Rupture process of the 2011 Tohoku‐oki earthquake and absolute elastic strain release
Abstract
[1] On 11 March 2011, the Tohoku‐oki earthquake in eastern Japan and the devastating tsunami that followed it caused severe damage and numerous deaths. To clarify the rupture process of the earthquake, we inverted teleseismic P‐wave data applying a novel formulation that takes into account the uncertainty of Green's function, which has been a major error source in waveform inversion. The estimated seismic moment is 5.7 × 1022 Nm (Mw = 9.1), associated with a fault rupture 440 km long and 180 km wide along the plate interface. The source process is characterized by asymmetric bilateral rupture propagation, but we also found continuous slips up‐dip from the hypocenter, which led to a large maximum slip (50 m), long slip duration (90 s), and a large stress drop (20 MPa). The long slip duration, large stress drop, extensional (normal faulting) aftershocks in a previously compressional stress regime, and low‐angle normal slips at approximately the depth of the plate interface suggest that the earthquake released roughly all of the accumulated elastic strain on the plate interface owing to exceptional weakening of the fault. The stress accumulated on the plate interface was about 20 MPa near the trench and 0–10 MPa in the down‐dip source region.
1. Introduction
[2] The Pacific plate subducts at a rate of about 85 mm/y beneath the Tohoku district along the Japan Trench [DeMets et al., 1990], where several large interplate earthquakes have occurred during the last century. The coupling rate on the plate interface has been estimated from GPS data [Nishimura et al., 2004; Hashimoto et al., 2009] and small repeating earthquakes [Uchida et al., 2004]. The behavior of the asperities on the plate interface off Miyagi prefecture has been investigated in detail [Umino et al., 2006]. From these analyses and historical records, several scenarios of large interplate earthquakes up to magnitude 8.2 have been considered (Headquarters for Earthquake Research Promotion, http://www.jishin.go.jp/main/index-e.html), although extensive sediment deposition by the large Jogan tsunami of 869 suggesting a larger event has recently been documented [Minoura et al., 2001].
[3] In this study, we estimate the detailed rupture process of the 2011 Tohoku‐oki earthquake from teleseismic P‐wave data using a newly developed inverse method [Yagi and Fukahata, 2011], which takes into account the uncertainty of Green's function that has been a major error source in waveform inversion. Based on the rupture process and normal fault aftershocks, we suggest that roughly all of the accumulated elastic strain on the plate interface was released by the 2011 Tohoku‐oki earthquake.
2. Inversion Analysis
[4] The 2011 Tohoku‐oki Earthquake is the biggest event in Japan since the initiation of modern seismic observation. To estimate the rupture process of the earthquake, we inverted teleseismic P‐wave data recorded at 51 broadband network stations (Figure S1 of the auxiliary material). Stations were selected to ensure adequate data coverage and quality. Observed waveforms were shifted so that first arrivals aligned with the first break at the hypocenter and then converted into velocity waveforms with a sampling interval of 1.2 s. For mitigation of aliasing and low frequency noise, we applied the Butterworth band pass filter between 0.001 and 0.38 Hz before the re‐sampling.
[5] Waveform inversion is widely used for constructing seismic source models, but models may differ substantially for the same earthquake [e.g., Beresnev, 2003; Vallée and Bouchon, 2004]. Waveform inversion is especially problematic for large earthquakes with a long source time function, because seismic data for such events are contaminated by various later phases, which are difficult to calculate accurately because of limited accuracy of the Green's function. To cope with this problem, we applied the newly developed inverse method [Yagi and Fukahata, 2011], in which uncertainty of the Green's function is taken into account. One of the clear advantages of this method is that the observed data for later phases are naturally reduced in weight. In this method, the smoothness of slip distribution is objectively determined from observed data based on Akaike's Bayesian Information Criterion (ABIC) [Akaike, 1980; Yabuki and Matsu'ura, 1992] and the non‐negative constraint for slip is not needed. We demonstrate the difference of the results between the new and the conventional methods in Figure S2 of the auxiliary material. As shown in Figure S2c of the auxiliary material, the misfit of the new formulation has stronger correlation with time than that of the conventional formulation. This is because the modeling error in the new formulation is defined as the convolution of a slip‐rate function at each point and a random error of Green's function. In the conventional formulation such correlated errors are regarded as signals with random errors.
[6] We calculated the theoretical Green's function by the method of Kikuchi and Kanamori [1991] with a sampling rate of 0.1 s. To explain the teleseismic waveforms, we modified the structure model obtained by an ocean bottom seismic survey [Miura et al., 2005]. We assumed that faulting occurred on a single flat plane and adopted a hypocenter (38.103N, 142.860E, depth 22 km), and fault mechanism (strike 200°, dip 12°) that were slightly modified from the JMA hypocenter and the Global Centroid‐Moment‐Tensor solution [http://www.globalcmt.org/] to minimize ABIC in preliminary analyses. We took a fault area of 500 km (NNE) × 200 km (ESE), which was expanded into bilinear B‐splines with an interval of 20 km. We also took a slip‐rate duration of 102 s on each space patch, which was expanded into linear B‐splines with an interval of 1.2 s. Based on preliminary analyses, we assumed the velocity of the rupture front to be 2.8 km/s, which yielded the start time of the linear B‐splines at each sub‐fault.
3. Results
[7] Figure 1a shows the inverted slip distribution with the moment rate function. The maximum slip was about 50 m in the up‐dip side from the hypocenter. The area of slip more than 5 m extends about 440 km long and 180 km wide along the plate interface. Slip‐rate functions of three representative patches are also shown in Figure 1a. Figure 2 shows snapshots of the slip distribution during the mainshock with the tsunami source regions of historical large earthquakes (Headquarters for Earthquake Research Promotion, http://www.jishin.go.jp/main/index-e.html). The locations of the red, green, and blue patches for slip‐rate functions in Figure 1a correspond to the source regions of the 1978, 1897b, and 1938a earthquakes in Figure 2, respectively.
[8] As shown in Figure 2 and Animation 1, the rupture propagated southeast during the first 20 s, breaking the southwestern part of the source region of the 1897b earthquake (green patch in Figure 1a). After that, the rupture was greatly accelerated in and around this area. At the same time, the rupture started at 20 s in the source region of the 1978 off Miyagi earthquake (red patch in Figure 1a), where the slip rate began to decelerate at 35 s but accelerated again keeping high slip rate until 80 s. After 40 s, the rupture started to propagate north and south, although the rupture velocity slowed down around the northern edge of the 1938c source region, where large postseismic slip events of 2005 off Miyagi (Mw 7.2) and 2008 off Fukushima (Mw 6.9) earthquakes (closed brown curves in Figure 1a) were reported [Suito et al., 2011]. The rupture reached off Ibaraki at 100 s and slip continued until 150 s around this area.
[9] The stress drop was calculated from the inverted total slip distribution (Figure 3b). The stress drop was larger (about 20 MPa) in the up‐dip region from the hypocenter and relatively lower (0–10 MPa) in the down‐dip source region. The average stress drop of 6 MPa is as twice as that of typical interplate earthquakes [Kanamori and Anderson, 1975].
4. Discussion
[10] Our source model reproduces the overall features of observed waveforms including high frequency components (Figure S1 of the auxiliary material). The first three‐days aftershocks delineate the large slip area (Figure 1a). Figure 1b shows strong ground motion data, in which we observe three notable phases. These phases are basically well explained by the theoretical arrival time from each peak of the slip‐rate functions at the 1978 (P1), 1897b (P2), and 1938a (P3) source regions (Figure 1), in which relatively stronger coupling has been estimated [Nishimura et al., 2004; Uchida et al., 2004; Hashimoto et al., 2009]. Figure 1 suggests that high frequency components of seismic waves were radiated in the up‐dip region as well as the down‐dip region, which contradicts existing analyses [e.g., Ide et al., 2011; Simons et al., 2011]. The synthetic displacements calculated from our total slip model are consistent with observed GPS data (Figure S3 of the auxiliary material). The slip distribution estimated from a joint inversion analysis of tsunami and GPS data (Tanioka, http://www.sci.hokudai.ac.jp/isv/ev-news-flash/#a-04) also resembles our slip model.
[11] As shown in Figure 1a, even though the rupture propagation time (about 10 s) to pass through a patch of 20 km is taken into account, the slip continues about 90 s in the maximum slip area, which resulted in a large stress drop. 90 s of rupture duration at a point is significantly longer than about 30 s expected from Geller's [1976] empirical relationship. In the 2010 Chile earthquake (Mw 8.8), which has a similar fault size to this earthquake, the maximum slip duration at a point was only 24 s [Delouis et al., 2010]. This long slip‐rate function, which is also suggested by strong ground motion analyses [e.g., Yoshida et al., 2011], means that dislocation across the plate interface continued to release elastic stress and strain, which is likely to indicate significant weakening of frictional strength on the fault plane. Thermal pressurization seems to be a plausible mechanism for this weakening [Wibberley and Shimamoto, 2005]. In the 1978 source region, 4.6 m slip occurred during the first phase (25 s), which means that the slip deficits accumulated after the 1978 earthquake were completely released during the first phase. Accordingly, 6.7 m slip of the second phase (46 s) appears to be induced by the extremely large up‐dip slip.
[12] Before the earthquake, E–W compression was prevailed in the most area of the Honshu arc except near the Izu collision zone [Terakawa and Matsu'ura, 2010]. After the 2011 Tohoku‐oki earthquake, however, a drastic change of earthquake mechanisms is observed (Figure 3a). Normal faulting has become active along the Pacific coastline around Fukushima. Rotation of the focal mechanisms about 45 degrees also occurred around northern Nagano. Above the ruptured area of large slips, there are so many normal fault aftershocks. Especially, some of them occurred at approximately the depth of the plate interface with a mechanism of low‐angle normal faulting [Ide et al., 2011]. We also confirmed the depth and mechanism for the largest event (Mw 6.6) from waveform inversion (Figure S4 of the auxiliary material).
[13] The plate interface is considered to be the site where absolute elastic strain accumulates (Figure 4). However, the absolute level of stress and strain has been difficult to estimate, because seismic data only allow us to determine the stress drop of an earthquake [Kanamori, 1994]. The debate about the strength of the San Andreas fault is a well‐known example of this problem [Scholz, 2000]. In typical seismic events such as the series of off Miyagi earthquakes (1936 M7.4, 1978 M7.5, 2005 M7.2) [Umino et al., 2006], only part of this absolute strain is released. Observed changes in a stress field are commonly small and limited in extent, even after a magnitude‐8 event. One exception is the 1968 Tokachi‐oki earthquake (Mw 8.2), in which low‐angle normal fault aftershocks were observed around the northwestern edge of the large slip area [Kanamori, 1971].
[14] The drastic change of earthquake mechanisms in the wide region of eastern Honshu means that at least a substantial part of the absolute elastic strain accumulated on the plate interface was released by the 2011 Tohoku‐oki earthquake. Low‐angle normal earthquakes at approximately the depth of the plate interface indicate that overshoot of slip occurred at least locally. In addition to them, many normal aftershocks above the large slip area suggest that roughly all elastic strain accumulated on the plate interface was exceptionally released in the mainshock. Our rupture model that suggests significant weakening of frictional strength strongly supports this idea.
[15] If the absolute elastic strain was released, this holds great significance. First, we can estimate the absolute stress level on the plate interface from the stress drop of this earthquake (Figure 3b), which is about 20 MPa near the trench and about 6 MPa in the average of the ruptured area. These values are consistent with the existent estimates of the absolute stress on the plate interface along the Japan trench, from heat flow data (<20 MPa) [Furukawa and Uyeda, 1989], force balance in the fore arc (∼20 MPa) [Seno, 2009], and stress tensor inversion for the aftershocks of the 1968 Tokachi‐oki earthquake (<5 MPa) [Magee and Zoback, 1993]. Stress tensor inversion in and around the source region of the 2011 Tohoku earthquake [Hasegawa et al., 2011] also shows nearly complete stress drop (∼20 MPa) at the earthquake. A difference of our estimate from these studies is that we have obtained a rough distribution of the absolute stress, which is high (∼20 MPa) near the trench and low (0–10 MPa) in the down‐dip source region. Such contrast of the stress state may be explained by the fault‐valve model [Sibson, 1992], in which stress is high near the trench because of approximately hydrostatic pore pressure whereas stress is low in the down‐dip region because pore pressure approaches lithostatic.
[16] Secondly, we can expect seismic activity on the ruptured area to become quiet for a substantial period. For example, in the source region of off Miyagi earthquakes, where the recurrence interval of the interplate earthquakes has been about 40 years [Umino et al., 2006], at least 130 years are required to recover the slip deficit that was released at the 2011 Tohoku‐oki earthquake. Such a quiescence of seismic activity was recorded in central Peru [Dorbath et al., 1990; Okal et al., 2006], where no large earthquake had occurred for about 200 years after the 1746 great event, although the usual recurrence interval is less than 100 years.
[17] Thirdly, periodic occurrence of large interplate earthquakes may be questioned, because large events seem to be controlled by dynamic weakening of the fault with non‐linear nature. In fact, the most well‐known sequence of large interplate earthquakes along the Nankai trough, Japan, shows repeated occurrence of them, but the periodicity is not good; the minimum interval is 90 years and the maximum 264 years [Ando, 1975]. Large variance of the recurrence interval (100–800 years) of outsized tsunami deposits along the Pacific coast of Hokkaido, Japan [Sawai et al., 2009] is also reported. Such pseudo‐cyclic behavior of large interplate earthquakes may be understood by constant accumulation of elastic strain due to steady plate motion and accidental release of elastic strain due to dynamic weakening that strongly depends on initial conditions. If so, prediction of M9 events may be fundamentally difficult.
Acknowledgments
[18] Waveform data obtained by FDSN and GSN were supplied by the IRIS‐DMC. We used hypocenters determined by JMA, strong ground motion data observed by K‐net, NIED, and moment tensor solutions determined by Global CMT project and F‐net, NIED. We thank B. Shibazaki and N. Nishimura for his useful information. We also acknowledge the comments by anonymous reviewers in improving the manuscript. This study was supported by grant‐in‐aid for scientific research 21540428 of the Japan Ministry of Education, Culture, Sports, Science and Technology to Y.Y. and Y.F.
[19] The Editor thanks two anonymous reviewers for their assistance evaluating this manuscript.
