Are the frictional properties of creeping faults persistent? Evidence from rapid afterslip following the 2011 Tohoku-oki earthquake

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 4, 6 67, doi:./grl.57, Are the frictional properties of creeping faults persistent? Evidence from rapid afterslip following the Tohoku-oki earthquake Jun ichi Fukuda, Aitaro Kato, Naoyuki Kato, and Yosuke Aoki Received May ; revised July ; accepted July ; published July. [] Geophysical observations and numerical studies have shown that creeping portions of faults have persistent ratestrengthening frictional properties and can act as barriers to earthquake rupture propagation. On the basis of GPS data following the M W 9. Tohoku-oki earthquake in Japan, we find that the evolution of afterslip and postseismic shear stress on the plate interface is inconsistent with persistent rate-strengthening frictional properties but is consistent with slip-rate-dependent frictional properties that exhibit less rate-strengthening with increasing slip rate. Such sliprate-dependent frictional properties tend to prevent creeping regions from acting as barriers to rupture propagation and therefore could be an important factor in determining the spatial extent of individual earthquakes. Citation: Fukuda, J., A. Kato, N. Kato, and Y. Aoki (), Are the frictional properties of creeping faults persistent? Evidence from rapid afterslip following the Tohoku-oki earthquake, Geophys. Res. Lett., 4, 6 67, doi:./grl.57.. Introduction [] Geodetic and seismic observations have documented spatial and temporal variations in seismic and aseismic slip on plate boundary faults, and observed slip behaviors have been interpreted to result from the spatially heterogeneous distribution of fault frictional properties in terms of the ratestate friction law [Boatwright and Cocco, 996; Scholz, 998; Kaneko et al., ]. In this framework, the steady state frictional shear stress ss on a fault is expressed as follows [Scholz, 998]: V ss = +(a b) eff ln () where V is the slip rate, a b is a friction parameter that represents the rate dependence of friction, eff is the effective normal stress, V is a reference slip rate, and is the steady state shear stress at V. For positive and negative (a b) eff, ss exhibits rate strengthening (RS) and rate weakening (RW), respectively [Scholz, 998]. In widely employed models of slip on a plate boundary fault, the plate interface consists of unstable RW patches surrounded by stable RS areas [Boatwright and Cocco, 996; Kaneko et al., ]. RW patches are the sites of repeated earthquakes, Additional supporting information may be found in the online version of this article. Earthquake Research Institute, University of Tokyo, Tokyo, Japan. Corresponding author: J. Fukuda, Earthquake Research Institute, University of Tokyo, -- Yayoi, Bunkyo-ku, Tokyo -, Japan. (jfukuda@eri.u-tokyo.ac.jp). American Geophysical Union. All Rights Reserved //./grl.57 V whereas RS regions are characterized by aseismic creep. Stress changes due to earthquakes on RW patches trigger aseismic afterslip in RS regions adjacent to the earthquake ruptures. The spatial and temporal evolution of afterslip inferred from geodetic data has been shown to be consistent with the predictions of such models [Perfettini and Avouac, 4; Miyazaki et al., 4; Hsu et al., 6; Perfettini et al., ]. [] RS regions can act as barriers to earthquake rupture propagation [Kaneko et al., ]. An earthquake that initiates in a RW patch can propagate into surrounding RS regions where it is arrested if the RS property is sufficiently strong (i.e., large positive (a b) eff ) relative to the stress perturbations arising from the earthquake. Otherwise, the earthquake can propagate through the RS regions and trigger seismic slip on neighboring RW patches. This indicates that the degree of RS in stable regions is an important factor in determining the spatial extent of individual earthquakes [Kaneko et al., ]. [4] Geodetic observations of afterslip afford the opportunity to explore the distribution of (a b) eff in RS regions and have shown that (a b) eff is spatially variable but does not dynamically vary with time during afterslip [Perfettini and Avouac, 4; Miyazaki et al., 4; Hsu et al., 6; Perfettini et al., ]. In addition, many numerical studies have assumed that the spatial distribution of (a b) eff in RS regions is a persistent property [Boatwright and Cocco, 996; Kaneko et al., ]. In contrast, several experimental and numerical studies have shown that portions of a fault that exhibit RS behavior at low slip rates can become less RS with increasing slip rate and can eventually become RW at higher slip rates due to several mechanisms [e.g., Reinen et al., 99; Shibazaki et al., ; Noda and Lapusta, ] including thermal weakening [Noda and Lapusta, ]. This nonpersistent nature of frictional properties in RS regions has a significant influence on the spatial extent of individual earthquakes [Shibazaki et al., ; Noda and Lapusta, ]; however, the frictional behavior of RS regions upon real faults has not been quantified for a wide range of slip rates. [5] The March M W 9. Tohoku-oki megathrust earthquake is the largest event worldwide whose early postseismic deformation was continuously recorded by a dense network of GPS receivers. Furthermore, this earthquake produced large stress changes in broad regions surrounding the coseismic rupture and thus provides an unprecedented opportunity to investigate the frictional behavior of RS regions on a real fault for a wide range of slip rates. In this study, we investigate the frictional behavior of afterslip areas using an inversion of postseismic GPS data after the Tohoku-oki earthquake. 6

2 // / mm/yr Figure. Map of cumulative afterslip for the period between the main shock and 7 October (color scale). Solid magenta line denotes the outer edge of the large slip zone of the main shock inferred from aftershock data [Kato and Igarashi, ]. Solid red line indicates the Japan Trench. Dashed gray lines denote isodepth contours of the upper surface of the Pacific plate at km intervals [Nakajima and Hasegawa, 6]. Yellow star denotes the epicenter of the main shock. Thick arrow shows the relative motion of the Pacific plate with respect to the North American plate [Sella et al., ]. Solid circles represent points where slip rate, slip, and shear stress histories are shown in Figures b,, and. Temporal variation in slip rate at points in Figure a.. Inversion [6] To estimate the spatial and temporal evolution of afterslip, we use daily coordinate time series from 49 stations of a continuous GPS network in northeastern Japan from March to 7 October (Text S in the supporting information). Coseismic displacements due to 54 aftershocks with M.5 are estimated and removed from the GPS time series (Text S and Figures S and S). [7] We assume that the corrected postseismic deformation during the first 7 months following the main shock was due to afterslip on the subducting plate interface, following Ozawa et al. []. The curved plate interface is modeled as a collection of triangular dislocation elements in a homogeneous elastic half-space [Thomas, 99] which tessellate a model of the plate interface geometry [Nakajima and Hasegawa, 6] (Figure S). We apply a time-dependent inversion method [Fukuda et al., 8] to the corrected GPS time series to estimate the spatial and temporal evolution of daily cumulative afterslip and afterslip rate on the model plate interface (Text S). [8] The estimated cumulative afterslip during the first 7 months following the main shock is concentrated downdip of the area of large coseismic slip (Figure a). The estimated evolution of afterslip shows that slip decelerates with time and that the locations of areas of large slip do not change significantly with time (Figure S5). This spatial and temporal evolution is similar to that described previously [Ozawa et al., ]. The maximum slip rate exceeds m/yr immediately after the main shock and is greater than m/yr during the first 5 days following the main shock (Figure b). The maximum slip rate immediately after the main shock is an order of magnitude or more higher than that for afterslip following the M W 8. Tokachi-oki earthquake (7 m/yr) [Miyazaki et al., 4] and the 5 M W 8.7 Nias earthquake (6 m/yr) [Hsu et al., 6]. Thus, the afterslip pattern following the Tohoku-oki earthquake enables us to study frictional behavior for higher slip rates than those considered previously [Perfettini and Avouac, 4; Miyazaki et al., 4; Hsu et al., 6; Perfettini et al., ].. Fault Frictional Properties [9] Previous studies have shown that the evolution of afterslip is consistent with steady state RS friction (equation ()) with a positive and constant (a b) eff. Following the Tokachi-oki and 5 Nias earthquakes, afterslip-related shear stress changes in afterslip areas evolved approximately linearly with the logarithm of slip rate, suggesting that afterslip is governed by steady state RS friction with constant (a b) eff [Miyazaki et al., 4; Hsu et al., 6]. The use of a spring-slider model that employs steady state RS friction with constant (a b) eff gives the following slip evolution with time t in response to a shear stress step at t =[Perfettini and Avouac, 4]: s(t) = (a b) eff k ln + V+ (e t/tc ) V pl where k is the spring stiffness, V + is the initial slip rate immediately after the stress step, V pl is the load point velocity, which is taken as the plate velocity [Hsu et al., 6; Perfettini et al., ], and t c is the characteristic decay time given by t c =(a b) eff /kv pl. Equation () successfully reproduces the temporal evolution of afterslip and postseismic deformation following many large earthquakes [Perfettini and Avouac, 4; Hsu et al., 6; Perfettini et al., ], () 64

3 (c).5 Inverted afterslip Fit of eq () during the first 5 days Fit of eq () after the 5st day (d) Moment (Nm) x 5 5 Figure. (a c) Comparison between inverted afterslip and the model of RS afterslip with constant (a b) eff (equation ()) for selected points on the plate interface (points in Figure a, respectively). Blue circles represent the inverted cumulative afterslip. Red and green curves represent the best fit of equation () to the inverted afterslip time series during the first 5 days following the main shock and to the time series after the 5st day following the main shock, respectively. (d) Same as Figures a c but for the moment of afterslip. again suggesting that afterslip is governed by steady state RS friction with constant (a b) eff. [] We fit equation () to the time series of cumulative afterslip obtained from the inversion by estimating (a b) eff /k and V + (Text S), revealing that equation () does not reproduce the time series of afterslip (Figures a c). A set of parameters that provides the best fit to afterslip during the first 5 days following the main shock significantly underpredicts the subsequent slip, whereas another set of parameters that best fits the slip time series after the 5st day following the main shock does not reproduce the rapid early afterslip in the first month (Figures a c). Similarly, equation () does not reproduce the time series of the afterslip moment (Figure d and Text S), indicating that the misfit between the inverted slip history and equation () is a robust feature. This result suggests that the temporal evolution of afterslip is inconsistent with steady state RS friction with constant (a b) eff. [] We next compute the spatial and temporal evolution of shear stress changes on the plate interface due to afterslip, using the inverted slip history [Thomas, 99]. The steady state RS friction (equation ()) with constant (a b) eff predicts a positive linear relation between shear stress and the logarithm of slip rate. However, in contrast to this prediction, shear stress changes plotted as a function of the logarithm of slip rate exhibit convex upward curves (Figure a), which is again inconsistent with steady state RS friction with constant (a b) eff. [] If afterslip is governed by steady state RS friction (equation ()), (a b) eff is given by d ss /d ln V, i.e., the slope of the stress-log(slip rate) curve. Thus, the stresslog(slip rate) curves (Figure a) suggest that (a b) eff is not a constant but is dependent on slip rate. We therefore determine (a b) eff as a function of slip rate by fitting a quadratic function to each stress-log(slip rate) curve and calculating the slope of the function (Figures S6 and b). We then calculate the afterslip as a function of time assuming a spring-slider model by solving equation () together with a quasi-static force balance equation given by d ss /dt = k(v pl V ) with the initial condition V(t =)=V +,where we use the rate-dependent (a b) eff determined from the stress-log(slip rate) curves (Figure b). We fit this model to the time series of cumulative afterslip by adjusting V + and k. The predicted afterslip histories perform well in reproducing the inverted slip histories (Figures d f). In addition, the stress-log(slip rate) relations from the afterslip model exhibit convex upward patterns similar to those from the inversion (Figure c). Thus, the model of afterslip with the rate-dependent (a b) eff successfully reproduces both the temporal evolution of afterslip and the convex upward stress-log(slip rate) relations that cannot be reconciled with the model with constant (a b) eff. [] As opposed to our results, Ozawa et al. [] argued that the model with constant (a b) eff (equation ()) can perform well in fitting time series of afterslip moment if the loading velocity V pl is adjusted as an unknown and 65

4 (d).5 Shear stress change (MPa) (c) Shear stress change (MPa) (e) (f) Figure. Shear stress change, in the same direction as the relative motion of the overriding plate with respect to the subducting plate, due to afterslip as a function of slip rate at selected points on the plate interface (points in Figure a). Slip-rate-dependent (a b) eff at points estimated from the stress-log(slip rate) curves shown in Figure a. (c) Shear stress change as a function of slip rate at points predicted from the model with rate-dependent (a b) eff shown in Figure b. (d f) Comparison between the inverted afterslip (blue circles) and the predicted afterslip from the model with rate-dependent (a b) eff shown in Figure b (red curves) for points, respectively. concluded that the evolution of afterslip is governed by the steady state RS friction (equation ()) with constant (a b) eff. However, we find that V pl must be significantly greater than the plate velocity (.84 m/yr [Sella et al., ]) to fit the afterslip and moment time series (V pl =..5m/yr for afterslip and V pl '.4 m/yr for moment). Furthermore, even if V pl is large enough to fit the afterslip time series, the steady state RS friction with constant (a b) eff does not predict the convex upward stress-log(slip rate) relations derived from the inversion (Figure a). We therefore conclude that the evolution of afterslip is inconsistent with a constant (a b) eff. [4] The estimated values of (a b) eff for slip rates lower than m/yr are on the order of. MPa (Figure b). These values are comparable with values of (a b) eff estimated from afterslip following previous M W 8.7 earthquakes with slip rates lower than m/yr [Perfettini and Avouac, 4; Miyazaki et al., 4; Hsu et al., 6; Perfettini et al., ]. For slip rates between and m/yr, the estimated values of (a b) eff are on the order of. MPa (Figure b), an order of magnitude smaller than previous estimates for lower slip rates. The rate dependence of (a b) eff is qualitatively similar to the laboratory-measured rate dependence of a b for antigorite serpentinite [Reinen et al., 99] in the sense that a higher slip rate leads to a reduced degree of RS. Alternatively, the rate dependence of (a b) eff could result from time-dependent eff due to temporal variations in pore fluid pressure. Elevated pore pressure in the afterslip area could induce postseismic fluid flow away from the area due to poroelastic effects [Koerner et al., 4]. Such fluid flow would gradually reduce the pore pressure in the afterslip area and could generate the rate dependence of (a b) eff. 4. Discussion [5] The reduced degree of RS at high slip rates promotes the propagation of seismic slip from a RW patch into surrounding RS regions [Kaneko et al., ]. Therefore, early interplate aftershocks initiated on RW patches surrounded by rapid afterslip could be promoted to rupture broader RS regions than preseismic and late postseismic earthquakes initiated on the same patches. Shimamura et al. [] reported that an M 5.9 interplate aftershock, which occurred 9 days after the Tohoku-oki earthquake in the afterslip area, ruptured the area of the M 4.8 repeating earthquake sequence offshore of Kamaishi (9. ı E, 4. ı N) [Matsuzawa et al., ], as well as an adjacent area where earthquakes had not been observed before the Tohoku-oki earthquake. Consequently, the radius of the M 5.9 rupture was five times as large as that of the M 4.8 repeating earthquakes [Shimamura et al., ]. This increase in rupture dimension could possibly be explained by enhanced rupture of the RS region adjacent to the M 4.8 repeating earthquake patch due to a reduced RS property associated with rapid afterslip. [6] There is growing evidence that great earthquakes (M W > 8) occur in regions that include the rupture areas of smaller earthquakes (M W 7 8) [e.g., Nanayama et al., ; Konca et al., 8]. The rate dependence of 66

5 (a b) eff found for the Tohoku-oki afterslip may provide an explanation of this noncharacteristic behavior. If an earthquake that nucleated on a RW patch produces a sufficiently large stress increase in surrounding RS regions, slip on the RS regions would be substantially accelerated, and reduced (a b) eff at high slip rates would prevent the RS regions from acting as barriers to rupture propagation. Consequently, the earthquake would rupture multiple RW patches, potentially resulting in a great earthquake. Otherwise, slip in RS regions would not be accelerated sufficiently and the RS regions would act as barriers to rupture propagation due to the larger (a b) eff at lower slip rates, resulting in a smaller earthquake that ruptures only a single RW patch. If the transition from RS to RW behavior occurs at higher slip rates [Reinen et al., 99; Shibazaki et al., ; Noda and Lapusta, ], it would further promote the rupture of multiple RW patches [Shibazaki et al., ]. Therefore, the rate-dependent behavior of (a b) eff in RS regions may provide a key to the occurrence of great earthquakes. To further understand the role of the rate dependence of (a b) eff in determining the spatial extent of earthquakes, it is important to quantify (a b) eff for real faults, considering slip rates higher than those employed here. [7] Acknowledgments. We thank P. Segall and K. M. Johnson for helpful comments, A. M. Bradley for providing computer codes, the Geospatial Information Authority of Japan for providing GPS data, the National Research Institute for Earth Science and Disaster Prevention for providing centroid moment tensor solutions, and the Japan Meteorological Agency for providing an earthquake catalog. This work was supported by JSPS KAKENHI 749. [8] The Editor thanks Laura Wallace and an anonymous reviewer for their assistance in evaluating this paper. References Boatwright, J., and M. Cocco (996), Frictional constraints on crustal faulting, J. Geophys. Res.,,,895,99. Fukuda, J., S. Miyazaki, T. Higuchi, and T. Kato (8), Geodetic inversion for space-time distribution of fault slip with time-varying smoothing regularization, Geophys. J. Int., 7, 5 48., doi:./j.65-46x.7.7.x. Hsu, Y.-J., M. Simons, J.-P. Avouac, J. Galetzka, K. Sieh, M. Chlieh, D. Natawidjaja, L. Prawirodirdjo, and Y. Bock (6), Frictional afterslip following the 5 Nias-Simeulue earthquake, Sumatra, Science,, 9 96, doi:.6/science.696. Kaneko, Y., J.-P. Avouac, and N. Lapusta (), Towards inferring earthquake patterns from geodetic observations of interseismic coupling, Nat. Geosci.,, 6 69, doi:.8/ngeo84. Kato, A., and T. Igarashi (), Regional extent of the large coseismic slip zone of the M w 9. Tohoku-oki earthquake delineated by on-fault aftershocks, Geophys. Res. Lett., 9, L5, doi:.9/gl5. Koerner, A., E. Kissling, and S. A. Miller (4), A model of deep crustal fluid flow following the M w = 8. Antofagasta, Chile earthquake, J. Geophys. Res., 9, B67, doi:.9/jb86. Konca, A. O., et al. (8), Partial rupture of a locked patch of the Sumatra megathrust during the 7 earthquake sequence, Nature, 456, 6 65, doi:.8/nature757. Matsuzawa, T., T. Igarashi, and A. Hasegawa (), Characteristic smallearthquake sequence off Sanriku, northeastern Honshu, Japan, Geophys. Res. Lett., 9, 54, doi:.9/gl46. Miyazaki, S., P. Segall, J. Fukuda, and T. Kato (4), Space time distribution of afterslip following the Tokachi-oki earthquake: Implications for variations in fault zone frictional properties, Geophys. Res. Lett.,, L66, doi:.9/gl94. Nakajima, J., and A. Hasegawa (6), Anomalous low-velocity zone and linear alignment of seismicity along it in the subducted pacific slab beneath Kanto, Japan: Reactivation of subducted fracture zone?, Geophys. Res. Lett.,, L69, doi:.9/6gl677. Nanayama, F., et al. (), Unusually large earthquakes inferred from tsunami deposits along the Kuril trench, Nature, 44, 66 66, doi:.8/nature864. Noda, H., and N. Lapusta (), Stable creeping fault segments can become destructive as a result of dynamic weakening, Nature, 49, 58 5, doi:.8/nature7. Ozawa, S., T. Nishimura, H. Munekane, H. Suito, T. Kobayashi, M. Tobita, and T. Imakiire (), Preceding, coseismic, and postseismic slips of the Tohoku earthquake, Japan, J. Geophys. Res., 7, B744, doi:.9/jb9. Perfettini, H., and J.-P. Avouac (4), Postseismic relaxation driven by brittle creep: A possible mechanism to reconcile geodetic measurements and the decay rate of aftershocks, application to the Chi-Chi earthquake, J. Geophys. Res., 9, B4, doi:.9/jb488. Perfettini, H., et al. (), Seismic and aseismic slip on the Central Peru megathrust, Nature, 465, 78 8, doi:.8/nature96. Reinen, L. A., J. D. Weeks, and T. E. Tullis (99), The frictional behavior of serpentinite: Implications for aseismic creep on shallow crustal faults, Geophys. Res. Lett., 8, Scholz, C. H. (998), Earthquakes and friction laws, Nature, 9, 7 4. Sella, G. F., T. H. Dixon, and A. Mao (), REVEL: A model for recent plate velocities from space geodesy, J. Geophys. Res., 7, 8, doi:.9/jb. Shibazaki, B., T. Matsuzawa, A. Tsutsumi, K. Ujiie, A. Hasegawa, and Y. Ito (), D modeling of the cycle of a great Tohoku-oki earthquake, considering frictional behavior at low to high slip velocities, Geophys. Res. Lett., 8, L5, doi:.9/gl498. Shimamura, K., T. Matsuzawa, T. Okada, and N. Uchida (), The rupture process of an earthquake on March, in the source area of the repeating earthquakes off Kamaishi, NE Japan, and its relation to the M9. Tohoku earthquake, Abstract S4C-74 presented at Fall Meeting, AGU, San Francisco, Calif., 5-9 Dec. Thomas, A. L. (99), PolyD: A three-dimensional, polygonal element, displacement discontinuity boundary element computer program with applications to fractures, faults, and cavities in the Earth s crust, MS thesis, Stanford Univ., Stanford, California. 67