Ariyoshi et al. Earth, Planets and Space 2014, 66:55 http://www.earth-planets-space.com/content/66/1/55 FULL PAPER Open Access A trial derivation of seismic plate coupling by focusing on the activity of shallow slow earthquakes Keisuke Ariyoshi1*, Toru Matsuzawa2, Ryota Hino3, Akira Hasegawa2, Takane Hori1, Ryoko Nakata1 and Yoshiyuki Kaneda1,4 Abstract To understand the effect of plate coupling on very low-frequency event (VLFE) activity resulting from megathrust earthquakes, we performed long-term multiscale earthquake cycle simulations (including a megathrust earthquake and slow earthquakes) on a 3-D subduction plate boundary model, based on a rate- and state-dependent friction law. Our simulation suggests that quiescence of shallow VLFEs off Miyagi may be explained by the location in the shallow central part of the 2011 Tohoku earthquake because of the locally strong coupling, while observed activation of VLFEs off Iwate (northern part of Tohoku district), Fukushima (southern part of Tohoku district), and Ibaraki (northern part of Kanto district) is explained by the location on the outer rim. The area and duration of the quiescence off Miyagi may be a new clue to evaluate the potential for plate coupling strong enough to cause the next megathrust earthquake. Keywords: Subduction plate boundary; Megathrust earthquake; Rate- and state-dependent friction law; Superhydrostatic pressure Background migrated for long distances along the strike direction in Broadband seafloor seismometers near the trench the down-dip range of the seismogenic zone for the (Sugioka et al. 2012) and dense inland networks of highly Nankai Trough (Obara and Sekine 2009), southwestern sensitive seismic stations (Matsuzawa et al. 2012) have en- Japan, and around the up-dip range off Tokachi (e.g., abled observation of very low-frequency earthquakes NIED 2014), southern Hokkaido. The reasons for the (VLFEs; Ito et al. 2007) in the shallow transition zone near differences in the location and activity of the VLFEs are the trench of subduction plate boundaries (Schwartz and not yet understood. Rokosky 2007) as well as a deep low-frequency earthquake From numerical simulations of VLFEs on the basis of a (at a depth about 30 km) (Obara and Sekine 2009). VLFEs rate- and state-dependent friction (RSF) law (Dieterich are thought to be of a slow earthquake group with a con- 1979; Ruina 1983) derived from rock laboratory experi- stant moment rate function (Ide et al. 2007). ments, Ariyoshi et al. (2012) pointed out that the recur- After the 2011 Tohoku earthquake (e.g., Yagi and rence interval of VLFEs decreases and the moment release Fukahata 2011), northeastern Japan (see Figure 1), rate increases during the preseismic stage of megathrust Matsuzawa et al. (2012) reported that shallow VLFEs be- earthquakes. Slow-slip events (SSEs), another type of slow came active locally off the Iwate, Fukushima, and Ibaraki earthquake with longer duration than VLFE, have also regions but were inactive off Miyagi. In addition, shallow been modeled in recent studies, which have succeeded in VLFEs seemed to occur in isolation there, while VLFEs reproducing SSE migration (Shibazaki and Shimamoto 2007) and have shown that the recurrence interval of SSEs also decreases during the preseismic stage of megathrust * Correspondence: [email protected] 1Research and Development Center for Earthquake and Tsunami, Japan earthquakes (Matsuzawa et al. 2010). Agency for Marine-Earth Science and Technology, Yokohama 236-0001, These simulation results could not directly explain Japan why the VLFEs were inactive off Miyagi, when large Full list of author information is available at the end of the article © 2014 Ariyoshi et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Ariyoshi et al. Earth, Planets and Space 2014, 66:55 Page 2 of 11 http://www.earth-planets-space.com/content/66/1/55 (a)WCM (b)SCM Seismic slip (m) 0 1 2 3 3.44 5 5.3 0 22 44 66 74 17 35 52 70 87 93 Seismic coupling (%) for weak/strong coupling model Figure 1 Subduction plate boundary model. (a) A 3-D view of a subduction plate boundary model with frictional parameter γ = a − b. (b) Frictional parameters (a, γ, dc) and the superhydrostatic pore pressure factor κ as functions of distance along the dip direction from the surface, −3 strong weak strong weak −3 where (a1, a2) = (2, 5) [×10 ], (γ1, γ2, γ3 , γ3 , γ4) = (0.7, 0.01, −0.98 , −0.3 , 4.9) [×10 ], (dc1, dc2, dc3, dc4) = (10, 0.3, 0.4, 400) [mm], and (κ1, κ2, κ3) = (1.0, 0.07, 0.13). Half the length of the minor axis (along the dip) of the elliptical asperity takes the following values: for the large asperity (LA), (R1, R2, R3) = (30, 33, 35) [km], and for the shallow small asperities (SA), (r1, r2, r3) = (2, 2.25, 2.5) [km], where the aspect ratios for the LA and SA are 1.25 and 1.5, respectively. The distances between the central points of the SA along the strike and dip direction are 2 and 2.5 km, respectively. The values of the frictional parameters and κ are based on rock laboratory results (e.g., Blanpied et al. 1998) and observational results (Ariyoshi et al. 2007), respectively. (c) Depth of plate interface drawn by B-spline curve with 16 fixed points: (ξ, φ) = (0, 4), (10, 4), (30, 5), (50, 5), (53, 8), (67, 8), (70, 8), (90, 8), (120, 10), (140, 12), (160, 17), (168, 22), (182, 22), (190, 22), (200, 22), (215, 27), where ξ and φ are distances along the dip direction from the surface and dip angle (in degrees), respectively. postseismic slip occurs around megathrust earthquakes, boundary is described by a quasi-dynamic equilibrium which is thought to promote VLFEs. Another question is (e.g., Rice 1993) between the shear stress (due to reverse whether the local difference in the shallow VLFE activity dip slip on the discretized faults) and the frictional stress off Tohoku may be partly explained by the inhomogeneity based on an RSF law. It is well known that RSF laws can of the frictional properties (Matsuzawa et al. 2012). This represent asperity models (Lay et al. 1982; Scholz 1990), seems to be inconsistent with VLFE migration at depth, if where an asperity is an area on a stuck fault. An earth- the frictional property in the shallower part of the transi- quake rupture usually begins at an asperity because of tion zone is largely homogenous along the strike direction friction gap. From the various friction laws available, we in the same way as the deeper earthquake (e.g., Schwartz adopted the aging (or slowness) law, which enabled us and Rokosky 2007), in which the VLFE migrates for long to reproduce slow earthquakes under the condition of distances (Obara and Sekine 2009). This is because VLFE weak frictional instability, which was relatively easier migration can be easily reproduced when the frictional than the slip law, as pointed out by Ampuero and Rubin properties are homogenous or weakly inhomogeneous (2008). The details are described later. along the strike direction, as shown in numerical simula- To perform multiscale earthquake cycle simulations, tions (e.g., Ariyoshi et al. 2009; Shibazaki and Shimamoto we assumed a single large asperity and numerous small 2007). The stress shadow effect, which is the relationship asperities arranged along the strike direction, as shown of present observations of low seismicity rates with the by the blue patches (γ = a − b < 0) in Figure 2, where a occurrence of past large earthquakes in major asperities and b are frictional parameters and γ < 0 means velocity (e.g., Maccaferri et al. 2013), may be another factor of weakening (Ruina 1983). In our model, a large asperity VLFE localization. Previous studies have not investigated generates megathrust earthquakes and a chain reaction this effect. of numerous small asperities generates a migration of In this study, we perform numerical simulations of slow earthquakes along the strike direction (Ariyoshi multiscale earthquake cycles, including a megathrust et al. 2009). The difference of slip behavior between the earthquake and VLFEs, on a three-dimensional subduc- regular earthquake (including the megathrust earth- tion plate boundary with high spatiotemporal resolution quake) and slow earthquakes is explained by asperity to understand the change in activity of VLFEs after size r or R (hereafter, we represent it as L) relative to nu- megathrust earthquakes. cleation size, where r and R are half the length of the minor axis (along the dip) of the elliptical large and Methods small asperities in Figure 2, respectively. For the aging Outline of modeling slow earthquakes under different law, a slip event does not occur in the asperity but plate coupling conditions creeps at a steady rate for L < Lmin. A slow earthquake The numerical simulation employed in the present study occurs for Lmin < L < L∞, and a regular earthquake occurs is similar to that described by Ariyoshi et al. (2013). In for L∞ < L, where asymptotic nucleation half-length 2 our study, the motion equation for a subduction plate L∞ = ηGbdc/σγ and minimum nucleation half-length Ariyoshi et al. Earth, Planets and Space 2014, 66:55 Page 3 of 11 http://www.earth-planets-space.com/content/66/1/55 (a) (c) log10 (V/Vpl) −6.0 −4.0 −3.0 −2.0 −1.0 −0.3 0.3 1.0 2.0 3.0 7.0 10.0 (b) (d) Figure 2 Slip isograms (0.5-m increments) of the simulated megathrust earthquakes.