mainshock. Using GPS data, they showed that there was significant post-seismic slip following the main-shock. Their findings placed most of the slip in an area to the northeast and southwest of the coseismic slip but we note that the results did not fit well the distribution of the vertical displacements. Baba et al. (2006) estimated a U-shaped 1-yr post-seismic slip distribution encircling the co-seismic slip, using GPS and ocean bottom pressure data. Miyazaki and Larson (2008) used 30-second GPS data to derive a model of post-seismic slip during the ~1 hour before the largest aftershock, and also for the first 4 hours after the mainshock. They concluded that there was significant post-seismic slip in the region between the slip maxima of the mainshock and that of the largest aftershock, as well as downdip of those zones. Fukuda et al. (2009), using 5 hours of GPS data immediately following the mainshock, also found slow post-seismic slip roughly in the area between the main, and the largest, aftershock.
Here, we re-examine this post-seismic slip episode by utilizing dilatational strain data from a Sacks-Evertson borehole strainmeter (Sacks et al., 1971) at the Urakawa Seismological Observatory of Hokkaido University (KMU) in southern Hokkaido, Japan (Fig. 1) with the objective of determining what additional constrains can be placed on the parameters of the post-seismic slip. Clearly, with only one strainmeter site we cannot claim a complete solution but we will see if our model based on strain changes can also satisfy the displacement data from those GPS sites in south-east Hokkaido in the general vicinity of the strainmeter site. Strain changes in near-surface crustal rock have contributions from barometric pressure changes, from Earth tides, and precipitation, in addition to any tectonic changes of importance to this study. Additionally, the continuity of the data stream is occasionally interrupted due to equipment failure or loss of power. To remove extraneous influences, we first apply a state-space model that was developed for detecting coseismic changes of groundwater levels (Kitagawa and Matsumoto, 1996; Matsumoto et al., 2003) to the strain data recorded at KMU. The resulting signal decomposition provides a corrected strain signal, showing a clear strain event consisting of contraction for about 4 days, and then expansion for about 23 days, following the 2003 Tokachi-oki earthquake. We assume, as did previous investigators, that the source for this strain event is coplanar with the mainshock and additionally that the slip is in the same direction as the coseismic slip and is uniform over our entire model surface.
2. Observation and Data Processing
Our primary data are 6 months of strain change observations, starting about 4 months before the 2003 Tokachi-oki earthquake, recorded by a SE strainmeter in a 110-m-deep borehole at KMU (Takanami, et al., 1998). The site is about 105 km from the earthquake epicenter (Fig. 1). The strainmeter has a sensitivity of about 10−11, large dynamic range and constant response to strain from zero frequency to 20 Hz (Sacks et al., 1971). The strain data are now logged on site and also sent by telemetry to the Institute of Seismology and Volcanology, Hokkaido University, Sapporo, Hokkaido, but, in 2003, we had only telemetered data. We also use GPS data from a number of sites in southeast Hokkaido to confirm the validity of our model and to provide constraints on the along strike length of the slow rupture source.
This time series shows a clearly anomalous strain change for at least 27 days following the earthquake. The data do not preclude continuing slip over a longer time interval as has been shown by Ozawa et al. (2004) but since we cannot readily recognize such strain changes we limit our analysis to the clearly observable strain event. We now seek to determine the source of this signal.
3. Propagating Fault Model for Post-Seismic Slip
Previous studies of post-seismic strain changes in locations of GPS sites (Ozawa et al., 2004; Miyazaki and Larson, 2008; Fukuda et al., 2009) solved for source models coplanar with the mainshock rupture. We also take that approach and additionally assume the same direction for the slip vector as for the mainshock (Geographical Survey Institute, 2004). This approach is supported by the work of Ito et al. (2004), who pointed out that the mechanisms of the aftershocks, distributed along the boundary between the Pacific and the North American plates, are similar to that of the main event, indicating a thrust fault with a nodal plane dipping to the northwest. The location of such aftershocks corresponds to the upper zone of the double-planed Wadati-Benioff seismic zone (DSZ) imaged along the southernmost Kuril trench using relocated hypocenters by Katsumata et al. (2003). We use the mainshock fault plane solution from the Geographical Survey Institute (2004).
By focusing on the strain data, we bring additional constraints on models for the post-seismic slip. Our approach is to look for the simplest model that will satisfy the strain record and then check by comparing calculated displacements with GPS observations in southeast Hokkaido from GEONET (GPS Earth Observation Network System) of the Geospatial Information Authority of Japan (GSI) and the temporary GPS survey by Takahashi et al. (2004). That the strain record is characterized by a change in sign during the course of the event is indicative of a propagating source. In contrast to horizontal displacements, vertical displacements and dilatation experience sign changes that are diagnostic of source depth. When we apply the very reasonable constraint that the source of the post-seismic slip is coplanar with the mainshock rupture (strike 240°, dip 23°) and the slip vector has the same rake angle (124°) as for the main-shock, as given by GSI (2004), we immediately find that the strain record supplies strong constraints on the extent of the source in the dip direction and also requires that the rupture propagates down-dip. To minimize the number of free parameters, we also assume that the slip amplitude is constant over the slow rupture surface and that the rupture front is a horizontal line source.
The schematic geometry of faults in Stages 1 and 2 is illustrated in Fig. 3(b). The fault parameters (fault areas, fault slips, rupture velocities, and depths) are 130×32 km2, 50 cm, 9 cm/s and 38 km for Stage 1, and 130×32 km2, 50 cm, and 3 to 0.7 cm/s (exponentially decreasing) and 50.5 km for Stage 2, respectively. The total seismic moment released slowly is 1.4×1020 N m (equivalent to M w = 7.4).
4. Comparison of Model with GPS Data
For GPS sites whose data plots are not shown, three close to Cape Erimo record significantly larger EW displacements than those calculated from our model, while some sites to the north have larger (negative) NS displacements. The discrepancy could be reduced by allowing some clockwise rotation of the slip vector as a function of strike direction from southwest to northeast. But, even without adding any complexity to our extremely simple model, the overall fit to all sites is very good given that we did not use these data to control the slip solution; clearly, our model captures the essentials of the post-seismic rupture. We do not fit well the horizontal displacements at GPS sites to the NE of our model; this is not surprising since our model is primarily based on the strain record from KMU to the southeast end of the model surface. That aspect could be improved by including additional slip in the vicinity of those GPS sites (e.g. see Ozawa et al., 2004) without any noticeable change in the calculated strain at KMU.
There have been several studies of this post-seismic slip event based on analyses of GPS data, e.g. Miura et al. (2004), Miyazaki et al. (2004), Ozawa et al. (2004), Murakami et al. (2006), and Uchida et al. (2009). The latter two present an analysis over a longer period than in our study. Compared with our very simple model, all of these studies solve for models with many more parameters. These solutions characteristically show large slip amplitudes shallow in the subduction zone (depth <20 km) at rather larger distances from the land-based observation points. The models also have slip concentration on the subduction interface under Hokkaido. We note that the shallow slip in those models is not compatible with the strain record (as noted above, slip in that area will result in a positive strain change at KMU). Also, that shallow slip causes negative vertical displacements at GPS sites close to the coast where the data show uplift; this has to be offset by adding slip patches under the land. Baba et al. (2006) show that the land-based GPS data provide poor resolution for slip in the shallow parts of the subduction zone. Previously-published models are in conflict with the observed strain change data whereas our very simple model, derived primarily to fit the strain data, also fits the GPS data very well for those sites in the vicinity of our model.
5. Relationship between Post-Seismic Slip and Aftershock Activity
We also note (Figs. 5(b) and 5(c)) that the post-seismic slip area is complementary to that with the large majority of aftershocks, as pointed out by Ito et al. (2004). Mochizuki et al. (2005) interpreted strong reflections at the plate boundary within the aseismic regions as implying aseismic slip between the plates. Aftershocks occur mainly to the east of about 144.2°E and south of 42.5°N, whereas continuing post-seismic slip dominates the post-seismic release to the west. Earlier GPS-based studies found post-seismic slip to the north of the 42.5°N limit. (As discussed above, we discount any post-seismic slip shallower in the subduction zone, i.e. to the east of 144.2°E and south 42.5°E, as proposed in earlier GPS-based studies, because such slip violates the strain observations, and a subsequent study by Baba et al. (2006) shows that the GPS data has very low resolving power for such slip.) This dividing line is not simply along a depth contour of the subduction, and so the differing characteristics are not simply a function of depth. It may be suggestive of differing fault zone rheologies. Machida et al. (2009) showed that the high V p /V s anomaly is positioned above the largest slip area of the 2003 Tokachi-oki earthquake, estimated by Yamanaka and Kikuchi (2003), and suggested that it may relate to fluid flow during the main shock.
We applied state-space modeling techniques to enable the removal of offsets, barometric pressure change effects, solid Earth tides, and precipitation effects, from the strain recorded by an SE strainmeter at KMU, southeast Hokkaido. Particularly noteworthy is the successful removal of the strains induced in a non-linear fashion by precipitation. The remaining trend is a significantly improved estimate of geodetic strain and clearly shows continuing post-seismic strain following the M 8 Tokachi-oki earthquake.
By assuming, for this post-seismic slip, a source coplanar with the seismic rupture plane, we are able to place strong constraints on the down-dip extent and amplitude of the post-seismic slip by using only the dilatational strain data. We limit the northeast extent of our model to match the coseismic rupture and then find that we match the GPS data surprisingly well with the other slip parameters determined solely from the strain data at a single station. We minimize the number of free parameters in the model by having the simplest possible geometry and slip parameters. We have two rectangular slip surfaces, one for each stage of the strain event that consists of contraction followed by expansion. These two sources have equal lengths and widths, and we impose a uniform slip vector over the complete source.
Miyazaki and Larson (2008) concentrated on GPS displacement changes during the first 4 hours after the main-shock, an interval during which we have no strain data due to power failure at the observation site. Their model has a slip patch contiguously up-dip from our model; if that slip propagated downward it would merge into our slip area. Ozawa et al. (2004) and Miyazaki et al. (2004) studied a longer time interval but, for the duration of our study, they proposed a large patch of post-seismic slip up-dip from the seismic rupture at a depth less than 20 km, in addition to slip at depths more comparable to those of our model. Such models are not compatible with the strain record; they produce a large expansion (positive) signal. Also, as we noted above, the GPS network has a rather low resolving capability for slip in those distance shallow area (Baba et al., 2006). Both studies use data from a large number of GPS stations and invoke quite a complex source model. The GPS data in those two studies show low amplitude changes continuing after the end of our Stage 2. Strain amplitudes for such small long-period changes would be below our detection threshold.
Additionally, we note an intriguing relation: the areas experiencing aftershocks and post-seismic slip are complementary, but are not separated by depth. We have no simple explanation for this but the observation appears to be robust.
The authors thank M. Acierno, B. Schleigh, and B. Pandit from DTM of Carnegie Institution of Washington, and T. Ogawa, M. Takada and Y. Tanioka from ISV of Hokkaido University for their valuable support. Reviews and corrections by two anonymous reviewers are greatly appreciated. GMT (Wessel and Smith, 1991) was used to produce the figures. We used the unified Japan Meteorology Agency (JMA) earthquake catalog with Hokkaido University, Hirosaki University, Tohoku University, Tokyo University, Nagoya University, Kyoto University, Kochi University, Kyushu University, Kagoshima University, Shizuoka Prefecture, Yokohama City, Tokyo Metropolis, JMA, Natural Research Institute for Earth Science and Disaster Prevention, National Institute of Advanced Industrial Science and Technology (AIST), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), and Hot Springs Research Institute of Kana-gawa Prefecture. Mapping for epicenters were carried out by using the Seismicity Analysis System TSEIS (http://wwweic.eri.u-tokyo.ac.jp/analysis.html).
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