Geophysical Research Letters

A deep outer-rise reverse-fault earthquake immediately triggered a shallow normal-fault earthquake: The 7 December 2012 off-Sanriku earthquake (MW 7.3)

Authors


Abstract

[1] Teleseismic body wave analysis revealed that the 7 December 2012 off-Sanriku earthquake (MW 7.3) at the outer rise of Japan Trench consisted of two successive subevents. The first subevent with reverse-fault mechanism (Event 1, MW 7.1) at 56 km depth was followed by, approximately 20 s later, the second subevent with normal-fault mechanism (Event 2, MW 7.2) at 6 km depth. Finite-fault slip models show that the slip of Event 1 was concentrated around the initial rupture point with the maximum of 2.7 m and that Event 2 had two asperities with the maximum of 4.5 m at both sides of the initial rupture point. The static Coulomb Failure Function analyses suggested that Event 1 triggered Event 2 and that both subevents were promoted by the 2011 Tohoku earthquake (MW 9.1).

1 Introduction

[2] Following the 11 March 2011 Tohoku earthquake of MW 9.1 (Global Centroid Moment Tensor: GCMT) (Figure 1), many normal-fault aftershocks, including a large earthquake of MW 7.6 (GCMT) on the same day, have occurred in the outer-rise region of Japan Trench, where the Pacific plate is subducting beneath the North American plate. The 7 December 2012 off-Sanriku earthquake of MW 7.3 (the hypocenter parameters given by the National Earthquake Information Center (NEIC) are as follows: origin time = 06:18:24 UTC; epicenter = 37.889°N, 144.090°E; and depth = 36.1 km) seemed to be one of such aftershocks. For this earthquake, however, variable mechanism solutions were determined by different institutions. The W-phase and body wave moment tensor solutions by the United States Geological Survey (USGS) show reverse faulting, whereas the CMT solution by the National Research Institute for Earth Science and Disaster Prevention (NIED) of Japan shows a normal faulting (Figure 1).

Figure 1.

The NEIC epicenter of main shock (red star), 1-month aftershocks (red circles) and mechanism solutions determined by the USGS and NIED (below the map) of the 7 December 2012 off-Sanriku earthquake. Gray stars show the NEIC epicenters of the 11 March 2011 Tohoku earthquake and the large outer-rise aftershock on the same day. Gray circles are the 1-month aftershock epicenters following 11 March 2011. Mechanism solutions in the map are the GCMT solutions. Slip distribution of the Tohoku earthquake estimated by Satake et al. [2013] is shown by colors indicated below the map. Inset of the map shows tectonic setting around the study area; AMR, NAM, PAC, and PHS denote the Amurian, North American, Pacific, and Philippine Sea Plate, respectively.

[3] In this study, in order to reconcile the discrepancy among the different focal mechanism solutions by the USGS and NIED, we perform teleseismic body wave analysis to estimate multiple point-source moment-tensor solutions. We will show that this earthquake consists of two successive M7-class subevents: a reverse-fault event in the deep outer-rise region (Event 1) and a normal-fault event in the shallow outer-rise region (Event 2). We then estimate finite-fault slip models for Event 1 and Event 2 by using the teleseismic body wave inversion. Finally, we calculate the static change in the Coulomb Failure Function (ΔCFF) caused by Event 1 for Event 2 as a receiver fault and that by a finite-fault model of the 2011 Tohoku earthquake for Event 1 and Event 2 as receiver faults to show that these earthquake sequences can be interpreted as static stress triggering by the 2011 main shock and Event 1.

2 Point Source Solutions

[4] We first determined the mechanism solutions of the 2012 off-Sanriku earthquake by using the moment tensor inversion of teleseismic body waves for multiple point sources [Kikuchi and Kanamori, 1991; http://www.eri.u-tokyo.ac.jp/ETAL/KIKUCHI/]. We used the UD component of the P waveforms recorded at 73 stations with the epicenter distance from 30° to 90° (Figure S1 in the Supporting Information). The waveform data were retrieved from the Data Management Center of the Incorporated Research Institutions for Seismology (IRIS), band-pass filtered in the frequency range of 0.004–1.0 Hz, and deconvolved into the ground displacements. The duration of the waveforms used in the analysis is 90 s from the calculated P wave arrival times. The velocity structures around the source region were set in reference to the CRUST 2.0 [Bassin et al., 2000] and ak135 [Kennett et al., 1995].

[5] We assumed two triangles with 9 s duration as source time functions. The rupture velocity was assumed to be 2.8 km/s (about 65% of average S wave velocity in the source region). We tested other rupture velocities ranging from 65% to 80% of the average S wave velocity, but the results as well as the variance between the observed and the synthetic waves were almost identical. We searched for two point sources on 9 × 7 grid points around the NEIC hypocenter with a 20 km spacing along the N25°E direction and a 10 km spacing in the depth direction. The direction of horizontal search is almost parallel to the 2012 aftershock distribution and strikes of the mechanisms determined by the USGS and NIED (Figure 1).

[6] The result shows that the 2012 off-Sanriku earthquake consisted of two successive subevents (Figure 2). The first subevent with a reverse-fault mechanism occurred in the deep outer-rise region (Event 1; depth, 56.1 km; strike, 171.8°; dip, 57.3°; rake, 68.5°), and the second subevent with a normal-fault mechanism occurred in the shallow outer-rise region at 20 km SSW from Event 1, which is the same location of the NEIC epicenter, at 22 s after the origin time (Event 2; depth, 6.1 km; strike, 23.7°; dip, 76.4°; rake, −94.5°). Seismic moments of Event 1 and Event 2 are 5.88 × 1019 Nm (MW 7.1) and 7.77 × 1019 Nm (MW 7.2), respectively. Total seismic moment is 8.84 × 1019 Nm (MW 7.2). The waveform comparisons for the moment tensor inversion are shown in Figure S2 in the supporting information.

Figure 2.

(a) Mechanism solutions and epicenters (black dots) of Event 1 and Event 2. Gray stars show the NEIC epicenter of the 2012 off-Sanriku and 2011 Tohoku earthquakes. (b) Source time functions of Event 1 and Event 2. (c) Composite mechanism solution of Event 1 and Event 2.

[7] Our mechanism solutions of Event 1 and Event 2 are similar to the USGS body wave moment tensor solution and the NIED CMT solution, respectively (Figures 1 and 2a). The composite mechanism solution of Event 1 and Event 2 is almost the same as the USGS W-phase moment tensor solution (Figures 1 and 2c). The GCMT catalog [http://www.globalcmt.org/] also shows two independent earthquakes: the reverse-fault earthquake of MW 7.2 occurred at 144.09°E, 38.01°N, and 57.8 km depth, and the normal-fault earthquake of MW 7.2 followed 12 s later at 143.83°E, 37.77°N, and 19.5 km depth.

[8] The 2012 off-Sanriku earthquake was a rare event that two M7-class events with opposite focal mechanisms occurred successively with a relatively short time interval. It has been reported that the reverse and normal-fault events occur in the deep and shallow outer-rise regions, respectively [Christensen and Ruff, 1988; Seno and Yamanaka, 1996], but their occurrence are usually interpreted as independent. The 2009 Samoa-Tonga earthquake of MW 8.1 was a doublet of an interplate reverse-fault event and a normal-fault outer-rise event occurred at almost simultaneously and its W-phase solution was also different from the GCMT solution [Beavan et al., 2010; Lay et al., 2010].

3 Finite-Fault Slip Models for Event 1 and Event 2

[9] We now attempt to estimate the slip distributions for Event 1 and Event 2 by using the teleseismic body wave inversion program (http://www.eri.u-tokyo.ac.jp/ETAL/KIKUCHI/). The finite-fault inversion needs an initial mechanism solution. Because the 2012 off-Sanriku event had opposite mechanism solutions for the two subevents, we used a procedure of estimating finite-fault slip model for each subevent by considering it as independent earthquake. The mechanism solutions of the point-source analysis (Section 2) were used as the initial mechanisms. We assumed that the steeply dipping nodal planes were the actual fault planes for the both subevents (orientation of the steep nodal plane is shown in Section 2). For Event 1, we actually tested both planes and found that the steep plane yielded slightly better variance than the shallowly dipping plane (0.587 vs. 0.591 s2). For Event 2, because of the very shallow depth and closeness to the trench axis, the shallowly dipping plane is unlikely to be the fault plane because it would extend across the plate boundary. The point-source location of Event 1 was assumed as the initial rupture point of Event 1. As for Event 2, the epicenter of the point source was used for the initial rupture point with the depth of 10.9 km so that the upper limit of the assumed fault plane coincides the sea bottom depth (about 6.0 km). The same velocity structure of Section 2 was used for the inversions. The rupture velocities of Event 1 and Event 2 were assumed to be 2.9 and 2.7 km/s (about 65% of average S wave velocity at each source depth), respectively. As in the point-source inversion, we also varied the rupture velocity between 65% and 80% of shear wave velocity. For Event 1, the variance changed little (0.58–0.59 s2). For Event 2, smaller rupture velocity (65% of shear wave velocity) yielded smaller variance (0.77 s2) than the larger rupture velocity (0.80 s2 for 80%). The rigidities for Event 1 and Event 2 were assumed 67 GPa and 57 GPa, respectively.

[10] We first estimated the slip distribution of Event 1. We placed 5 × 5 grid points with 10 km spacing along the strike and dip directions on the fault plane (Figure 3). The subfault source time functions were parameterized by five overlapping 1.5 s duration triangles with a 0.75 s separation. The 73 UD components of the P waveforms, the same as Section 2, were used in the inversion. Durations of the waveforms used in the inversion are 120 s from the theoretical P wave arrival times.

Figure 3.

(a) Source time functions and finite-fault slip models for Event 1 and Event 2. Stars show initial rupture points of two events. Contour interval of slip distribution is 0.5 m. (b) (left) Map projection and (right) vertical projections on the cross sections along lines AB and CD in the map. Mechanism solutions in the map are obtained by the teleseismic body wave inversions in this study. Red rectangles show map projections of the fault planes in Figure 3a. Red small letters besides the rectangles indicate upper line of fault planes on Figure 3a. White large star and green/blue small stars in cross sections show the 2012 hypocenter and initial rupture points of Event 1/Event 2, respectively.

[11] The inversion result shows that the slip of Event 1 was concentrated around the initial rupture point, with the maximum and average slips of 2.7 and 0.42 m, respectively (Figure 3a). The average rake value, total rupture duration, and seismic moment were estimated as 77.8°, about 13 s, and 6.41 × 1019 Nm (MW 7.1), respectively. The agreement between the observed and synthetic waveforms is good for the large initial pulses but worse for the later phases, which seem to be originated from Event 2 (Figure S3 in the Supporting Information).

[12] We next estimated the slip distribution of Event 2. We first calculated residual waveforms, i.e., the observed waveforms minus the Event 1 synthetic waveforms, and used them for the inversion (Figure S4 in the Supporting Information). The durations are 90 s beginning 19 s after the P wave arrival times (3 s before the Event 2 occurrence). We placed 9 × 3 grid points with 10 km spacing along the strike and 5 km spacing along the dip direction on the fault plane (Figure 3a). The subfault source time functions were parameterized by six overlapping 1.5 s duration triangles with 0.75 s intervals.

[13] The slip distribution of Event 2 has two large slips at the both side of the initial rupture point (Figure 3a). The maximum and average slips were 4.5 m and 1.33 m, respectively. The rake was slightly variable, with an average value of −89.7°. Total rupture duration and seismic moment were estimated as 24 s and 8.67 × 1019 Nm (MW 7.2), respectively. The agreement between the observed (residual) and synthetic waveforms is not very good at a first glance. Although Event 1 is modeled well, the residual waveforms still include complex phases from Event 1 such as later phases due to the incomplete velocity structure (Figure S5 in the Supporting Information). Unlike the case for Event 1 (Figure S3 in the Supporting Information), in which the first pulses show good match, the largest amplitudes were attempted to match in this inversion. If we focus on the largest peaks, especially at the stations where the amplitudes were large, the agreement is not as bad. The major slip distribution of Event 2 is located beneath the seafloor, similar to those of other outer-rise normal-fault earthquakes, e.g., the 13 January 2007 Kuril event of MW 8.1 [e.g., Lay, et al., 2009] and the 6 July 2011 Kermadec event of MW 7.4 [Todd and Lay, 2013].

4 Earthquake Triggering Due to the Change of Stress Field

4.1 Did Event 1 Trigger Event 2?

[14] In order to examine whether Event 1 triggered Event 2, we calculated static change in ΔCFF caused by Event 1 for Event 2 as a receiver fault.

[15] The ΔCFF is defined as ΔCFF = Δτ − μΔσ, where Δτ is the shear stress changes resolved on a given failure plane (positive value in the fault slip direction), Δσ is the normal stress changes (positive value in the compressive direction), and μ ′ is the apparent coefficient of friction [e.g., Stein et al., 1992; King et al., 1994]. Positive ΔCFF values promote failures and negative ones suppress failures. In calculating ΔCFF, we assumed an elastic half-space [Okada, 1992], an apparent coefficient of friction of 0.4, a rigidity (shear modulus) of 62 GPa, and a Poisson's ratio of 0.25. We also calculated ΔCFF changes in the case of μ′ = 0.0 and 0.8 here and in Section 4.2. The distributions do not change significantly and they support the results of μ′ = 0.4 (Figures S6–S8 in the Supporting Information).

[16] Figure 4 shows that the ΔCFF for Event 2 is positive around the rupture area of Event 2, although ΔCFF in other area is negative or almost zero. The size of positive ΔCFF region is consistent with the rupture size of Event 2. Therefore, we conclude that Event 1 triggered Event 2, or a deep reverse-fault earthquake caused a shallow normal-fault event.

Figure 4.

Horizontal distribution at the depth of 10.9 km and vertical distributions on the cross sections along lines AB and CD of the ΔCFF by Event 1 for Event 2 as a receiver fault. Other symbols are the same as in Figure 3b.

[17] In addition to the triggering mechanism due to static stress change, dynamic stress change by the seismic waves from Event 1 may also affect the occurrence of Event 2 [e.g., Hill et al., 1993; Anderson et al., 1994], because the time difference between Event 1 and Event 2 was only about 20 s. Since the average S wave velocity around source regions is about 4.3 km/s and the distance between rupture areas of Event 1 and Event 2 is about 45 km, the S wave from Event 1 arrives at the source region of Event 2 in approximately 10 s. Thus, the dynamic stress change due to the S wave from Event 1 might also trigger the initial rupture of Event 2.

4.2 Were Both Events Triggered by the 2011 Tohoku Earthquake?

[18] Following a giant or great interplate earthquake, it is common that the normal-fault earthquakes occur in the shallow outer-rise region [e.g., Christensen and Ruff, 1988]. The 2011 Tohoku earthquake produced many normal-fault aftershocks in the shallow outer-rise region, including M7-class events (Figure 1). The occurrence of these aftershocks has been interpreted in terms of ΔCFF by using various fault models of the 2011 earthquake [e.g., Lay et al., 2011; Toda et al., 2011]. However, the interaction between the 2011 Tohoku earthquake and Event 1, or the reverse-fault event in the deep outer rise, has not been revealed yet.

[19] We therefore calculated ΔCFF by the 2011 Tohoku earthquake for Event 1 as a receiver fault. For comparison, we also calculated ΔCFF for Event 2. Since the sources of Event 1 and Event 2 are close to the trench axis, the ΔCFF for both events strongly depend on the slip distribution near the trench of the 2011 Tohoku earthquake fault models. However, various fault models using different data sets, e.g., teleseismic waveforms, near-field strong motion waveforms, tsunami waveforms, or crustal deformation, provide different slip patterns on the plate interface. Yokota et al. [2011] showed that, by resolution tests for various data sets, a fault model estimated from tsunami waveform data provides the best estimation of slip distribution near the trench. We therefore used Satake et al.'s [2013] fault model (Figures 1 and 5) estimated from tsunami waveform data recorded on coastal tide gauges, offshore OBP gauges and GPS buoys. The model has the largest slip (~70 m) close to Event 1 and Event 2 (Figure 5). The upper depths of shallowest subfaults of the Satake et al.'s [2013] fault model were at the seafloor, and we assumed the seafloor depth was 6 km, so we calculated ΔCFF in such a way that seafloor was free surface.

Figure 5.

(a) Horizontal distribution at the depth of 56.1 km and the vertical distributions on the cross sections along lines AB and CD of the ΔCFF for Event 1 by the 2011 finite source model. The other symbols and rectangles are the same as in Figure 3b. (b) Horizontal distribution at the depth of 10.9 km and the vertical distributions of the ΔCFF for Event 2 by the 2011 finite source model.

[20] Figure 5a shows that the horizontal distribution of ΔCFF for Event 1 at the depth of 56.1 km is broadly positive and the largest around the rupture area of Event 1. This is because the 2011 slip was largest near the trench and also at the rupture areas of the 2012 earthquake. The vertical distributions also show that Event 1 occurred in the positive ΔCFF areas. The NEIC hypocenter of 2012 off-Sanriku earthquake is also located in the positive areas. Therefore, we concluded that the 2011 Tohoku earthquake triggered Event 1 or the M7-class reverse-fault earthquake in the deep outer rise.

[21] The ΔCFF distribution for Event 2 in Figure 5b has similar features shown in previous studies [e.g., Lay et al., 2011]. The horizontal ΔCFF distribution at the depth of 10.9 km is entirely positive. The ΔCFF is largest around the rupture area of Event 2 because of the same reason mentioned above. The vertical cross sections in Figure 5b show that the ΔCFF values are significantly high in the shallow outer-rise regions. Thus, it is natural that Event 2, or the normal-fault event, occurred in this region. Static stress change by the 2011 Tohoku earthquake was much larger, nearly two orders of magnitude, than the change by Event 1. Event 2, however, occurred just after Event 1 within the positive ΔCFF area by Event 1 despite the much smaller level of the static change in ΔCFF. It is certain that the occurrence of Event 2 was influenced by stress change due to Event 1. In summary, the 2011 Tohoku earthquake had raised the occurrence possibility of a normal-fault earthquake in this region, and the static (and dynamic) change of stress field by Event 1 gave the coup de grâce to the occurrence of Event 2.

Acknowledgments

[22] The authors thank Takeo Ishibe and two anonymous reviewers for critically reading the manuscript and providing valuable comments. We calculated ΔCFF by using the program coded by Takeshi Kimura based on the subroutine programs developed by Okada [1992]. Figures were generated using generic mapping tools [Wessel and Smith, 1998].

[23] The editor thanks two anonymous reviewers for assistance evaluating this manuscript.

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