Crustal Deformation Following Great Subduction EarthquakesControlled by Earthquake Size and Mantle RheologyTianhaozhe Sun1,2 , Kelin Wang1,3 , and Jiangheng He3

1School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada, 2Now at Department ofGeosciences, Pennsylvania State University, University Park, PA, USA, 3Pacific Geoscience Centre, Geological Survey ofCanada, Natural Resources Canada, Sidney, British Columbia, Canada

Abstract After a great subduction earthquake, viscoelastic stress relaxation causes opposing motion ofEarth’s surface in the strike-normal direction, with the dividing boundary located roughly above thedowndip termination of the rupture. As the effect of the viscoelastic relaxation decays with time, the effect ofthe relocking of the megathrust becomes increasingly dominant to cause the dividing boundary to migrateaway from the rupture zone, eventually leading to wholesale landward motion. The evolution of thepostseismic deformation is controlled not only by mantle viscosity but also by the size of the earthquake.Large coseismic fault slip induces greater stress perturbation that takes a longer time to relax, and a greaterrupture length along-strike results in a pattern of postseismic viscous mantle flow less efficient for stressrelaxation. Here we employ spherical-Earth finite elementmodels of Burgers rheology to quantify postseismicdeformation processes for ten 8.0 ≤Mw ≤ 9.5 subduction earthquakes. Using geodetic data as constraints, wereconstruct spatiotemporally continuous evolution of the postseismic deformation following eachearthquake. We comparatively examine the “reference time” when the dividing boundary of the opposingmotion passes through the map view location of the 50-km depth contour of the subduction interface.Our results suggest a positive dependence of the reference time on earthquake size, although site- and/orevent-specific factors such as subduction rate, afterslip, and postseismic locking state of the megathrustalso affect the evolution. Upper mantle viscosities constrained by available geodetic observations showsomewhat different values between subduction zones located far from one another.

1. Introduction

Following a great subduction earthquake, postseismic deformation occurs due to continuing slip (afterslip) ofparts of the subduction fault, relocking of the fault, and relaxation of the coseismically induced stresses in theviscoelastic upper mantle (viscoelastic relaxation). From deformation patterns presently observed at differentsubduction zones, each representing a different stage of the earthquake deformation cycle, a common evo-lution history can be pieced together, at least for giant (Mw ≥ 9) earthquakes (Wang et al., 2012). The earlierpart of the deformation cycle features opposing motion of the land and trench areas, and the dividingboundary of the opposing motion gradually migrates landward, eventually leading to wholesale landwardmotion, similar to the interseismic situation before the earthquake (Wang et al., 2012) (Figure 1, upper inset).Over the past two decades, the Global Navigation Satellite Systems (GNSS), especially the Global PositioningSystem (GPS), have yielded geodetic observations of crustal deformation associated with a number of sub-duction earthquakes and thus enable us to examine the deformation process in a systematic manner.

In this work, we conduct a comparative study of postseismic deformation following great to giant (Mw 8–9.5)earthquakes (Figure 1). Building on the study of Wang et al. (2012) which examined threeMw ≥ 9 earthquakes,we include seven 8 ≤Mw< 9 events and two additionalMw ≥ 9 events, thus providing a rather complete doc-umentation to date of geodetically constrained postseismic deformation of Mw ≥ 8 subduction earthquakes.For each earthquake, we review critical postseismic geodetic observations and construct three-dimensional(3-D) finite element models (Figure 1, lower inset) to simulate the postseismic deformation process.Compared to most previous studies that are usually focused on individual earthquakes, a global study of thistype will better illuminate the common physical process.

The aforementioned opposing motion begins immediately after the earthquake (Figure 1, upper inset). Whilemost of the upper plate adjacent to the rupture zone moves seaward, the near-trench area just above therupture zone moves in the opposite direction. The primary cause for this opposing motion is viscoelastic

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Journal of Geophysical Research: Solid Earth

RESEARCH ARTICLE10.1029/2017JB015242

Key Points:• In postseismic deformation following

great subduction earthquakes, thedividing boundary of opposingmotion migrates away from thetrench

• How fast the dividing boundarymigrates, measured using areference time, depends on Earth’sviscoelastic rheology and earthquakesize

• Comparative modeling of ten8.0 ≤Mw ≤ 9.5 earthquakes suggests apositive dependence of the referencetime on earthquake size

Supporting Information:• Supporting Information S1

Correspondence to:K. Wang,kelin.wang@canada.ca

Citation:Sun, T., Wang, K., & He, J. (2018). Crustaldeformation following great subductionearthquakes controlled by earthquakesize and mantle rheology. Journal ofGeophysical Research: Solid Earth, 123,5323–5345. https://doi.org/10.1029/2017JB015242

Received 15 NOV 2017Accepted 2 JUN 2018Accepted article online 9 JUN 2018Published online 29 JUN 2018

©2018. Her Majesty the Queen in rightof Canada. Reproduced with permissionby Natural Resources Canada.

relaxation of the stresses asymmetrically induced by the megathrust earthquake; that is, the earthquakeinduces much greater tension landward than seaward of the rupture zone (Sun & Wang, 2015). SeafloorGNSS observations following the 2011 Mw 9 Tohoku-oki earthquake show the dividing boundary of theopposing motion to be located roughly above the downdip termination of the rupture zone (Sun et al.,2014; Watanabe et al., 2014), where the greatest incremental tension was generated (Sun & Wang, 2015).Because the effect of megathrust relocking becomes increasingly dominant as the effect of viscoelasticrelaxation decays with time, landward motion gradually prevails. The dividing boundary thus migrateslandward, which can be observed as progressive reversal of GNSS sites away from the trench, eventuallyleading to wholesale landward motion (Wang et al., 2012).

We are particularly interested in the migration of the dividing boundary of the opposing motion. The “speed”of this migration and the spatial extent of the opposing motion are inferred to be associated with not onlymantle rheology but also the size of the earthquake (Wang et al., 2012). Because a larger earthquake causesa larger stress perturbation, the ensuing viscoelastic relaxation lasts longer, and the opposing motioninvolves a large area and is longer-lived (Wang et al., 2012; Figure 2). Another reason is that a larger earth-quake usually features a longer rupture along strike, so that the flow of mantle material during relaxationis geometrically constrained to occur predominantly in the dip direction (Wang et al., 2012). For a smallerearthquake, it is easier for the mantle material to flow in from both ends of the rupture, and the additionalalong-strike flow helps to speed up the relaxation (Figure 2). By synthesizing postseismic observations andmodeling the process of opposing motion for a range of earthquake magnitudes, we are able to investigatesystematically the effects of earthquake size and mantle rheology on the evolution of the deformation. Theresults also help understand what and how event- and site-specific factors in terms of fault behavior, struc-ture, and plate kinematics affect the deformation.

2. Mantle Rheology and Modeling Strategy2.1. Bi-Viscous Burgers Rheology

Following our previous work (Hu & Wang, 2012; Sun et al., 2014; Sun & Wang, 2015; Wang et al., 2012), weemploy a bi-viscous Burgers rheology for the upper mantle in our models. The Burgers rheology is one of

Figure 1. Earthquakes investigated in this study, model structure, and schematic illustration of postseismic deformation.Locations and approximate rupture areas of the ten 8.0 ≤ Mw ≤ 9.5 subduction earthquakes modeled in this work areshown in red (Tables 1 and S1), and those of the twoMw ≥ 9.0 events studied by Wang et al. (2012) but not included in thiswork are shown in yellow. Lower inset shows model structure. An elastic “cold nose” beneath the fore-arc crust representsthe stagnant part of the mantle wedge (Wada & Wang, 2009). Upper inset schematically illustrates horizontal motion ofthree sites (A, B, and C color coded in lower inset) after an earthquake (t = 0) and their sense of horizontal motion at threedifferent times (t1, t2, and t3) after the earthquake. The dividing boundary of opposing motion migrates away from thetrench, leading to eventual wholesale landward motion (t3).

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the simplest approximations of the time-dependent mantle rheology. It can be envisioned to be seriallyconnected Kelvin solid and Maxwell fluid that represent the transient rheology and steady state rheology,respectively (Peltier et al., 1981; Pollitz et al., 2006; Wang et al., 2012). A more complex rheology mayinvolve multiple Kelvin components or a nonlinear relationship between stress and strain rate. For thepurpose of identifying the first-order physical process in this work, we think the Burgers rheology is adequate.

Upon sudden loading, the Kelvin solid deforms initially as a Newtonian fluid with the deformation rate con-trolled by the transient viscosity ηK but eventually transitions to a Hooke solid with the deformation deter-mined by its rigidity μK. The Maxwell fluid exhibits an opposite time-dependent behavior, that is, initialelastic deformation controlled by its rigidity μM transitioning to eventual viscous deformation controlledby the steady state viscosity ηM. The steady state (or Maxwell) viscosity is higher than the transient (orKelvin) viscosity. Accordingly, the Burgers rheology features two material relaxation times, with a smallerKelvin time τK = ηK/μK and a larger Maxwell time τM = ηM/μM.

Because the subduction zone system consists of geological units of different material properties, the timescale of its viscoelastic stress relaxation cannot be characterized by the material relaxation time of the uppermantle alone. Besides, the relaxation process is strongly dependent on the size of the preceding earthquake.

Figure 2. Generic models to illustrate the effects of rupture length and slip amount on the evolution of postseismic defor-mation. Eachmodel is symmetric in the strike direction, and only the northern half is shown. Each row shows time-averagedsurface velocities over two time intervals after a megathrust (rake = 90°) earthquake, of which the slip magnitude iscontoured at every 10 m (starting from 0 m). The same fault geometry (depth contoured at 10 km intervals with dashedlines), elastic plate thickness (30 km), mantle viscosities (ηK=5 × 1017 Pa s, ηM=1 × 1019 Pa s), and locking (slip deficit)distribution are used for all three models. Models M1 and M3 have the same earthquake magnitude (Mw = 9.1, assuming arigidity of 40 GPa); models M2 (Mw = 8.8) and M3 have the same rupture length. The three green circles along the lineof symmetry show three sites above the 20, 50, and 120-km depth contours of the fault, roughly corresponding to pointsA, B, and C, respectively, in Figure 1. Ten to 15 years after the earthquake, while all the three sites move landward in modelM2, the most inland site in models M1 and M3 still moves seaward.

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Therefore, it is convenient to define a system relaxation time that scales with the earthquake size (Wang et al.,2012). For example, for the steady state component, the system relaxation time is

TM ¼ Mo=M0o

� �τM (1)

whereMo is the seismic moment of the earthquake andM0o is a reference moment.Mo andMW are related by

log Mo=M0o

� � ¼ 1:5 MW �M0W

� �, where M0

W corresponds to M0o. A lower-magnitude earthquake has a smaller

system relaxation time and thus is expected to be followed by shorter-lived opposing motion.

2.2. 3-D Spherical-Earth Finite Element Model

For numerical simulation, we use a 3-D spherical-Earth finite element model which employs 27-node isopara-metric elements throughout the model domain. The effect of the gravitational force is approximately incor-porated using the stress-advection approach (Peltier, 1974). Fault slip, including thrust-faulting coseismic slip,afterslip, and the normal-faulting type back slip used for simulating the effect of megathrust locking (seesection 2.3), is incorporated using the split-node method (Melosh & Raefsky, 1981). We use small time steps(<0.1τK) immediately after the earthquake to model the postseismic deformation in the transient phase andincreasingly larger steps for later deformation.

Our models include actual subduction fault geometry and long-wavelength surface topography. We gener-ally use the global Slab1.0 model (Hayes et al., 2012) for the fault geometry, except for Japan Trench, EasternAlaska, and the northernmost part of the Middle America Trench, where fault geometries are consideredbetter constrained by local scale earthquake relocation results, seismic reflection profiles, and/or receiverfunction analyses (see Table S1 in the supporting information for references). We use constant thicknessesfor the elastic oceanic plate and the arc and back-arc parts of the elastic upper plate. Similar to Sun et al.(2014), we include an elastic mantle wedge corner beneath the fore-arc crust to represent the stagnant “coldnose” of the mantle wedge (Wada & Wang, 2009; Figure 1, lower inset).

For finite element mesh construction, it is convenient to have distant model boundaries roughly parallel withor perpendicular to the average strike direction of the subduction zone and to have more or less parallel mer-idians. We therefore conduct a coordinate transformation for some subduction zones, such as Eastern Alaska,Southern Kuril, Southern Peru, and Northern Sumatra, to have the new “equator” approximately normal tothe trench crossing the rupture area. This new coordinate system also makes it convenient to partitionGNSS displacements and their time series into trench-normal and trench-parallel directions (see figures insections 4 and 5).

The bottom boundary of our models is at 500 km depth. The lateral boundaries are more than 1,000 km fromthe rupture area and have minimal effects on model results. At the four lateral boundaries, the displacementis fixed in the normal direction but free in the tangential directions. The bottom boundary is fixed, and the topboundary is free in all directions.

2.3. Modeling Strategy

Following Wang et al. (2001) and Hu et al. (2004), we separately model the “earthquake effect” and the “faultlocking effect” and then combine the results to have the total deformation field.

The earthquake effect includes seismic rupture followed by viscoelastic stress relaxation and afterslip.Assigning a well determined static coseismic slip distribution is an important first step. For each earth-quake, we use a published coseismic slip model if its application to our finite element mesh yields surfacedeformation in good agreement with coseismic observations. For some earthquakes, we need to modifythe original slip models by scaling up or down slip values in order to better match observations. Suchmodifications are necessitated by differences in fault geometry and/or rigidity values between the originalmodels and ours. If the adaptation of published slip models cannot fit coseismic observations, we con-struct our own slip distributions using single or multiple elliptical patches. The slip distribution within eachpatch is of a bell shape and is assigned using the method of Wang et al. (2013), featuring peak slip at thecenter of the patch and smooth decrease in all directions. Parameters for these elliptical patches and theirslip distribution are given in Table S2.

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Estimating afterslip in the viscoelastic Earth is challenging because geodetic observations reflect both viscoe-lastic relaxation and afterslip. Most published afterslip distributions for the earthquakes studied here werederived using purely elastic models. Studies that did consider viscoelastic relaxation, such as for the 1964Alaska, 2011 Tohoku-oki, 2010 Maule, and 2003 Tokachi-oki earthquakes, typically did not include the transi-ent rheology and sometimes did not include a subducting slab. Therefore, we do not directly apply the pub-lished afterslip models. Instead, we estimate the spatiotemporal distribution of afterslip, together with otherkey model parameters such as viscosities, via trial-and-error by visually comparing model results and obser-vations. For the afterslip distribution of most of the earthquakes, we use elliptical patches as described in theprevious paragraph. For the 1964 Alaska, 1995 Jalisco, and 2001 Peru earthquakes, afterslip is not assignedbecause the effect of viscoelastic relaxation alone is adequate in explaining the basic pattern of postseismicobservations. To define the temporal evolution of afterslip, we use the cubic function described in Hu andWang (2012). The adopted duration of the afterslip following each earthquake is reported in Table 1.

In modeling the locking effect, we assign a constant rate of slip deficit (or back slip; Savage, 1983) to the faultnodes. Full locking is simulated using a rate equal to the subduction rate and incomplete locking using alower rate. The assigned slip deficit rate may change along strike as required by GNSS observations. Modelsurface velocities initially change with time in response to a suddenly imposed slip deficit rate, but the systemeventually stabilizes to a steady state. We wait until the surface velocities become constant, typically aftermore than 300 years for a Maxwell mantle viscosity of the order of 1019 Pa s. For along-strike variations ofthe locking state, we refer to published locking models obtained by inverting interseismic GNSS velocities(see Table S1 for references). Because these studies assumed an elastic Earth, they usually overestimatethe downdip width of the locked zone (Li et al., 2015; Wang & Tréhu, 2016). We use narrower locked zonesin our models, with the slip deficit rate tapering to zero in the downdip direction to a depth no greater than30–50 km. Except for the Tohoku-oki earthquake, all our GNSS observations were from land stations, and theyusually have no sensitivity to megathrust locking or creep near the trench (Wang & Tréhu, 2016). We thus usea very simple locking distribution in the dip direction and focus on the more pronounced effects of along-strike variations.

The campaign and continuous GNSS data included in this work have all been published by other researchers.We obtained digital values from the original publications or from their authors (see ensuing sections for indi-vidual earthquakes). Where a dense network of continuous GNSS sites was available, we only selected a sub-set of the sites optimally distributed to represent the spatiotemporal pattern of postseismic deformation. TheGNSS motion discussed in this paper is always with respect to the stable part of the upper plate. For subduc-tion zones featuring secular motion of upper-plate crustal blocks, such as northern Sumatra (Bradley et al.,2016) and eastern Alaska (Li et al., 2016), we apply appropriate corrections as will be detailed in later sections.

To compare postseismic deformation between different earthquakes, we use as a common location refer-ence the vertical projection of the 50-km depth contour of the subduction fault on Earth surface, called

Table 1Summary of Earthquakes and Model Parameters

Figureno. Earthquake Mw

Coseismicslip model

Afterslipduration (year)

Peakafterslip (m)

Mantle wedge viscosity (Pa s) Oceanic mantle viscosity (Pa s)

ηK ηM ηK ηM

S1 1960 Chile 9.5 Moreno et al. (2009) NA 0 1 × 1018 2 × 1019 1 × 1019 1 × 1020

3 1964 Alaska 9.2 This work NA 0 1 × 1018 7 × 1018 1 × 1019 1 × 1020

4 2011 Tohoku-oki 9.0 Iinuma et al. (2012)a 10.0c 3.8c 5 × 1017 2 × 1018 2.0 × 1018 1 × 1020

5 2010 Maule 8.8 Moreno et al. (2012) 4.5 2.2 1 × 1018 3 × 1018 6.7 × 1018 1 × 1020

6 2005 Nias 8.6 Konca et al. (2007)b 7.5 3.9 5 × 1017 2 × 1018 5.0 × 1018 1 × 1020

7 1995 Antofagasta 8.0 This work 1.0 0.2 1 × 1018 3 × 1018 1 × 1019 1 × 1020

8 2007 Pisco 8.0 Remy et al. (2016) 2.0 0.7 1 × 1018 3 × 1018 1 × 1019 1 × 1020

9 1995 Jalisco 8.0 This work NA 0 2.5 × 1017 1 × 1018 2.5 × 1018 1 × 1020

10 2001 Tokachi-oki 8.1 This work 12.0 3.8 2.5 × 1017 7 × 1017 2.0 × 1018 1 × 1020

11 2001 Peru 8.4 This work NA 0 2 × 1018 5 × 1018 1 × 1019 1 × 1020

aOriginal slip values are scaled down by a factor of 0.92. bOriginal slip values are scaled up by a factor of 1.3. cThe values listed here are for the deep afterslipnorth of the coseismic slip. For other afterslip patches, see Wang et al. (2018).

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R-50. Our models constrained by available geodetic observations allow us to predict a continuous spatiotem-poral postseismic deformation pattern. We thus can find the time after each earthquake when the dividingboundary of the opposing motion passes through R-50, referred to as the reference time. The product ofthe reference time and subduction rate is called the reference length.

3. Crustal Motion Following Mw ≥ 9 Subduction Earthquakes3.1. The 1700 Mw 9.0 Cascadia, 1960 Mw 9.5 Chile, and 2004 Mw 9.2 Sumatra Earthquakes

Synthesizing present-day deformation patterns at Sumatra, Southern Chile, and Cascadia, Wang et al. (2012)demonstrated a common deformation cycle of great subduction earthquakes. For these giant (Mw ≥ 9) earth-quakes, the process of viscoelastic relaxation is very long. For example, at the Chile margin, ~40–50 years afterthe 1960 Mw 9.5 earthquake, opposing motion of the coastal and inland areas can still be observed(Khazaradze et al., 2002) and may last for ~70 years as predicted by Hu et al. (2004) using a Maxwellviscoelastic model.

In this work, we do not reconstruct models for Sumatra and Cascadia, where modern land-based GNSS obser-vations show wholesale seaward motion and wholesale landward motion, respectively. For our purpose,further modeling will not add much to what has been learned by Wang et al. (2012, and references therein)for these end-member cases. However, for Chile, where the opposing motion of the coastal and inland GNSSsites is ongoing, we made an effort to refine the previous model. In particular, to improve the prediction ofGNSS velocities, we allow the degree of locking of the subduction fault to vary along the strike based onMoreno et al. (2010) and Métois et al. (2012). We have also added the “cold nose” mentioned in section 2to the new Chile model. Although we use a bi-viscous mantle rheology, to be consistent with our modelsfor all the other earthquakes, GNSS observations three to four decades after the 1960 Chile earthquake arenot sensitive to the transient viscosity. To the first order, the new results are similar to those in Wang et al.(2012), so the results are displayed only in Figure S1 in the supporting information. The fault geometry is rela-tively uniform along strike. However, because of heterogeneous coseismic rupture and interseismic locking,viscoelastic relaxation is not uniform along strike. In our model, the dividing boundary of opposing motionreaches R-50 earlier near the northern end of the rupture zone due to a combination of a relatively low coseis-mic slip and a wide zone of interseismic locking. It passes through R-50 (section 2.3) in different places alongthe margin over a period of about 30–45 years after the earthquake.

3.2. The 1964 Mw 9.2 Alaska Earthquake

Similar to the 1960 Mw 9.5 Chile earthquake, the 1964 Mw 9.2 Alaska earthquake has a long rupture lengthwhich extended 600–800 km from Prince William Sound along the Kenai Peninsula to Kodiak Island(Plafker, 1965; Plafker et al., 1994). Mutually different coseismic slip models have been published for thisevent (e.g., Holdahl & Sauber, 1994; Ichinose et al., 2007; Johnson et al., 1996), and it is difficult to fit geo-detic observations when applying these slip distributions to our finite element model. Therefore, wedevelop our own coseismic slip model. For triggering postseismic deformation, it is the net coseismic slipthat matters. Details of the dynamic rupture process (e.g., Christensen & Beck, 1994; Kanamori, 1970) areless important, but the identification of three pulses in the earthquake source time function provides gui-dance for us to understand the patchiness of the rupture (e.g., Christensen & Beck, 1994; Ichinose et al.,2007; Figure 3a).

The Alaska earthquake occurred long before the age of GNSS. Coseismic deformation was estimated fromleveling and tide level change data (Plafker, 1965) and triangulation surveying data (Figure 3a; Snay et al.,1987). Using these data as constraints, we construct a coseismic slip distribution consisting of three overlap-ping elliptical patches (Figure 3a) with a constant rake of 100° (Table S2). The resultant coseismic deformationmodel captures the basic pattern of the observed deformation (Figure 3a), such as the >2-m subsidence onthe Kenai Peninsula and Kodiak Island (Plafker, 1965) and the ~10-m seaward displacement near the PrinceWilliam Sound (Snay et al., 1987). These data have greater uncertainties compared to modern GNSS observa-tions, and we do not attempt to fit themmore precisely. In particular, because postearthquake campaign sur-veys were conducted a few months to a few years after the earthquake, the observed displacements musthave included some postseismic deformation. Also, for simplicity, we neglect the possible slip of a splay faultnear Montage Island (Holdahl & Sauber, 1994; Plafker, 1965).

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About 30–50 years after the earthquake, GNSS velocities show opposing motion between sites on the south-east coasts of the Kenai Peninsula and Kodiak Island and other sites further inland (Figure 3c; Freymuelleret al., 2008; Li et al., 2016). This pattern has sustained over the period (~20 years) of GNSS observations,although a couple of slow slip events beneath the Cook Inlet at depths of 40–60 km caused slight transientperturbations to the deformation pattern (Li et al., 2016, and references therein). In a previous study, Suitoand Freymueller (2009) employed long-lasting afterslip and viscoelastic relaxation in a 3-D Cartesian finiteelement model of Maxwell rheology to explain the seaward motion of the inland GNSS sites. They then usedan elastic model to obtain a megathrust locking distribution after removing the modeled postseismic signalsfrom observed GNSS velocities.

Figure 3. Coseismic and postseismic deformation of the 1964 Mw 9.2 Alaska earthquake. Depth below sea level of themegathrust, based on Li et al. (2013) and Kim et al. (2014), is contoured at 10-km intervals (light violet dashed lines).(a) Coseismic horizontal displacements based on triangulation survey (Snay et al., 1987) and model-predicted displace-ments using the shown slip distribution. Purple contours (in m) show model-predicted vertical displacements. The blackline encompasses the rupture area (Plafker et al., 1994) inferred from precise leveling and tidal elevation data (Plafker,1965). (b–d) Model-predicted postseismic velocities over three different periods as labeled in each panel. The blackcontours (in m) show the same coseismic slip distribution as in (a). Global Navigation Satellite Systems (GNSS) velocity databetween 1992 and 2004 (Li et al., 2016) are shown in (c). Along-strike variations in the slip deficit rate are based on Li et al.(2016). To account for themotion of the Peninsula block (see inset; Li et al., 2016), a constant velocity of 6.5mm/yr in the strikedirection has been added to GNSS sites located in it. In this figure and all the other map view figures in this paper, the arrowoffshore shows subduction direction (Table S1). For this model and other models that require a rotation of coordinates, aninset is provided to show the actual orientation of the margin. In the inset: The box outlines map area shown in the rest of thefigure. PWS: Prince William Sound; MI: Montage Island; CI: Cook Inlet; KP: Kenai Peninsula; KI: Kodiak Island.

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Ourmodel differs from Suito and Freymueller (2009) mainly in the spherical-Earth geometry and the inclusionof viscoelasticity in modeling fault locking (see section 2). Similar to the case of the 1960 Chile earthquake,GNSS observations 30–50 years after the 1964 Alaska earthquake are not sensitive to the transient viscosity.With the thicknesses of both elastic plates set at 30 km, the preferred steady state viscosity of the mantlewedge is 7 × 1018 Pa s (Table 1). Model tests suggest that lower or higher viscosity values cannot depictthe present-day location of the dividing boundary of the opposing motion. According to this model, thedividing boundary passed through R-50 (section 2.3) in different places along the margin about 25–35 yearsafter the earthquake.

3.3. The 2011 Mw 9.0 Tohoku-Oki Earthquake

Different from the1964 Mw 9.2 Alaska and the 1960 Mw 9.5 Chile earthquakes, coseismic and postseismicdeformation of the 2011Mw 9.0 Tohoku-oki earthquake was very well recorded, thanks to the dense geodeticnetwork in Japan including seafloor GNSS sites in and around the rupture area and many other types ofobservations. These observations have provided critical information on the coseismic rupture and short-termpostseismic deformation (e.g., Freed et al., 2017; Iinuma et al., 2012; Sun et al., 2014, 2017). For a review oflessons learned from observed crustal deformation associated with the Tohoku-oki earthquake, the readeris referred to Wang et al. (2018) and references therein.

We expand the finite element model of our previous work (Sun et al., 2014; Sun &Wang, 2015) to predict crus-tal deformation of the Japan Trench subduction zone over the next few hundred years. Model results for thecoseismic deformation (Figure 4a) are identical to those in Sun et al. (2014) and Sun and Wang (2015). Resultsfor the short-term (0–1 years) postseismic deformation differ slightly from those in the two previous publica-tions because of fine adjustment of the afterslip distribution in this work. Heterogeneous locking of themegathrust is assigned to fit the GNSS observations, but there are some uncertainties in the degree of lockingin the creeping segments (Wang et al., 2018). Assuming the locking pattern stays unchanged, we predictGNSS site velocities averaged over time intervals of 30–40 years and 180–200 years after the earthquake(Figures 4c and 4d). The reference time when the dividing boundary of opposing motion will pass throughR-50 is predicted to be about 18–20 years, a time between the frames shown in Figures 4b and 4c.

The relatively low viscosities used in our Tohoku-oki model (Table 1), as compared to the values used forother subductions (Wang et al., 2012 and this work), may reflect site-specific processes affecting the thermalstate and structural features. But the lower values may also be due to the inability of the Burgers bodyadopted by our model in describing what might be a more complex mantle rheology of the actual Earth. Itis quite possible that deformation over the first 5 years after the earthquake is still in the transient phase,and the actual steady state mantle viscosity that controls the longer-term (decades to centuries) deformationshould be higher. This is a subject deserving further research.

4. Subduction Earthquakes of 8.5 ≤ Mw < 9

In this section, we discuss the postseismic deformation of the only twoMw 8.5–8.9 subduction earthquakes inthe modern GNSS era, the 2005Mw 8.6 Nias and 2010Mw 8.8 Maule earthquakes. We will show that the land-ward migration of the dividing boundary of opposing motion after these two earthquakes is faster than afterthe Mw ≥ 9 events.

4.1. The 2010 Mw 8.8 Maule Earthquake

The 2010 Mw 8.8 Maule earthquake is a well observed event. The part of the Chile subduction fault thatruptured during this earthquake, located just north of the 1960 Mw 9.5 rupture, had long been identifiedas a seismic gap. Therefore, a large number of GNSS sites were installed there before the earthquake by var-ious research groups (Klotz et al., 2001; Moreno et al., 2011; Ruegg et al., 2009), providing records of crustaldeformation in both the coseismic and short-term postseismic phases. Also, the shorter trench-coast distance(~100 km) as compared to the Japan Trench (>200 km) allows the coseismic slip of this earthquake to be rea-sonably well determined with land-based GNSS observations, except for the most near-trench area.

Published rupture models of the Maule earthquake feature an elongated rupture area of ~450 km long and~100 kmwide (Delouis et al., 2010; Lay et al., 2010; Lorito et al., 2011; Moreno et al., 2012; Vigny et al., 2011). In

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this work, we directly use the model of Moreno et al. (2012; Figure 5a) that was derived by inverting GNSS,InSAR, and land-level changes data using a finite element model in many ways similar to ours.

Some of the postseismic studies for the Maule earthquake employed elastic models to study the effect ofafterslip only (Bedford et al., 2013; Lin et al., 2013), and some invoked viscoelasticity (Bedford et al., 2016;Klein et al., 2016; Li et al., 2017). Klein et al. (2016) used a finite element model of Burgers rheology but didnot directly include the effect of fault relocking. Bedford et al. (2016) included the locking effect but assumedMaxwell rheology; the model can explain an observed change in the motion direction of coastal GNSS sites

Figure 4. Coseismic and postseismic deformation of the 2011Mw 9.0 Tohoku-oki earthquake. Depth below sea level of themegathrust is contoured at 10-km intervals (light violet dashed lines). (a) Coseismic horizontal displacements of land(Ozawa et al., 2011) and seafloor (Kido et al., 2011; Sato et al., 2011) Global Navigation Satellite Systems (GNSS) sites andmodel-predicted displacements using the slip distribution of Iinuma et al. (2012) scaled by 0.92. (b–d) Model-predictedpostseismic velocities over three different periods after the earthquake as labeled in each panel. The black contours showthe same coseismic slip distribution as in (a) in m. The gray contours (in m) in (b) show afterslip distribution (Wang et al.,2018). Land and seafloor GNSS velocity data over 0–1 year (Ozawa et al., 2012; Sun et al., 2014; Watanabe et al., 2014) areshown in (b). Along-strike variations in slip deficit rates are based on Suwa et al. (2006) and Hashimoto et al. (2009).

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from trenchward (westward) to northerly, as affected by the slightly oblique subduction of the Nazca Plate(DeMets et al., 2010). Li et al. (2017) also assumed Maxwell rheology but with a heterogeneous mantleviscosity in the arc and back arc to explain the postseismic uplift of the arc region.

Our new model is similar to that of Bedford et al. (2016) but with a Burgers rheology (Tables 1 and S1),considered to be more appropriate for modeling short-term postseismic deformation. Invoking the transi-ent viscosity leads to the prediction of less afterslip. Our model-predicted GNSS velocities for two timewindows are shown in Figures 5b and 5c. Observed and modeled time series for a few coastal and inlandGNSS sites are shown in Figure 5d; this subset is adequate in representing the general evolution of thedeformation. A group of GNSS sites (ARCO, CONT, CONZ, CBQC, and PCLM) that cover a wide range alongthe coast reversed their direction of motion from seaward to landward within the first few years(Figure 5d), causing the pattern of opposing motion to emerge on land (Figure 5c). The dividing boundaryof opposing motion is predicted by our model to go through R-50 at slightly different times along strike,about 10–13 years after the earthquake.

4.2. The 2005 Mw 8.6 Nias Earthquake

The 2005Mw 8.6 Nias earthquake ruptured an ~350-km segment of the Sunda megathrust offshore of north-ern Sumatra, abutting the coseismic slip area of the 2004 Mw 9.2 Sumatra earthquake to the north (Briggset al., 2006). GNSS observations from fore-arc islands at relatively short distances from the trench (~60 km)provided important constraints for the coseismic slip (e.g., Briggs et al., 2006; Konca et al., 2007). Publishedrupture models show buried slip that did not breach the trench. In this work, we use the coseismic slip modelof Konca et al. (2007; Figure 6a) that was obtained by jointly inverting teleseismic data, GNSS displacements,and vertical displacements inferred from coral records (Briggs et al., 2006). When mapping slip vectors fromKonca et al.’s (2007) planar fault to our curved fault, we need to scale up their slip values by a factor of 1.3 inorder to fit GNSS observations.

The fore-arc GNSS observations yield important information also on the postseismic deformation in the nearfield. Large trenchward displacement (0.8 m) of the fore-arc site LHWA occurred over the first 9 months afterthe earthquake. Using an elastic model, Hsu et al. (2006) inferred>1-m afterslip over this period updip of therupture zone. Sun and Wang (2015) used a 2-D finite element model to demonstrate that the amount of the

Figure 5. Coseismic and postseismic deformation of the 2010 Mw 8.8 Maule earthquake. (a) Coseismic Global NavigationSatellite Systems (GNSS) displacements (Moreno et al., 2012; Vigny et al., 2011) and model-predicted displacementsobtained by applying the coseismic slip distribution of Moreno et al. (2012) to our finite element mesh. See (d) for thelabeled sites. Sites CONZ and CONT coincide at this plotting scale. For the data of Vigny et al. (2011), only those fromcontinuous sites are shown here. These data were not used by Moreno et al. (2012) to constrain the slip model; model-predicted displacements of these sites are shown in lighter blue. Depth below sea level of the megathrust is contoured at10-km intervals (light violet dashed lines). (b and c) Postseismic velocities over two different periods predicted by ourmodel. Observed GNSS velocities at some sites over 0–1 year are shown in (b). The solid contours (every 4 m) show thesame coseismic slip distribution as in (a). Thin dashed contours (every 0.5 m) in (b) show cumulative afterslip over 4.5 years.Along-strike variations in the slip deficit rate are based on Moreno et al. (2010). (d) Observed (red) (Bedford et al., 2016)and modeled (blue) eastward displacements at selected GNSS sites. See Figure S2 for the north and vertical components.The four sites labeled with location coordinates are farther than 400 km from the trench and therefore not shown in (a).

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shallow afterslip could be even greater (>2 m) if mantle viscoelasticity is considered. The lack of coseismicslip with the presence of large afterslip is understood to imply a velocity-strengthening behavior of theshallowest portion of the megathrust (Wang & Hu, 2006).

In this work, we use GNSS observations over a longer period (Feng et al., 2015). Our model parameters areshown in Tables 1 and S1. The results suggest a fast continuing seaward motion of the fore-arc region dueto the shallow afterslip immediately after the earthquake (Figure 6b). Within 3–5 years, the locking of thesubduction fault causes the fore-arc GNSS sites to reverse their motion, similar to the Maule example,

Figure 6. Deformation due to the 2005 Mw 8.6 Nias earthquake. Depth below sea level of the megathrust is contoured at10-km intervals (light violet dashed lines). (a) Coseismic Global Navigation Satellite Systems (GNSS) displacements (e.g.,Briggs et al., 2006) and model-predicted displacements using the coseismic slip distribution of Konca et al. (2007) scaled by1.3. Inset shows the map area of this figure and location of the Sumatra fault. (b and c) Observed and model-predictedpostseismic velocities over two different time periods. Because of data gap and seismicity perturbation, observed velocitiescannot be obtained for all the sites. The black lines are 2, 6, and 10-m contours of the coseismic slip distribution shown in(a). Thin black dashed contours (in m) show cumulative afterslip over 7.5 years. A constant velocity of 1.7 cm/yr in thestrike direction has been added to fore-arc GNSS sites, to account for the right-lateral motion of the strike-slip Sumatra fault(see inset). The error ellipses of GNSS velocities in 0–1 year represent standard error (derived in this work). The errors for thelater period are difficult to quantify, due partly to perturbations by numerous Mw 6–7.8 earthquakes in this region(Feng et al., 2015). Along-strike variations in the slip deficit rate are based on Chlieh et al. (2008) and Prawirodirdjo et al.(2010). (d) Observed (red) (Feng et al., 2015) and modeled (blue) trench-normal displacements of GNSS sites. See Figure S3for the trench-parallel and vertical components. Locations of these sites are shown in (b) except for NTUS (103.68°E, 1.35°N)that is over 700 km from the rupture area.

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while the inland site SAMP is still moving seaward (Figure 6d). The dividing boundary of opposing motionpasses through R-50 in our model about 6–10 years after the earthquake.

To account for the right-lateral motion of the strike-slip Sumatra Fault (Figure 6), we have added a constantvelocity (1.7 cm/yr) in the strike direction to the fore-arc “sliver” seaward of this fault (Bradley et al., 2016). Thisresults in a rather good fit to the strike-parallel component of GNSS time series (Figure S3). A similar methodin dealing with fore-arc sliver motion was used by Wang et al. (2007) in studying the postseismic deformationof the 1960 Mw 9.5 earthquake.

5. Subduction Earthquakes of Mw < 8.5

In this section, we discuss the postseismic deformation of five Mw 8–8.5 subduction earthquakes for whichrelevant geodetic observations are available. We will show that these earthquakes are followed by rathershort-lived (one to a few years) opposing motion. The dividing boundary of the opposing motion sweepsthrough the geodetic network very fast. Observing the short-lived opposing motion with campaign-stylemeasurements requires frequent occupation of campaign sites within a limited time window.

In assigning the coseismic slip distributions of these “small-size” great earthquakes, we use a simple ellipticalslip patch and a constant slip rake (Table S2) as explained in section 2, except for the 2007Mw 8.0 Pisco earth-quake for which we directly apply a published rupture model.

5.1. The 1995 Mw 8.0 Antofagasta Earthquake

The 1995 Mw 8.0 Antofagasta earthquake ruptured an ~150-km segment of the subduction fault, about1,000 km north of the 2010 Mw 8.8 Maule rupture (section 4.1). The rupture terminated to the north beforebreaking into a seismic gap where anMw ~9 earthquake occurred in 1877 (Delouis et al., 1997). Published rup-ture models of this earthquake that were obtained using seismic, campaign GNSS, and InSAR data (Chliehet al., 2004; Delouis et al., 1997; Ruegg et al., 1996) suggest a single slip patch. The coseismic deformation pre-dicted using an elliptical patch (Table S2) in our finite element model agrees with campaign GNSS data fromRuegg et al. (1996), Klotz et al. (1999), and Chlieh et al. (2004; Figure 7a).

Although only campaign observations were available to provide snapshots of crustal deformation followingthis earthquake (Khazaradze & Klotz, 2003; Klotz et al., 2001), the broad spatial coverage of themeasurements

Figure 7. Coseismic and postseismic deformation of the 1995Mw 8.0 Antofagasta earthquake. Depth below sea level of themegathrust is contoured at 10-km intervals (light violet dashed lines). (a) Coseismic horizontal displacements based oncampaign Global Navigation Satellite Systems (GNSS) surveys (e.g., Chlieh et al., 2004) and model-predicted displacementsusing the shown slip distribution. (b and c) Observed postseismic velocities based on campaign GNSS surveys(Khazaradze & Klotz, 2003; Klotz et al., 2001) andmodel prediction over the first 2 years after the earthquake. The black linesare contours (inm) of the coseismic slip distribution shown in (a). The gray dashed ellipses in (b) encompass areas of>0.1 minferred afterslip over the first year. Slip deficit rates are based on Chlieh et al. (2011). The error ellipses for the GNSSobservations are from the original publications.

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helps to demonstrate clearly how quickly the dividing boundary of opposing motion must have migratedlandward through the network (Figure 7). With primary parameters given in Tables 1 and S1, we constructa continuous deformation history constrained by these campaign data (Figure 7). In this model, thedividing boundary passes through R-50 as quickly as 0.5–1 years after the earthquake.

The campaign data for the period of 0–1 years (Figure 7b) feature rather low signal-to-noise ratio, but the dataclearly show that the dividing boundary of opposing motion in the margin-normal direction was already onland during this time. However, we cannot explain the relatively large margin-parallel (northward) motion ofsome of the sites and why such motion disappeared or diminished in years 1 and 2. It may be associated witha proposed lower degree of locking just north of the rupture zone (Li et al., 2015). More peculiar is the beha-vior of the three coastal sites near the rupture zone. Their observed motion slowed down in years 1 and 2when other sites accelerated their landward motion as expected (Figures 7b and 7c). We think it may reflecta transient phenomenon such as delayed afterslip of parts of the megathrust somewhere offshore.

5.2. The 2007 Mw 8.0 Pisco Earthquake

The 2007Mw 8.0 Pisco, central Peru, earthquake has a rupture length similar to 1995 Antofagasta. The ruptureterminated to the south where the Nazca ridge is subducting (Remy et al., 2016; Sladen et al., 2010). Therewere no GNSS measurements prior to the earthquake, but five continuous sites were installed ~20 days afterthe earthquake and recorded postseismic deformation (Figure 8; Perfettini et al., 2010; Remy et al., 2016). Weapply to our finite element model the rupture model that Remy et al. (2016) derived by inverting InSAR data.The rupture model of Sladen et al. (2010) based on joint inversion of InSAR, teleseismic, and tsunami datashows a similar slip distribution.

All the available GNSS sites quickly stopped moving seaward or reversed their direction (Figure 8). Theyclearly show how the motion changed with time (Figure 8d). With parameter values shown in Tables 1 andS1, our postseismic deformation model can reproduce the main pattern of these observations. In this model,the dividing boundary of opposing motion goes through R-50 around 1–1.5 years after the earthquake. Thequick motion reversal suggests a rapid resumption of megathrust locking, but the exact timing of the reversalof specific sites may be affected by along-strike variations in the degree of locking. For example, compared tosite JUAN, the more southerly site GUAD, located even slightly closer to the rupture zone, reversed its motionslightly more slowly (Figure 8d). Because of the lower degree of locking in the south, associated with the sub-duction of the Nazca ridge (Villegas-Lanza et al., 2016; Wang & Bilek, 2014), it takes a little longer for the lock-ing effect to overshadow the effect of viscoelastic relaxation.

Figure 8. Model-predicted coseismic and postseismic deformation of the 2007 Mw 8.0 Pisco earthquake. Depth below sea level of the megathrust is contoured at10-km intervals (light violet dashed lines). (a) Coseismic displacements predicted with the shown slip model of Remy et al. (2016). The five GNSS stations (labeled onmap) were installed ~20 days after the earthquake. Inset shows the location and orientation of the map area in this figure. (b and c) Postseismic velocities overtwo time periods after the earthquake. The black contours (in m) show the same coseismic slip distribution as in (a). The gray dashed contours show the 2-yearcumulative afterslip in m. Along-strike variations in the slip deficit rate are based on Villegas-Lanza et al. (2016) and Chlieh et al. (2011). (d) Observed (red) (Remy et al.,2016) and modeled (blue) landward displacements of the GNSS sites. See Figure S4 for the trench-parallel and vertical components.

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5.3. The 1995 Mw 8.0 Jalisco Earthquake

The 1995 Mw 8.0 Jalisco earthquake ruptured an ~150-km-long segment along the northernmost part of theMexico subduction zone, where the very young (<10 Ma) Rivera Plate is subducting at a rather slow rate(Table S1; DeMets & Traylen, 2000; DeMets &Wilson, 1997). More than 10 campaign GNSS sites were surveyedin the Jalisco area and further inland before the 1995 earthquake, and another ~10 sites were establishedshortly after the earthquake. Most of these sites were occupied about 5–6 times over the first 4 years afterthe earthquake (Hutton et al., 2001). In addition to these campaign sites, the only operating continuous siteCOLI, ~40 km from the coast and slightly south of the rupture area (Figure 9a), provides important informa-tion on the temporal variation of the deformation. Márquez Azúa et al. (2002) employed an elastic dislocationmodel (Okada, 1985) and viscoelastic and poroelastic finite element models to explain the observed motionof COLI. In their work, the effect of megathrust locking was modeled using the elastic model.

Our model parameters are given in Tables 1 and S1, and results are shown in Figure 9 in comparison withavailable GNSS data. Three to 4 years after the earthquake, most of the sites are still observed and modeledto be moving seaward, except along the coast (Figure 9). The landward migration of the dividing boundary ofopposing motion is thus slower than that of the Antofagasta or Pisco earthquake (sections 5.1 and 5.2),despite the similar Mw. This is obviously the consequence of a very slow subduction rate at this margin(Table S1). Similar to incomplete megathrust locking discussed in the preceding subsection, a slower subduc-tion rate allows less contribution to postseismic deformation from fault locking. In our model, the dividingboundary moves through R-50 7–8 years after the Jalisco earthquake. We are unable to explain the

Figure 9. Coseismic and postseismic deformation of the 1995 Mw 8.0 Jalisco earthquake. Depth below sea level of themegathrust, based on Pardo and Suarez (1995) and Suhardja et al. (2015), is contoured at 10-km intervals (light violetdashed lines). (a) Observed (Melbourne et al., 1997) and model-predicted horizontal coseismic displacements using theshown slip distribution. COLI (green circle) was the only continuous Global Navigation Satellite Systems (GNSS) site. (b–e)Model-predicted postseismic velocities over four different time periods after the earthquake as labeled. GNSS velocities basedon campaign surveys (Hutton et al., 2001) are shown where available. The solid contours (in m) show the same coseismicslip distribution as in (a). (f) Observed (Márquez Azúa et al., 2002) (red) and modeled (blue) horizontal displacements of COLIbefore and after the Jalisco earthquake (t = 0). Inset in (a) shows the location and orientation of the map area in this figure.

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significant margin-parallel component of postseismic motion of the GNSS sites, especially in years 3 and 4(Figure 9c), since the subduction direction is almost margin-normal. There may be other local geologicalprocesses that are not accounted for by the postseismic deformation model, which add uncertainties toour results.

5.4. The 2003 Mw 8.1 Tokachi-Oki Earthquake

The 2003Mw 8.1 Tokachi-oki earthquake ruptured an ~100-km-long segment along the southern Kuril trench(Figure 10). Paleoseismic and historical records suggest that this part of the subduction fault has produced anumber of Mw 8–9 earthquakes. Another Mw 8 earthquake occurred in 1952 (Hirata et al., 2003), and a muchlarger event ruptured at least a 300-km-long segment along the strike ~350 years ago (Nanayama et al., 2003;Sawai et al., 2004).

Similar to the 2011Mw 9.0 Tohoku-oki earthquake (section 3.3), the Tokachi-oki earthquake is a well observedevent. Many rupture models were obtained by various groups using different data sets, including static andhigh-rate GNSS data (Miura et al., 2004; Miyazaki, Larson, et al., 2004; Nishimura, 2011; Ozawa et al., 2004),seismic waves (Yagi, 2004; Yamanaka & Kikuchi, 2003), tsunami waveforms (Hirata et al., 2003; Taniokaet al., 2004), or by joint inversion of more than one type of data (Koketsu et al., 2004; Romano et al., 2010).Most of these published rupture models suggest a single slip patch at relatively large depths (30–45 km).Using a nearly circular patch, our finite element model predicts coseismic deformation in good agreementwith the GNSS data (Figure 10a).

Figure 10. Deformation due to the 2003 Mw 8.1 Tokachi-oki earthquake. Depth below sea level of the megathrust is con-toured at 10-km intervals (light violet dashed lines). (a) Observed (e.g., Larson & Miyazaki, 2008) and model-predictedhorizontal coseismic displacements using the shown slip distribution. Inset in (c) shows the location and orientation of themap area in this figure. (b and c) Postseismic velocities over two different time periods after the earthquake as labeled.Observed postseismic velocities are shown for labeled sites. Low signal-to-noise ratio and seismicity perturbations do notallow reliable derivation of observed velocities after the first 3 years. The solid contours (in m) show the same coseismicslip distribution as in (a). The gray dashed contours (in m) show cumulative afterslip over 12 years. Along-strike variations inthe slip deficit rate are based on Suwa et al. (2006) and Hashimoto et al. (2009). (d) Observed (red) (Itoh & Nishimura, 2016)and modeled (blue) trench-normal displacements of Global Navigation Satellite Systems sites labeled in (b). SeeFigure S5 for the trench-parallel and vertical components. Observed displacements after the 2011 Mw 9.0 Tohoku-okiearthquake (~7.5 years) are not shown.

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Most postseismic deformation studies for this earthquake focused on afterslip in an assumed elastic Earth(Baba et al., 2006; Miyazaki, Segall, et al., 2004; Ozawa et al., 2004; Sato et al., 2010). They suggest substantialafterslip updip of the rupture zone, the most direct geodetic evidence being a>20-cm uplift recorded by twoocean-bottom pressure gauges seaward of the rupture (Baba et al., 2006). Itoh and Nishimura (2016)employed a layered-Earth model (without a slab) of Maxwell rheology to study the effects of both afterslipand viscoelastic relaxation but without megathrust locking.

Our 3-D model differs from that of Itoh and Nishimura (2016) by including a slab. The viscosity values aregiven in Table 1. In terms of the large and sustained afterslip updip of the rupture area, our model resultsagree with previous studies (Figure 10). Right after the earthquake, because of the large depth of the rupture,the dividing boundary of the viscoelastic opposing motion should be in the coastal area, above the downdiptermination of the rupture. In other words, viscoelastic relaxation alone would cause landward motion ofsome the coastal GNSS sites right after the earthquake (model tests not shown here; see also Itoh andNishimura, 2016). To explain the actually observed continuing seaward motion of the coastal GNSS sites, alarge amount of afterslip updip of the rupture is required.

Due to viscoelastic relaxation and the long-lasting shallow afterslip, GNSS sites farther than 100 km from therupture zone had been smoothly moving seaward until being interrupted by the 2011 Mw 9.0 Tohoku-okiearthquake that occurred ~400 km to the south. After initial seaward motion for 4 years due primarily to

Figure 11. Coseismic and postseismic deformation of the 2001 Mw 8.4 Peru earthquake. Depth below sea level of themegathrust is contoured at 10-km intervals (light violet dashed lines). AREQ (green circle) was the only continuousGlobal Navigation Satellite Systems site in operation. (a) Observed (e.g., Chlieh et al., 2011; Perfettini et al., 2005) and mode-predicted horizontal coseismic displacements using the shown slip distribution. (b–d) Model-predicted postseismicvelocities over three different time periods after the earthquake as labeled. The solid contours (in m) show the samecoseismic slip distribution as in (a). Along-strike variations in the slip deficit rate are based on Chlieh et al. (2011) andVillegas-Lanza et al. (2016). (e) Observed (Bevis & Brown, 2014) and modeled postseismic landward displacements of AREQ.Inset in (a) shows the location and orientation of the map area in this figure.

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the shallow afterslip, sites near the coast reversed their motion direction (Figure 10d). The dividing boundarywent through R-50 3–4 years after the earthquake. Opposing motion occurred on land sometime before the2011 Tohoku-oki earthquake, as can be seen, for example, by comparing the trench-normal component ofsites 0138 and 0012 shown in Figure 10d.

5.5. The 2001 Mw 8.4 Peru Earthquake

The 2001 Mw 8.4 Peru earthquake ruptured an ~200-km-long segment of the Peru subduction zone(Figure 11), where a great Mw 8.8–9 earthquake in 1868 had ruptured a longer segment extending farthersouth (Bilek & Ruff, 2002; Comte & Pardo, 1991). Although seismological studies (e.g., Bilek & Ruff, 2002;Giovanni et al., 2002) indicate two major pulses of moment release, rupture models derived by invertingGNSS and InSAR data generally show a simple slip distribution (e.g., Chlieh et al., 2011; Pritchard et al.,2007). All the GNSS sites that provided coseismic displacement values are campaign sites, except AREQ(Pritchard et al., 2007; Ruegg et al., 2001). Using an elliptical rupture patch, our finite element model predictsthe basic pattern of the observed GNSS displacements (Figure 11a). The observed displacements must haveincluded some postseismic deformation, because the campaign sites were not reoccupied until weeks tomonths after the earthquake.

Various models have been proposed to explain the postseismic time series of AREQ, the only continuous sitein operation, located 225 km from the Peru trench and landward of the main slip area (Bevis & Brown, 2014).Melbourne et al. (2002) attributed the continuing seaward motion of the site to afterslip downdip of the rup-ture area. Perfettini et al. (2005) used a 1-D semianalytical model that includes an afterslip zone and a viscousshear zone along the downdip extension of the seismogenic plate interface. Hergert and Heidbach (2006)used a 2-D finite element model that includes nonlinear Maxwell rheology for the lower crust. No 3-D modelshave been published to study viscoelastic relaxation and megathrust relocking.

The primary parameters of our postseismic deformation model for this earthquake are given in Tables 1 andS1. Model results are shown in Figure 11, with the predicted time series for AREQ compared with its GNSSrecord. The model well explains the gradual motion reversal of AREQ ~6 and 7 years after the Peru earth-quake (Figure 11e), although it does not precisely fit the earliest part of the AREQ displacements. Theobserved very fast displacement in the first month could be due to some afterslip that is not included inour model or a more complex transient rheology than considered here. In this model, the dividing boundaryof opposing motion goes through R-50 around 4 years after the earthquake.

6. Conclusion

Using R-50 as a location reference, we summarize in Figure 12 our results for all the earthquakes studied inthis work in lieu of the conclusion of the study. As described in section 2.3, our models depict a spatiotempo-rally continuous postseismic deformation history for each earthquake constrained by available geodeticobservations. From this modeled history, we obtain the “reference time” when the dividing boundary ofthe opposing motion passes through R-50 (Figure 12a). To reflect the effect of plate kinematics, we show inFigure 12b the “reference length,” defined as the product of the reference time and the local subduction rate,as a function of earthquake magnitude. The reference length represents the amount of plate convergence (orslip deficit if the fault is fully locked) accrued during the period of the reference time.

For different earthquakes, the geodetic constraints have different spatial and/or temporal coverages. An idealsituation of a dense network of continuous GNSS sites evenly distributed over a broad region and covering along enough time span is rare. When continuous GNSS observations are few or not available, frequentcampaign-mode measurements are very useful. For the Mw 8.0 Antofagasta, Mw 8.0 Jalisco, Mw 9.2 Alaska,and Mw 9.5 Chile earthquakes, most or all of the data were collected in campaign surveys. Frequent occupa-tions of sites after the Antofagasta earthquake helped to define the rapidly evolving deformation at differentsites. The more stable modern GNSS velocities observed in Alaska and Chile represent one stage of theirearthquake deformation cycle. For 1995 Jalisco and 2001 Peru, our models are constrained mainly by cam-paign data, but in each case a sole continuous record helps to improve the model’s prediction of the timeevolution of the postseismic deformation. For the Mw 8.0 Pisco, Mw 8.1 Tokachi-oki, Mw 8.6 Nias, Mw 8.8Maule, and Mw 9.0 Tohoku-oki earthquakes, a greater number of continuous GNSS sites are available, buteither the spatial coverage or the time span of the measurements is limited. For example, the five sites for

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Pisco are less than 100 km apart and form a spatially confined cluster. Sites for the Nias earthquakes arealmost all located on fore-arc islands less than 100 km from the trench. GNSS observations for the Tohoku-oki and Maule earthquakes are dense and continuous, but it is still too early for them to observe thedividing boundary of the opposing motion pass through R-50.

Nonetheless, a comparison of the model results for the 10 earthquakes indicates a clear trend: In general, thegreater the earthquake, the longer time it takes for the dividing boundary of opposing motion to reach R-50(Figure 12). For great earthquakes that feature a compact rupture area but huge slip such as Mw 9.0 Tohoku-oki, the long duration of the opposing motion is mainly because of the large stress perturbation induced bythe rupture (Figure 2). For great earthquakes that feature a long rupture in the strike direction but less slip,such as Mw 9.2 Sumatra, the long duration is mainly because of the less efficient postseismic viscoelasticstress relaxation, with the viscous mantle flow tending to be more confined to the dip direction (Figure 2).

7. Discussion7.1. Site-Specific Factors

Besides the primary control by earthquake size, the reference times of the individual examples also reflect theeffects of other site-specific factors. Examples follow.

1. The larger reference time of the Jalisco earthquake (Figure 12a), compared to otherMw 8.0 earthquakes, ismore strongly influenced by plate kinematics. Here the slower subduction rate leads to a smaller contri-bution by fault relocking to postseismic deformation, slowing down the evolution of the opposingmotion. In comparison, the reference length of the Jalisco earthquake lies within the trend in Figure 12b.

2. Similarly, incomplete locking of segments of a subduction fault also leads to a slower evolution. For earth-quakes with relatively long along-strike rupture lengths, such as the 1964 Alaska and 1960 Chile earth-quakes, variations in the slip deficit rate in the strike direction lead to a wide range of the reference time.

3. Although the reference time of the 2003 Tokachi-oki earthquake fits the trend in Figure 12, shallow after-slip played a more dominant role than viscoelastic relaxation. The large depth of the rupture zone in thisearthquake would normally result in a dividing boundary of opposing motion in the coastal area, but thelarge shallow afterslip completely negated this effect and caused the dividing boundary to be located off-shore over the first ~3 years. Similarly, the large shallow afterslip following the Nias earthquake causedcontinuing seaward motion of fore-arc GNSS sites over the first ~5 years, partially offsetting the effectof viscoelastic relaxation (Sun & Wang, 2015).

The Tokachi-oki example illustrates one shortcoming of defining the reference location using the same depthcontour (50 km) for all the margins. This definition fails to take into consideration complications in slip distri-bution. In particular, the downdip extension of earthquake rupture varies among events and is potentially

Figure 12. (left) The “reference time” for each earthquake, defined as the time when the landward migrating dividingboundary of opposing motion passes R-50, and (right) the same results shown as “reference length.” R-50 is the mapview location of the 50-km depth contour of the subduction interface (section 2.3). Reference length is the product of thereference time and subduction rate. For a large earthquake, the reference time may vary along strike, so a bar is used torepresent the range of values.

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important in controlling the postseismic deformation. However, to compare these earthquakes in a simplemanner, a better alternative in defining the reference location is difficult to find.

The cumulative postseismic seaward motion of R-50 until it reverses direction at the reference time amountsto a small fraction of its coseismic motion (results not displayed), ranging from 2% for the 1995 Antofagastaearthquake to 22% for the 2011 Tohoku-oki earthquake. There is no obvious relationship with earthquakesize; for example, the values for both the 2007Mw 8.0 Pisco event and the 1960Mw 9.5 Chile event are about10%. It may depend on site- or event-specific conditions such as the degree of megathrust locking, depth dis-tribution of coseismic slip and afterslip, and so forth.

Global Navigation Satellite Systems observations of the 10 earthquakes studied in this work allow us to con-strain mantle viscosities of multiple subduction zones. The viscosity values appear to be site-specific to somedegree. For segments of the same subduction zone or for adjacent subduction zones, the inferred viscosityvalues are similar. For example, for all the studied earthquakes in the Chile and Peru margins since 1995, tran-sient viscosities of 1–2 × 1018 Pa s and steady state viscosities of 3–5 × 1018 Pa s are preferred. However, thesesteady state viscosities are lower than the value (2 × 1019 Pa s) preferred for the 1960Mw 9.5 Chile earthquakein the same margin. It is possible that deformation following the more recent earthquakes has not yet fullyentered the steady state phase, although it has beenmodeled to be already in the steady state by our modelsof bi-viscous Burgers rheology. For subduction zones far from one another, somewhat different viscosityvalues are inferred. For example, in comparison with Chile and Peru, viscosity values preferred for theJapan and Kuril margins are lower by a factor of 2–5.

7.2. Margin-Parallel and Vertical Components of Postseismic Deformation

Because of the theme of this study, we have focusedmainly on themargin-normal component of postseismicdeformation. Observed margin-parallel motion usually reflects the same deformation process. The motioncan be significant especially in areas near the strike termini the rupture zone, as is the most obvious northand south of the latitudes of the Tohoku-oki rupture area (Figure 4b). Some of themargin-parallel componentmay reflect long-term motion of upper-plate crustal blocks in response to oblique subduction, such as at theSumatra margin discussed in section 4.2 (Figure 6c).

More difficult to understand is the vertical motion. Where observations are available, we display the GNSStime series of the vertical component in the supporting information together with their horizontal compo-nents. When studying the opposing motion of GNSS sites, we made no effort to fit the vertical component.Yet at some sites, the model-predicted vertical motion is in good or reasonable agreement with observations.At some other sites, the comparison with observations is rather poor. The poor comparison in some cases canbe explained by the simplicity of our structure model. The vertical component is muchmore sensitive to localand small-scale structural heterogeneities than is the horizontal component (Wang et al., 2018), but we prefersimple models in order to focus on the first-order physical process. However, some of the poor fit cannot beimproved by introducing more complex structures. The most intriguing is the dramatic difference betweenthe overall temporal characteristics of the horizontal and vertical components at some sites, such as CONZin Chile (Figure S2) and 0012 in Japan (Figure S5). Their margin-normal displacement shows very fast motionat first andmuch slower motion later, suggesting an inherent time scale that is consistent with current under-standing of fault friction and viscoelastic relaxation, but the vertical component indicates no such time scale.Either something is wrong with the data or something is fundamentally missing in the current understandingof earthquake deformation by the scientific community. This is an important topic of research that theauthors are currently pursuing.

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