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# Chilean megathrust earthquake recurrence linked to frictional contrast at depth

## Abstract

Fundamental processes of the seismic cycle in subduction zones, including those controlling the recurrence and size of great earthquakes, are still poorly understood. Here, by studying the 2016 earthquake in southern Chile—the first large event within the rupture zone of the 1960 earthquake (moment magnitude (Mw) = 9.5)—we show that the frictional zonation of the plate interface fault at depth mechanically controls the timing of more frequent, moderate-size deep events (Mw < 8) and less frequent, tsunamigenic great shallow earthquakes (Mw > 8.5). We model the evolution of stress build-up for a seismogenic zone with heterogeneous friction to examine the link between the 2016 and 1960 earthquakes. Our results suggest that the deeper segments of the seismogenic megathrust are weaker and interseismically loaded by a more strongly coupled, shallower asperity. Deeper segments fail earlier (~60 yr recurrence), producing moderate-size events that precede the failure of the shallower region, which fails in a great earthquake (recurrence >110 yr). We interpret the contrasting frictional strength and lag time between deeper and shallower earthquakes to be controlled by variations in pore fluid pressure. Our integrated analysis strengthens understanding of the mechanics and timing of great megathrust earthquakes, and therefore could aid in the seismic hazard assessment of other subduction zones.

## Main

Models of recent, large, subduction-zone earthquakes have revealed spatial relations between zones of high pre-seismic locking on the interface and regions of large coseismic slip, mechanically indicative of so-called asperities1,2,3,4,5. Although such relationships can be interpreted as evidence for heterogeneous fault friction properties3,6, little is known about the physical controls on the spatial distribution of creep, locking and slip on a seismogenic interface. Possible hypotheses include the varying degrees of geometric complexity7,8, the nature and thickness of the trench sediments9, variable fluid release at different depths10,11,12,13, differential loading along the plate interface associated with the geologic structure of the upper plate14,15,16 and fault zone rheology17,18. Each of these proposed physical mechanisms may independently influence dynamic, mechanical, and hydraulic properties of the subduction interface and consequently its frictional strength (stress required to initiate earthquake slip) and kinematics.

The lack of precision and completeness in deformation records between great earthquakes, and the rarity in recording major events affecting the same segment have restricted the characterization of the earthquake cycle to short snapshots. Thus, our understanding of the cycle in terms of frictional conditions along the plate interface is limited. The 25 December 2016 southern Chile earthquake19 (moment magnitude (Mw) = 7.6; Fig. 1) is the first sign of seismic reactivation within the segment that failed during the 1960 megathrust earthquake—the largest recorded by modern seismology20,21. Therefore, exploring the relationship between both events could provide insights into the persistence of asperities and a better understanding of slip behaviour (locking, creeping and seismic slip) with respect to spatiotemporal variations in frictional properties on the plate interface.

## The 2016 Southern Chile earthquake

The first-order kinematics of the 2016 event19 resembles previous Chilean megathrust events (that is, 1985 Central Chile22, 1995 Antofagasta23, 2007 Tocopilla24) in that most slip occurred along the deeper portions of the seismogenic region of the megathrust, within the transitional rheological separation to aseismic sliding25,26. Furthermore, such deeper, zone-C events26 with Mw = 7–8 are more frequent than great (Mw > 8.5) shallower events in subduction zones27 and thus play an important role in the process of stress build-up and release of seismic energy.

The 2016 earthquake ruptured the deeper portion of an area thought to represent a locked asperity, based on decadal-scale geodetic monitoring28 (Fig. 1). Kinematic models suggest that this patch previously released its full slip deficit in 1960 with over 10 m of slip29. We report near-fault, static surface displacements of the 2016 mainshock recorded by nine continuous GPS stations and synthetic aperture radar (SAR) differential interferograms (Fig. 1b and Supplementary Figs. 1–4). The largest recorded horizontal and vertical displacements occurred at Guafo Island (located ~20 km from the epicentre). To derive the slip distribution, we jointly inverted the GPS and InSAR data. Our preferred slip solution (Fig. 1) suggests a simple rupture composed of a single slip patch with a maximum slip of 2.9 m at 22 km depth. This amount is consistent with the release of ~80% of the total plate motion accumulated there since 1960. This is in agreement with the degree of pre-2016 locking, implying that the 2016 earthquake released most of the elastic strain accumulated over 56 years in this area. The epicentre and aftershocks of this event were located just up-dip of the zone of highest coseismic slip, similar to the location of the background seismicity recorded before 201630 (Fig. 2a). Interestingly, the aftershock sequence featured relatively low magnitudes (Mw < 5.5) and event numbers rapidly decayed with time (Supplementary Fig. 6), suggesting the regions surrounding the mainshock were below the critical conditions for failure.

The seismogenic zone in this area has been inferred to be shallow and controlled by a hot and young (13 Ma) incoming Nazca Plate30. The seismic to aseismic transition along the interface has been mapped at ~30 km depth and coincides with an isotherm of ~325 °C, close to the tip of the hydrated mantle wedge at the intersection of the slab with the continental Moho31 (Fig. 2c). Below this limit, neither interseismic microseismicity30 nor aftershocks of the 2016 event have been recorded, indicating a rheological regime where creep is dominant.

Using offshore multichannel seismic reflection data (Supplementary Fig. 7), we mapped the morphology and distribution of Tertiary forearc basins. We find that Guafo Island lies over a sedimentary basin, which has a thickness of ~750 m at the depocentre. A patch of high interseismic locking and large 1960 slip release is coincident with a region of negative anomalous gravity32 in the basin area (Fig. 2). The relation between gravity lows (basins) and concentration of coseismic slip (high locking) has been linked with elevated effective coefficients of friction and thus higher shear fault strengths (greater resistance) that cause long-term (million year timescale) topographic depressions14,33. The continental basement has a local high (ridge) that delimits the eastern border of the basin. This ridge structure correlates with a relative gravity high, which coincides with the downdip end of the locked zone as well as of the downdip extents of the 1960 and 2016 coseismic ruptures. Such a gravity high has been observed globally along subduction zones32, and has been inferred to represent an expression of the long-term stability of the downdip limit of the seismogenic zone. Likewise, the ridge structure could be caused by the transformation of interseismic strain into permanent geologic strain via faulting, folding and/or buckling of the inner forearc at the transition between unstable (seismic) and stable (aseismic) sliding32.

## Stress build-up along the seismogenic zone

Heterogeneity in frictional strength at the plate interface is a first-order control on earthquake rupture and frequency34. The spatial correlation between the forearc structure and the kinematics of both the 1960 and 2016 events suggests a depth-varying frictional segmentation along the seismogenic zone (Fig. 2c), with the shallower segment being the highly coupled portion of the fault (higher shear strength state at depths shallower than 20 km), and the deeper segment localized in the narrow transition from unstable to stable slip (the rupture zone of 2016 event at 20–30 km depth).

Inspired by the observed correlation, we investigated the frictional structure of the seismogenic zone with a mechanical model designed to simulate the evolution of stress build-up due to the steady subduction35 of a coupled asperity under the Coulomb friction failure criterion. Our model outputs the spatiotemporal evolution of tractions (stresses on the fault plane) for a heterogeneous frictional seismogenic zone under tectonic stress loading. We do not attempt to model the complex dynamics of rupture6,36 and subsequent healing37, which are of short duration compared with the period of stress build-up of a 2016-class earthquake (56 yr assuming that the 1960 event released all stress in the 2016 zone). In our model, a higher coefficient of effective friction clamps a segment of the fault (no sliding) until the frictional forces overcome the fault strength and the coupled section begins to slide. Aseismic slip occurs around areas with a lower effective coefficient of friction, where the weaker interface fails due to a smaller resisting shear strength. The clamp model produces a deformation halo of low creep rate surrounding the coupled asperity that in turn causes higher strain rates downdip, effectively loading these areas while shielding updip portions of the asperity (Supplementary Fig. 9) due to the shadowing of stresses38.

It is important to note that the size of the coupled asperity and the frictional contrast around the asperity control both the pattern of strain energy concentration at the downdip end and the rupture interval (time when a fault segment begins sliding without building extra stress) (Supplementary Fig. 9). Accordingly, larger asperities require more time to reach the critical failure state. We tested a wide range of frictional contrasts based on the distribution of locking degree to define the boundary of the coupled asperity. We found a significant spatial correlation between the shear stress accumulation after 50 yr of interseismic loading in the deeper fault portion and the slip of the 2016 earthquake when the shallow segment of the fault is clamped (Fig. 3a). This finding suggests that the shallow segment mechanically behaves like a coupled asperity that induces strain and stress accumulation in the deeper seismogenic segment. This is also supported by its kinematics, as this fault section released the highest slip during the 1960 event (slip >25 m) and its centre is fully locked (locking degree >0.9; Fig. 2). Our model shows that following a deeper-class earthquake, the shallower coupled segment will continue stressing and straining the transition between the shallower and deeper segments, but with a reduced ring-shaped area (Fig. 3b). After 100 yr of loading, a subsequent rupture of the entire coupled segment could also drive failure of the down-dip region, producing a Mw > 8.5 earthquake.

## Failure lag time

Given the lag time between the 1960 and 2016 events, we further investigated the effective friction coefficients for both the shallow and deep fault segments that would favour the rupture of the deep segment after 60 ± 5 yr of interseismic loading. In doing so, we assume that tectonic stress guides the loading of the system and seismic stress drop represents pre-earthquake stress conditions on the fault. In addition, we assume that a giant 1960-class event fully releases the accumulated elastic stresses, as proposed for the 2011 Tohoku earthquake39. We focus on characterizing the downdip frictional zonation across the 2016 rupture zone, and thus we do not attempt to explore along-strike variations. The rupture times of the fault segments are assessed as the initial time when the fault cannot hold the accumulated stresses in the system, marking the onset of unstable sliding. The results indicate the range of coefficients of friction combinations (between the shallow and deep segments) that can produce the observed 56-year lag time for rupture of the deep segment (Supplementary Fig. 10). The effective friction coefficient of the deep segment needs to be <0.01 and always lower than that of the shallow segment, which ranges between 0.01 and 0.04 (Supplementary Fig. 10). This result suggests that the seismogenic zone is weak, with an effective friction coefficient of generally <0.04, as suggested by thermal modelling studies40.

The rupture time of the deep segment depends not only on its own effective friction coefficient but also on the transfer of stress from the shallow segment. Hence, the spatiotemporal evolution of stress build-up, and thus timing of ruptures, can be controlled by the contrast in effective friction between the shallow and deep seismogenic segments (Supplementary Fig. 11). We cannot yet directly establish the value of the friction coefficient of the shallow segment, and therefore its rupture time. We can, however, use the stress drop of the 2016 event (Supplementary Fig. 12) as a proxy for the expected stress in this region. Thus, to accumulate shear stresses in the range of the stress drop after 56 yr of steady subduction, the effective friction coefficient of the deep segment needs to be 30–40% of the value of the shallow segment (Fig. 4a). We can narrow the rupture time of the shallow segment to an optimal range of 110–140 yr of interseismic loading (Fig. 4a), similar to the recurrence time of historical Mw > 8 ruptures41. The proposed differential along-dip mechanical behaviour of the seismogenic zone allows an elastic slip deficit accumulation period on the shallow segment to be twice as long as on the deeper segment; such a longer period may thus result in great tsunamigenic earthquakes.

## Frictional contrast and pore pressure relationship

Our model suggests that differences in lithostatic load (Supplementary Fig. 14) alone cannot produce the short-term mechanical behaviour of a coupled asperity. High normal stress couples the fault below the seismogenic limit, whereas low normal stress induces a reduction of fault resistance in the shallow segment, opposite to its mechanical behaviour (Supplementary Fig. 15). Hence, variations on the effective friction coefficient are expected to offset the normal stress14. It has long been recognized that pore fluid pressure can counteract the normal stress, weakening the absolute strength and stability of a fault10,42. Likewise, gradients in fluid pressure can induce fault strength segmentation11,13, with drained conditions promoting fault coupling12,13.

By assuming that the pore fluid pressure gradient is the main parameter varying the frictional resistance, we estimated the values of the pore pressure ratio (λ = pore pressure/lithostatic stress) based on the predicted values of effective friction coefficient (Fig. 4b). We ignored additional factors beside pore pressure alone, such as heterogeneity of the shear zone and accumulation of damage37, that may play a role in frictional variations. In absence of these additional complexities, our results suggest that λ in the deep segment has to be >0.98 to permit its rupture after ~56 years of loading. In contrast, in the shallow segment λ = 0.95–0.96 is needed in order to accumulate the shear traction matching the stress drop of the 2016 event. Our results not only support the anti-correlation between locking degree and λ proposed by previous studies10,12, but also demonstrate that overpressure results in a faster release of shear stress, potentially causing more frequent earthquakes of moderate size. Pore fluid may thus exert similar stresses to the lithostatic load, providing an explanation for the apparent weakness of the fault in the transition between unstable and stable frictional behaviour. In our study area, this transition ends around the slab-Moho discontinuity, where temperatures are inferred to be 300–400 °C (ref. 31), and where serpentinite and other hydrous minerals may release fluids into the seismogenic zone maintaining pore pressure close to lithostatic values (Fig. 5).

Localized hydration at the base of the continental plate will form an effective permeability seal because of associated volumetric dilation caused by the hydrous mineral phases, forcing fluids to move upwards along the interplate fault zone and increasing pore pressure43. In addition, high pore pressures within the plate interface in southern Chile may be partly attributed to its geological history. Here, the forearc basement consists of metamorphic rocks from a Permo–Triassic accretionary complex44. Geophysical images and exhumation history suggest rock units exposed at the surface are continuous to interplate depths44,45 (Fig. 5). These units are associated with duplex structures interpreted to reflect continuous basal accretion of underthrusted trench sediments44. Such duplexes are formed by low-angle thrust sheets dominated by subhorizontal foliations. These pervasive structures are locally cut by submetric vertical quartz veins interpreted as syn-exhumation tension gashes filled with silica-rich fluids pumped by seismogenic processes43,44. The predominant horizontal fabrics of basally accreted material may constitute an additional permeability seal (stratigraphic fluid barrier) precluding the ascent of trapped fluids, in contrast to intrusive continental framework rocks that are usually associated with vertical cooling fabrics. Subhorizontal fabrics in southern Chile may thus play a role in restricting vertical fluid migration pathways and enhancing interplate pore pressure.

The interseismic GPS deformation field shows a landward reduction from 50 mm yr–1 to 12 mm yr–1 in a distance of only 100 km, indicating a high degree of crustal shortening just above the deeper section of the seismogenic zone (Fig. 5). This observation corroborates our conceptual model of the deeper segment being interseismically strained. This mechanical behaviour appears to have a major impact on the long-term morphology of subduction margins as suggested by the relation of forearc basins with seismic asperities14,15,16 and the permanent emergence of coastlines above deeper seismogenic segments46.

In summary, we propose that a variation in pore fluid pressure induces a downdip zonation of frictional strength along the plate interface. The frictional contrast at depth may thus control the lag time between deeper seismic ruptures (such as the 2016 event) and great shallower megathrust earthquakes (such as the 1960 event). Hence, deeper 2016-class earthquakes may be considered as a first phase of energy release that precedes failure of the shallower region during great earthquakes. Rupture of the shallow segment could drive failure of the downdip region even if the latter has experienced more-frequent smaller events, resulting in a 1960-class earthquake. Although our model assumes uniform properties along-strike, in nature the frictional contrast may vary along strike, making the failure time different at different along-strike segments. The central part of the 1960 rupture zone seems to be highly locked28 in a wider along-strike segment than in the 2016 region. This suggests that either the fault strength is uniform over a larger along-strike segment or that the friction contrast at depth is relatively low, allowing a bigger area to be clamped over a longer period. Our model predicts that as interseismic strain builds up, more 2016-class events should occur along the 1960 rupture zone. These forthcoming events will allow a better understanding of along-strike frictional variations. Further development of this modelling strategy, such as incorporating variations of frictional behaviour in the strike direction, could be used to estimate the critical failure threshold of asperities and their time-dependent seismic potential.

## Methods

### GPS data processing and coseismic offset estimations from time-series

Data from all available continuous GPS stations with coseismic data were compiled and processed using the Earth Parameter and Orbit System (EPOS) software47 in the ITRF 2014 reference frame. IGS08 phase centre variations and FES2004 ocean tide loading were used with hourly tropospheric wet zenith delays estimated as random-walk parameters and Vienna mapping functions in a grid file database. The reprocessed precise satellite orbit and clock products were generated together with station coordinates by EPOS and combined with IGS products in order to reduce the impact in estimating Earth rotation parameters.

We estimated the coseismic offset of the GPS data from the continuous stations FUTF, GUAF, MELK, MUER, PMO1, PTRO, GLLN, RMBA, TPYU installed by the National Seismological Center of Chile (CSN) and the University of Potsdam, Germany. The resulting time series were automatically cleaned for all data and/or error outliers. The coseismic offset was estimated using an iterative least-square inversion that also solves for additional signal components48,49 like the linear (interseismic) plate rate, antenna offsets, seasonal and semi-seasonal variations and coseismic offsets from relevant earthquakes in the vicinity, based on the NEIC (National Earthquake Information Center, https://earthquake.usgs.gov) earthquake catalogue and with a threshold given by the magnitude–distance relationship. The variance of the resulting coseismic offsets was estimated using the averaged data fit normalized by overall length of the time series50. Supplementary Figure 1 shows the time series and the parameters estimated for each station used in our analysis.

### InSAR data

C-band and L-band Synthetic Aperture Radar (SAR) data acquired by the European and Japanese space agencies (ESA, JAXA), respectively, were used in this study. They include a pair of ascending and descending C-band SAR data acquired in interferometric wide-swath (IW) mode from the Sentinel-1 (S1) satellite and a pair of descending L-band SAR data acquired in ScanSAR mode (full aperture) by Advanced Land Observing Satellite 2 (ALOS 2). S1 interferograms were constructed from images acquired on 12 December 2016 and 10 January 2017 for descending and 21 December 2016 and 14 January 2017 for ascending pairs, whereas the ScanSAR ALOS-2 interferogram was constructed from images covering 1 December 2016 and 12 January 2017. The S1 interferograms were processed with the GAMMA software51. The spectral diversity method52 was applied for precise coregistration of SAR data. ALOS-II ScanSAR processing53 was done using SARscape (http://www.sarmap.ch/wp/). A 90 m digital elevation model that was derived from the NASA Shuttle Radar Topography Mission (SRTM) was used as the reference topography model54 for the topography-related phase correction and geocoding of all the interferograms. The coseismic wrapped interferograms (Supplementary Fig. 2) were unwrapped using the minimum cost flow (MCF) method55 (Supplementary Fig. 3).

The unwrapped data were visually checked for unwrapping errors, which were either corrected or excluded from the modelling (for example mountainous areas). We then subsampled the data using the quad-tree approach56(Supplementary Fig. 4). In parallel, we calculated the corresponding line of sight (LOS) and the centre of mass of all valid data within one subsampled cell that was used as observation coordinate. Overall, we obtained 520 data points for the Sentinel 1 ascending data set, 550 points for the Sentinel 1 descending data set and 230 data points for the ALOS descending data set.

In the modelling, we accounted for a phase jump of a multiple of 2π between the main land, Chiloé Island and Guafo Island by introducing three additional parameters for InSAR phase ambiguities between these subsets. As the first-order proxy for estimating the noise level of the data we used the inverse of the width of the subsampled quads57.

### Slip inversion

Plate interface slip was modelled using over 600 triangular patches with a mean area of 65 km2 meshed to represent the undulating plate interface model58. Slip on each patch was represented by Green’s functions of dislocation in an elastic half-space59 and two slip vectors were solved for at each patch. These two slip vectors bound the horizontal azimuthal motion of each patch between the bearings of 250 and 290 degrees. In the inversion for slip, the lower bound of slip for each slip direction was defined as zero, so that all modelled slip has a thrust component. A maximum slip for each slip direction was set at 5 m. The bounding azimuths were selected to represent a realistic direction of plate interface motion based on the focal mechanics of moment tensor inversions along this subduction margin. The inversion problem was formulated in the L2 regularization sense so that the procedure enacted the following optimization:

$${\rm{minimize}}\parallel w\times \left(d-G\times m\right){\parallel }_{2}+\beta \parallel m\parallel$$

subject to:

$$0\le m\le 5$$

where d is the data vector containing the GPS, G are the Green’s functions, m is the solution vector corresponding to the amounts of slip for each Green’s function, w is the vector of weights for each data point, and β is the weighting of the regularization. Accordingly, this optimization is the solution of the Tikhonov damped, bounded, weighted least squares problem. Data are first weighted by their respective errors with a uniform error of the InSAR estimated to be 6 cm from the lateral variability of the data. The data are then further weighted in the inversion so that InSAR LOS data are weighted 10 times as strongly as GPS displacements. The choice of ratio between weighting of GPS and InSAR was based upon the approach of ref. 60. The optimization was regularized with the L2 norm of the parameter values. The favoured damping coefficient was selected using a trade-off curve between model misfit and damping coefficient (Supplementary Fig. 5). The optimization was performed using the Matlab package CVX OPT61.

Checkerboard tests were performed revealing regions of the interface that are better resolved and the sizes of kinematic heterogeneity that can be isolated (Supplementary Fig. 5). In the region containing the mainshock and aftershock seismicity, the results of the checkerboard tests confirm that the modelled slip distribution is in a relatively well resolved region of the plate interface and that the shape of the recovered slip distribution is broader than the finest scale that can be resolved.

### Seismicity

We used raw waveform data from seismic networks C and C1 available on IRIS (https://ds.iris.edu/SeismiQuery/) to detect and locate aftershock seismicity after the 25 December earthquake. Initially, we ran a recursive STA/LTA trigger algorithm over the raw data and searched for events with coherent arrivals at at least five stations. After manually picking P and S phases for these events, we also visually checked the raw waveform data at station GO07 (which is closest to the main shock) and identified additional smaller events that were missed in the first step. All events that were visible on at least four seismometer stations were also handpicked and added to the dataset. This yielded a total of 262 earthquakes detected in the time interval between the main shock and 31 January 2017, nearly all of which are located in the main shock area. We also ran the STA/LTA algorithm over the two years of data preceding the main shock, but found no significant precursory activity. However, network coverage in the region has increased only recently, which means smaller events before 2015 may have been missed. For relocation, we employed joint hypocentre determination62 to the manual P and S picks, keeping the velocity model fixed to the local model30. Due to the relatively small number of stations at close distances and their unfavourable geometry (most stations are located to the NE of the main shock; no coverage at western azimuths), hypocentral depths are not well defined, but epicentres should be relatively reliable.

We also determined moment tensors for five of the largest aftershocks with a previously reported technique63. Only these five events had sufficient signal-to-noise ratios at long periods to be thus inverted. We required the solutions to be deviatoric, and used the period band between 15 and 35 s. The epicentres for these events were fixed to their catalogue position, and inversions with different trial centroid depths were performed. The trial depth with the lowest misfit solution was then chosen as the optimal centroid depth. All five aftershocks show low-angle thrust mechanisms, and their depths are situated close to the plate interface as defined previously58, giving us confidence that the aftershock seismicity is indeed situated on the plate interface. Since moment tensor inversion is less dependent on event–station geometry than hypocentral location, these centroid depths should be more reliable than the ones from the event catalogue. The aftershocks sequence is characterized by a rapid decay in the number of events (Supplementary Fig. 6).

### Multichannel seismic reflection data

Multichannel seismic reflection data were acquired offshore of Guafo Island during the SPOC using R/V Sonne in 2000/2001. (Supplementary Fig. 7). The signals for the seismic reflection experiment were generated by a tuned set of 20 air guns with a total volume of 51.2 l. The multichannel seismic reflection data were analysed using standard processing, including re-binning, normal move out correction, stacking, deconvolution and post-stack time migration. A predictive deconvolution with two gates, for the shallow sedimentary events and the deeper crustal events, was applied before the stack.

A space and time variant frequency filter prior to a post-stack migration completed the processing flow64. The seismic recording system is characterized by a record length of 14,332 ms, a sampling rate of 4 ms, and a LC-Filter of 3 Hz. The shots were triggered in time intervals of 60 s on full minutes UTC. At a speed of 5 knots that results in a shot point distance of 154 m. A constant hydrophone spacing of 25 m (108 channels) was chosen for the seismic processing, resulting in a common mid-point distance of 12.5 m and a maximum fold of 27 (ref. 64). Results of the seismic reflection processing are used to characterize the depth-varying structural features (Supplementary Fig. 7). A reflective zone shows the upper limit of the continental basement, which defines the lower limits of a sedimentary basin. Guafo Island lies in the centre of this forearc basin, which has a sediment thickness of ~750 m at its depocentre (Fig. 2b).

### Mechanical modelling

The purpose of this model is to estimate the spatiotemporal evolution of stress build-up along the seismogenic zone, and its relationship to the lag time between the 1960 and 2016 earthquakes. We performed 3D geomechanical simulations using the PyLith software65. Our model consists of an elastic downgoing slab (oceanic plate) and an upper crustal unit (overriding continental plate) that sit on top of oceanic and continental asthenospheric units, respectively (Supplementary Fig. 8). We specified a Young's modulus of 100, 120 and 160 GPa, for the continental, oceanic and mantle layers, respectively28. The Poisson’s ratio was set to 0.265 and 0.30 for the continental and oceanic crusts66, respectively.

To simulate the steady interseismic subduction of the oceanic plate, we implemented the previously reported Elastic Plate Model35. In this model, the plate subduction is kinematically represented by the superposition of creep along the entire base of the oceanic crust and on the top of the slab below the seismogenic zone (Supplementary Fig. 8). We specified two fault interfaces with kinematic fault conditions, representing the base of the slab (Fault3) and the creeping part below the seismogenic zone (Fault2). On those interfaces, we prescribed a homogeneous constant creeping equal to the plate convergence velocity (6.6 cm yr–1), but with opposite sense of movement. The seismogenic fault (Fault1) extends between 0 and 30 km depth and is divided at 20 km depth into two segments (the shallower and deeper seismogenic segments) with different coefficients of effective friction (Fig. 2). The frictional behaviour of the seismogenic zone is modelled with the Coulomb failure criterion:

$$\tau =\mu^{\prime} \times \left({\sigma }_{n}^{\prime} \right)+c$$, where τ is the shear strength of the fault, μ′ is the effective friction coefficient, σn′ is the fault normal stress and c is the cohesion. Here, fault activation occurs when the driving forces exceed τ. For simplicity, our model neglects gravity body force but specifies normal tractions consistent with overburden (lithostatic load) as initial stress state along the frictional fault. We simulate the mechanical behaviour of a coupled asperity by clamping a section of the fault, so that it has a higher friction than the non-asperity region of the fault.

In our mechanical model, tectonic forces (slab pull) load the system and fault strength controls the levels of stress that the fault can support before sliding. We do not model the complex dynamics of rupture nucleation, dynamic interaction between asperities, or rupture propagation. Rather, we focus on the static friction that needs to be overcome to begin the process of fault motion, and not the subsequent evolution of material properties during a seismic event. Therefore, our model contributes to the conceptual understanding into the level of stress that the seismogenic zone can support before breaking in medium to large earthquakes. Other significant assumptions we make include: (i) the stress drops in the earthquakes must represent almost all of the pre-earthquake shear stress on the faults, and so the faults must be able to support only a few tens of megapascals of shear stress before slipping in earthquakes; (ii) the 1960 earthquake totally released the stress in the 2016 rupture zone; (iii) frictional strength is uniform along-strike in the study area.

We tested different values of the effective friction coefficient for both fault segments; running a total time of 360 yr of steady interseismic loading. We define the onset of instable fault behaviour as the rupture time. In this study, we assumed that the fault instable behaviour occurs when the fault creep rate exceeds 3 cm yr–1. We also varied this threshold value between 1 and 5 cm yr–1 and found that this variation does not significantly impact the retrieved rupture times.

Supplementary Fig. 10 shows the rupture times of all tested effective friction coefficient combinations for the two segments. Results indicate that both segments must be weak with a low coefficient of effective friction (generally <0.1) to maintain a reasonable rupture time (generally <300 yr), which is consistent with previous studies18,67. These results give a range of friction combinations that produces rupture of the deeper segment after 56 yr of loading (Supplementary Fig. 10). For the deep segment to rupture at 60 ± 5 yr (black circles in Supplementary Fig. 10b), the rupture time of shallow segment depends on the ratio of the effective friction coefficients between the two segments.

We estimated the change of Coulomb failure stress (CFS)68 predicted by our optimal slip distribution (Supplementary Fig. 12). We use a homogeneous coefficient of friction μ = 0.5 (ref. 69). The CFS values (<1.5 MPa) are in keeping with those expected from such a moderate size earthquake. We estimate the optimal range effective friction coefficient combinations that induce accumulation of stress build-up similar to the stress drop at the 2016 rupture zone, and use this frictional ratio to estimate the rupture time of the shallow segment. In order to accumulate shear stresses in the range of the stress drop of the 2016 event, the effective friction coefficient of the deep segment has to be 30–40% of the value of the shallow segment (Fig. 4a). For this friction coefficient combination, the shallow segment fails after 110–140 yr of loading.

The low effective friction coefficients of our model can be interpreted to be the result of high pore fluid pressure. High pore fluid pressure acts to locally reduce the effective normal stress on faults, which are able to fail at lower shear stresses than if the fluid were absent10.

The effective friction coefficient $$\mu ^{\prime} ={\mu }_{0}\times \left(1-\lambda \right)$$, can be used to incorporate pore pressure into the Coulomb stress criterion, where $${\mu }_{0}$$ is a typical frictional sliding coefficient and the value of λ, so-called the pore pressure ratio, represents the degree to which pore pressure counteracts the total stress generated by the overburden stress. Considering the typical frictional sliding coefficient as 0.5 in southern Chile subduction zone69, we derived the pore pressure ratio of the two segments by the formula of $$\lambda =1-\mu ^{\prime} /{\mu }_{0}$$. Figure 4b shows the parameter space of λ of the two segments that allows the deep segment ruptures after a reasonable amount of time. For the deep segment, λ has to be >0.98 to permit its rupture after 56 years of loading. It is expected that in the shallow segment λ 0.95–0.96 in order to accumulate shear traction matching the stress drop of the 2016 event.

### Stress anomaly

To gain insight into the heterogeneity of the initial static stress distribution at the plate interface we make use of normal stress anomalies reported previously70. The anomaly is derived from vertical stress (lithostatic load) and then projected into the normal of the subduction interface. Since there is no external horizontal component involved, it is more exactly expressed as normal component of the vertical stress anomaly. Using a 3D density model further developed from the gravity forward modelling reported previously71, the vertical stress effects of density anomalies at the computation depth, that is the interface of the subducting plate in the 3D model, are incorporated into the model. Density anomalies are defined as bodies of a rock density that deviate from the standard three-layer reference model used during gravity forward modelling of the 3D density model. Isostatic or flexural effects are not considered. Topographic masses add to the vertical load and therefore we added the lithostatic stress effect of topographic masses by using ETOPO1 heights and a standard density of 2,670 kg m−3. The sum of the results in the vertical component is then projected into the interface normal. The static stress anomaly grid was computed on a ~3 minutes grid. For the 3D model, therefore, normal stresses are carefully calculated.

Our mechanical clamping models indicate that including the normal stress anomaly (due to density contrast in the forearc) (Supplementary Fig. 14), with a constant value for the effective friction coefficient, cannot produce the coupling pattern of the asperity (Supplementary Fig. 15) and therefore variations of effective friction along the plate interface are needed to clamp the fault.

### Code availability

Numerical simulations were calculated in Pylith65, which is available on the Computational Infrastructure for Geodynamics web site (https://geodynamics.org/cig/software/pylith/). Codes developed in this study to simulate stress build-up under interseismic loading are available from the corresponding author upon reasonable request. The GAMMA and SARScape software used to compute the interferograms can be accessed at www.gamma-rs.ch and www.sarmap.ch/page.php?page=sarscape, respectively.

### Data availability

The GPS data that support the findings of this study are available in the GNSS data repository of the Centro Sismologico Nacional, Chile (http://gps.csn.uchile.cl/data/). GPS data from stations GUAF and MELK (before 2016) are available from the corresponding author upon reasonable request. C-band Synthetic Aperture Radar imaging from the Sentinel mission is available from the Copernicus Open Access Hub (https://scihub.copernicus.eu). ALOS original data are copyright to the Japanese Aerospace Exploration Agency and are not publicly available.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

This work is supported by the German Science Foundation (DFG) grants MO3157/2-3 (M.M., J.R.B.) and SCHU2460/3-1 (C.S.), Millennium Scientific Initiative (ICM) grant NC160025 "CYCLO - the seismic cycle along subduction zones" (D.M., A.T.), Chilean National Commission for Scientific and Technological Research (CONICYT) grant PAI-MEC 2016 (M.M.), FONDECYT 1150321 (D.M.), and Helmholtz Graduate Research School GeoSim (S.L.). ALOS original data are copyright of the Japanese Aerospace Exploration Agency and provided under proposal 1161 (M.Mo.). This study was encouraged by discussions with B. Schurr and I. Urrutia. We thank Armada de Chile for hosting our cGPS stations GUAF (Faro Guafo) and MELK (Melinka).

## Author information

### Affiliations

1. #### GFZ Helmholtz Centre Potsdam, German Research Centre for Geosciences, Telegrafenberg, Potsdam, Germany

• M. Moreno
• , S. Li
• , J. R. Bedford
• , M. Motagh
• , S. Metzger
• , C. Sippl
• , Z. Deng
•  & O. Oncken

• M. Moreno

• S. Li

• D. Melnick
5. #### Millennium Nucleus The Seismic Cycle Along Subduction Zones, Valdivia, Concepción, Chile

• D. Melnick
•  & A. Tassara

• J. C. Baez
7. #### Institute of Photogrammetry and GeoInformation, Leibniz Universität Hannover, Hannover, Germany

• M. Motagh
•  & S. Vajedian
8. #### Institut für Planetare Geodäsie, Technische Universität Dresden, Dresden, Germany

• B.D. Gutknecht
9. #### Departamento de Geofísica, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile

• E. Contreras-Reyes

• A. Tassara

### Contributions

M.M. and S.L. conceived the original idea, which was elaborated with J.R.B., D.M. and O.O. M.M. and S.L performed all numerical simulations. J.R.B. performed the slip inversions. S.M., M.Mo. and S.V. processed the InSAR data. J.C.B. and Z.D. processed the GPS data. S.M. performed the time series analysis of GPS data. B.D.G. performed the stress anomaly model. C.S. processed the seismological data. E.C. performed the processing of seismic reflection data. D.M. installed cGPS stations. The manuscript was written by M.M. with comments from D.M., J.R.B., S.L., C.S., S.M., O.O., E.C. and A.T.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to M. Moreno.

## Supplementary information

1. ### Supplementary Information

Supplementary Figures

### DOI

https://doi.org/10.1038/s41561-018-0089-5

• 1.
• Daniel Melnick
• , Shaoyang Li
• , Marcos Moreno
• , Marco Cisternas
• , Julius Jara-Muñoz
• , Robert Wesson
• , Alan Nelson
• , Juan Carlos Báez
•  & Zhiguo Deng

Nature Communications (2018)

• 2.
• Amy L. Williamson
•  & Andrew V. Newman

Pure and Applied Geophysics (2018)