The detectability of shallow slow earthquakes by the Dense Oceanfloor Network system for Earthquakes and Tsunamis (DONET) in Tonankai district, Japan
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In order to understand the characteristics of shallow very low-frequency (VLF) events as revealed by recent ocean-floor observation studies, we perform a trial simulation of earthquake cycles in the Tonankai district by taking the characteristics of the 1944 Tonankai earthquake and assuming that slow earthquakes occur on numerous small asperities. Our simulation results show that the increase of moment release rate of shallower VLF events in the pre-seismic stage of a megathrust earthquake is higher than that of deeper VLF events. This increase may make leveling change due to VLF swarms detectable at Dense Oceanfloor Network system for Earthquakes and Tsunamis (DONET). We also introduce the time series of hydraulic pressure data at DONET, comparing with the leveling change expected from our numerical simulation. Since leveling change due to shallower VLF swarms is so local as to be incoherent, removal of the moving-averaged data from the data stacked by four nearby observation points in the same node may be useful to detect the short-term local leveling change.
KeywordsVery low-frequency event Nankai Trough Leveling change Earthquake cycle simulation
As an additional matter concerning the forthcoming megathrust earthquakes along the Nankai Trough, the 2011 M w 9.1 earthquake off the Pacific coast of Tohoku (hereafter, the 2011 Tohoku earthquake) is thought to have ruptured off the coasts of Miyagi, Iwate, Fukushima, and Ibaraki, covering some tsunami source regions of large (M 7–8 class) earthquakes (e.g., Yagi and Fukahata 2011). It is possible that the 2011 Tohoku earthquake may correspond to the recurrence of the 869 Jogan earthquake (e.g., Ozawa et al. 2011), which was followed by the 887 Nin’na earthquake which gave rise to the rupturing of the source regions for both the 1946 M w 8.1 Nankai (Kanamori 1977) and 1944 M w 7.9 Tonankai (Kikuchi et al. 2003) earthquakes (Ishibashi 1999) with probably greater magnitude than the single event of either earthquake. This history of megathrust earthquakes around Japan indicates that the next megathrust earthquake in Tonankai may follow soon after the 2011 Tohoku earthquake and rupture not only Tonankai but also the Tokai and Nankai regions simultaneously with magnitude comparable to the 1707 M 8.7 Hoei earthquake (e.g., Furumura et al. 2011) in some cases.
Since DONET-I is located above the source region of the 1944 Tonankai earthquake (e.g., Kikuchi et al. 2003) as shown in Fig. 1, DONET is expected to detect the arrival of S-waves and tsunami by about several tens of seconds and several minutes earlier than inland- and shore-observation networks, respectively (Kaneda et al. 2009). Delivering seismic and hydraulic pressure data in real time, DONET is also expected to monitor the state of parameters such as seismicity and crustal deformation around a Tonankai earthquake by responding to its pre-seismic change, as observed for the 2011 Tohoku earthquake from inland seismometers (Kato et al. 2012) and bottom-up hydrostatic pressures (Ito et al. 2013), but higher sensitivity observation near the source regions of target earthquakes has been needed.
Owing to recent campaign observations using broadband ocean-bottom seismometers near DONET-I, Sugioka et al. (2012) reported that very low-frequency (VLF) events (Ito et al. 2007) are generated by slip along the plate boundary beneath the sedimentary wedge. This means that VLF events occur in the shallow transition zone of a subduction plate boundary (Schwartz and Rokosky 2007) as well as in the deeper part (Ito et al. 2007). However, it has not yet been well established how shallower VLF events are to change in the pre-seismic stage of the forthcoming Tonankai earthquake.
From a numerical simulation study of the deeper slow earthquakes (Ide et al. 2007), including VLF events, Ariyoshi et al. (2012) pointed out that the recurrence interval becomes shorter and the moment release rate becomes higher in the pre-seismic stage of megathrust earthquakes. As another slip event of the slow earthquake group, slow-slip events (SSE) have been modeled in recent studies, which succeeded in reproducing SSE migration (Shibazaki et al. 2012) and have pointed out that the recurrence interval of SSE also becomes shorter in the pre-seismic stage of megathrust earthquakes (Matsuzawa et al. 2010). However, long-term cycle simulation of shallower slow earthquakes has not yet been modeled.
In this study, we develop the modeling of a subduction plate boundary around the source region of a Tonankai earthquake by modeling shallower slow earthquakes as well as deeper ones around a megathrust earthquake in order to understand the long-term cycle of the shallower slow earthquake from the view of detectability by DONET-I.
Owing to the recent higher performance of CPUs, the modeling of a seismic cycle on a subduction plate boundary in a uniform elastic half-space of three dimensions (3-D) by applying the rate- and state-dependent friction (RSF) law (Dieterich 1979; Ruina 1983) has been successfully developed (e.g., Liu and Rice 2005; Shibazaki et al. 2012; Matsuzawa et al. 2010). Being essentially the same as previous studies, the present method of simulation is customized to fit the model of coexisting megathrust and slow earthquakes (Ariyoshi et al. 2009, 2012) on a bended plate boundary of a subduction zone (e.g., Kato and Hirasawa 1999).
Setting the subduction plate boundary model
Numerical simulation of the subducting plate motion
Frictional parameters for megathrust- and slow-earthquakes
We adopt the concept of slow earthquakes reproduced by Ariyoshi et al. (2012), which explains slow earthquake migration from the viewpoint of interaction among numerous close-set small asperities generating VLF events on the skirt of a greater asperity. In the present study, an asperity is denoted by a region with a – b = γ < 0, following Boatwright and Cocco (1996). The plate interface is demarcated into six parts, as shown in Fig. 2c (1) one large asperity (LA), (2) 120 shallower (small) asperities (SA), (3) 120 deeper (small) asperities (DA) (4) a shallow stable zone, (5) a deep stable zone, and (6) a transition zone (γ ~ +0).
To set the super-hydrostatic pore pressure factor κ(z), we assume that a high pore pressure system exists locally around 30 km depth due to the dehydration derived from facies change in the slab (Kato et al. 2010) and/or permeability contrast at the Moho (Katayama et al. 2012). Ariyoshi et al. (2007a) estimated that the value of κ is 0.1–0.5 for the shallower part (<30 km) and 0.1 for the deeper part (>30 km depth) based on the post-seismic slip propagation speed. The ratio of fluid pressure to normal stress on the plate interface is estimated to be 0.94 near the fault plane of the 2011 Tohoku earthquake by inverting focal mechanisms of earthquakes (Hasegawa et al. 2011), which corresponds to κ ~ 0.1. Katayama et al. (2012) estimated the pore pressure as a function of depth. They show that pore pressure nearly reaches lithostatic pressure locally at the depth of the Moho, with a corresponding age more than ~20 Ma, where the age of the Philippine Sea plate is thought to be 15–30 Ma (Müller et al. 2008).
The constant parameters in the present study are V pl = 4.0 × 10−2 m/year (or 1.3 × 10−9 m/s), G = 30 GPa, β = 3.75 km/s, ρ rock = 2.75 × 103 kg/m3, ρ w = 1.0 × 103 kg/m3, g = 9.8 m/s2, V 0 = 1 μm/s, μ0 = 0.6, and Poisson’s ratio ε = 0.25.
Dependency of model parameters on numerical simulation results
All cells are smaller than the characteristic length scale L b = Gd c /σb (Rubin and Ampuero 2005), which is related to the minimum size of nucleation zones and to the characteristic size of the process zone of propagating transients, including in the frictionally stable region (γ > 0). We check the cell size dependency by making other models with half size (twice finer) calculation cells in SA (or DA). Their characteristics of the simulation results for SA (or DA) is similar to the original model. We uniformly set the initial shear stress at the steady state friction value at a rate of 0.9 V pl, where the value of initial slip velocity is independent of simulation results.
We also perform dozens of trial simulations by changing frictional parameters γ (γ 3: 3.0 to 4.8 [×10−3]), κ (κ 2 and κ 3: 5–15 %) and d c (d c2 and d c3: 0.3–1 mm) so as to generate a megathrust earthquake on the LA and VLF events on both SA and DA, respectively, under the conditions of L b being largely constant. The results of these simulations show qualitatively similar characteristics and will be described in the following sections.
Earthquake cycle simulation results
Characteristics of megathrust earthquakes
Compared with the co-seismic slip distribution of the 1944 Tonankai earthquake shown in Fig. 1, the simulated co-seismic slip distribution in Fig. 3 has a similar peak value (~3.5 m) around (34N, 137E). In addition, the 1944 Tonankai earthquake has a similar magnitude (M w 7.9; Kikuchi et al. (2003)) and its recurrence interval is about 100–150 years (e.g., Ishibashi 1981). From these results, we consider this simulated megathrust earthquake as the likely scenario for a future Tonankai earthquake in order to investigate the characteristics of slow earthquakes for the long-term period of the megathrust earthquake cycle.
Similarities and differences between shallower and deeper slow earthquakes
In the pre-seismic stage of the simulated megathrust earthquake, Fig. 5b shows that the strongly sticking area fades away from the SA belt due to a partial weakening of coupling around the LA. Strictly speaking, the velocity field in the SA belt appears higher than in the DA belt (indicated by the warmer color in Fig. 5b). This suggests that the stress field promoting thrust-type slip driven by the pre-seismic slip of megathrust earthquakes has a more positive effect on the SA belt than on the DA belt, which causes slow earthquakes in the SA belt and a more active and higher moment release rate than that in the DA belt as shown in Fig. 4. That is, the SA belt near the free surface is more sensitive to the stress field caused by slip around the LA belt than the DA belt.
Crustal deformation due to shallower slow earthquake swarms
Long-term crustal deformation
Figure 6 shows the difference between science nodes (A–E in Fig. 1b); long-term (longer than several years) leveling change and temporal acceleration of the uplift at nodes closer to the LA (e.g., A- and E-nodes) is greater than that at nodes closer to the trench (e.g., C-node) mainly because of the shorter distance from LA where pre-seismic slip occurs around there as shown in Fig. 5b.
The node closer to the LA shows greater difference among leveling observation points in the same node (e.g., difference between E-18 and E-20 in Fig. 1b) than that closer to trench (e.g., C-9 and C-12), which is more significant after the time indicated by broken lines in Fig. 6. This is because the difference of distance from LA to leveling observation points in the same node closer to the trench (e.g., differential of distance between <C-9 to LA> and <C-12 to LA>) is relatively smaller than that in a node closer to the LA (e.g., differential between <E-18 to LA> and <E-20 to LA>).
In Fig. 5, the gray-colored DONET-I array shows the crustal deformation of the horizontal component magnified 50,000 times for 2.5 years in the inter-seismic (Fig. 5a; almost overlapped with red-colored DONET-I array) and pre-seismic (Fig. 5b) stages of the simulated Tonankai earthquake. From Fig. 5, we find that the horizontal deformation at DONET-I appears too small to be detected for all nodes in the inter-seismic stage of the simulated Tonankai earthquake (Fig. 5a), but is significantly greater for all nodes in the pre-seismic stage. In addition, the difference of horizontal deformation among observation points in the same node for the node closer to the LA (e.g., the difference of horizontal deformation between E-18 and E-20) tends to be greater than that for the node closer to the trench (e.g., the difference between C-9 and C-12), which is similar to the characteristics of leveling change as mentioned above in the pre-seismic stage. These results suggest that seafloor geodetic measurements using the GPS/acoustic technique (e.g., Kido et al. 2006) with electric power supply from DONET may be helpful in continuously monitoring long-term crustal deformation due to pre-seismic slip of a future Tonankai earthquake.
These characteristics are common to both Coffin and Bird models. Since the Bird model has a shorter distance from the LA to the observational points than the Coffin model, crustal deformation in the Bird model tends to be greater than in the Coffin model. This result suggests that precise determination of the subduction plate structure plays an important role on quantitatively evaluating the crustal deformation on the ocean-floor observation points.
Short-term leveling change accompanied by slow earthquake swarms
For E-node, Fig. 6 shows short-term (shorter than several days) leveling change due to slow earthquake swarms appears significantly for both Coffin and Bird models. However, its characteristics are different between the two models. In B-node, short-term leveling change appears significantly only for the Bird model (B-8), while it only appears in A-node (A-2, A-3 and A-4) for the Coffin model. These results mean that the crustal deformation is so localized because of the short distance between the sources of the slow earthquake swarms and the receivers of DONET-I, which requires a denser network around the epicenters of shallower slow earthquakes when we detect them by stacking data of the short-term leveling change.
On the points of E-17 and E-18, the short-term leveling change is uplift for the Coffin model while depression for the Bird model. These differences can be generally explained on the basis of dislocation theory in case of dip slip on a buried fault (e.g., Segall 2010), where vertical displacement on the free surface is uplift with relatively steep slope around the updip edge of a fault and depression with relatively slight slope around the downdip edge of a fault. In case of the Coffin model as shown in Fig. 2b, E-17 and E-18 are located on the updip part of SA while E-19 and E-20 (but no significant change because of too far from the SA belt) on the downdip part of SA belt, while all of observation points for E-node are on the downdip part in case of the Bird model as shown in Fig. 2a, which is consistent with the theoretical analysis.
Therefore, precise determination of slow earthquake hypocenters and trench location is very important to estimate the short-term leveling change at DONET in advance from numerical simulations.
For nodes responding significantly to slow earthquake swarms in Fig. 6, the rate of leveling change tends to be higher toward the origin of the simulated Tonankai earthquake. In the pre-seismic stage of a megathrust earthquake, the moment release rate of slow earthquakes, which is expected to be proportional to slip velocity averaged in SA or DA under the condition of fixed fault area, becomes higher as shown in Fig. 4a due to pre-seismic slip around the LA (Ariyoshi et al. 2012), which explains the higher rate of leveling change. The ability of DONET to detect the short-term leveling change in the pre-seismic stage of a future Tonankai earthquake will be discussed in the next section.
Detectability of shallower slow earthquakes by DONET
In order to detect leveling change by hydraulic pressure gauges, it is necessary to remove noise and drift components from raw data. From previous long-term seafloor measurements of Paroscientific pressure gauge (e.g., Polster et al. 2009) which is used for DONET, the estimated noise level is about 10–20 Pa, and drift rate is about 5–10 kPa/year with a time constant of about 50–200 days. Figure 6 illustrates the long-term leveling change at DONET-I; the rate of the long-term leveling change is shown to be about 10 (C-node)–100 (A, E-nodes) Pa/year, which is lower than the estimated drift component. Figure 6 also shows the time constant of long-term leveling change is significantly longer than 1 year. These results mean that we can estimate the drift component by subtracting crustal deformation calculated in Fig. 6 if our simulation results can reproduce pre-seismic slip quantitatively, while it may be difficult for us to extract the long-term crustal deformation from hydraulic pressure gauge data at a single point of DONET-I if our simulation results explain crustal deformation just qualitatively. Since the trend of long-term change in all nodes is uplift, stacking data in the same node and/or combination of several nodes, which should be removed the sensor drift and noise components individually for each hydraulic pressure gauge, may be helpful to detect the long-term crustal deformation.
Focusing on the differential data in Fig. 8, we find that its fluctuation is about several tens of Pa (several millimeters for leveling change), which is comparable to the leveling amount of short-term change as shown at E-17 of the Coffin model in Fig. 7 (about 2 mm: 20 Pa). From Fig. 7, we see that the short-term leveling change is incoherent in the same node. Supposing that a hydraulic pressure gauge responding to shallower VLF swarms at only one observation point in a node as seen for E-17 of the Coffin model in Fig. 7 for simplicity, the differential data is expected to contain three quarters of its value (15 Pa in case of 20 Pa at E-17 in Fig. 7 when the change at E-20 is negligible). This estimation suggests that short-term local leveling change driven by shallower VLF swarms might be buried by the fluctuation in the case of using only hydraulic pressure gauges.
As shown in Fig. 8, we now have a continued daily solution of hydraulic pressure gauge data as a simple test run by using a moving average from 100 Hz sampling data in a 6 h time-interval. Since some VLF events may have a duration time shorter than 1 s as shown at E-17 in Fig. 7, in the future we have to enhance the sampling of the differential data from daily to higher than 1 Hz to detect the temporal and local leveling change due to shallower VLF swarms. In the hydraulic pressure gauges of DONET, water temperature gauges are also installed, which helps us to reduce the noise component in both the stack and differential data by temperature correction (Inazu and Hino 2011).
DONET has broad-band seismometers buried in the ocean floor at nearly the same location as the hydraulic pressure gauges (Nakano et al. 2013a, b), which enable us to estimate the fault parameters of shallow VLF events. Since the dip angle of the basal plane of the overriding wedge (décollement) is steeper than that of oceanic plate near the trench (e.g., Ikari and Saffer 2012), shallow VLF events on a décollement (Sugioka et al. 2012) or on mega-splay faults (Ito and Obara 2006) are expected to cause a leveling change higher than our simulation results (Fig. 7) in the case of a dip angle of a VLF event significantly steeper than 5°. When we also use the origin time and hypocenter location of a VLF event automatically detected by seismometers, the accuracy of detecting VLF events on the basis of leveling change of DONET is expected to become higher.
The case of a Tonankai earthquake triggered by Tokai/Nankai earthquakes
As mentioned in section “Setting the subduction plate boundary model”, we adopt a periodic boundary condition along the strike direction to take nearby megathrust earthquakes and slow earthquake migration in the Tokai and Nankai regions into account. This condition means that a Tokai and Nankai earthquake occurs simultaneously with a Tonankai earthquake. However, the actual earthquake generation cycle along the Nankai-Suruga trough is thought to be complicated. There are numerous examples of this complicated generation cycle (e.g., Ishibashi 1981). The 1096 Eicho earthquake is thought to have ruptured at least the Tonankai area and possibly the western part of the Tokai area, which was followed by the 1099 Kowa earthquake rupturing the Nankai area. The 1498 Meio earthquake is thought to have ruptured at least the Tokai and Tonankai areas and possibly the eastern part of the Nankai area. The 1707 Hoei earthquake is thought to have ruptured almost the whole extent of the source segments including the Tokai, Tonankai and Nankai areas. The 1854 Ansei earthquake is thought to have simultaneously ruptured the Tokai and Tonankai areas, then the Nankai area 30 h after. The 1946 Nankai earthquake occurred 2 years after the 1944 Tonankai earthquake. As mentioned above, those previous studies (e.g., Ishibashi 1981) on these historical earthquakes along the Nankai Trough suggest that the Tonankai earthquakes have occurred with a time-lag between a Tokai or Nankai earthquake or almost simultaneously. In this section, we discuss the case of a Tonankai earthquake triggered by Tokai and Nankai earthquakes.
From numerical simulations of earthquake cycles on a subduction plate boundary, the propagation speed of post-seismic slip is higher in the shallower part when effective normal stress is proportional to the depth (Ariyoshi et al. 2007a, b). Applying this simulation result to historical earthquakes along the Nankai Trough, we interpret that the rupture initiation of the 1946 Nankai earthquake was located on the southeastern edge of the source region (e.g., Kanamori 1972) and was triggered by post-seismic slip of the 1944 Tokai earthquake propagating westward from the shallower part of the subduction plate boundary. In another numerical simulation similarly based on RSF law, Hyodo and Hori (2010) reproduced a complex cycle of Nankai earthquakes following the Tonankai earthquakes 4.9–457 days after, where all of the rupture initiations were from a similar location to the 1946 Nankai earthquake. This means that the 1854 Ansei earthquake may also have ruptured from the southeastern edge of the Nankai area. From these results, if the next Tonankai (or Nankai) earthquake is triggered by a Nankai (or Tonankai) earthquake, the post-seismic slip of the preceding megathrust earthquake will propagate in the shallower part of the transition zone between Tonankai and Nankai earthquakes.
Compared with a single event, slip amount in a seismogenic segment increases in each of the co-, pre- and post-seismic stages when an earthquake occurs shortly after another earthquake in a nearby seismogenic segment (Ariyoshi et al. 2009). This means that Nankai earthquakes following Tonankai earthquakes with a short time delay have pre-seismic slip greater than that that of a single event. Since DONET-I and DONET-II are located on the southwestern part of the simulated Tonankai earthquake and near the southeastern edge of the Nankai earthquake zones, crustal deformation, including leveling change due to pre-seismic slip, may become detectable in the case of there being a short time delay from the initiation of a nearby megathrust earthquake.
In this study, taking advantage of an FFT algorithm, we assume a subduction plate boundary bended only along the dip direction (2.5-Dimension) so as to perform multi-scale (LA and SA) earthquake cycle simulation by discretizing at most about one million calculation cells, which is very difficult for a 3-D subduction plate boundary model (e.g., Hyodo and Hori 2010) because of the huge calculation cost without using FFT. Since crustal deformation at DONET is sensitive to the shape and location of the subduction plate boundary, it is a our future study aim to develop a large-scale numerical simulation of megathrust- and slow-earthquake cycles on a 3-D subduction plate boundary based on structural surveys (e.g., Nakanishi et al. 2008).
Since leveling change due to slow earthquakes at DONET is expected to be local and incoherent in the same node because of the short distance between their sources and the (DONET) receiver, it is useful to remove an average from original data in the same node in order to extract a signal.
In the pre-seismic stage of megathrust earthquakes, the crustal deformation rate driven by slow earthquakes tends to become higher, which is greater for the shallower VLF events than that for deeper ones. This means that a combination of seismometers to decide origin time and hydraulic pressure gauges to estimate leveling change may be a helpful tool to robustly detect crustal deformation.
If the next Nankai/Tonankai earthquake also follows the nearby Tonankai/Nankai earthquake with a short time delay such as the 1854 Ansei earthquake, the detectable crustal deformation at DONET is expected to become more predominant due to larger pre-seismic slip of the Nankai/Tonankai earthquake. This temporal change would help us to judge the possibility of triggering nearby megathrust earthquakes in advance.
The authors would like to thank H. Matsumoto for discussion about the evaluation of the noise component in hydraulic pressure. Two anonymous reviewers helped us to improve the manuscript in a better readable way. The present study used the Earth Simulator and the supercomputing resources at the Cyberscience Center of Tohoku University. GMT software (Wessel and Smith 1998) was used to draw a number of the figures. Hydraulic pressure data shown in Fig. 8 was conducted by the DONET program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT). This study was partly supported by MEXT for Young Scientists (B), 23710212, 2013 and for Geofluids program.
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