A Review of the Rupture Characteristics of the 2011 Tohoku-Oki Mw 9.1 T Earthquake

Tectonophysics 733 (2018) 4–36

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Tectonophysics

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Review Article A review of the rupture characteristics of the 2011 Tohoku-oki Mw 9.1 T earthquake

Thorne Lay

Department of Earth and Planetary Sciences, University of California Santa Cruz, Santa Cruz, CA 95064, USA

ARTICLE INFO ABSTRACT

Keywords: The 2011 March 11 Tohoku-oki great (Mw 9.1) earthquake ruptured the plate boundary megathrust fault off- 2011 Tohoku-oki earthquake shore of northern Honshu with estimates of shallow slip of 50 m and more near the trench. Non-uniform slip Japan subduction zone extended ~220 km across the width and ~400 km along strike of the subduction zone. Extensive data provided Megathrust faulting by regional networks of seismic and geodetic stations in Japan and global networks of broadband seismic sta- Ground displacements tions, regional and global ocean bottom pressure sensors and sea level measurement stations, seafloor GPS/ Tsunami generation Acoustic displacement sites, repeated multi-channel reflection images, extensive coastal runup and inundation Fault slip distribution Seafloor geodesy observations, and in situ sampling of the shallow fault zone materials and temperature perturbation, make the Finite-source model event the best-recorded and most extensively studied great earthquake to date. An effort is made here to identify Rupture parameters the more robust attributes of the rupture as well as less well constrained, but likely features. Other issues involve Earthquake physics the degree to which the rupture corresponded to geodetically-defined preceding slip-deficit regions, the influ- Fault friction ence of re-rupture of slip regions for large events in the past few centuries, and relationships of coseismic slip to precursory slow slip, foreshocks, aftershocks, afterslip, and relocking of the megathrust. Frictional properties associated with the slip heterogeneity and in situ measurements of frictional heating of the shallow fault zone support low stress during shallow sliding and near-total shear stress drop of ~10–30 MPa in large-slip regions in the shallow megathrust. The roles of fault morphology, sediments, fluids, and dynamical processes in the rupture behavior continue to be examined; consensus has not yet been achieved. The possibility of secondary sources of tsunami excitation such as inelastic deformation of the sedimentary wedge or submarine slumping remains undemonstrated; dislocation models in an elastic continuum appear to sufficiently account for most mainshock observations, although afterslip and viscoelastic processes remain contested.

1. Introduction Japan (ERCJ), 2009; Fujiwara et al., 2009; Geller, 2011). The fraction of the relative plate motion convergence across the megathrust ac- As old Pacific plate underthrusts beneath Japan at ~8.3 cm/yr, commodated over time by earthquakes versus slower slip remains un- spatially variable friction on the plate boundary causes strain to build certain, but historical activity (Fig. 1) prior to 2011 indicated a low up in the rock around locked regions of the megathrust fault while regional seismic coupling coefficient of ~0.2 along Honshu (e.g., steady or episodic slow sliding occurs in other regions. Elastic energy Scholz and Campos, 1995; Pacheco et al., 1993; Peterson and Seno, accumulates around the stuck regions until friction is overcome and 1984). sudden shear displacement occurs as an earthquake, reducing the sur- On 2011 March 11, rupture of a frictionally locked region in the rounding strain energy abruptly and radiating seismic waves that central portion of the 220 km wide megathrust fault commenced in- spread outward to eventually shake the surface. Motions of the seafloor nocuously, with a magnitude 4.9 earthquake (e.g., Chu et al., 2011), but generate tsunami if the seafloor displacement is large enough. Afterslip the rupture failed to arrest, continuing to expand for 150 s, spreading and aftershocks then cause further sliding while the sticking portions over the full width of the boundary and along its length for 400 km likely quickly relock. For hundreds of years this process has involved (Fig. 1). The rupture expanded relatively slowly in the up-dip direction, localized portions of the plate boundary repeatedly rupturing in with fault slip of ~30 m near the hypocenter, spanning a region that earthquakes of up to about magnitude 8.2, thus the Japanese earth- had not failed since a great event in 869 CE, increasing to about 50 m or quake hazard scenarios prior to 2011 envisioned this to be the typical more near the trench. The rupture expanded more rapidly and errati- activity expected in the future (e.g., Earthquake Research Committee of cally down-dip to below the Honshu coast with slip of 1–5 m extending

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.tecto.2017.09.022 Received 25 July 2017; Received in revised form 7 September 2017; Accepted 25 September 2017 Available online 28 September 2017 0040-1951/ © 2017 Elsevier B.V. All rights reserved. T. Lay Tectonophysics 733 (2018) 4–36

seismic and geodetic stations across Japan, along with multiple offshore seafloor geodetic sites and tsunami sensors of various types. Together with global broadband seismic networks, Pacific-wide ocean-bottom pressure sensors, rapid field deployments to measure tsunami runup and inundation along the coasts of Honshu and Hokkaido, and even prompt deep drilling into the toe of the megathrust that recovered fault zone core samples and measured temperature increases from frictional heating, there are unprecedented data before, during and after this great earthquake. So, it is also the best-studied earthquake to date, with the diverse observations of the entire sequence having been addressed in hundreds of scientific publications. The outpouring of international research publications has directly ensued from the vast data sets combined with open data sharing of the geophysical community. Multiple general overview papers (e.g., Lay and Kanamori, 2011; Ritsema et al., 2012; Pararas-Carayannis, 2014; Lorito et al., 2016) and reviews of the early literature (e.g., Hino, 2015; Tajima et al., 2013) provide broad perspectives of the seismic history, regional seismicity, ground deformation history, early characterizations of the faulting and tsunami generation process, shaking effects, tsunami impacts, afterslip, triggering of regional earthquakes, ionospheric per- turbations, and other aspects. This review, written just over six years after the event, builds directly on the early review by Tajima et al. (2013), and has three goals: first, to focus on what we have learned about the rupture process of the mainshock; second, to provide a fairly comprehensive summary and reference list of the many rupture investigations, tracking the evolution of models from early rapid assessments to the current generation which provides some consistency of overall faulting characteristics; and third, to discuss some key un- resolved questions regarding the 2011 Tohoku-oki rupture characteristics.

Fig. 1. Map of large earthquakes around the 2011 Tohoku earthquake region. The green fi region is the 1 m slip contour for the 2011 rupture (Yue and Lay, 2011). Aftershocks from 2. Megathrust slip de cit and an Mw 7.3 foreshock the USGS-NEIC catalog with depths < 50 km through March 31, 2011 are shown by green dots with radius scaled proportional to magnitude. The yellow and red patches The extensive deployment of geophysical instrumentation in Japan indicate estimated rupture zones of previous large earthquakes. The white arrow indicates prompted by the disastrous 1995 Kobe earthquake provided over a the direction of motion of the Pacific plate relative to Honshu. decade of dense observations prior to the 2011 Tohoku earthquake fi (Modi ed from Ritsema et al., 2012). from ground motion monitoring with > 1200 continuous GPS stations (GEONET); quantification of regional seismicity down to very small magnitudes using thousands of seismic stations in high quality borehole networks (Hi-net), broadband networks (F-net), strong motion net- southward along the Miyagi, Fukushima and Ibaraki Prefectures works (KiK-net, K-NET), and offshore ocean bottom seismometer de- (Fig. 1). Multiple source regions of large earthquakes of the last century ployments; new observations of seafloor position with deployment of re-ruptured sequentially, with short-period seismic waves released by cabled and campaign GPS/Acoustic ocean-bottom position sensors; and this down-dip rupture being enhanced relative to the up-dip rupture. sea wave quantification with extensive offshore and harbor sea wave The huge slip on the shallow megathrust produced a strong band of and tidal gauges. The same instrumentation captured the mainshock ocean floor displacement that generated a narrow tsunami pulse riding signals, aftershocks and postseismic deformation. on a broader pulse from the wide-spread displacements at greater The on-land GEONET data from 1995 to 2002 provided the first depth. This compound sea wave swept onto the coastlines of Honshu opportunity to characterize the upper plate deformation associated and Hokkaido, contributing to the most costly natural disaster ever in with variable frictional locking of the megathrust, yielding direct term of economic losses from the earthquake and tsunami. Fortunately, measures of strain accumulation as the plates converge to guide as- warning of the impending tsunami arrival was widely broadcast and sessment of possible future earthquake occurrence. Nishimura et al. acted on, and even though the predicted tsunami heights of 3 to 6 m (2000) and Mazzotti et al. (2000) used the GPS data from 1995 to 1997 were underestimated relative to the actual 10 to 15 m runup experi- to estimate current interseismic coupling ratio from back-slip modeling, enced along the Sendai coast, many lives were saved as people evac- finding decoupling and strong afterslip persisting for > 1 year near the uated to higher ground. Along the rugged Sanriku coast in northern 1994 Sanriku-oki earthquake (at a latitude just north of 40°), a region of Honshu, the tsunami runup reached almost 40 m, slightly exceeding low coupling and low seismicity just off the Sanriku coast from 39.5°N prior great tsunamis produced by near trench events in 1896 and 1933 to 40°N (Nishimura et al., 2000), and strong coupling south of 39.5° (Fig.1). near the region of the ensuing 2011 rupture. As the time window of GPS This was the 2011 Tohoku-oki earthquake, with a seismic moment observations expanded, Nishimura et al. (2004), Suwa et al. (2006), magnitude Mw = 9.1; the fourth largest event recorded by seismolo- Hashimoto et al. (2009), and Loveless and Meade (2010) analyzed the gical instrumentation dating back to 1900. The loss of life (about increasingly precise deformation velocities to map the spatially het- – 19,688 fatalities or missing) and damage (~$142 $222 billion) were erogeneous coupling in greater detail (Fig. 2). The region off of the horrific(Kazama and Noda, 2012), and the induced catastrophic failure 1978 Miyagi-oki earthquake showed a large slip deficit, with the down- of the Fukushima nuclear reactor continues to be an environmental dip limit of the locked fault extending to depths of 50–60 km (Suwa disaster. However, the earthquake occurred in the most densely geo- et al., 2006). Slip deficit was also detected offshore of Fukushima where physically-instrumented region of the world, with huge networks of large earthquakes ruptured in 1936 to 1938. All of these studies

5 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 2. Estimates of slip deficit (back slip rate) and coupling fraction on the megathrust boundary offshore of Honshu and Hokkaido obtained from geodetic measurements of upper plate deformation made prior to the March 12, 2011 Tohoku-oki earthquake. (a) Back slip rates with a contour interval of 2 cm/yr from Suwa et al. (2006). Dashed lines indicate the slab depth every 50 km. (b) The blue and red contours, respectively indicate slip-deficit and slip-excess at intervals of 3 cm/yr estimated by Hashimoto et al. (2009). The plate interface is indicated by gray dots. Arrows indicate the relative plate motion as the Pacific (PA) plate underthrusts the North American (NA) plate. (c) Coupling fraction (speed of estimated slip divided by long- term elative motion of the blocks indicated by thin lines) estimated Loveless and Meade (2010). Reproduced/modified by permission of American Geophysical Union; and Nature Geoscience.

assumed no slip deficit on the shallow portion of the megathrust, thus geodesy is essential for addressing this issue. the inferred locked regions are concentrated on the near-coast down- Offshore measurements of seafloor position seaward of Miyagi were dip half of the megathrust. Loveless and Meade (2010) accounted for in fact being made during this time interval (as discussed below), but deformation on upper plate faults using crustal blocks, but this has the up-dip extent of offshore strain accumulation and fault locking was relatively minor effects, thus the offshore locking distributions are si- not yet resolved. The assumption that the shallow part of the subduc- milar, albeit not identical, among the different investigations (Fig. 2). tion zone is weak, with slip velocity strengthening friction of sediments These publications preceded the 2011 event, and contributed greatly to and no viable strain accumulation was broadly accepted. So, this ex- the now globally applied strategy of geodetic slip deficit modeling on traordinary first-ever mapping of megathrust locking was largely re- the subduction zone scale to inform seismic hazard assessment. conciled with the likelihood that future events on the plate boundary The heterogeneous megathrust frictional locking models were pri- would conform to the size and distribution of prior deeper seismic ac- marily discussed in the context of large historical earthquakes off the tivity in Fig. 1. When a large thrust event occurred at 02:45 UTC near coast of Honshu during the past century (Fig. 1). Comparison of Figs. 1 38.32°N, 143.28°E (Japan Meteorological Agency, JMA) on 2011 March and 2 indicates that the down-dip regions of higher slip deficit corre- 9 with Mw 7.3 (e.g., Marsan and Enescu, 2012; Ohta et al., 2012), it spond quite well to regions of prior large events close to the coast with seemed to be generally compatible with this scenario. And then the magnitudes in the range 7.5 to 8.2, with the low seismic region off of 2011 March 11 event proved otherwise. The short-term precursory Sanriku (see Ye et al., 2012) having reduced slip deficit in all of the process prior to and following the March 9 event, now recognized as a models. Strong coupling detected offshore of Hokkaido in all the models foreshock, will be discussed later. First the basic rupture process of the spanned the region of the 2003 Hokkaido Mw 8.3 thrust event, which March 11 event will be discussed. re-ruptured the 1952 zone. This event reinforced the value of the geodetic coupling determinations. The 1933 Sanriku earthquake was a 3. 2011 mainshock rupture characteristics great intraplate normal faulting event, so it was not directly linked to ‘ coupling, and the 1896 earthquake was a distinctive tsunami earth- The 2011 March 11 mainshock struck at 14:46:18.1 local time ’ quake (Kanamori, 1972; Tanioka and Satake, 1996b), believed to have (05:46:18.1 UTC) 24 km deep at 38.103°N, 142.861°E (JMA). This is ruptured on the very shallow megathrust with a long source process about 45 km southwest of the March 9 Mw 7.3 foreshock. The final US time and relatively weak generation of short-period seismic waves, but Geological Survey National Earthquake Information Center (USGS- huge tsunami excitation. The 1611 event is less well characterized, but NEIC) origin time (05:46:24.12 UTC) and location (38.297°N, may have been a similar tsunami earthquake near the trench. While 142.373°E, 29 km deep) are delayed and shifted westward relative to well-documented, awareness of the 1896 thrust event did not prompt the JMA value. This caused some early images of the source radiation to fi the slip-de cit modelers to allow coupling to extend to the trench. In be offset from those found using the JMA location. The discrepancies hindsight, this seems like a poor choice, but the onshore geodetic data are largely due to the very weak initial radiation from the rupture, provide intrinsically poor resolution of coupling or earthquake slip in detectable only by the near-field high frequency sensors in Japan, with the shallow megathrust, as discussed below, so it was not possible to some influence of 3D mantle structure. The characteristics of the evaluate the actual degree of shallow locking. Tsunami earthquakes mainshock are discussed next. that rupture the shallow megathrust are now recognized to be widespread, although infrequent (e.g., Lay et al., 2012), and so today it would be questionable to assume no slip deficit in the shallow mega- 3.1. Long-period source measures thrust even if onshore GPS data cannot detect whether it exists. Seafloor Early estimates of the overall size of the 2011 Tohoku earthquake

6 T. Lay Tectonophysics 733 (2018) 4–36 were primarily constrained by long-period seismic wave inversions for scale lengths will be more valuable for great earthquake total size equivalent point-source parameters. These can be obtained as soon as a quantification. sufficient number of on-scale long-period seismic recordings are available. Hayes et al. (2011) describe W-phase inversions at the USGS- 3.2. Rupture initiation NEIC, where by 19.6 min after the origin there was an internal release with Mw 9.0. NEIC broadcast a W-phase solution with Mw 8.94 by The 2011 mainshock rupture initiated with weak radiation in the 47.6 min. The USGS-NEIC had a research Centroid Moment Tensor first 4 s, producing P waves compatible with an Mw 4.9 event near a (rCMT) solution with Mw 8.9 by 27 min, which was distributed by relocated position of 38.19°N, 142.68°E (Chu et al., 2011). Radiation 32 min. The final USGS CMT solution has seismic moment from this phase of the rupture is low enough to be missed in most tel- 22 M0 = 4.54 × 10 Nm (Mw 9.0) with dip, δ = 14°, strike, ϕ = 187°, eseismic signals, accounting for the later origin time found by the and rake λ = 68°. Duputel et al. (2011) note that real time W-phase USGS-NEIC. The onset was visible on regional Hi-Net stations, but inversions running at the USGS, Pacific Tsunami Warning Center Fukahata et al. (2012) could not see motion in GEONET hr-GPS stations (PTWC) and Institut de Physique du Globe de Strasbourg (IPGS) all had before 20 s after the origin, with the first significant moment release results with Mw 8.8–9.0 within 30 min, and by 45 min these converged originating 35 km west of the JMA location, which is close to the USGS- to Mw 9.0 with dip, δ = 14°. The final IPGS W-phase solution has an NEIC hypocenter. Uchide (2013) inverts the space-time history of the almost pure double couple solution with δ = 9°, ϕ = 193°, and first 20 s of the rupture using regional Hi-Net, KiK-net and F-net data, 22 λ = 78°, with M0 = 5.59 × 10 Nm (Mw 9.1). Ammon et al. (2011) and infers that after the first 4 s of the rupture the peak slip rate was performed W-phase inversions within hours of the event, finding a faster than 1 m/s and had a 3.0 km/s rupture velocity, expanding north 22 seismic moment of M0 = 3.9 × 10 Nm (Mw 9.0) with a 71 s centroid and northeastward for about 12 s to near the coseismic slip zone of the time. Polet and Thio (2011) discuss rCMT solutions, having determined Mw 7.3 foreshock, and then bilaterally in the down-dip direction for the Mw 8.9 within 23 min and Mw 9.0 by 12 h later. Nettles et al. (2011) next 20 s, with large shallow up-dip slip dominating thereafter. describe the final Global Centroid Moment Tensor (GCMT) solution The emergent signals from the onset of rupture pose challenges for 22 which has M0 = 5.31 × 10 Nm (Mw 9.1), with a best double couple early warning systems tuned to the initial detection of short-period with δ = 10°, ϕ = 203° and λ = 88°, and a centroid time of 69.8 s. energy. Hoshiba and Iwakiri (2011) and Hoshiba et al. (2011) evaluate They determined Mw 7.9 for the largest aftershock 30 min after the the early warning limitations for the first 30 s, with an estimate of Mw mainshock, located to the south offshore from Chiba Prefecture. 7.2 at 8.6 s, and the amplitudes by 30 s being only slightly larger than Larger estimates of seismic moment are found for solutions with those observed for the Mw 7.3 foreshock. The first few seconds of the shallower dip, due to the long-period wave excitation dependence on signals were not depleted in high frequencies to give an indication of the product M0sin(2δ). Tsai et al. (2011) explored the tradeoff between any difference from M ~6 size foreshocks (Hoshiba and Iwakiri, 2011). M0 and δ, finding that long period Rayleigh and Love waves do have From an analysis of 446 east-component strong motion recordings at some resolution of the separate parameters for the 2011 event if azi- distances from 120 to 530 km, Colombelli et al. (2012) found that by muthal weighting is balanced. Using an a priori geometry of the 35 s some early warning measures can provide estimates of Mw 8.4, but megathrust from model Slab 1.0 (Hayes et al., 2012), estimates of Mw signal saturation precludes reliable gauging of the eventual size. from 9.01 to 9.11 are obtained, depending on position along dip and Earthquake warning procedures active at the time of the event relied on 22 local δ. Their preferred M0 = 4.2 × 10 Nm (Mw 9.02) has δ = 12°. narrow band, short-time window estimates of earthquake magnitude The same dip is recovered for pure double couple solutions with (JMA estimated Mw 7.9 by 2.5 min), thus they underestimated the ϕ = 195°. Shao et al. (2011) explored multiple double couple analysis actual size of the event and associated tsunami potential (Ozaki, 2011). for the long period waves, but found that a single double couple with This real-time information is discussed further in earlier reviews 22 M0 = 5.06 × 10 Nm, and δ = 10° and ϕ = 199°, provides a good fit. (Ritsema et al., 2012; Tajima et al., 2013). Okal (2013) determined an ultra long period mantle wave magnitude 22 22 with M0 = 4.1 × 10 Nm and an average of 3.5 × 10 Nm for long 3.3. High frequency radiation characteristics period normal modes. He could not detect any significant difference in duration from mode data versus shorter period data, indicating that Short-period seismic waves were radiated throughout the rupture there was no ultra-low frequency spectral increase and no long tail on process, and they provide a probe of the rupture dynamics that is pri- the moment rate function. marily sensitive to expansion of the leading edge of the rupture front, While point-source measures are intrinsically inadequate re- rapid changes in rupture expansion velocity, and slip accelerations. presentations of the faulting which extended over a large spatial extent Analyzed on their own, short-period signals do not resolve total slip at a across a megathrust interface that varies in dip from 3° to 30°, the given location, although they may bound the overall duration of rup- overall size of the event can be summarized as ture to first order. Teleseismic and regional data recorded on short- 22 ~M0 = 4.9 ± 0.7 × 10 Nm (Mw ~9.1) with average dip of 9° to period regional networks, broadband networks, and accelerometer 14°. Following the convention of adopting the final W-phase or GCMT networks have been used to image attributes of the 2011 Tohoku rup- solutions as a standard, the 2011 Tohoku event is specified as having ture, finding complex relationships with the total slip distribution

MW = 9.1. This is the fourth largest earthquake to be seismically re- (Fig. 3). The total duration of high frequency radiation at teleseismic corded, after the 1960 Chile (Mw 9.5), 1964 Alaska (Mw 9.2) and 2004 distances was estimated as about 170.5 s by Hara (2011). He inferred Sumatra-Andaman (Mw 9.15) events. The associated mass displace- an Mw = 8.96 from the maximum displacement amplitude, with two ments are large enough to perturb long-wavelength gravity across the distinct rupture processes; expansion to the southwest with high fre- region, and this was detected in spaceborne gravimetry data from the quency radiation and to the east with large moment. Gravity Recovery and Climate Experiment (GRACE) system. Han et al. Regional and global networks of short period P wave recordings (2011), Wang et al. (2012b), and Zhou et al. (2012) describe analyses of have been back-projected to the source region to image the space-time GRACE data, finding moments in the range 4.0 to 5.0 × 1022 Nm, with history of coherent bursts of energy in the short-period wavefields. dependence on assumed source dip. Postseismic deformation could Koper et al. (2011a) used ~1 s period P waves from arrays of stations in contribute up to 10% to the estimated moments, so comparisons were North America and Europe, finding initial down-dip propagation at made for various slip and afterslip models to try to separate the relative 1 km/s followed by faster 2 to 3 km/s rupture to the southwest beneath contributions. The GRACE data are limited to > 300 km scale length the coast of Honshu. Comparison with early finite-fault models showed resolution, but do show minor differences relative to different slip that localized concentrations of short-period radiation were in rela- models. Future gravity missions that hold potential to resolve 100 km tively low slip areas down-dip from the large-slip region east of the

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hypocenter, indicating depth-varying frequency dependence of seismic radiation from the megathrust. Meng et al. (2011) and Simons et al. (2011) applied the Multiple Signal Classification (MUSIC) algorithm to 0.5–1 Hz data from USArray and Europe, finding a similar two-stage evolution of the radiation (Fig. 4a), with initial slow expansion at 1 km/ s and then faster expansion to the north and southwest after 35 s. Other early back-projections are generally similar (e.g., Ishii, 2011; Wang and Mori, 2011a; Zhang et al., 2011; Kiser and Ishii, 2012; Satriano et al., 2014). In an extension of short-period back-projection methods, Yao et al. (2012) apply an iterative method with subevent signal stripping and correlation alignment. This reveals 16 subevents in the 1–5 s period band, most around or west of the hypocenter at early times, then expanding north at 2 km/s and southwest at 3 km/s. There is again a lack of short-period radiation from the up-dip region. Back-projections of P wave signal from multiple narrow bands from 0.5 to 8 s period by Koper et al. (2011b) indicate that longer period energy tends to image at up-dip positions relative to shorter periods. This is consistent with the general tendency for the short-period ~1 Hz energy to locate below the coast while slip-inversions show large slip at shallow depth (Fig. 3). Similar results are found by Wang and Mori (2011b) and Kiser and Ishii (2012). Meng et al. (2012) attempt to mi- tigate artifacts in beamforming style back-projections that might cause artificial up-dip migration of lower frequency images. They use a re- Fig. 3. Variations in seismic radiation from the rupture zone of the 2011 Tohoku ference window strategy in MUSIC for data from North America and earthquake. The black rectangles indicate estimated locations of high frequency Europe, finding no trenchward shift of energy with periods of 8 to 16 s. (> 0.15 Hz) strong ground motions determined by Kurahashi and Irikura (2011). Loca- However, this contrasts with results of imaging short-period energy – tions of coherent bursts of teleseseismic short-period energy in the period band 0.7 3s sources by compressive sensing, which involves sparse inversion for imaged by back projection (Koper et al., 2011b) are shown by the circles, scaled pro- ff portion to relative energy with time lapse indicated by lower color scale. The white star sources of coherent energy for di erent frequencies (Yao et al., 2011). indicates the epicenter for the rupture model obtained by inverting broadband teleseismic This method shows clear trenchward shift of energy from 10 to 20 s P waves by Lay et al. (2011a). The vectors indicate the slip direction and magnitude for period relative to the 2 to 5 s period band. Yagi et al. (2012) suppress the hanging wall displacement relative to the Pacific slab. Note that the high frequency the depth-varying interference with surface reflections by convolving P- radiation originates from down-dip of the large-slip area imaged by longer period signals. wave data with Green's functions for different positions on the mega- fi Reproduced/modi ed by permission of American Geophysical Union. thrust. This approach finds short-period (0.5 to 2.0 s) radiation only down-dip from the hypocenter whereas long-period radiation (2.0 to 10 s) comes from both up- and down-dip. The along-dip variation in frequency content is supported by back-

Fig. 4. Back-projection of (a) teleseismic short period (1–2 s) P waves recorded by USArray (squares) and European stations (circles) (Meng et al., 2011), and (b) Rayleigh waves using periods from 13 to 100 s (Roten et al., 2012). The black lines in (a) indicate the average slip distribution estimated by Simons et al. (2011). The pink line it the down-dip limit of megathrust activity. In (a) the USGS-NEIC hypocenter (white star) is the reference position, while in (b) the JMA hypocenter (yellow star) is the reference position, so there is some baseline shift between the short-period and long-period images, but the patterns are clearly oﬀset.

8 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 5. Finite-fault slip distributions for the March 11, 2011 Tohoku earthquake inverted from teleseismic observations. (a) Model P-MOD2 (Lay et al., 2011a). GCMT focal mechanisms of the mainshock and the first three weeks of aftershocks are shown, along with vectors indicating the long-term motion of the Pacific plate relative to Japan (MORVEL model). White star is the epicenter of Zhao et al. (2011). (b) Model of Ide et al. (2011), with moment rate function in the inset. Focal mechanisms of the mainshock, March 9, 2011 Mw 7.2 foreshock and two normal faulting aftershocks are shown along with JMA seismicity. (c) The final solution from the USGS-NEIC from body wave and surface wave modeling (Hayes, 2011), with hypocenter at the USGS-NEIC location. (d) Final model from inverting body and surface waves from Shao et al., 2011. Red star is the JMA epicenter and red dots are the first 6 days of aftershocks.

projection of lower frequency Rayleigh waves, filtered in the 13 to of four strong motion sensors, Nakahara et al. (2011) applied a wave 100 s period range from 384 strong-motion records (Roten et al., 2012). field coherency measure for 0.5 to 2.0 s energy to resolve an initial Fig. 4b shows the position of Rayleigh wave emitters, with a three stage northerly, then a southwestward distribution of short-period energy sequence; first slow rupture down-dip, then energetic rupture between release. The dense Metropolitan Seismic Observation Network in Tokyo the JMA hypocenter and the trench within 60 s, and final bilateral was similarly used in semblance-enhanced stacking analysis of 0.05 to expansion north and south at 3 to 3.5 km/s. 0.5 Hz recordings (Honda et al., 2011), projecting the energy to the Regional short-period seismic recordings down to 0.1 s period have fault plane to find large radiation off the coast of Miyagi prefecture and also been used to image locations of energy from the 2011 rupture. The little radiation offshore of Ibaraki. Using many stations, Kurahashi and proximity of recording stations in Japan provides good sensitivity to the Irikura (2011, 2013) detected five localized strong ground motion along-strike distribution of energy. For example, using just a small array generation areas (SMGAs), with locations shown in Fig. 3. These locate

9 T. Lay Tectonophysics 733 (2018) 4–36 west of the hypocenter, along Sanriku and to the south along Fu- et al. (2011a). Their updated model (Fig. 5a) used local velocity kushima and Ibaraki. Asano and Iwata (2012) used an empirical Green's structure information indicating strong P velocity reduction near the function (EGF) method to similarly locate four SMGAs for 10 to 0.1 s toe of the trench (e.g., Miura et al., 2005), finding 22 period energy beneath the coast in the vicinity of the prior large Miyagi- M0 = 4.0 × 10 Nm, with average displacement of ~20 m, and peak oki events (1978 and 2005) and Fukushima-oki events (1938) (Fig. 1). displacement of 62 m in the shallowest model row next to the trench. They estimate stress drops of these subevents of 6.6 to 27.8 MPa. Reducing rigidity as depth shallows causes the estimated peak slip to Kumagi et al. (2013) image sources of 0.2 to 0.1 s period S waves, increase by a factor of ~40% near the trench. Peak slip is not well- finding locations on the deeper megathrust with three subevents along resolved in finite-fault inversions, both due to dependence on fault the coast. Maercklin et al. (2012) back-project local strong motion data model parameterization and on the choice of rigidity. This should be to characterize a two-stage rupture, with very large slip of up to 50 m at kept in mind when comparing slip models throughout this review. The shallow depth over a 100 to 150 km wide zone followed by south- rupture duration is 150 s for this model. This model predicts on-land westward extension. Their image using 2.5 to 5 s data is rather in- GPS statics quite well. Ide et al. (2011) inverted 50 broadband P waves, coherent, but slip near the hypocenter and along Fukushima is imaged finding that the rupture (Fig. 5b) had a weak initial phase, then pro- in 10 to 20 s and 5 to 10 s passbands. pagated down-dip, then up-dip, then down-dip again, re-rupturing the There is little doubt that there is depth-dependence in the coseismic central portion of the megathrust. They infer two modes of rupture, radiation as generally depicted in Fig. 3, but this will not be captured in with shallow, relatively low short-period energy release with large most finite-source inversion models discussed next because the Green's dynamic overshoot, and deep rupture that radiated energetic short- functions are not accurate for short-period energy and short-period period signals. Their estimate of shallow slip is 30 m, but they note that signals have low amplitude relative to the long-period signals, so the it could be larger. Dynamic overshoot of a compliant hanging wall was inversions do not put weight on them. Explicit joint consideration of the attributed to shear stress being reduced to below dynamic friction level results of kinematic inversions for slip and back-projection of short- on the shallow megathrust. Shao et al. (2011) inverted P and SH waves period energy underrepresented in such inversions is necessary to and surface waves for a sequence of models over several days, refining capture the full rupture process (e.g., Koper et al., 2011a; Satriano travel time alignments, with the final model (Fig. 5d) having large near- et al., 2014). trench slip of up to 60 m with two subevents down-dip. This model has 22 M0 = 5.8 × 10 Nm. The slip peaks somewhat down-dip from the 3.4. Coseismic slip distribution estimates trench, but the velocity model does not have as low of a shallow rigidity reduction as used by Lay et al. (2011a). Satriano et al. (2014) and Yagi Many estimates of finite-fault slip distribution and/or the space- and Fukahata (2011) obtain basically similar models using teleseismic P time evolution of the slip have been produced for the 2011 Tohoku wave inversions. Yagi and Fukahata (2011) include allowance for un- earthquake. All of the methods require construction of Green's functions certainty in Green's functions, and obtain a moment of 5.7 × 1022 Nm, for a distributed grid on the fault model, appropriate for the specific with long slip durations in the shallow fault of up to 90 s, and peak slip signals used in an inversion for the slip model. This is an ill-posed of 50 m. problem suffering from use of simplified Earth models, band-limited The regional strong motion data, heavily filtered to extract the low signals, kinematic constraints imposed on the rupture process, and in- frequency ground motion time series, have been used to construct finite trinsic limitations of the observation geometry. A brief summary is fault models as well. Suzuki et al. (2011) used 36 S waves filtered from provided of the models obtained using only teleseismic and/or regional 0.01 to 0.125 Hz to image slip, finding a large area with > 20 m of slip seismic recordings, only on-land static deformations, time-varying and peak slip of 48 m east of the hypocenter near the trench axis. Their 22 geodetic observations, on-land and offshore static deformations, only model has M0 = 4.42 × 10 Nm with slip extending as far north as tsunami observations, and various joint combinations of different data 40°N. Comparison with the acceleration records indicates that there is sets. As better appreciation has been gained for the limitations of in- strong frequency dependence with depth for the rupture. Takewaki dividual data sets, which can be severe, models obtained from joint (2011), Kumagi et al. (2012), and Wang et al. (2013) also inverted inversions appear most likely to best represent the source process. heavily filtered strong motion records. Yoshida et al. (2011a) inverted However, there are caveats for joint inversions due to the questionable 0.005–0.05 Hz signals from strong motion recordings of F-net and KiK- isolation of coseismic signals from postseismic signals for geodetic ob- net, finding a three stage rupture model with moderate slip down-dip of servations, the possibility of additional tsunami excitation by inelastic the hypocenter, 47 m of slip near the trench up-dip of the hypocenter, deformation or submarine slumping, and selection of the appropriate and then southward rupture. An average rupture velocity of 2.2 km/s weighting for different data sets and measures of the degree to which was found, but higher rupture velocities of 3–4 km/s occur in the down- they are each fit. dip regions. Yoshida et al. (2011b) compare separate inversions of teleseismic P and regional strong motion records filtered from 0.01 to 3.4.1. Seismic wave inversions 0.15 Hz. In both cases the main slip is east of the hypocenter with The first models for the finite-fault slip distribution for the 2011 slip > 25 m indicated by the strong-motion inversion. All of the slip is event were produced using only seismic waves, primarily from global imaged in the shallower half of the fault plane. Note that these models broadband seismic networks, as these data are openly accessible in near do not characterize well the along-coast distribution of regional and real-time. Hayes (2011) and Hayes et al. (2011) report on rapidly im- short-period energy sources south of 37.5° in Figs. 2 and 3, indicating plemented inversions of P and SH body waves and long period surface that the latter regions have < 5 m slip during the main rupture. waves for automated and adjusted models by the USGS-NEIC. Within 22 the first couple of hours a slip model with M0 = 4.04 × 10 Nm and 3.4.2. Onshore geodetic inversions peak slip of 18 m distributed 300 km along strike, slightly up-dip of the The GEONET GPS observations provide > 1200 measures of static hypocenter was obtained. Subsequent adjustment using the interface deformation for the 2011 Tohoku earthquake. The largest on-land model of Slab 1.0 moved slip trenchward and more concentrated along displacement was 5.3 m. This data set is unprecedented, and even more 22 strike with peak slip of over 32 m and M0 = 4.9 × 10 Nm, in a model remarkable is that these stations are sampled at 1 Hz, so they capture (Fig. 5c) publically released about 10 h after the event. There is minor the full time-evolution of the displacement at each site from the passage moment rate after 150 s in these models. The rupture velocity was of seismic waves to the static offsets. This enabled the phenomenal variable, ranging from 1.25 to 3.25 km/s. animation of hr-GPS displacements across Japan from the 30 s kine- Lay et al. (2011a) updated initial models derived from broadband matic position estimates produced by the ARIA project displayed in teleseismic P waves used in comparison with back-projections by Koper Grapenthin and Freymueller (2011). Many studies have made use of

10 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 6. Finite-fault slip distributions for the March 11, 2011 Tohoku earthquake inverted from only geodetic observations. (a) Inversion of static GPS displacements from Koketsu et al. (2011). The JMA locations are shown for the epicenter (orange star), March 9, 2011 Mw 7.3 foreshock (white circle) aftershocks larger than 7 (orange circles) and other aftershocks (yellow circles). (b) Inversion of high-rate GPS signals by Yue and Lay (2011). The larger circles indicate the GE- ONET stations used among all stations (circles). (c) Slip distribution including oﬀshore and onshore deformation observations from Iinuma et al. (2012). Slip contour is 10 m. (d) Slip distribution from GPS with free slip at the trench and accounting for seaﬂoor deformation from Ozawa et al. (2012).

only the static motions, in part because numerous codes have been aftershocks; the Mw 7.9 in the south 30 min after the mainshock, and developed to invert static deformations for earthquake slip distribu- an Mw 7.3 event offshore of Sanriku. Diao et al. (2011) performed GPS- tions. Such inversions provide no information about rupture timing, but only inversions finding slip of around 23 m near the hypocenter. can provide good resolution of the spatial distribution of slip if the Imakiire and Koarai (2012) estimate that the area with slip exceeding observation configuration is favorable. For the 2011 event, the GPS 4 m is 400 km long and 200 km wide, with peak slip of ~27 m near the coverage is one-sided, producing severe limitations on the along-dip epicenter, similar to Ozawa et al. (2011). Evans and Meade (2012) resolution for slip placement. This is exacerbated by the common re- invert 298 onshore GPS observations using a sparsity promoting quirement in many of the codes that the slip pinches to zero in poorly method with l1 regularization, finding a band of slip from 30 to 50 km resolved parts of the fault model and on its edges. deep extending 500 km along strike with a maximum slip of 64 m. Inversions of GEONET static measurements alone are generally well These models demonstrate that the very smooth distributions of some represented by the inversion of Koketsu et al. (2011) shown in Fig. 6a. models are not required. They also invert for afterslip, finding a narrow This inversion uses Green's functions for a half-space. Slip of 25 to 40 m band distributed down-dip of the large-slip zone. While explicitly ad- is typically found in the vicinity of the hypocenter, extending along the dressing the intrinsic limited along-dip resolution of the GPS data, there subduction zone by 250 to 400 km, with relatively little internal is no clear basis for minimizing the slip dimensions along dip, and such structure. Iinuma et al. (2011) found 35 m peak slip around the 1981 a model will likely not provide a good fit to the tsunami data. and 2003 Miyagi-oki source regions. With a very smooth slip zone ex- These on-land GPS based models are generally consistent, but in tending almost 400 km along strike, Ozawa et al. (2011) estimated peak contrast to the seismic models in Fig. 5, they have smoother slip dis- 22 slip of 27 m near the epicenter and M0 = 3.43 × 10 Nm (for rigidity tributions with peak slip near the hypocenter. Yue and Lay (2011) in- of 40 GPa). They also estimated smooth afterslip with a peak off San- verted the complete time-varying ground motions from GEONET sta- riku but extending over the entire coseismic slip zone. Nishimura et al. tions, filtered to periods longer than 25 s. This explicitly incorporates (2011) obtained slip distributions for the mainshock with 40.9 m slip in seismic wave information into the inversion, as the peak signals and the north and 4.7 m in the south, and for the largest two thrust their time dependence are well represented. A model with maximum

11 T. Lay Tectonophysics 733 (2018) 4–36

22 slip of 60 m near the trench and M0 = 4.8 × 10 Nm was obtained 3.4.4. Geodetic inversions including offshore ground deformation (Fig. 6b), with a more compact slip distribution than static GPS inver- The availability of offshore seafloor geodetic data discussed in sions. Subfault durations of 30 to 70 s were estimated, with re-rupturing Section 3.4.3 has proved transformative for geodetic models of the of the central portion of the fault as detected in teleseismic inversions 2011 Tohoku earthquake slip distribution as well as for the study of (e.g., Ide et al., 2011). The time-dependence provides the moment rate megathrust faulting in general. Discrepancies between slip models like function shown in Fig. 6b, with contributions from the up-dip and those in Figs. 5 and 6a have often been attributed to differences in in- down-dip portions of the slip being indicated. The static displacements trinsic resolution of seismic and geodetic data, both of which clearly are as well fit as for the static-only inversions, so the extra time-de- have some advantages and some limitations, but this issue has usually pendent information adds significant constraint on the problem. not been resolved by direct deformation measurements. Recognizing that seafloor geodetic data have their own uncertainties (afterslip may 3.4.3. Direct measures of offshore and near trench displacement occur before seafloor positions are re-measured, submarine slumping or The 2011 Tohoku earthquake is exceptional in having numerous wedge faulting may occur, etc.), once the data became available, they seafloor displacement measurements extending all the way to the were quickly incorporated into geodetic models of the fault slip. trench. This is largely unprecedented for a great megathrust earth- Ito et al. (2011a) combined GEONET statics and the seafloor geo- quake, and has demonstrated the immense value of seafloor position detic sites off of Miyagi and Fukushima in estimating coseismic fault measurements before and after future great earthquakes, as there has slip, finding that the region of large slip was generally complementary always been uncertainty in up-dip extent of coseismic faulting for plate to the source regions of large earthquakes during the past 100 years, boundary thrust faults. Sato et al. (2011) reported observations from 5 although some slip did re-rupture the source zones of the 1936, 1938 GPS/Acoustic seafloor geodetic sites, 4 of which lie offshore Miyagi and 1978 events (Fig. 1). They obtained a maximum slip of 60 m, with near the 2011 main slip zone and the last is offshore of Fukushima. concentrated large-slip southeast of the hypocenter, extending to near These were re-measured from March 28 to April 5, finding 5 to 24 m the trench. Ito et al. (2011b) considered the frontal wedge uplift of 5 m offsets (with 50 to 60 cm error) toward the east-southeast and ~3 m and displacements of 58 m at TJT1 and 74 m at TJT2 to estimate slip on uplifts. The largest slip (at MYGI) is centrally above the mainshock slip the fault of 80 m near the trench. The basic structure of this frontal zone, and if it represents coseismic deformation, at least 30 m of slip wedge was proposed by Tsuji et al. (2011) based on faults in reflection must have occurred on the fault in that region. Offsets at KAMS (23 m) profiles. The increase in displacement relative to the 31 m at GJT3 just and KAMN (15 m) from 36°N to 39°N indicate that large slip extends at to the west was attributed to extension within the toe of the wedge least this far north, as found in the seismic models (Fig. 5). Kido et al. during the earthquake, likely involving normal faulting under the (2011) provided seafloor geodetic measurements with the GPS/ landward slope, as further argued by Tsuji et al. (2013). The normal Acoustic method for two additional sites one month after the main- faulting is estimated to be < 1 m. It was suggested that the presence of shock. These are 100 km (GJT4) and 50 km (GJT3) from the trench, and faults within the wedge could weaken the hanging wall, promoting horizontal displacement of 15 m and 31 m were measured, respectively, dynamic overshoot. The region of large displacement was found to be the latter being the largest direct seafloor displacement measured by consistent with back-tracking of impulsive crests in tsunami recordings this method. The estimated error is only 1 m. GJT4 only had 2 out of 5 (discussed later), with those recorded at cabled sites TM1 and TM2 seafloor transponders respond, so it is less reliable. The 7 GPS/Acoustic suggesting a 40 km wide source zone comparable to the frontal wedge seafloor displacements have almost parallel motions and provide stable dimension. estimates of static deformation above the main slip zone. An unknown Pollitz et al. (2011) combine the onshore and 5 offshore deforma- amount of postseismic deformation is likely to have occurred at these tion statics in an inversion with a layered spherical model. Their fault sites prior to the measurements, but the static values have been ex- plane has variable dip and a strike of 195°. The maximum slip of 33 m tensively used in finite fault models as discussed below. was on the shallowest part of the model, up-dip from the 1936 and 1978 Fujiwara et al. (2011) performed repeated multibeam bathymetric Miyagi-oki events, but not extending to the trench. The model has 22 imaging near the trench, finding a 40 km wide area 7 to 10 m shallower M0 = 4.06 × 10 Nm. A similar data distribution was inverted by and with 50 m east-southeast motion toward the trench relative to prior Hashimoto et al. (2012), using the same model geometry as in com- observations in 1999. Ito et al. (2011b) used local benchmark dis- puting their earlier coupling model (Hashimoto et al., 2009). They find placements obtained by acoustic ranging before and after the main- maximum slip of 27 m centered below the hypocenter, with little slip shock at the frontal wedge. An ocean-bottom pressure observation in- near the trench. In contrast, Feng and Jónsson (2012) perform inver- dicates 5 ± 0.5 m of uplift (station TJT1) on the wedge, and average sions with GEONET, 5 offshore GPS/Acoustic data and InSAR data with displacements 58 m (TJT1) to the east and 74 m (TJT2) east-southeast a model that has > 35 m slip above 10 km depth near the trench. The with uncertainties of about 20 m. Kodaira et al. (2012) used differences InSAR data contribute little for this event given the excellent GPS in seismic refl ection data from 1999 and 11 days after the 2011 event to coverage, but do help to identify anomalous GPS observations. Wang infer that fault rupture did reach the sea floor. They observe disruption et al. (2012a) analyzed a similar combined data set, applying correc- of the reflectivity in a triangular wedge of sediments 3 km long and tions for postseismic contributions. They found only 1 m correction for 350 m thick, with 50 m of horizontal motion. Sliding of the wedge up seafloor sites and < 0.4 m for InSAR, so the resulting models are not and down across horst structure in the incoming Pacific plate appears to strongly influenced by the corrections. The inclusion of the seafloor have caused gravitational instability and slumping, but large overall data, and to some extent the InSAR data, produce asymmetry in the slip horizontal displacement appears reliable. distribution with northward extension of a more concentrated slip Tsuji et al. (2013) report post-earthquake seafloor observations patch than GPS inversion alone. The seafloor data increase the slip to a along the same dive points made before the earthquake using manned maximum of 50 m near 5 km depth for a model with 22 submersible and deep-tow camera systems. They had to take into ac- M0 = 3.14 × 10 Nm (assuming rigidity of 40 GPa). By inversion of count several tens of meters of movement of some of the dive locations, the GEONET and seafloor data Imakiire and Koarai (2012) find the slip with the changes of seafloor morphology indicating open fissures and model shifts eastward and peak slip increases to 56 m relative to their high heat flow near a landward-dipping normal fault five months after inversions of GPS data only. Diao et al. (2012) find a similar up-dip shift the event. The data demonstrates extensional and inelastic deformation and increase in peak slip to 45.8 m when seafloor data are included. of the overriding wedge. The normal faulting may account for lateral Wang et al. (2013) include 5 seafloor observations and find a 50 m peak variation in the seafloor observations between the GPS/Acoustic mea- slip up-dip of the epicenter. The large shallow slip is similar to that surements of Sato et al. (2011) and Kido et al. (2011) and the larger estimated by Fujiwara et al. (2011). motions found by Ito et al. (2011b). Updated geodetic models utilizing all 7 GPS/Acoustic seafloor

12 T. Lay Tectonophysics 733 (2018) 4–36 observations were obtained by Iinuma et al. (2012) and Ozawa et al. GPS static displacement-based estimates of the slip magnitude and (2012). Both models have more concentrated slip zones, extending distribution for offshore megathrust faulting even given an extensive farther offshore with increased slip relative to the on-land GPS inver- geodetic network, unless the full time-series of hr-GPS recordings is sions. Iinuma et al. (2012) find 50 m slip adjacent to the trench in a utilized. Even a modest number of offshore measurements provide great compact region with dimensions 40 km × 120 km (Fig. 6c). Ozawa improvement in resolution. However, even for the 2011 event, one et al. (2012) solve for pre-slip, coseismic and afterslip. The coseismic must be cautious about the limited coverage, especially to the north, slip model (Fig. 6d) has a similar up-dip concentration to the model of given the large parallel displacements seen at the northernmost seafloor Iinuma et al. (2012), but also has an additional narrow southward ex- stations, and there is always concern about postseismic contribution to tension of slip. The updated model of postseismic slip is much more offsets, which motivates quick re-measurement of the seafloor sites. concentrated than in Ozawa et al. (2011), and locates down-dip of the large coseismic slip at depths > 30 km. The pre-slip from 2003 to 2011 3.4.5. Inversions with only tsunami data is caused by the moderate size Miyagi-oki events and their afterslip. The tsunami data set for the 2011 Tohoku event is also unrivaled Silverii et al. (2014) invert 421 GEONET and 7 GPS/acoustic observa- among great earthquakes. Tsunami waves reaching 5 to 6 m amplitude tions, obtaining a model with 40 m of slip at the trench and > 55 m in at coastal ocean bottom pressure sensors and GPS gauges surrounding their second row of sub-faults down-dip. Slip near 50 m close to the the source (Fujii et al., 2011) supplementing Pacific wide deep-ocean trench is also found in the model by Zhou et al. (2014), which inverts seafloor pressure sensor recordings with good azimuthal and range 1232 GPS along with the 7 seafloor observations. They considered distributions relative to the source. Mori et al. (2011, 2012) document a uniform dip and variable dip models. Checkerboard tests demonstrate field survey by 300 scientists of tsunami runup and inundation the poor short wavelength resolution for GPS statics on-land over the with > 5300 measurements along 2000 km of eastern Japan coastlines. outer half of the megathrust, with clear improvement in resolution The compiled measurements provide an overall depiction of the tsu- when also inverting the seafloor data. Inversions with either zero-slip or nami impact, which includes 5.4 km inundation on the Sendai plain free-slip boundary conditions, and either gradient or Laplacian (Mori et al., 2011; Goto et al., 2012b) with a maximum inundation smoothing were examined, along with fixing or freeing the rake vectors. height of 19.5 m and runup locally reaching almost 40 m along the Slip extension to the trench and narrowing of the slip zone occur if a rugged Iwate coasts fronting the rupture zone (Mori et al., 2011; Lin free slip boundary condition is used and if rake is fixed. Perfettini and et al., 2012). The unprecedented hydrographic datasets have been ex- Avouac (2014) invert GEONET and 6 sea floor observations, again tensively analyzed to determine the earthquake source process and its finding a compact slip zone with 30 to 50 m slip near the trench, relationship to the resulting tsunami and impacts along the eastern whereas peak slip is around 25 m when only inland data are used. As Japan coasts. discussed below, they infer that a large fraction of the shallow slip is Tsunami waves propagate at much lower speeds than rupture ex- postseismic given the time delay prior to the seafloor measurements, pansion and seismic waves and their amplitudes and periods are in- which is at odds with other interpretations of postseismic slip dis- trinsically sensitive to the coseismic seafloor deformation. The records tribution. from well-positioned stations around the source thus allow reliable The consistent tendency for slip to increase and for the slip zone to inference of the initial sea level source and associated seafloor de- concentrate spatially with the inclusion of the seafloor data in geodetic formation. The deformation can be mapped into fault slip, but can also inversions is consistent for most of these homogeneous structure capture other tsunami sources such as submarine landslides. While models. Numerical methods have also explored the stability of the re- seismic and geodetic inversions for finite-fault models of large earth- sults for more complicated representations of the medium. quakes tend to be highly parameterized and very detailed, inversions of Kyriakopoulos et al. (2013) used 3D finite element modeling of the tsunami observations tend to be simpler in parameterization and lower Green's functions for models with a relatively weak upper plate and stiff in resolution due to the long-period nature of the waves. Horizontal underthrusting plate. Matching the data requires less slip than if displacement plays a big role in tsunami excitation for dipping sea floor homogeneous properties are assumed because the slip is more widely bathymetry (Tanioka and Satake, 1996a). distributed, and there is asymmetry in motion across the fault, with Many analyses of the 2011 tsunami recordings explicitly assume larger motion of the hanging wall. Calculations using checkerboard that megathrust faulting produced the tsunami excitation, and map the tests reaffirm the added resolution provided by the seafloor data. An tsunami information directly into slip distributions. Saito et al. (2011) adjoint-based 3D finite element method is applied to GPS and 5 seafloor achieved this by first performing an inversion for the instantaneous displacements, including topography, bathymetry and medium het- tsunami generation using ocean bottom pressure and GPS wave gauge erogeneities by Pulvirenti et al. (2014). They find broad slip distribu- recordings with linear dispersive Green's functions, and then specifying tion east of the hypocenter, with large slip at the trench exceeding a faulting geometry and inverting for slip from the tsunami source. 40 m, but checkerboard tests indicate there is still poor resolution near They estimated 30 m slip 20 km deep with 25 m slip extending to near the trench. Their model resembles that of Iinuma et al. (2012) in the trench (Fig. 7d). The peak sea level height perturbation at the Fig. 6c. Grilli et al. (2013) also use 3D finite element modeling for the trench was 8 m. Two cabled ocean bottom pressure gauges off Kamaishi seismic model of Shao et al. (2011) and a model based on finite-element (TM1, TM2) indicate a two-stage tsunami with a long wavelength Green's function fitting of onshore and offshore geodetic data to for- smooth 2 m amplitude wave with a superimposed short wavelength 5 m ward model tsunami excitation. The preferred FEM source with Mw 8.8 amplitude wave (Maeda et al., 2011). The analysis of these records has concentrated slip near the trench with peak slip of 51 m, and using using a simple 4-depth increment model indicates 42 m of slip near the the time sequence for the slip based on Yue and Lay (2011) it provides a hypocenter and 57 m near the trench axis south of the rupture area of better prediction of near-field tsunami waveforms, but both models the 1896 Meiji Sanriku tsunami earthquake. The model produces fair underpredict runup along the Sanriku coastline from 38°N to 39°N. fits to recordings at Deep-ocean Assessment and Reporting of Tsunami As indicated in Fig. 6, there has been significant evolution of slip (DART) sites, but signals are late to the north, suggesting that slip needs models inferred from geodesy, from the long smooth models with to extend farther north into the 1896 rupture zone. ~30 m peak slip near the hypocenter (as in Fig. 6a), to much more Rapid tsunami analysis by NOAA using the MOST method estimated spatially concentrated and up-dip slip models with peak slip of 50 to the tsunami source within 1.5 h, providing a basis for successful real 60 m at shallow depth when using hr-GPS time series (Fig. 6b) or from time flooding forecasts around the Pacific(Wei et al., 2013). The NOAA inclusion of up to 7 offshore GPS/Acoustic measurements in static in- tsunami source model involves 6 of the tsunami source cells along the versions. Given the huge on-land data set, this is a very sobering result; megathrust in the Tohoku region, all located seaward of the hypo- for a wide megathrust environment, little confidence can be placed in center, with 4 distributed along the trench, extending to 40.7°N

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Fig. 7. Finite-fault slip distributions for the March 11, 2011 Tohoku earthquake inverted from only tsunami observations. (a) Tsunami waveform inversion of ocean-bottom pressure, GPS wave gauges and coastal tide gauges by Fujii et al. (2011). (b) Inversion by Koketsu et al. (2011), in which the fault had to be extended seaward relative to the GPS solution in Fig. 6a, in order to match the tsunami data. (c) Inversion by Satake et al. (2013) with a grid extending farther north than in (a) and using multiple time windows extending up to 6 min from the origin. (d) Estimated for slip distribution from inverted initial tsunami height distribution by Saito et al. (2011).

(covering the 1896 rupture zone). The scaling of pre-computed re- peak in the two-component waveforms. Their inverted slip model has 22 sponses to match nearby DART recordings indicate 8–9 m initial sea M0 = 3.8 × 10 Nm, with no slip north of 39°N. Koketsu et al. (2011) floor uplift concentrated along the trench. This model provides better and Yokota et al. (2011) invert just tsunami observations as well, prediction of the ~40 m runup along the Sanriku coast north of 39°N comparing with inversions of other data and joint inversions. Koketsu than the USGS-NEIC seismic model (Fig. 5c), and it predicts regional et al. (2011) found that to fit the tsunami signals, they had to extend the GPS buoys and wave gauges fairly well. The total energy transmitted by fault model farther toward the trench (Fig. 7b) than in inversions of tsunami waves was estimated as 3.9 × 1015 J using the two closest other data sets (e.g., Fig. 6a shows their on-land geodetic inversion for DART recordings and the MOST method (Tang et al., 2012). comparison). Direct fault model inversion of tsunami waveforms using 33 tide Satake et al. (2013) perform a multiple time window inversion of 53 gauges, GPS wave gauges, and bottom pressure sensors was performed tsunami waveforms from ocean-bottom pressure, GPS, coastal wave and by Fujii et al. (2011). They infer that large slip on the central mega- tide gauges using linear shallow water equations and nonlinear equa- thrust was responsible for the large Sendai inundation, with slip > 40 tions for coastal stations for finite difference Green's functions. The slip m along the trench axis (Fig. 7a) giving rise to the short wavelength model has 25 m of slip near the hypocenter, in the vicinity of the 869

14 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 8. Inversion for initial sea surface displacement for the March 11, 2011 Tohoku earthquake from tsunami recordings. (a) Posterior median model from Dettmer et al. (2016). Source areas of the 869 Jogan (red dashed line) and 1896 Sanriku earthquakes (blue dashed line, gray star), are shown. (b) Cumulative source model inverted assuming variable rupture velocity, dispersive waves and 15 km Gaussian basis functions from Hossen et al. (2015b).

Jogan tsunami source region (Fig. 7c). This slip produces the initial rise concentrated up-dip of the hypocenter with peak slip of about 25 m at of the tsunami waveforms as well as the inundation in the Sendai and the trench. Løvholt et al. (2012) forward model tsunami at Pacific Ishinomaki plains. Huge slip of up to 69 m near the trench 3 min after buoys and inundation in ten areas for 4 scenario slip models, demon- rupture initiation extends along strike over 400 km with > 10-m slip. strating that heterogeneous slip is needed to even begin to match runup The slip extends through the 1896 zone. This near-trench slip is re- observations. They infer slip of 15–20 m across a 150 km wide zone, sponsible for the peak tsunami amplitudes and maximum heights on the however, the fits to data are not exceptional. MacInnes et al. (2013) northern Sanriku coast. The average slip on the fault is 9.5 m, with compute tsunami for 10 source models. Many of the models yield 22 M0 = 4.2 × 10 Nm. They estimate that horizontal motion is re- predictions within 20% of the observations from 38° to 39°N, including sponsible for 20–40% of the wave amplitudes. Slip models with 44 or extent of inundation of the Sendai plain. This supports the existence of 55 subfaults were considered with inclusion of narrow up-dip subfaults large initial seafloor uplift around 38°N, 143.25°E. However, most yielding slip all the way to the trench. The calculated runup for models models did not reproduce the extreme runup north of 39°N, leading the with a 3 min delay in shallow slip fits the data somewhat better than for authors to suggest a need for an additional tsunamigenic source such as instantaneous slip, but predicted peak runups are only as much as 25 m. splay faulting or submarine slumping. Some studies use the tsunami observations to evaluate and improve Many technical issues for tsunami modeling have been explored slip models from other data inversions. Comparison of early seismic slip using the 2011 recordings. Modeling inundation with buildings is very models that assumed the USGS-NEIC hypocentral location with the challenging and limits prediction of observations, as discussed by Baba arrival times of nearby DART stations to the east indicated a need for et al. (2014). The importance of wave dispersion and nonlinear effects seaward shift of the models by ~40 km east-southeast (Lay et al., for models of the 2011 tsunami are explored by Saito et al. (2014), 2011b). Yamazaki et al. (2011) perturb the orientation of the seismic using the initial tsunami height model from Saito et al. (2011). If dis- slip model from Lay et al. (2011a) (Fig. 5a) to improve the fit to DART persion is not included, initial heights are overestimated, even for re- and 9 near-field tsunami observations, rotating the strike by 10° and the latively short paths. Linear dispersive Green's functions are used in dip by 2°, but finding good fits for the large shallow slip model. time-dependent tsunami generation inversions by Hossen et al. (2015a). Yamazaki et al. (2013) use the perturbed model to calculate resonance While it is of clear interest to determine faulting parameters com- modes along the Honshu coast. Similarly perturbed versions of the Lay patible with the tsunami observations, the possibility of non-faulting et al. (2011a) seismic model were further used to compute standing origins or faulting poorly constrained by other geophysical measures wave surges along the Hawaiian Islands and to successfully model always exists. Thus, many studies of tsunami signals focus on the de- tsunami amplitudes and flow speeds recorded at insular shelves, wa- termination of the tsunami source area and/or initial sea surface dis- terways and harbors (Yamazaki et al., 2012; Cheung et al., 2013; placement by various forms of reverse time imaging. Hayashi et al. Benjamin et al., 2016). Bai et al. (2015) extend these forward models to (2011) estimated the tsunami source area as being 50 km wide and Pacific wide tsunami and standing wave calculations. Petukhin et al. 200 km long from back-tracking first arrival times at offshore wave (2017) use tsunami observations to ‘tune’ finite-fault inversions of long- gauges, GPS buoys, cabled ocean bottom pressure gauges and tsunami period strong-motion recordings in a similar manner to the teleseismic buoys. The picking of wave arrival times is difficult and the inferred analysis of Yamazaki et al. (2011). They find a model with slip source area extends well north of 40°N, into the 1968 rupture zone,

15 T. Lay Tectonophysics 733 (2018) 4–36 where coseismic slip did not occur. Tsushima et al. (2011) and sets, but more importantly, it exploits complementary sensitivity to Takagawa and Tomita (2012) determine initial sea level height by a different aspect of the rupture provided by each data type, essentially linear wave back-propagation method like that applied by Saito et al. constraining portions of the null space of separate models. For example, (2011) finding a similar concentration of high sea level seaward of the tsunami waveforms are particularly effective in constraining the sea- hypocenter. ward and along-strike extent of the source region, potentially stabi- A Bayesian approach with a wavelet decomposition of the dis- lizing the poor up-dip resolution of land-based geodetic data. placement field is used to reconstruct initial sea level displacement and Parameterization of joint inversions is, however, intrinsically compli- its uncertainty by Dettmer et al. (2016). The posterior median model is cated by the varying resolution of different datasets and choice of re- shown in Fig. 8a. The method adaptively adjusts parameterization relative weighting of the diverse data. lative to resolution, giving a parsimonious representation. Up to 8 m sea There have been numerous joint inversions using seismic and geo- level displacement occurs near the trench eastward from the hypo- detic data. Ammon et al. (2011) combined teleseismic P waves, Ray- center, with a well-resolved finger of uplift extending to north of 40° leigh wave source time functions, and hr-GPS observations in a kine- along the trench, spanning the 1896 rupture zone. Hossen et al. (2015a) matic inversion, with the rupture velocity increasing from 1.5 to apply time reversal imaging to reconstruct instantaneous initial sea 2.5 km/s in accord with back-projection constraints. Assuming uniform surface displacements, comparing results with the method of Saito et al. rigidity, they found a 40 m peak slip zone centered just up-dip of the (2011) and finding a quite compatible basic pattern of large uplift be- NEIC hypocenter. Kinematic finite fault inversions of broadband tween the hypocenter and the trench. A linear tsunami waveform in- seismic data and GPS observations are shown in the Supplement of version for sea surface displacement using Gaussian wavelet basis Simons et al. (2011), which show slip significantly closer to the trench functions was applied by Hossen et al. (2015b) to obtain the cumulative than the geodetic-dominated model presented in the main text. Chu sea surface displacement shown in Fig. 8b. The peak water height is et al. (2011) found that slip inverted from GPS and teleseismic data 8 m. They found that accounting for dispersion, even over the relatively depends on the source location; using their revised seaward location short paths to regional recording sites, model parameterization, and shifts the slip closer to the trench. allowing for rupture kinematics (rather than instantaneous displace- Wei et al. (2012) invert static displacements from 797 GPS stations, ment) are all important factors for the 2011 event. Fig. 8b shows a 5 seafloor displacements, and strong motion records from 14 K-Net finger of northward sea surface uplift tracking the trench axis. The stations to obtain the model shown in Fig. 9a. The strong increase in slip imaging and location of this feature is very sensitive to dispersion in the in the shallow megathrust was attributed to acute dynamic weakening, signals and to assuming finite source time. Hossen et al. (2015b) sug- possibly involving thermal pressurization. Checkerboard tests indicate gest that it might be consistent with a submarine mass failure producing that the strong motion data alone have limited resolution of slip up-dip debris accumulation in the bathymetric low along the trough, but from the hypocenter, while on-land static inversion resolves slip out to faulting in the 1896 zone could also be responsible. Baba et al. (2017) the hypocenter, but has no resolution of slip near the trench. Inclusion use the initial sea surface displacements from Saito et al. (2011) and of seafloor deformation data in geodetic inversions still provides low Hossen et al. (2015b) as initial source conditions, performing accurate resolution in the northern and southern regions of the megathrust. The far-field calculations with Boussinesq terms, seawater density, elastic combined inversion appears well-resolved to ~39.5°N. Erratic rupture loading, and gravitational potential energy change. Including the latter velocity fluctuations from 1 to 2 km/s and slip velocity of up to 2 m/s in three features provides progressively increasing time shifts at distant the shallow high-slip region were found in the models. stations with little waveform affect, allowing times of remote DART Inversions of teleseismic, local strong motion and terrestrial and signals to be accurately predicted. Inclusion of the Boussineq terms has seafloor static geodetic data were conducted by Lee et al. (2011). They important waveform effects. find > 50 m slip during a 160 s rupture duration with the large slip Jiang and Simons (2016) apply probabilistic imaging of seafloor patch up-dip of the hypocenter (Fig. 9b). The initial rupture velocity displacements in a Bayesian framework, incorporating uncertainty in is < 1.5 km/s, then increases to 2.5–3.0 km/s as in the model of dispersive tsunami waves. Their average model has a peak uplift of 5 m Ammon et al. (2011). Repeated slip occurred on central segments of the near the inner-outer forearc transition, with 2 m of uplift at the trench model, as in Ide et al. (2011). Lee (2012) inverts 18 teleseismic axis along about 50 km. They infer uplift and tilting of the 40 km wide broadband P waves and 451 GPS statics finding a model similar to that toe. Slip deficit in the shallow region could be due to inelastic de- of Lee et al. (2011). A large slip zone with peak slip of about 35 m is formation or could be accommodated by afterslip. Their images do not found up-dip from the hypocenter at depths of 5 to 30 km, and a sec- show clear northward extension of along trench uplift, but have very ondary slip patch with 15 m slip extends down-dip from the hypo- diffuse uplift in the north. The differences between their mean model center. The estimated rupture duration is 180 s. Kubo and Kakehi and those shown in Fig. 8 are substantial and inference of tilting and (2013) also jointly invert telseismic, GPS and 5 seafloor displacements, strong reduction of slip to the trench appears tenuous. exploring the maximum slip duration and rupture expansion velocity in These initial sea level reconstructions all place peak sea level or sea kinematic inversions. They find similar near-trench patterns for seismic, fl oor uplift 30 to 40 km west of the trench near 38.0° to 38.3°N, con- geodetic, and joint (Fig. 9c) inversions. The peak slip in the joint in- sistent with large slip on the megathrust in this vicinity, as found in the version is 43 m, up-dip from the hypocenter. Wang et al. (2013) invert tsunami fault model inversions in Fig. 7a, b and c, the hr-GPS inversion strong motion and GPS data including 5 seafloor displacements. They in Fig. 6b and the geodetic inversion with offshore displacements in find slip up-dip from the hypocenter with peak slip of 25 m. Fig. 6c, and the seismic wave inversions in Fig. 5a, c and d. This The hr-GPS time-varying displacement recordings intrinsically strongly indicates that most, if not all of the tsunami excitation is di- combine seismic and geodetic information (e.g., Ammon et al., 2011; rectly related to faulting on the megathrust, not to inelastic deformation Yue and Lay, 2011), and these data have been further combined with of the toe or submarine slumping. additional seismic data in what can be called seismo-geodetic inversions. Yue and Lay (2013) perform joint inversions of hr-GPS signals, 3.4.6. Inversions with multiple data sets teleseismic P waves, Rayleigh wave source time functions and 5 ocean The discipline-specific models of the 2011 rupture discussed above bottom deformation statics, obtaining the model in Fig. 9d. This has a 22 all have limitations stemming from the configuration and nature of the M0 = 4.2 × 10 Nm and a large-slip patch of up to 60 m slip up-dip data used. The various examples of success in using fault models de- from the hypocenter. There is down-dip extension of minor slip to the rived from one data set to forward model other data sets indicate the south, corresponding to the regions of high frequency radiation in potential for joint inversion or iterative modeling of the different data Fig. 3. Filtered (> 5 s period) strong motion recordings from KiK-net types. This is intended to find a self-consistent model for multiple data and K-net were inverted with hr-GPS recordings by Frankel (2013), who

16 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 9. Cumulative slip from time-varying rupture models from joint inversion of seismic and geodetic data. (a) Model of Wei et al. (2012), obtained using 797 on-land GPS and 5 offshore seafloor displacements along with 14 accelerometers. There are 5 segments (S0 to S4) with varying dip. The moment rate function is shown in the inset. Blue and Pink vectors are predicted displacements on top of white observations. (b) Inversion of teleseismic P waves, on-land and seafloor static deformations and strong motion records by Lee et al. (2011). (c) Inversion of teleseismic P and PP phases, 351 on-land GPS and 5 offshore seafloor displacements by Kubo and Kakehi (2013). Afterslip (broken lines) from Ozawa et al. (2011) are shown, along with interplate aftershocks from F-net CMT solutions. (d) Joint inversion of 1-Hz GPS, 5 seafloor displacements, teleseismic P waves, and Rayleigh wave source time functions by Yue and Lay (2013). Observed and predicted static displacements are shown.

finds a model involving 3 subevents, one up-dip from the hypocenter similarity of seismic inversions and tsunami inversions and some of the with peak slip of 65 m. The model underpredicts the observed seafloor better resolved geodetic inversions support the premise that faulting displacements. Some of the mismatch could be due to afterslip, but it is produced all of the observations. unlikely to be the entire explanation. Koketsu et al. (2011) explored whether a unified model could be Joint inversions of seismic and/or geodetic observations with tsu- developed, first performing separate inversions of strong motion, tele- nami signals represent the most comprehensive attempts to reconcile all seismic, on-land GPS statics (Fig. 6a), and tsunami (Fig. 7b) data sets. of the observations with models of faulting. This does raise questions of Their seismic and geodetic models all have slip concentrated below or whether all of the processes are directly produced by faulting or whe- along strike from the hypocenter. Joint inversion of the seismic and ther inelastic or slumping contributions may lead to intrinsic in- geodetic data sets concentrates slip just down-dip of the hypocenter. compatibilities in joint inversions. As noted above, the general Slip does not extend to trench, but provides a reasonable fitto5

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Fig. 10. Finite-fault slip distributions for the March 11, 2011 Tohoku earthquake joint inversions of geodetic, seismic and tsunami observations. (a) Joint inversion of tsunami and geodetic data by Romano et al. (2014). Green contours are the slip distribution for the March 9, 2011 Mw 7.3 foreshock. Magenta dashed area is the location of the 1896 rupture. Black circle is location of the JFAST drilling site. (b) Joint inversion of seis- mogeodetic and tsunami gauge data by Melgar and Bock (2015). (c) Mean posterior slip distribution from static inversion of GEONET GPS, seafloor geodetic stations (triangles), tsunami gauges (circles), and DART stations from Minson et al. (2014). Red contours are for the Mw 7.9 aftershock slip. (d) Joint inversion of seismic, hr- GPS, static GPS, seafloor geodesy and tsunami waveform data by Bletery et al. (2014). The inset shows the far-field moment rate function.

seafloor displacements. However, separate tsunami inversion could not Yokota et al. (2011) instead invoke inelastic deformation near the toe, fit the data well with a similar model, and they had to add an up-dip invisible to seismic and geodetic data as a possible explanation for the row to the model with slip up to 40 m locating near the trench. They did tsunami under-prediction. not invert the tsunami data with other data types, so they did not Static GPS displacements on-land and 12 seaward DART sea floor achieve a truly unified inversion. Yokota et al. (2011) followed up on pressure gauge recordings were inverted by Simons et al. (2011) using a this with a joint inversion including the tsunami data, finding that it Bayesian procedure. Emphasis was placed on fitting the GPS data, as the shifts the largest slip region (up to 35 m slip) up-dip to between the fits to the tsunami signals were not very good. The mean model has slip hypocenter and the trench, but the model considered does not extend to in the center of the hypocenter, similar to the GPS only inversions de- the trench, so it cannot really resolve whether very near-trench slip scribed earlier, and in contrast to the kinematic slip models with up-dip occurred. Their tsunami-only inversion placed the slip on the upper slip near the trench from the combined GPS data and teleseismic data edge of the model, and their checkerboard solutions show there is poor inversions shown in the paper's supplement. Gusman et al. (2012) geodetic resolution in the upper third of the fault, but good tsunami jointly inverted 17 tsunami waveforms from DART, tide gauge, sea resolution. Thus it seems likely that extending the fault model to the bottom pressure gauges and GPS buoys, static GPS data and 5 seafloor trench would further shift the slip distribution, and may improve (with displacements, obtaining a model with peak slip of 44 m and slip of increased slip) the systematically under-predicted tsunami waveform 41 m near 38.2°N at the trench. Peak sea surface uplift of 9 m was found 22 amplitudes they show in the supplement. Koketsu et al. (2011) and just east of the hypocenter. M0 = 5.5 × 10 Nm for this model. Peak

18 T. Lay Tectonophysics 733 (2018) 4–36 slips are underestimated for some of the short wavelength pulses, so they find the peak slip is at depth and not at the trench and they assert inclusion of additional non-faulting tsunami excitation from block uplift that data with large trench deformation from Ito et al. (2011b) and of the toe of the wedge (e.g. Tanioka and Seno, 2001) was explored, Kodaira et al. (2012) may have been affected by landsliding and the resulting in a very narrow 11 m high sea level uplift right along the Fujiwara et al. (2011) data have significant displacement on at least one trench. This improves the waveform fits at several of the tsunami sta- secondary fault. The mean posterior model in Fig. 10c predicts 40 m tions. Romano et al. (2012) similarly invert data from DART buoys, 7 horizontal and 6 m vertical motion at the toe compared to 50 m hor- pressure sensors, coastal wave gauges, and GPS-buoys, static onshore izontal and 7–10 m vertical in Fujiwara et al. (2011). The model fits the GPS and 7 GPS/acoustic measurements. Their solution has 48 m peak tsunami signals well. The model of Bletery et al. (2014), obtained by slip just southeast of the hypocenter and up to 35 m close to the trench joint inversion of high-rate GPS, static GEONET, seafloor, teleseismic, near 38.2°N. The slip is larger and shifted seaward relative to inversions strong motion, and tsunami buoy data places peak slip near the trench, of just onshore GPS statics. with some slip extending northward to 39.5° and beyond, and peak slip Joint inversion of GPS statics, 5 seafloor displacements, and 7 DART of 60 m at the trench near 38.3°N (Fig. 10d). Minson et al. (2014) assert waveforms was performed by Hooper et al. (2013). They find a model that their models are free from non-physical regularization, but it is with slip extending to the trench with 57–74% of the maximum slip of curious that their mean model is systematically shifted southward and 73 to 81 m. Their model provides good prediction of the pattern of down-dip relative to other joint inversions in Fig. 10, which are rela- runup and inundation along the coast, although it under-predicts peak tively consistent. Somehow the Bayesian methods do not seem to ade- amplitudes along Sanriku by about 10 m. Omission of the DART data quately capture the stable behavior of separate joint inversions so it is leads to severe (> 20 m) under-prediction of tsunami amplitudes along unclear how meaningful the mean models are. Sanriku even when seafloor geodetic data are included. The importance of horizontal motion of the dipping bathymetry is demonstrated, 4. Outstanding issues about the rupture especially for creating the peak short wavelength tsunami which originates near the trench. The foregoing review of rupture models for the 2011 Tohoku Wei et al. (2014) perform joint inversion of tsunami waveforms and earthquake shows progressive convergence of slip models, with slip on-land geodetic data. They used tsunami inundation models from Wei being increasingly localized along strike and concentrated up-dip, ex- et al. (2013) to provide a distribution of seafloor uplift estimates. Their tending all the way to the trench with slip ~50 m near 38.2°N. Over joint inversion model has a 12° dip, and has large slip of up to 50 m time the rupture models have progressed from quite smooth re- trenchward from the hypocenter. The joint model does not predict the presentations to more detailed slip distributions, especially for the runup along Sanriku as well as the tsunami inundation model of Wei geodetic and tsunami models. In part, this reflects improved modeling, et al. (2013), but does better than the seismic model of Hayes et al. inclusion of offshore data, and the complementary sensitivity of dif- (2011). It has minor slip north of 39°, and little seafloor uplift in the ferent data sets used in joint inversions. Increasing confidence in some area despite the presence of such in the inundation model. The joint slip features of the models may also motivate reduced smoothing and model appears to be dominated by the GPS fitting, and thus provides damping of the inversions. Models have also progressed from simple only moderate fit to the regional buoy and remote DART waveforms. planar dipping faults in a half-space or 1D plane layered structure to The most recent set of joint inversions including tsunami observa- more realistic numerical models with 3D bathymetry, wedge structure, tions are shown in Fig. 10.A3Dfinite-element model was used to in- dipping plate structure, volumetric velocity heterogeneity, and dip- clude structural complexities in joint inversion of tsunami and geodetic varying or laterally undulating fault geometry. It is difficult to evaluate data by Romano et al. (2014), yielding the slip model shown in Fig. 10a. the relationship between more complex inferred faulting and the in- They note a close spatial relationship between their slip model and local creasingly complex model parameterizations, so no attempt is made to tomographic high P wave velocity anomalies (Zhao et al., 2011). Di- do so here. Some of the differences among current models may re- minishing slip extends northward along the trench throughout the 1896 present the different parameterizations, but the similarity of the ma- rupture zone, and slip appears to be low in the region of the Mw 7.3 jority of joint inversion models (Fig. 10) suggests that different para- foreshock. The model predicts about 40 m slip near the JFAST drilling meterizations are at least not overwhelming the source information. site. Melgar and Bock (2015) inverted three-component displacement However, there are many remaining questions about the basic nature of and velocity seismo-geodetic records (from combined hr-GPS and the rupture, including relationships with prior coupling, prior earth- nearby strong motion instruments) for 20 stations along with 8 offshore quake ruptures and precursory slow slip, aftershocks and afterslip, tsunami recordings from moored GPS buoys and ocean bottom pressure frequency dependence of seismic radiation across the fault, extent of sensors to obtain the kinematic model in Fig. 10b. Their seismo-geo- rupture in the near-trench region, stress drop, and dynamical processes detic only and joint inversions are similar to the seismo-geodetic in- of fault weakening. These key issues are now discussed in the context of version of Yue and Lay (2013) (Fig. 9d) in having a localized zone of the existing suite of rupture models. 50 m slip adjacent to the trench. Inclusion of the tsunami data localizes slip closer to the trench and increases the duration of the shallowest 4.1. Relationship to prior coupling and megathrust ruptures source time function. Calculation of runup for the joint model does not match the peak runup north of 39.5°N. The along-strike northward In general, models of fault locking available prior to the rupture extension of slip into the 1896 zone was viewed as evidence that the (Fig. 2) accurately identified an along-strike domain of strain accu- shallow region of the megathrust can accumulate strain. mulation, but relative to the better resolved slip models, they seriously Monte Carlo Bayesian static and kinematic inversions were per- underestimated the degree of up-dip slip that could occur. Hashimoto formed by Minson et al. (2014) using 6 h-GPS, 738 static GPS, 7 sea- et al. (2012) updated their slip deficit map without using a constraint of floor displacements, near-field and far-field tsunami data, providing an up-dip free slip. This shifts the inferred zones of locking along Honshu ensemble of samples of the posterior probability density function for and Hokkaido seaward (Fig. 11.a), improving consistency with early which the mean is shown in Fig. 10c. The peak slip in the mean model is land-based geodesy inversions for slip, but still not capturing the po- 74 m, and most slip is concentrated in depth range of 10–20 km, unlike tential for near-trench short-wavelength tsunami generating slip. the other joint models in Fig. 10. Slip decreases toward the trench, with Loveless and Meade (2011) also updated their coupling estimates by significant displacement at the toe only in a small region around 38.6°. removing assumptions of no up-dip interseismic strain accumulation, No slip is indicated along the trench north of 39°N, so this model im- which allows coupling to extend to the trench (Fig. 11b), and they find plies little re-rupture of the 1896 zone. The rupture velocity tends to that about half of the early slip models are more consistent with the decrease as depth shallows in this model. The authors emphasize that original coupling models while others have slip more seaward.

19 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 11. Updated retroactive computations of interplate slip-deficit in which the coupling is allowed to extend farther seaward (even if it is not resolved to do so by the data). These models from broaden the zones of inferred interplate coupling relative to the models before the earthquake in Fig. 1. (a) The updated slip-deficit model of Hashimoto et al. (2012) is shown in blue with contour intervals of 3 cm/yr. The yellow star indicates the USGS-NEIC epicenter. The white circle is the Mw 7.3 foreshock. Aftershock locations for the first three days are shown by yellow circles. The green region superimposes a slip model with 4 m slip contours inverted from GPS static and offshore displacement data, which largely overlaps the region of strong coupling. (b) The updated coupling fraction estimate of Loveless and Meade (2011), without constraint of zero strain accumulation at the up-dip end of the model.

Consideration of the more recent models indicates that most are more zone has approximately tripled from values before the event, to near 0.6 compatible with the revised coupling estimates. This suggests that it is afterwards (Scholz and Campos, 2012). misleading to impose an up-dip free slip condition if there is no actual Long-term seismicity patterns are also valuable for characterizing constraint from the on-land data. Of course, it is hard to evaluate the plate boundary stress state prior to the 2011 rupture zone. Asano coupling at depths shallower than a laterally extensive locked zone due et al. (2011) examine moment tensors for events on and off the plate to stress shadowing effects (e.g., Bürgmann et al., 2005). Sato et al. boundary, with the distribution of interplate thrust activity fringing the (2013) retrospectively incorporate the offshore GPS/Acoustic mea- mainshock large-slip zone. Lin and Wu (2012) map cumulative seismic surements for the 9 years prior to the 2011 mainshock into assessment moment for events from 1976 to 2011, finding that larger moment is of interplate coupling improving the spatiotemporal variation. Weak located in the down-dip area of the 2011 mainshock rupture than in the interplate coupling off Fukushima Prefecture relative to Miyagi Pre- up-dip area. Up-dip moment is located where slow slip activity and fecture is clearly documented, enhancing the trend found from onshore repeaters are observed. Ye et al. (2013) analyzed the region off Sanriku data. with low seismicity, few M > 5 events, and lack of large historical A valuable additional constraint on the depth extent and distribu- ruptures, designating this the Sanriku Low Seismicity Region (SLSR). tion of coupling is provided by occurrence of repeating small events, This includes the region of the M ~5 Kamaishi repeater (Matsuzawa which appear to involve stick-slip patches surrounded by quasi-static et al., 2002). Postseismic slip peaks in this region (e.g. Ozawa et al., slow slip regions on the boundary (Uchida et al., 2004). Prior to the 2011), and mainshock slip was low, likely only extending into the 2011 event these were extensively detected near the 1989, 1992 and southwest portion of the SLSR. Thus it appears to have delimited the 1994 M ~7 earthquakes off Sanriku, with migrations of seismicity for 2011 rupture to the northwest. This weakly coupled zone also causes the 1994 event indicating slow slip in the prolonged postseismic de- the land based geodetic models to have even further reduced resolution formation that occurred over the next year. Examination of repeating of slip directly up-dip near the trench where the 1896 Meiji tsunami earthquakes over the entire megathrust (Uchida and Matsuzawa, 2011), earthquake occurred. exploiting the Hi-Net detection capabilities, indicates high coupling There is also evidence of a large-scale long-term slow acceleration of from 1993 to 2000 in the 2011 large-slip zone by the absence of re- aseismic slip on the megathrust from 1996 to 2011, apparent after the peating sequences, whereas repeating events in the northern, western contributions from earthquake with magnitudes of 6 to 8 are removed and southern regions indicate slow slip deformation and lower strain from continuous GPS records (Mavrommatis et al., 2014, 2015; Yokota accumulation in areas surrounding the large-slip zone of the 2011 and Koketsu, 2015). Fig. 12 shows the pattern of forward accelerating rupture. This information can help to overcome the limited resolution slip along Miyagi and Fukushima over a large region near the coast. from on-land geodesy for localizing the strain accumulation off shore by Sequences of repeating earthquakes offshore central Honshu show ac- estimating localized slip-rates with good spatial resolution. Based on celerating rates, and joint inversion of GPS and seismicity data refines both the size of the 2011 earthquake and the geodetic estimates of fault the forward slipping image (Fig. 12b). This decadal transient super- zone locking, the estimated seismic coupling coefficient for the Honshu imposes on the geodetic velocities used to infer coupling, so the

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Fig. 12. (a) Map of GPS station accelerations estimated by Mavrommatis et al. (2014) (black arrows). Colors (blue to red) represent dip-slip component of estimated slip acceleration on the plate interface from 1996 to 2011. Triangles show repeating earthquake locations, with yellow indicating decelerating recurrence and cyan indicating accelerating recurrence. Gray circles are and white squares are less reliable repeaters. Contours are coseismic slip distribution for the 2011 event in 10 m intervals from Hooper et al. (2013). (b) Preferred model of slip accelerations from joint inversion of GPS and repeating earthquakes. Observed GPS accelerations shown in black arrows with 2σ error ellipses, predicted in green. From Mavrommatis et al. (2015).

combined information could help to identify truly locked regions. The There has been substantial focus on the 2011 9 March Mw 7.3 driving stress this transient applied to the mainshock slip zone is about foreshock, as this event was both preceded by a month long slow slip/ 0.01 MPa (Yokota and Koketsu, 2015). seismicity migration and followed by afterslip that expanded to near the Tidal triggering of background seismicity in the large-slip region of mainshock hypocenter. Two sequences of migrating seismicity brack- the 2011 rupture zone over a decade prior to the event was detected by eting the foreshock were analyzed by Kato et al. (2012). The first oc- Tanaka (2012), but no correlation is found after the mainshocks. This curred before the foreshock, in mid-February, migrating at 2 km/day to supports the notion that the region was extensively critically stressed near the 7.3 foreshock, and the second migrated at 10 km/day after the and susceptible to triggering by increases in tidal shear stress. Evidence foreshock toward the subsequent mainshock epicenter. Small repeating for seismic quiescence beginning about 20 years before the 2011 event events in the migrating seismicity suggest that these sequences were in the deeper region of the megathrust has been reported by Katsumata accompanied by slow-slip transients. (2011). Miyazaki et al. (2011) used on-land GPS to constrain the slip of the Two transient slow slip events in 2008 and 2011 occurred near the foreshock and its afterslip. They find that the rupture expanded down- 2011 hypocenter. Ito et al. (2013) discuss temporary OBS, ocean dip from the hypocenter, and that over the next 50 h there was com- bottom pressure sensor, and on-shore volumetric strain recordings for parable moment in the foreshock afterslip that expanded to near the both sequences. The December 2008 event was accompanied by an Mw mainshock hypocenter. From this, they infer that the afterslip of the 7.3 5.7 event, with slow deformation lasting for a week located in the large- foreshock triggered the mainshock onset, although the spatial resolu- slip region of the 2011 rupture. This suggests either small-scale het- tion of their model is poor. Munekane (2012) also modeled the GPS erogeneity or temporal variation in frictional behavior. Slow slip locally time series, finding 0.41 m maximum slip for the foreshock and a decay preceded the March 9 foreshock with a 1-month duration from Feb- time of 0.63 days for its afterslip. Gusman et al. (2013) constrained slip ruary 2011 to the Mw 7.3 foreshock. Ito et al. (2015) report evidence of the Mw 7.3 foreshock using tsunami inversion. They calculate an for 5 to 8 Hz tremor episodes from OBS observations. However, no increased Coulomb stress of 1.6–4.5 bar near the mainshock hypo- significant precursory deformation above 2 to 4 cm was detected in the center. The foreshock afterslip migrated with decreasing velocity over day before the mainshock by Hino et al. (2014), who corrected con- two days in the analysis of Ando and Imanishi (2011), with a reduced tinuous ocean-bottom pressure records for tidal and nontidal fluctua- slip region within the mainshock coseismic slip model of Iinuma et al. tions. While postseismic deformation for the Mw 7.3 foreshock was (2012) (Fig. 6c) surrounding the zone of the foreshock. Geodetic in- apparent, no preslip with moment greater than Mw 6.2 in the vicinity of version for the foreshock and its afterslip using GPS, ocean-bottom the foreshock hypocenter or > 6 along the interface near the trench pressure sensors and the on-land KNK volumetric strain site by Ohta occurred. Hi-net tilt records were examined by Hirose (2011) for pre- et al. (2012) indicates that the afterslip region, with peak slip of over cursory tilt change in the short term (days) to medium term (month) to 0.4 m, has some overlap with the Mw 7.3 coseismic slip area that had a look for preslip to the 2011 event. He found no signal of preseismic tilt peak slip of 1.5 m. Both lie within the mainshock's 20 m slip contour change or preslip larger than Mw 6.2 on the deeper megathrust or estimated by Iinuma et al. (2012) (see Fig. 13.a). The afterslip again larger than Mw 7.3 near the hypocenter. appears to migrate to the hypocenter of the mainshock. Marsan and

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Fig. 13. Spatial distribution of event faulting types (a) before (July 1984 to 11 March 2011, 14:45) and (b) after (11 March 2011, 14:46 to December 2013) the Tohoku earthquake. Contours of slip distributions for major interplate events are shown in black. In (a) main source areas for the 1994 Sanriku-oki earthquake (M7.6) and the larges 9 March 2011 foreshock (Mw 7.3) are shown by yellow and light blue areas, respectively. Black ellipsoids (regions (A)–(D)) indicate earthquake clusters including aftershock areas of the 2003 Mw 7.1 (D) and 2005 Mw 7.2 (A) intraplate earthquakes. In (b), the area with coseismic slip of ≥30 m from the Tohoku earthquake (Iinuma et al., 2012) is light blue. The slip areas for two large aftershocks on 11 March 2011 (Mw 7.4, Mw 7.7) are shown by gray-ﬁlled contours (Kubo et al., 2013; Muto et al., 2014). Black ellipsoids (regions (E)–(H)) indicate earthquake clusters including aftershocks of the major intraplate earthquakes that occurred at 15:25 JST, 11 March 2011 (Mw 7.5), on 14 March (Mw 6.9), and 7 December (Mw 7.3) 2012. Stars indicate epicenters of major earthquakes. From Nakamura et al., 2016.

Enescu (2012) use continuous F-net recordings to search for non-cat- 200 km long with magnitude ~8.4. Namegaya and Satake (2014) re- alog events down to magnitude 1.2, better defining the two-day long analyze the data for the 869 event using constraints from observations sequence after the March 9 foreshock. They observe an interval of 3 h for 2011 of how deep the flow depths were at the points of sandy de- with increased low frequency noise during migration of seismicity to- posits (which had been conservatively used as maximum inundation ward the mainshock hypocenter. They argue that an aseismic transient levels previously). For the 2011 event flows depths of 1 m and flow is not required to account for the sequence, and that any aseismic slip speed of 0.6 m/s at the sites of sand deposits extends the inferred in- played only a minor role in the triggering cascade of events, leading to undation zone for the 869 event, leading to an estimated rupture length the mainshock initiation. of 200 km and minimum magnitude of ~8.6 (Fig. 8a shows the location The 2011 mainshock ruptured regions of prior major ruptures that of their uniform slip model for the 869 event). Satake et al. (2013) note appear to have been accumulating slip deficit in the geodetic coupling that the Sendai inundation does not resolve contribution from huge models. The region of the 1938 events off Fukushima and Ibaraki near trench slip for the 2011 event, so the same must hold for the 869 (Fig. 1) was ruptured with low slip in 2011. This area has no history of event. While there must be large uncertainties in the location of the 869 large events prior to 1938. The up-dip portion of the megathrust in this event, it is very likely that the 2011 event re-ruptured the same region southern area does not appear to have slipped in the mainshock. Simons at a minimum. et al. (2011) note that this region was not prominent in the coupling The other important prior event of interest is the 1896 tsunami models and could have large afterslip. The repeating earthquake ac- earthquake (Fig. 8a shows the location of the Tanioka and Satake, tivity in this region suggests low coupling and significant quasi-static 1996b source region for this event). The runup and inundation ob- slip, so it may have delimited the mainshock rupture the same way as servations for this earthquake are quite similar to those for the 2011 the SLSR did to the northwest (Ye et al., 2012). event along the Sanriku coast north of 39°N (e.g., Mori et al., 2011, The last great earthquake that generated massive inundation of the 2012; Tsuji et al., 2014), but the 1896 event did not induce large in- Sendai plane was the 869 July 13 Jogan earthquake. This event was undation of the Sendai plain. While some of the models for the 2011 studied prior to the 2011 event by Minoura et al. (2001), who mapped rupture discussed above do have 5 to 15 m of near-trench slip over- well sorted fine sand over the coastal planes of Sendai and Soma, ex- lapping part of the 1896 rupture zone (e.g., Yamazaki et al., 2013; tending 4 km inland. They estimated a 1000 year recurrence of mag- Romano et al., 2014; Bletery et al., 2014), many do not have much slip nitude ~8.3 events. The 869 event was also modeled by Satake et al. north of 38.8°. The tsunami-only inversion of Satake et al. (2013) has (2008) and Namegaya et al. (2010). Still, awareness of this earthquake slip of up to 30 m near the trench in the 1896 zone, but in their model, was not widespread prior to 2011. Sugawara et al. (2013) compare the this slip takes place over several minutes after the 150 s duration of the 2011 and 869 tsunami on the Sendai plane, arguing that the magnitude main rupture inferred from seismic and geodetic data. The initial tsu- of the 869 Jogan event is still not well constrained, partly because an nami source inversions of Dettmer et al. (2016) and Hossen et al. ash deposit limits exposure of the tsunami sands. Sawai et al. (2012) use (2015a) shown in Fig. 8 suggest an elongated source region along the estimates of the 869 inundation and subsidence in modeling a rupture trench. Dettmer et al. (2016) argue that the large extent supports a

22 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 14. Determinations of afterslip distributions for the 2011 Tohoku earthquake. (a) Postseismic displacements for 12–25 March 2011 from Ozawa et al. (2011). (b) Updated, and much contracted afterslip distribution (red contours) along with the coseismic slip estimate from Ozawa et al. (2012) with 8 m contour intervals. (c) Cumulative distribution of estimated postseismic slip (red areas) from Iinuma et al. (2016). The color scale for the cumulative slip is indicated at the bottom. The blue dashed contours represent the coseismic slip model of Iinuma et al. (2012). Gray contours are slip regions of previous large events.

faulting source, while Hossen et al. (2015b) argue that a submarine driving stress for megathrust faulting north and south of the large-slip mass failure could account for the narrow source, which would gen- zone are calculated as ~0.1 MPa. erate dispersive waves. A submarine mass failure was identified in this Kosuga and Watanabe (2011) examined seismic activity on the region by Tappin et al. (2014), but it is not clear exactly when or how northern margin of the 2011 rupture, where the 1994, 1988 and 1968 quickly this may have occurred. major ruptures occurred. Regions down-dip from the 1896 earthquake that failed in 1992 and 1989 have lots of aftershock activity, but the 4.2. Relationship to aftershocks and afterslip farther down-dip (SLSR) region along the coast primarily has small, repeating events. They infer that the reduced strain in the areas of slow The dense seismic networks in Honshu provide superb resolution of slip and recent ruptures acted as a barrier to the mainshock rupture. An ff the locations and focal mechanisms for aftershocks of the 2011 Tohoku OBS deployment from August to October 2011 near the trench axis o earthquake. Extensive moment tensor inversions of the smaller events Miyagi shows that most aftershocks are intraplate, with few events lo- were considered by Asano et al. (2011), who find that thrust aftershocks cating on the plate boundary and none being on the plate boundary in near the fault plane are seldom located in the large slip area, and that the most seaward 45 km of the megathrust (Obana et al., 2013). They normal faulting occurs in both the upper and lower plates. The ten- infer total stress drop on the megathrust as the explanation. The ab- dency for on-fault thrust events to fringe the large-slip zone is further sence of even small events on the shallow megathrust, including in documented by Kato and Igarashi (2012). They suggest that the irre- locations of preceding repeater events (Uchida and Matsuzawa, 2013) gular domain bounded by interplate, repeating, and down-dip com- indicates that no afterslip was occurring there. They also report several pressional events where the rate of interplate aftershocks changed trench-normal compressional events at the landward end of the 45 km significantly, corresponds to edges of the mainshock slip zone. They wide aseismic wedge, which they attribute to relocking of the mega- infer that the accumulated stress was almost entirely released in the thrust. large slip zone, while stress increased in surrounding areas. Analysis of continuous recordings using template waveforms has Kato et al. (2011) argue that a wholesale stress change occurred in added many aftershock detections. Lengliné et al. (2012) analyze 227 fi the upper plate based on normal faulting in northern Ibaraki. Imanishi continuous recordings from Hi-Net stations for the rst 12 h after the et al. (2012) study the normal faulting sequence near the Pacific coast mainshock, increasing the catalog of small events by 40%. The seis- at the Ibaraki-Fukushima border. They infer that the mainshock stress micity extends around the margins of large-slip in the mainshock, pri- change was up to 1 MPa for east-west tension, but stress tensor inver- marily along the coast, but also farther up-dip along Fukushima and sion indicates that the region was already in tension prior to the Ibaraki Prefectures. They observe progressive expansion of the down mainshock, so extensional stress was augmented, not reversed. Focal dip aftershock area along strike to the south and locally around some mechanisms before the mainshock in the inland areas of northern To- patches of high activity. The activity decays with time, and could in- hoku have extensive compressional activity, with local stress field volve a cascade of static stress triggers or afterslip driven expansion. A changes indicated by variability (Yoshida et al., 2012), and the com- comprehensive analysis of repeating earthquakes from 1997 to 2013 pressional activity is dramatically reduced across Japan after the event. using template methods for separate P and S windows by Nakamura The limited regions of newly activated normal faulting may be influ- et al. (2016) recovers 5401 interplate repeaters before and after the enced by prior stress heterogeneity. Overall, it appears that compres- mainshock (Fig. 13). Focal mechanism information is used to char- sional elastic stress was largely released, but inland stresses did not acterize the events, and comparison with the slip model of Iinuma et al. extensively reverse. Calculation of Coulomb failure stress changes for a (2012) displays the cessation of interplate activity in the large slip area. model of mainshock slip by Hiratsuka and Sato (2011) support < 2 This is again attributed to nearly complete stress drop and slow inter- MPa, increases in driving stress on normal faults in the mainland, but plate stress recovery. larger extensional driving stresses exist in the wedge above the mega- Geodetic estimates of afterslip integrate the contributions from thrust and in the shallow region of the underthrusting slab. Changes in aftershock deformation with slow slip deformation of the megathrust.

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For the 2011 event, early models of afterslip such as that of Ozawa et al. Acoustic postseismic displacements at 7 stations 1 year after the event (2011) (Fig. 14a) have peak values offshore of Sanriku, but also with a structure that has a viscoelastic mantle wedge below Honshu and widespread afterslip over the entire megathrust. Later models tend to a low viscosity layer in the subducting plate. At station GJT3, the ob- concentrate afterslip in the down-dip portion of the megathrust deeper served motion over the year is close to 0.5 m, which exceeds even the than about 30 km, complementary to the increasingly seaward location increased convergence rate detected by Tomita et al. (2015) by over a of the estimated mainshock slip. The model of Ozawa et al. (2012) is factor or two. Nearby stations KAMS and MYGI are pretty consistent shown in Fig. 14b, and similar results are found by Imakiire and Koarai with that rate, and this persists over the next 3 years, as do the addi- (2012) and Evans and Meade (2012). These models assume all post- tional sites deployed in 2012 (Tomita et al., 2017). It seems likely that seismic deformation is caused by afterslip. However, Johnson et al. GJT3 was affected by some of the upper plate faulting that occurred, so (2012) assert that the first 8 months of afterslip cannot be restricted to the enhanced rate is likely to be a local effect. Nonetheless, Sun et al. outside regions of historical major ruptures along Miyagi and Fu- (2014) manage to fit the data at GJT3 and MYGI pretty well with their kushima without giving excessively large afterslip. From this they argue complex viscoelastic structure and strong asymmetry in extensional that velocity-weakening regions can have afterslip, in conflict with the deformation west and east of the megathrust. Freed et al. (2017) also rate-state asperity model. It is not clear that the spatial resolution of use 3-D viscoelastic fi nite elements modeling to invert for combined afterslip or knowledge of the precise slip zones of older events allow a viscoelastic relaxation and afterslip. They find that both processes conclusive statement. contribute comparably, but with spatial differences. Flow due to creep Silverii et al. (2014) invert GPS observations for afterslip in the first within the lower half of the Pacific lithosphere is a possible explanation 4 months after the mainshock, comparing the distribution with their for the westward motions in the shallow toe. Viscoelastic modeling is estimate of the mainshock slip. Afterslip extends down-dip of the co- generally not well constrained and is subject to uncertainty in the seismic slip to ~80 km deep. It peaks and decays more slowly near the boundary conditions and stress history, but the argument from these SLSR region offshore of Sanriku. They find that it overlaps the studies that short-term viscoelastic effects may be important and com- 30–50 km deep region where the 1978 and 2005 Miyagi-oki events petes with afterslip to produce the time varying surface motions is occurred, and there is slow slip off Chiba to the south of the Mw 7.9 clearly valid. aftershock offshore of Ibaraki. They view the fault as rheologically There is also ambiguity in the afterslip distribution due to boundary heterogeneous with ductile matrix interspersed with brittle asperities, condition assumptions in the modeling and contributions from early rather than arguing for complex friction like Johnson et al. (2012). afterslip to mainshock models. Perfettini and Avouac (2014) derive However, there is a lot of overlap with the mainshock slip zone in this afterslip for models with either locked or unlocked trench boundary model. conditions and varying degrees of smoothing. They find some deep Some of the postseismic motion could have contribution from vis- afterslip offshore of Sanriku fringing the down-dip edge of their coelastic relaxation. Analysis of 1.5 years of time-dependent GPS data mainshock slip region but also an extensive zone of afterslip over- by Diao et al. (2014) examines this possibility. If afterslip is assumed to lapping the mainshock zone, in contrast to the model of Ozawa et al. be the dominant process, models place afterslip down-dip of the (2012). Perfettini and Avouac (2014) argue that the difference is due to mainshock rupture area from 20 to 80 km depth, with a maximum the earlier work assuming a locked trench (an assumption that is not 22 cumulative slip of 3.8 m and M0 = 2.3 × 10 Nm (Mw 8.84). Slightly shown to be unjustified) and using a large degree of smoothing. In the 22 reduced afterslip is found (M0 = 2.1 × 10 Nm) if viscoelasticity is first 279 days, afterslip in their model is 40% of the coseismic moment. included. The afterslip pattern largely coincides with the aftershock The inferred large shallow postseismic slip is used to partition the co- distribution and with zones of calculated increased Coulomb failure seismic and early postseismic slip contributions to the offshore de- stress from the mainshock slip. The afterslip Coulomb stress change is formation in the first month before the seafloor stations were re-mea- about 10% of that for the mainshock. sured. Constraint on the slip azimuth has a big effect on estimated peak Yamagiwa et al. (2015) consider viscoelastic relaxation and afterslip coseismic slip (50 m when unconstrained, 25 m when constrained). for 2.5 years of time-dependent GPS data, augmented by repeated Their preferred coseismic model has only 25 m slip near the trench. It is measurements of GPS/Acoustic positions at six seafloor sites. Two of argued that the large afterslip in the coseismic zone decayed much the seafloor measurements among the offshore 5 sites discussed by Sato faster than downdip, which is necessary because no afterslip occurred et al. (2011) were found by Watanabe et al. (2014) to have reversal of near the JFAST drillhole one year after the event. The suggestion that motion (landward) relative to the coseismic displacements by 2014. there is huge postseismic slip in the mainshock slip zone is provocative, The landward motions are faster than long-term plate convergence rate but clearly at odds with the near total lack of interplate aftershock of 8.3 cm/yr, so they reflect viscoelastic increase in convergence rate seismicity as seen in Fig. 13b, with the rapid reversal of motion of the and re-locking of the shallow megathrust. Tomita et al. (2015) mea- GPS/Acoustic stations near the trench, and with the evidence for ex- sured the relative motion of the Pacific plate seaward of the Japan tensional stress state in the shallow toe, discussed below. Trench as 18.0 ± 4.5 cm/yr from September 2012 to September 2014. The occurrence of repeating events is commonly inferred to indicate This viscoelastic response accounts for the high westward motions. slow slip and it is generally thought likely that repeating aftershocks Yamagiwa et al. (2015) invert for coseismic slip finding peak slip of indicate where afterslip occurs. Uchida and Matsuzawa (2013) examine 50 m at depths shallower than 35 km along with 10–20 m of slip in repeating events prior to and after the 2011 mainshock, inferring areas seaward of Iwate and Ibaraki Prefectures (including slip from Mw postseismic slip of 1.6 m over the 9 months following the mainshock, in 7.4 and 7.9 events in each region). Afterslip was inverted for as well, the area surrounding the large-slip zone. The postseismic slip rate in- yielding a down-dip concentration off Sanriku and Miyagi similar to the creases near the margins of the main slip zone, consistent with outward models of Ozawa et al. (2012) (Fig. 14b), Diao et al. (2014), and Silverii propagation of afterslip. They also note small increases in rate in the et al. (2014), which had not incorporated offshore data. Hu et al. (2016) 3 years preceding the mainshock, which they attribute to ‘unfastening’ further examine time-dependence of afterslip using a 3D spherical of the locked area margin. This study was extended by Uchida et al. viscoelastic finite element model, focusing on stress-driven afterslip in a (2015), examining the postseismic response from repeating events with 2 km thick shear zone away from areas of historic ruptures. They use magnitudes from 2.5 to 6.1. Repeating sequences exhibit an increase of decaying rates of repeating earthquakes to constrain the shallow shear 0.3 magnitude units relative to prior repeating events for sequences of 3 zone rheology. Viscoelastic relaxation of the mantle wedge alone causes or more earthquakes in the down-dip region. Near the Kamaishi re- postseismic uplift and seaward motion, opposing effects of relaxation of peaters in the SLSR, magnitude increased by 1 magnitude unit and the the slab upper mantle. quasi-static slip rate is estimated to have increased by a factor of 6 after Viscoelastic calculations by Sun et al. (2014) modeled the GPS/ the 2011 event, with repeat times dropping from 5.5 years to 9 months,

24 T. Lay Tectonophysics 733 (2018) 4–36 although this activity appears to be slowing with time. Uchida et al. slip, and suggest that dip changes and contrast of crust/slab and (2015) suggest that this may represent an aseismic to seismic transition mantle/slab lithologies may influence coupling, with high stress in the under the ephemeral fast loading rate by the postseismic slip. slab-mantle contact resulting in high frequency radiation during rup- Hatakeyama et al. (2017) explore this possibility in detail, for the SLSR ture. region, documenting emergence and rapid disappearance of repeaters Other great earthquakes exhibit similar tendency for high frequency in regions lacking prior events. Loading-rate-dependent slip behavior to originate deeper on the megathrust, so Lay et al. (2012) proposed appears to be important for regions with relatively weak seismic cou- along-dip segmentation of megathrusts with Domain A being at pling. Such a process would likely have increased seismicity in the depths < 15 km where tsunami earthquakes occur with low short- large-slip area of the mainshock if large postseismic loading were oc- period energy release, Domain B being the region of large slip in most curring there, whereas interplate faulting actually decreased. interplate ruptures from 15 to 35 km deep, and Domain C being a re- Shirzaei et al. (2014) jointly invert GPS and repeating earthquake gion of modest slip with high short-period radiation. Somewhat simi- data to constraint spatio-temporal variation of afterslip, applying cor- larly, Yomogida et al. (2011) and Koyama et al. (2012) invoke along- rections for three viscoelastic relaxation scenarios. They find a re- dip double segmentation of the megathrust off Japan with shallow high lationship between modeled afterslip, slip inferred from repeating slip and deeper slip in M ~7.5 events. Along-strike variations are earthquakes on the megathrust and cumulative number of aftershocks clearly important in the Japan zone as well, as discussed above. within 15 km from the megathrust. Aftershocks are thus attributed to The issue of how much slip extended to the trench during the 2011 afterslip directly. event is still not completely resolved. The preponderance of the better- Using time dependent GPS and seafloor deformation statics, Iinuma resolved fault models and the seafloor observations support slip of > et al. (2016) use a finite element method to characterize and separate 30 m at the trench, with 50 to 60 m being reasonable near 38.2°N. Sun viscoelastic components from the postseismic deformation, and invert et al. (2017) compile the slip patterns for 45 rupture models along a for afterslip with the configuration shown in Fig. 14c. They find rather transect intersecting the trench around 38°N near the JFAST site remarkable complementary patterns of afterslip relative to the co- (Fig. 15). The models (identified in the supplement) include 24 that seismic slip model for the 2011 mainshock and to large slip zones of incorporated sea floor deformation observations and 15 that used tsu- prior major earthquakes offshore of Fukushima and Ibaraki and in the nami data as constraints. Early, poorly resolved on-land-only geodetic north off of Sanriku. Three large afterslip regions are found; one in the models are not included. The near-trench variation is still striking, SLSR region off Sanriku, one down-dip of the mainshock overlapping given the high quality data sets that are available. Sun et al. (2017) the 1978 Miyagi-oki region, and one up-dip on the megathrust seaward model the high-resolution bathymetry difference from 1999 to 2011 of the Mw 7.9 aftershock off Ibaraki, in the region with no historic reported by Fujiwara et al. (2011) using an elastic finite element model, earthquakes. In contrast to the models of Johnson et al. (2012) and accounting for differential bathymetry and internal deformation of the Perfettini and Avouac (2014), this model clearly supports conventional upper plate. Their preferred model has an average of 62 m (with esti- frictional properties with regions of stable sliding separate from regions mated 5 m error) of slip over the 40 km wedge closest to the trench. of stick-slip sliding. Comparison with the distribution of repeating Models in Fig. 15 with comparable slip at the trench include models 44 earthquakes (Fig. 13b) shows that the afterslip regions have some re- (Yamazaki et al., 2011), 39 (Satake et al., 2013), 33 (Maeda et al., peaters, as expected, although more are concentrated down-dip. The 2011), and 32 (Lay et al., 2011a). Sun et al. (2017) argue that this occurrence of repeaters appears valuable for constraining the regions of region is unlikely to have had creep prior to 2011 due to either locking afterslip (e.g., Shirzaei et al., 2014; Hu et al., 2016; Iinuma et al., 2016). of the fault or stress-shadowing from down-dip locking, and that At this time, there are very different end-member models of afterslip, afterslip contribution is unlikely given the absence of interplate after- and these influence assessments of coseismic slip. Incorporating the shocks and large stress drop in the mainshock zone. supplementary information from seismology, a preference can be given Large slip concentrated near the trench is particularly eff ective for to the models in Fig. 14b and c, but these models do depend on as- generating short wavelength tsunami, which enhances the potential for sumptions that need further validation. runup on steep coastal margins (e.g., Shimozono et al., 2014). The recorded runup heights and inundation on the Tohoku and Hokkaido 4.3. Depth-varying radiation behavior and slip to the trench coasts clearly provide a valuable dataset for evaluation of source models (e.g., Wei et al., 2012; Grilli et al., 2013; MacInnes et al., 2013; While the seismic wave observations for the 2011 Tohoku earth- Satake et al., 2013), and potentially for constraining aspects of the quake consistently indicate that the deeper part of the rupture zone rupture not resolvable by seismic, geodetic, and even offshore tsunami radiated relatively more short-period energy despite having lower slip, waveform recordings. However, the coastal interaction involves non- it is not clear if this is a property of the fault zone or a dynamic feature linear effects and requires very high-resolution bathymetry and topo- of the great rupture. One way to evaluate this is to seek similar behavior graphy, so runup and inundation observations have not been explicitly in other events. Analysis of magnitude differentials for interplate events incorporated into the model construction discussed above. Yamazaki on the megathrust by Rushing and Lay (2012) shows that scattered mb- et al. (2017) have now done so, starting with a perturbed (dip-varying), Mw anomalies increase with depth by ~0.2 magnitude units from 10 to down-scaled (larger-subfault dimensions) version of the seismic slip 55 km depth, favoring an increase in relative short-period radiation model of Lay et al. (2011a) and conducting extensive forward modeling with depth. Teleseismic analysis of rupture durations for 90 events from of regional and remote tsunami waveforms and the extensive runup and 1992 to 2011 along the Japan megathrust indicates that shallower, near inundation measurements along the coast. They then up-scale (back to trench thrust-events have longer durations, mainly for events near the original subfault dimensions) the tsunami-controlled model and invert 1896 tsunami source region, whereas down-dip thrust-events have teleseismic P waves with constraints on rake and moment for bins of shorter duration (Bilek et al., 2012). Regional strong-motion and Hi-Net subfaults to find a self-consistent model (Fig. 16). Large slip, of up to signal analysis of events with Mw 6.0 to 7.6 along the megathrust in- 56 m, along the trench extends to 39.6°N in this model, enabling good dicates enhanced 5 to 10 Hz ground shaking from deeper megathrust match to runup measurements in excess of 30 m and coastal inunda- events, and these events have higher corner frequencies (Ye et al., tions along Sanriku. The iterative inversion ensures that the model is 2013). Lateral variations in attenuation, with increasing Q toward the fully compatible with teleseismic data as well as with forward predic- coast, enhance the high frequency ground shaking for deeper events. tions of onshore and offshore coseismic geodetic data. The high frequency radiation appears to come from depths below the The GPS/Acoustic network was greatly expanded in September upper plate crust-slab contact. Satriano et al. (2014) analyze short- 2012 with an additional 20 sites from ~36.1°N to ~40.7°N, including period back-projections and low frequency kinematic inversions for sites farther north than the network that captured the coseismic slip in

25 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 15. Compilation of 45 slip models (identified in Supplementary Table S1 listing) along the corridor indicated in the inset. Solid and dashed lines show models that do or do not include seafloor displacement data as constraints. In the inset, position of the JFAST drill hole is indicated. Modified from Sun et al. (2017).

2011 (e.g., Tomita et al., 2017). These data help to constrain afterslip Fig. 16. Note that the range of stress drop over the latter variable slip both north and south of the mainshock large-slip zone. Two sites at model is substantial (Fig. 17a), with peak values of 37 MPa in the large- 39°N to 39.3°N show parallel westward motions similar to those in the slip zone. Melgar and Bock (2015) estimate stress drop of 20 MPa in the mainshock slip zone of Iinuma et al. (2012) despite locating north of shallow trench. Bletery et al. (2014) find two large slip patches with that slip zone. Stations farther north show trench parallel motion, while stress drop exceeding 8 MPa relative to large surrounding regions with those near the trench seaward of Ibaraki show seaward motion con- 1 MPa. Simons et al. (2011) find stress drop varying from 2 to 10 MPa sistent with continuing afterslip. While the co-seismic slip at these sites across their model. is not directly measured, it is reasonable to infer that slip extended to at Given the slip variation among models and the dependence of stress least 39.3°N, and that there is no significant afterslip in the 1896 rup- drop values on choice of slip threshold, Brown et al. (2015) compiled 40 ture zone, favoring significant rupture of that region during the main models, attempting to represent them in a uniform fault mesh frame- 2011 faulting. Thus, an exotic source such as a slump or inelastic de- work, with smoothing of the models and computing the average stress formation is not required to account for the runup (although that pos- drop for 5 m slip contours (Fig. 17b). This is a difficult process due to sibility cannot be ruled out). some models having large slip on their edges, so the calculations have substantial uncertainty. For some models, there are apparently errors in estimating the stress distribution, as appears to be the case for the Yagi 4.4. Stress drop, radiated energy, frictional heating and Fukahata (2011) model, based on comparison with the stress change calculations made in that paper, and the Maercklin et al. (2012) The coseismic stress drop and radiated energy are critical earth- study emphasizes short-period in the back-projections that give a very quake rupture parameters that can be estimated for the 2011 Tohoku irregular slip distribution to the stress calculation that is not really earthquake. With slip varying over the megathrust, stress drop varies as comparable to the others. Nonetheless, the mean value for 40 models well, so an average value is not particularly meaningful if it is for the using the area of the 5 m slip contour and assuming uniform rigidity of entire rupture zone. Estimates of stress change from the coseismic slip 40 GPa is 2.3 ± 1.3 MPa. For 38 of the models that have a 30 m are also relative to an unknown initial stress, which cannot be directly contour the estimated stress drop average at that threshold is measured from the mainshock signals. 10.8 ± 4.4 MPa. These values are low by at least a factor of two re- Several estimates of main shock radiated energy have given lative to the estimates from individual studies, but the trend of in- E = 4.2 × 1017 J(Lay et al., 2012), 5.1 × 1017 J (USGS-NEIC), and R creasing stress drop in the high slip regions is sensible. In some models 9.1 × 1017 J(Ide et al., 2011). These estimates give moment scaled − the peak stress drop exceeds 40 MPa, and almost all models are values of E /M of ~0.8–2.0 × 10 5, which is typical of large mega- R 0 smoothed in their construction. Average stress drop of about 5 MPa is a thrust events (Ye et al., 2016), and significantly higher than for tsunami reasonable value for the 2011 event. earthquakes (Okal, 2013; Ye et al., 2016). To evaluate whether the stress drop is a large fraction of the elastic Average stress drops for the 2011 event are also similar to those of shear stress or not, changes in the stress regime around the fault can be other large megathrust events, which span the range 1 to 10 MPa (Ye assessed. Multiple reflection profiles along the coast since 1966 (Tsuru et al., 2016). Lee et al. (2011) estimate an average stress drop of 7 MPa et al., 2002) identify a sedimentary unit wedge shape with very low for their model, Yagi and Fukahata (2011) estimate 20 MPa, and seismic velocity of 2 to 3 km/s in the forearc tapering down to the Yamazaki et al. (2017) find an average of 6 MPa for the model in

26 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 16. Slip model obtained by iterative inversion of seismic data and forward modeling of tsunami gauge data and coastal runup and inundation by Yamazaki et al. (2017). The slip model has peak slip of 56 m located 20 to 40 km down-dip from the trench. The shallow slip patch in the north is needed to account for peak runup north of 39°. This model provides good fit to the geodetic data. It is also compatible with the reconstructions of initial sea surface height shown in Fig. 8, explicitly mapping the tsunami data into a fault slip model consistent with teleseismic and geodetic observations. megathrust about 4 km deeper than the trench, with a backstop reverse fault interface reaching the surface from 10 to 30 km from the trench. Fig. 17. Stress drop estimates for the 2011 Tohoku earthquake. (a) The shear stress re- The wedge was further imaged as having a branch normal fault with the sulting from fault displacement from the joint inversion of Yamazaki et al. (2017). The east side up 40 km from the trench (about 30 km west of the local shear stress change is highly variable in direction and magnitude, spanning from 0 to 37 MPa. The average stress drop is estimated to be 6.1 MPa when the fault model is backstop reverse faults within 10 km of the trench) in multi-channel trimmed to remove subfaults that have < 15% of the moment of the peak subfault, and it fl seismic re ection data acquired in 1999 and by submersible observa- is estimated to be 5.9 MPa using the slip-weighted procedure of Noda et al. (2013). (b) tions in 2008 (Tsuji et al., 2011). Ito et al. (2011b) suggest that the Relationship between average stress drop and the slip contour used to define the aver- branch reverse fault in the wedge was not activated by the 2011 aging area for 40 rupture models, compiled by Brown et al. (2015). earthquake based on vertical motions at seafloor sites TJT1 and TJT2. Breaks in the seafloor slope were connected to a backstop reverse fault and a branch reverse fault. Tsuji et al. (2013) provide evidence for tensional features and some normal faulting from their post-earthquake mechanisms before and after the event, finding an increase in dip of the submersible deployment. Conin et al. (2012) argue that activation of maximum compressive directions by 30–35°. They infer that the de- splay fault normal faulting in the toe of the wedge can only be achieved viatoric stress was mostly released and that the plate interface is weak, if the friction coefficient on the megathrust drops to near zero (coeffi- so that a 21–22 MPa stress drop would be near total. Further stress cient of friction μ < 0.05). Critical taper theory is applied to explore tensor inversions by Hasegawa et al. (2012) indicate an upper plate normal faulting in the overriding plate and large shallow slip by Cubas stress change from compression in the convergence direction to et al. (2013). The forearc morphology and internal structure appear minimum stress direction toward the large near-trench slip area after- consistent with a critical Coulomb wedge, which can be reconciled with ward. They do not see corresponding changes in principal stress in the high internal pore pressure ratio and low effective basal friction (μ lower plate. Compressional stress in the upper plate toe before the event ~0.1–0.32). Activation of normal faulting in the wedge indicates ef- indicates that strain accumulation occurs there. The stress changes of fective basal friction under the inner wedge of μ < 0.015 to allow the 5–15 MPa in the upper plate and the stress directions are more con- wedge to achieve an extensional state, possibly as a result of transient sistent with a model with high stress change near the trench like that of dynamic weakening induced by the seismic rupture. To achieve 5 m Lay et al. (2011a) than with large near-hypocenter slip models. Stress uplift of the toe by block rotation with ~1.1 m normal faulting at the inversions for events near the megathrust by Hardebeck (2012) simi- backstop requires the value to drop to μ ~0.003. larly find rotation of the maximum compressive stress axis from shallow Evidence for near total stress drop in the mainshock faulting is also plunging before the event to ~45° plunging after the event, in- provided by the regional stress field change in the surrounding plates. ferring > 80% of the pre-mainshock stress being relieved for the To- Hasegawa et al. (2011) performed stress tensor inversion using focal hoku event. The stress axes rotated back quite rapidly in the postseismic

27 T. Lay Tectonophysics 733 (2018) 4–36 interval. and fluids. Kennett et al. (2011) and Yamamoto et al. (2011) also find Another strategy for measuring the stress state in the toe was en- enhanced P to S velocity ratios (Vp/Vs) ratios in the region of large slip abled by the JFAST drilling into the fault zone. Lin et al. (2013) and that could be due to presence of fluids and sediments. Tajima and Brodsky et al. (2017) argue that horizontal stress orientations and Kennett (2012) relate heterogeneous slip on the megathrust to patterns magnitudes estimated from borehole breakouts along with the apparent of P and S wave velocity variations. They suggest that the lack of ex- increase in displacement toward the trench favors nearly total stress pansion of the aftershock sequence for 2011 is due to cascading failure drop. The frontal portion of wedge was under trench-normal com- of the rupture across the heterogeneous surface. Holes in the main slip pression before the mainshock based on orientations of minor faults and zone are found where large events had occurred previously and after- bedding and the stress state changed from thrust to normal faulting shocks fill in slip deficit in areas of low slip in the mainshock. (nearly vertical compression axis, with small range of deviatoric stress). Local irregularity of the megathrust may also affect rupture processes. Zhan et al. (2012) determined focal mechanism and depths for 4.5. Factors affecting frictional variations interplate events, finding 5° to 10° steeper dips for events in the large slip zone. This could be due to changes in slope of the megathrust, Direct sampling of the megathrust in a region of large coseismic slip rough topography on the boundary, or off-plate boundary ruptures. is a unique feature of the 2011 Tohoku earthquake. The JFAST borehole drilling and core-sampling demonstrated that the toe of the wedge has 4.6. Dynamic rupture effects megathrust deformation localized within a zone < 5 m thick com- prised of pelagic scaly clay (Chester et al., 2013; Kirkpatrick et al., The many kinematic and static displacement models for the 2011 2015). A one meter long core sample was retrieved. Multiple discrete Tohoku earthquake provide first-order information about the rupture, faults were distributed over a 5–15 m thick fault zone. Commonly clays but the dynamic rupture processes are not well constrained. A large show velocity strengthening at low slip velocity. Faulkner et al. (2011) variety of dynamic models have been explored, guided by the fault slip consider low (0.5 mm/s to 5 mm/s) slip-velocity and high (1.3 m/s) models, but the physics of failure has to be prescribed and there is much slip-velocity experiments with clay samples. Slip strengthening was uncertainty involved in doing so. Rupture modeling thus spans a wide indeed observed at slow slip velocity for dry and wet conditions. Strong range from conceptual to spontaneous failure modeling. slip weakening occurs with increasing slip velocity for dry clay, with Multi-scale asperity models have been considered as representations smaller values and smaller stress reduction for wet conditions. The dry of the Japan megathrust, accommodating the diverse range of large condition weakening could be due to flash heating at asperity contacts, events and re-triggering of rupture areas of earlier events (Hori and frictional melt lubrication, silica gel formation or thermal decomposi- Miyazaki, 2011). Aochi and Ide (2011, 2014) and Ide and Aochi (2013) tion. Weakening under wet conditions was attributed to rapid thermal compute spontaneous dynamic rupture in systems with variable cir- pressurization (e.g., Di Toro et al., 2011). This suggests that rupture cular patches with fracture energy proportional to patch size. Cascading likely will not nucleate in low-normal stress clay-rich faults, but rupture ruptures occur in these models, with slow rupture in the high fracture may not be inhibited if it nucleates down-dip and propagates upward energy large slip regions, similar to the 2011 event. Mitsui and Iio through the clay-rich zone. (2011), and Mitsui et al. (2012a, 2012b) compute numerical models for Frictional experiments were conducted on the recovered JFAST mechanical systems with conditionally stable barriers, with dynamic samples at low (< 1 mm/s) sliding velocities (Ikari et al., 2015) and thermal pressurization as a dynamic weakening mechanism. The oc- high sliding velocities of up to 1.3 m/s (Ujiie et al., 2013). The smectite currence of earlier major (M ~7) failures enhances stress accumulation content of the clay causes the clay-rich layer to be weak (μ ~0.2–0.26) for the mainshock, with the stress state in the shallow fault strongly relative to the wall rocks (μ > 0.5), which have high amorphous silica influencing whether hydrothermal weakening occurs to produce large content with diagenetic cementation and low clay content. At high shallow slip. velocity very low peak stress drops were observed and steady state Numerical models with rate- and state-dependent friction, with shear stress was sustained. These laboratory findings indicate coseismic strong asperities and higher effective normal stress in the shallow fault weakening due to the presence of weak smectite clay and thermal have been examined by Kato and Yoshida (2011) and Yoshida and Kato pressurization could have occurred in the shallow megathrust. The (2011). The latter study considers pore pressure distribution, assuming likelihood of very low shear stress during failure of the shallow toe of that permeability depends on effective stress and that pore collapse can the megathrust is supported by a small (0.31 °C) temperature anomaly lead to variation from hydrostatic pore pressure at shallow depth to found 1.5 year after the mainshock near the base of the borehole lithostatic at greater depth. This could account for a strong shallow (Fulton et al., 2013). This maps to μ ~0.08, and an average shear stress asperity controlling the overall system. Duan (2012) models 3D spon- during slip of 0.54 MPa in the shallow toe is inferred assuming a 50 m taneous rupture with a high stress patch, approximating a seamount coseismic slip. 70 × 23 km2 up-dip of the 2011 hypocenter. The patch has lower pore Kimura et al. (2012) consider the forearc structure, noting promi- fluid pressure and the strength delays rupture expansion up-dip until a nent reflectors beneath the lower slope (east of the branch normal fault high stress drop event occurs, driving failure to the trench. The largest noted by Tsuji et al., 2011) with negative polarity in reflection profiles slip is expected near the hypocenter in this case. that may correspond to locations of high-pressure fluids. Their inter- Inelastic deformation of the wedge may serve as an energy sink, pretation implies that dehydration of underthrust sediments dominated causing slip to reduce as it approaches the trench. Ma (2012) and Ma by pelagic clays could concentrate fluids 50 to 60 km west of the de- and Hirakawa (2013) compute dynamic poroelastic yielding and information front, reducing effective normal stress and enabling runaway elastic deformation of the wedge in 2D models. Inelastic uplift occurs rupture from the deeper fault to extend to the trench. landward of the trench in these models, which could contribute to Larger scale properties around the megathrust may also influence tsunami excitation even though there is no trench slip. For the 2011 frictional properties. P and S wave seismic tomography by Huang et al. event, the predicted profile of up-lift differs from the observed seafloor (2011) was used by Zhao et al. (2011) to relocate 339 foreshocks and deformation (e.g., Jiang and Simons, 2016) and the model is at odds 5609 aftershocks and to relate slip and seismicity to the velocity with the extensive evidence for large displacement at the toe. The high structure. This work was extended by Huang and Zhao (2013). High P seismic velocities inland from the backstop fault in the wedge suggest velocity along the megathrust extends up-dip from the hypocenter to quite strong upper wedge material as well, which may have inhibited the trench, in the region of large-slip (as discussed by Huang and Zhao, significant inelastic failure in this event. 2013, and Romano et al., 2014), with lower velocities to the north and Numerous other 2D models have explored various parameteriza- south. The lower velocities were attributed to the presence of sediments tions of dynamic failure for the 2011 event. A boundary integral

28 T. Lay Tectonophysics 733 (2018) 4–36 equation method was applied by Goto et al. (2012a) to model multi- event occurred. Kawamura et al. (2012) identify possible submarine event generation in 2D dynamic ruptures for the first 50 s of the 2011 landslides several tens of km in length and width on the trench land- rupture. Dynamic parameters were set based on kinematic slip inver- ward slope from high-resolution bathymetric surveys and seafloor ob- sion results from Yoshida et al. (2011a). Linear slip weakening friction servations. These features stop at the toe of the trench slope. It is sug- was assumed. Free surface reflections prove important for expanding gested that under strong dynamic friction drop the toe collapses slip down-dip and making a second rupture stage. Huang et al. (2012, seaward, producing strong ocean displacement. Tappin et al. (2014) 2014) also consider 2D dynamic rupture models with linear slip- consider a source area near 39.5°N using pre- and post-event bathy- weakening friction and a free surface. Depth-dependent initial stress is metry. They interpret structure there as a 500 km3 submarine mass assumed, and the stress state is very different in the shallow and deep failure that dropped down and rode up on the toe producing a narrow region. Reflected waves in the front wedge enable high transient stress tsunami pulse that might account for the runup and inundation along drop and large slip, but the models do not produce significant over- the Sanriku coast from 39 to 40°N. The predicted amplitude of seismic shoot. and geodetic signals is so low that it would not be observable. This Kozdon and Dunham (2013) model 2D dynamic rupture with rate- scenario appears plausible, but it remains poorly constrained by ob- and state-dependent friction and with standard dependence of shear servations. The similarity of the 1896 and 2011 runup along Sanriku strength on slip velocity. Their model includes the free surface and suggests the more straightforward explanation that both were caused rupture extending to the trench. The shallow section of their model is by shallow tsunami earthquake slip of the shallow megathrust. velocity strengthening, which should be frictionally stable, and nor- mally this would cause rupture to arrest tens of kilometers down-dip 5. Discussion and conclusions from the trench. Rupture nucleates in a deeper velocity weakening section. Velocity strengthening could taper slip toward the trench, but This lengthy review has tracked the evolution of models for the the compliant wedge is susceptible to dynamic failure with dynamic rupture process of the 2011 Tohoku earthquake over the past 6 years. stresses from surface reflections driving the rupture through the velo- Most, but certainly not all, of the key contributions are cited, although city-strengthening region to the trench. Slip can be uniform or increase the discussion here can do justice to none of the individual studies. It is over distances > 50 km from the trench. Mechanisms for extreme dy- important to keep in mind that the earthquake process is continuing, as namic weakening or shallow asperities with large stress drop are not indicated in Fig. 18. The down-dip and offshore motion seaward of required in this case. Noda and Lapusta (2013) consider models with Fukushima have continued eastward throughout 6 years due to after- rate-strengthening material at low slip rates and coseismic weakening slip. The region around the main slip zone has re-locked and is moving due to rapid shear heating of pore fluids, allowing a transition to un- westward at the heightened convergence velocity caused by viscoelastic stable slip in regions that creep between events. This mechanism can relaxation of the deeper portion of the deformed slab or the underlying facilitate rupture breakthrough of creeping sections that are typically asthenosphere. This extends northward from the geodetic model re- assumed to be barriers. Their model did not include a free surface and ferenced in this figure, overlapping the northern slip zone of the models co-seismic slip always tapers close to the up-dip limit of faulting. Faults in Figs. 10a,b,d and 16. Over time, one expects progressive westward with a mix of rate-strengthening friction and rate weaking friction are migration of the reversed displacement front caused by the combined also considered by Perfettini and Avouac (2014). Thermal pressuriza- effects of the fault having relocked and strain accumulation progres- tion is invoked as a mechanism to transition the shallow stable sliding sively overwhelming diminishing afterslip, although there will be regions to rapid failure as a function of stressing rate so they do not overall slowing as the transient response of the plate relaxes back to the impede seismic rupture. Cubas et al. (2013) also consider shear heating long-term rate. More comprehensive modeling of viscoelastic effects dynamic weakening effects as a means to explain large shallow slip, and will better separate afterslip and coseismic slip in future modeling, so Cubas et al. (2015) produce 2D model sequences with rupture with even the most advanced models in this review will evolve, just as the thermal pressurization in a shallow patch of the megathrust with rate- deformation around the megathrust continues to do. strengthening friction favored for the shallow patch to produce The diversity of models for the rupture process of the 2011 Tohoku 1000 year recurrence time of the shallow failure. earthquake makes one hesitate to provide summary evaluations, as Three-dimensional dynamic rupture of a fault model with an a priori many issues remain concerning choice of boundary conditions, treat- distribution of asperities has been explored by Galvez et al. (2014) ment of poorly-constrained afterslip contributions to offshore geodetic using an unstructured version of SPECFEM3D. The results of finite-fault data used in fault models, uncertainty in secondary sources like sub- inversions and back-projections were used to guide the distribution of marine slumping that may decouple different data sets so that they asperity sizes and locations on the fault plane, and the modeling re- should not be inverted jointly, etc. The community working on this produces the depth-variations of the source radiation frequency de- event has not converged on a consensus model, and one cannot dependence. This modeling was extended in Galvez et al. (2016) to ex- mocratically average models in some way to converge on a sensible plore repeated rupture of the hypocentral portion of the megathrust as model. But, it is reasonable to define attributes of a strawman reference in the model of Ide et al. (2011) and Lee et al. (2011). A double-slip- model that distills the features that appear most stable and/or plausible. weakening friction model with two sequential strength drops can pro- Such a summary of the event was given in the introduction and a few duce a similar rupture pattern. The secondary strength drop is attrib- points are re-emphasized here. uted to large slip activation of thermochemical weakening processes. In terms of the primary slip zone, the joint models including tsunami information in Figs. 10 a,b,d, and 16 provide good characterization of 4.7. Possibility of submarine slumping the rupture, with ~50 m of slip near or at the trench about 38° to 38.3°N. Shallow slip in the upper 10 km of the megathrust (from 8 to While it does not appear impossible to reconcile seismic, geodetic, 15 km below the ocean floor) extends along strike from at least 37°N to and tsunami observations, including coastal runup and inundation 39.5°N, diminishing north and south of the central peak, which is near along Sanriku with fault displacement models (Yamazaki et al., 2017), the site of the JFAST drill hole. This is the Domain A zone of tsunami it is always possible that some additional process decouples the various earthquake-like behavior discussed by Lay et al. (2012). From 10 to data sets, and the most discussed possibility is that a submarine land- 35 km depth, the large-slip region, with > 20 m of slip narrows to slide or slump near the trench occurred. The forceful assertions of Grilli about ~150 km along strike, with the hypocenter within this zone, in et al. (2013), MacInnes et al. (2013), and Tappin et al. (2014) that an what is called Domain B. Modest slip of 5 to 10 m is spread along strike, additional tsunami source is needed to match the Sanriku runup and with down-dip Domain C concentrations of < 5 m offshore of Miyagi inundation is probably not correct, but it is still possible that such an and offshore of Fukushima. These regions of prior M ~7.5 events

29 T. Lay Tectonophysics 733 (2018) 4–36

Fig. 18. Postseismic ground deformation from the original (green vectors, measured from September 2012 to January 2014) and augmented (black vectors, measured from September 2012 to May 2016; note that “This study” in the inset label refers to Tomita et al., 2017) array of GPS/Acoustic sites oﬀshore of central Honshu coast. Gray vectors onshore are GEONET measurements from September 2012 to November 2015. Yellow and red contours correspond to the PRA (primary rupture area) 20-m slip and the VLSA (very large slip area) 50-m contours of slip for the model of Iinuma et al. (2012). From Tomita et al. (2017).

during the past century appear to have re-ruptured with more high the tsunami data. The large-slip zone appears to have re-locked rapidly frequency radiation than the shallower regions. The slip offshore of with no afterslip, as the toe of the wedge very quickly resumed west- Fukushima is relatively low and is not evident in all of the slip models. ward motion and there was no disruption of the JFAST drill hole to There is no significant coseismic slip in the Sanriku Low Seismicity indicate large shallow afterslip nearby. Zone (Ye et al., 2012), but this region has high, sustained afterslip with The rupture likely encompassed the rupture zones of the 869 Jogan accelerated recurrence of repeating events after the mainshock that are and 1896 Meiji earthquakes. Even the peak slip of 50 m, combined with larger magnitude than prior to the mainshock. The region up-dip of the 8.3 cm/yr of tectonic convergence, only accounts for 600 years of strain slip off of Fukushima has very little coseismic slip and is also a zone of accumulation in the peak slip regions. This raises questions about the large afterslip (Figs. 14, 16), suggesting reduced probability of a great historic record and the limited knowledge we have of locations for earthquake there. events like the 1611 rupture and other earlier events. The evidence for The distribution of repeating events supports the geodetic inver- total shear stress drop during this event is more compelling than for any sions that find a highly complementary distribution of afterslip and prior subduction zone event, with peak values of > 30 MPa and coseismic slip. The seafloor deformation observations, including GPS/ average value near 6 MPa. The large slip and total stress drop in the Acoustic measurements, ocean bottom pressure sensors, and repeated peak slip region support the notion of dynamic weakening mechanisms reflection profiling, along with the tsunami data recorded offshore and such as thermal pressurization, although rate- and state-dependent in onshore runup and inundation, provide critical constraints on the slip friction models can be reconciled with key aspects of the rupture. distribution, under the assumption that these data originate from shear However, the wedge geometry and dynamic interaction of surface re- faulting on the megathrust. Early assertions that one data type or an- flections with the shallow megathrust may have enabled large shallow other cannot be reconciled with such faulting do not appear to hold up, slip without a dynamic weaking mechanism. The shallow megathrust as joint analyses perform well, even for the demanding peak runup core samples support very low frictional resistance for high slip rate measurements along the Sanriku coast. The total source process time sliding, compatible with shallow slip achieving total stress drop. While can be accounted for within 150 s and need not be extended to match details of the rupture will continue to be investigated, along with many

30 T. Lay Tectonophysics 733 (2018) 4–36 modeling assumptions, these attributes appear to be pretty robust at the great Mw 9.0 Tohoku-oki earthquake. Earth Planet. Sci. Lett. 308, 277–283. http:// dx.doi.org/10.1016/j.epsl.2011.06031. time of this review. Colombelli, S., Zollo, A., Festa, G., Kanamori, H., 2012. Early magnitude and potential Supplementary data to this article can be found online at https:// damage zone estimates for the great Mw 9 Tohoku-oki earthquake. Geophys. Res. doi.org/10.1016/j.tecto.2017.09.022. Lett. 39, L22306. http://dx.doi.org/10.1029/2012GL053923. Conin, M., Henry, P., Godard, V., Bourlange, S., 2012. Splay fault slip in a subduction margin, a new model of evolution. Earth Planet. Sci. Lett. 341–344, 170–175. http:// Acknowledgements dx.doi.org/10.1016/j.epsl.2012.06.003. Cubas, N., Avouac, J.P., Leroy, Y.M., Pons, A., 2013. Low friction along the high slip patch I appreciate my many collaborators who have studied this earth- of the 2011 Mw 9.0 Tohoku-oki earthquake required from the wedge structure and extensional splay faults. Geophys. Res. Lett. 40, 4231–4237. http://dx.doi.org/10. quake with me and the many colleagues who have shared their analyses 1002/grl.50682. with me in meetings and publications. Lingling Ye, Kwok Fai Cheung, Cubas, N., Lapusta, N., Avouac, J.-P., Perfettini, H., 2015. Numerical modeling of long- and Domenico Giardini provided comments on the manuscript. I thank term earthquake sequences on the NE Japan megathrust: comparison with observations and implications for fault friction. Earth Planet. Sci. Lett. 419, 187–198. http:// Guest Editor Shiqing Xu and reviewers Gavin Hayes and Roland dx.doi.org/10.1016/j.epsl.2015.03.002. Bürgmann for their extensive helpful comments and suggestions. 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