# Interseismic Coupling and Slow Slip Events on the Cascadia Megathrust

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## Abstract

In this study, we model geodetic strain accumulation along the Cascadia subduction zone between 2007.0 and 2017.632 using position time series from 352 continuous GPS stations. First, we use the secular linear motion to determine interseismic locking along the megathrust. We determine two end member models, assuming that the megathrust is either a priori locked or creeping, which differ essentially along the trench where the inversion is poorly constrained by the data. In either case, significant locking of the megathrust updip of the coastline is needed. The downdip limit of the locked portion lies ∼ 20–80 km updip from the coast assuming a locked a priori, but very close to the coast for a creeping a priori. Second, we use a variational Bayesian Independent Component Analysis (vbICA) decomposition to model geodetic strain time variations, an approach which is effective to separate the geodetic strain signal due to non-tectonic and tectonic sources. The Slow Slip Events (SSEs) kinematics is retrieved by linearly inverting for slip on the megathrust the Independent Components related to these transient phenomena. The procedure allows the detection and modelling of 64 SSEs which spatially and temporally match with the tremors activity. SEEs and tremors occur well inland from the coastline and follow closely the estimated location of the mantle wedge corner. The transition zone, between the locked portion of the megathrust and the zone of tremors, is creeping rather steadily at the long-term slip rate and probably buffers the effect of SSEs on the megathrust seismogenic portion.

## Keywords

Cascadia megathrust slow slip events interseismic coupling variational bayesian independent component analysis## 1 Introduction

The Cascadia megathrust hosted an *M* ∼ 9 earthquake in 1700, producing a tsunami that was reported in Japan (Satake et al. 2003). Additional *M* ∼ 9 in the last 10 000 years have been documented from turbidite sequences (Goldfinger et al. 2017), tsunami deposits and coastal geological evidence (Atwater 1987; Clague and Bobrowsky 1994; Atwater and Hemphill-Haley 1997; Kelsey et al. 2005; Wang et al. 2013; Kemp et al. 2018). However, since 1700, the megathrust has remained relatively silent. At present, the background seismicity is very quiet except at its Northern and Southern ends (Wang and Trehu 2016).

The interseismic loading retrieved from surface geodetic measurements allowed to estimate the degree of locking of the megathrust and create maps of interseismic coupling (defined as the ratio of slip deficit rate along the megathrust, determined from the geodetic interseismic data, and the long-term slip rate). Interseismic coupling maps are useful for seismic hazard assessment as locked portions of the megathrust are indeed expected to potentially slip in large interplate earthquakes as has been observed in several seismically active regions (e.g. Chlieh et al. 2008; Moreno et al. 2010; Loveless and Meade 2011). Previous inversions of geodetic strain rate measured onshore indicate that the megathrust is locked to some degree in the interseismic period (Hyndman et al. 1997; Wang et al. 2003). We use the secular velocity field from 352 continuous GPS (cGPS) stations corrected for post-glacial rebound using the model of Peltier et al. (2015), to determine an interseismic coupling map for the 2007–2017 period. We also determine temporal variations of slip along the megathrust over that time period to clarify the relative position of the portions of the megathrust that are locked in the interseismic period and those that are producing transient slip events. The geodetic position time series from Cascadia show strong temporal variations which indicate episodic aseismic slip events, commonly called Slow Slip Events (SSEs) (Dragert et al. 2001; Miller et al. 2002). These slip events are mostly aseismic but are correlated in time and space with tremors (Rogers and Dragert 2003; Wech and Bartlow 2014), which presumably occur on the plate interface (Wech and Creager 2007). It is, therefore, likely that SSEs are related to episodic slip along the megathrust. SSEs are, however, not the only source of variation of the geodetic time series from their secular trend. These variations can be related to various causes. The larger earthquakes in the area may have caused some offsets and transient post-seismic deformation. The geodetic time series also show variations that are seasonal and likely due to surface load variations as has been observed in various other settings (Blewitt et al. 2001; Bettinelli et al. 2008; Fu et al. 2012). Temporal variations in geodetic series can also be spurious due to the ITRF realization generally used to express position in a global reference frame (Dong et al. 2002).

In this study, we analyse the geodetic position time series from Cascadia with the objective of separating the terms due to the various temporally varying factors and to interseismic coupling. To that effect, we apply to the detrended position time series a variational Bayesian Independent Component Analysis (vbICA) (Choudrey and Roberts 2003), a signal processing technique which has proven to be effective in extracting different sources of deformation (afterslip, SSEs, and seasonal signals) in geodetic time series (Gualandi et al. 2016, 2017a, b, c). We next perform an inversion of the Independent Components (ICs) related to SSEs, following the general approach of the principal component analysis-based inversion method (Kositsky and Avouac 2010). With this vbICA-based Inversion Method, (vbICAIM), we produce a kinematic model of the spatio-temporal variation of slip on the Megathrust from 2007 to 2017. We also determine the pattern of interseismic coupling along the megathrust from inverting the secular geodetic signal due to interseismic strain.

The remaining of the manuscript is organized as follows. We first introduce the data considered in this study in Sect. 2. We then describe how we extract the signals related to the different sources of interest. In Sects. 4 and 5, we present the results of the inversion to retrieve interseismic coupling and the SSEs kinematics, respectively. Final remarks and further discussions conclude the manuscript.

## 2 Data

We use daily sampled position time series in the IGS08 reference frame from the Pacific Geodetic Array (PANGA) and the Plate Boundary Observatory (PBO) maintained by UNAVCO and processed by the Nevada Geodetic Laboratory (http://geodesy.unr.edu, last access August 2017). Most of the available continuous GPS (cGPS) stations were deployed in 2007, and we consider the time range that goes from 2007.0 to 2017.632. We use only time series with at most 40% of missing data and we exclude all the stations in the proximity (< 15 km) of volcanoes to avoid contamination by volcanic signals. We also discard station BLYN because of spurious large displacements of unknown origin that were clearly not observed at nearby stations. The final selection includes *N*_{GPS} = 352 cGPS stations (Fig. 1a). We then refer all the stations to the North America reference frame using the regional block model of Schmaltze et al. (2014). The position time series are then organized in a *M *× *T* matrix *X*_{obs}, where *M* = 3 × *N*_{GPS} is the total number of time series (East, North, and Vertical direction per each station), and *T* = 3883 is the total number of observed epochs.

Two tremor catalogues are used in this study, one from Ide (2012) between 2007 and 2009.595, and one from the Pacific Northwest Seismic Network (PNSN) catalogue from 2009.595 to 2017.632 (https://pnsn.org/tremor).

## 3 Signal Extraction

Our goal is to retrieve: (1) the secular strain rate due to the average pattern of locking of Cascadia’s megathrust, and (2) the SSEs history on the megathrust in the considered time span.

To attain our first goal, we use the long-term linear trend estimated from a ‘trajectory’ model (Equation S1) in which each position time series is modelled using a combination of predetermined functions. We use a linear combination of a linear trend, annual and semi-annual terms, co-seismic step functions and exponential post-seismic functions. This approach provides a reasonable estimate of the linear trend with limited bias introduced by the non-linear terms. We do not model at this step the SSEs, but they do have a limited influence on the secular motion estimate since their typical returning period is much smaller than the overall observed time span, as it will be verified a posteriori. The secular geodetic velocities estimated from this approach are used to determine interseismic locking ratio on the Cascadia megathrust (Sect. 4). We use the long-term linear trend and the offsets that are simultaneously estimated by the trajectory model (Equation S1 and Supplementary Material) to correct the position time series. These time series are then the input for the variational Bayesian Independent Component Analysis (vbICA) algorithm. A brief description of the vbICA algorithm is offered in the next Sect. 3.1.1. We then describe its application to the extraction of post-seismic relaxation (Sect. 3.1.2), seasonal deformation (Sect. 3.1.3), and SSEs displacement (Sect. 3.1.4).

### 3.1 Sse Surface Deformation Extraction

#### 3.1.1 vbICA Algorithm

*X*) to be reconstructed by a linear combination of a limited number (

*R*) of Independent Components (ICs). The centring step is performed by removing from a time series its mean value. Each IC is fully characterized by a spatial distribution (

*U*

_{r}), a temporal function (

*V*

_{r}), and a relative weight (

*S*

_{r}). None of these quantities is a priori determined, allowing the data to reveal their inner structure. These quantities are organized in matrices, such that the following approximation holds (Gualandi et al. 2016):

*U*and

*V*have unit norm columns,

*S*is a diagonal matrix, and

*N*characterizes the noise, assumed to be Gaussian. Recall

*M*= 3 ×

*N*

_{GPS}is the total number of time series (East, North, and Vertical direction per each station) and

*T*= 3883 is the total number of observed epochs. This notation is similar to that of Principal Component Analysis (PCA), but here the constraint of orthogonality between the columns of

*U*is relaxed, as well as between the columns of

*V*. Moreover, any ICA algorithm is not aiming at the diagonalization of the variance–covariance matrix of the data and, thus, the diagonal values in

*S*do not represent a percentage of the dataset variance explained. Both

*U*and

*V*are non-dimensional, while

*S*and

*N*are in the same unit as

*X*(mm). In contrast to standard ICA algorithms (e.g. FastICA, Hyvarinnen and Oja, 1997), vbICA allows for more flexibility in the description of the temporal sources

*V*since it can model multimodal time function distributions. More details can be found in Gualandi et al. (2016) and references therein.

#### 3.1.2 Post-seismic Relaxation

Earthquakes affecting GPS time series from the North and South section (USGS)

Section | Magnitude | Year | Month | Day | Latitude | Longitude | Depth |
---|---|---|---|---|---|---|---|

North | 6.4 | 2011 | 9 | 9 | 49.535 | 126.893 | 22 |

7.8 | 2012 | 10 | 28 | 52.788 | 132.101 | 14 | |

5.5 | 2013 | 8 | 4 | 49.661 | 127.429 | 10 | |

6.5 | 2014 | 4 | 24 | 49.639 | 127.732 | 10 | |

South | 6.5 | 2010 | 1 | 10 | 40.652 | 124.693 | 28.7 |

5.9 | 2010 | 2 | 4 | 40.412 | 124.961 | 23 | |

5.6 | 2012 | 2 | 13 | 41.143 | 123.79 | 27.4 | |

5.7 | 2013 | 5 | 24 | 40.192 | 121.06 | 8 | |

6.8 | 2014 | 3 | 10 | 40.829 | 125.134 | 16.4 | |

5.7 | 2015 | 1 | 28 | 40.318 | 124.607 | 16.9 | |

6.6 | 2016 | 12 | 8 | 40.454 | 126.194 | 8.5 |

Due to the complexity of the tectonically active region in the proximity of northern Vancouver island in the North and of the triple junction point in the South (Table 1), it is challenging to obtain a clean source separation using the data from the entire network of stations. A first attempt to apply the vbICA to the whole dataset did not bring a clean separation between post-seismic events occurring at the northern and southern edges of the subducting plate. We, therefore, decided to first divide the study area into two sectors, split by the latitude 45° and limited to the east by the longitude − 121°, as shown in Fig. 1a.

In the South, six M5.5 + events (Table 1) have visibly induced detectable geodetic signals (stars in Fig. 1a and green lines in Fig. 3) and all are strike-slip events (USGS). In the North, similarly, three strike-slip M5.5 + earthquakes have occurred and affected GPS stations (Table 1, Figs. 1a, 2). There is one *M*7.8 with a reverse mechanism that occurred in 2012 (Table 1, star out of frame in Figs. 1a and 2), which might have induced post-seismic deformation on the megathrust or on a crustal fault of the North American plate (Hayes et al. 2017). The mainshock occurred 363 km from the closest GPS station (HOLB). Its rupture extended ~ 100–150 km along strike. This event seems to have affected the northernmost stations. In either case, we make a distinction between afterslip and SSEs and thus correct our dataset *X* for the displacement associated with all the retrieved post-seismic ICs. The stations corrected for post-seismic deformation are listed in Table S1.

#### 3.1.3 Seasonal Deformation

#### 3.1.4 SSEs Displacement

Finally, we apply a vbICA on the residual displacement time series. The SSEs signal is buried in the noise and the percentage of variance explained grows very slowly as the number of components increases. The number of components is chosen based on the Negative Free Energy (NFE) of the decomposition, which balances the fit to the data and the complexity of the model (Choudrey and Roberts 2003; Gualandi et al. 2016). The NFE indicates how close the approximating probability density function (pdf) of the hidden variables of the model is to the true posterior pdf. When the NFE reaches its maximum value, the Kullback–Leibler divergence between the aforementioned pdfs is minimum. When passing from 32 to 33 ICs the NFE decreases, and we thus select 32 components for our final decomposition (Fig. S1). Among these 32 ICs, we ascribe 15 of them to the kinematics of SSEs (components 1–15 in Fig. S2). The remaining 17 sources are considered as either noise (components 16–25) or local effects (components 26–32) (Fig. S2).

## 4 Interseismic Coupling

*P*= 3339, and they have triangular shape, with a characteristic length of ∼ 15 km. The Green’s functions are calculated using Okada (1992) dislocation model. We use the same regularization scheme of Radiguet et al. (2011), which allows to give an interseismic back-slip a priori model as input. Two a priori interseismic back-slip models are tested, one with a fully locked fault (coupling equal to 1), and the other with a fully creeping fault (coupling equal to 0). We expect the poorly resolved areas, specifically near the trench where no data are available, to stay near the a priori model. Those two a priori models define thus the 2 extreme cases where the fault trench is either fully locked or creeping. A rake direction constraint is imposed using the plate rate direction from Schmalzle et al. (2014) block model. We adopt as smoothing parameter the a priori uncertainty on the model parameters

*σ*

_{0}, while fixing the correlation distance

*λ*to the average patch size. Taking the locked a priori model, varying

*σ*

_{0}produces the L-curve shown in Fig. S3. We select

*σ*

_{0}= 10

^{−0.1}for our preferred inversion that yields the best trade-off between misfit and smoothness of the slip distribution. We use the same parametrization for the creeping a priori model. We calculate the interseismic coupling map dividing each sub-fault’s back-slip rate, given by the inversion, by its associated block model plate rate. The coupling maps for the two cases are given in Fig. 6. The fit to the data and the residuals are shown in Fig. 7. The resolution and restitution maps are shown in Fig. S4. The sensitivity to the regularisation parametrisation is shown in Fig. S5.

The two interseismic coupling maps (Fig. 6) show a partially locked shallow portion of the fault. The position of the locked zones, however, differs from one model to the other. Interestingly, the a priori fully creeping fault has locked areas that are closer to the coast than the a priori fully locked fault.

## 5 Slow Slip Events Kinematics

### 5.1 SSES Inversion

Once the surface deformations associated with the SSEs are isolated, we perform a static inversion of the spatial distribution related to the 15 extracted temporal functions. This approach follows the one adopted in Gualandi et al. (2017a, b, c). The principle is the same as the one described in Kositsky and Avouac (2010), but a vbICA is replacing the PCA decomposition of the data. We invert the selected ICs on the same geometry used for the interseismic velocities, and we adopt the same regularization scheme. A null a priori model is imposed, which implies that we expect a null a posteriori solution where the data do not require for slip on the fault. No constraints on the rake direction are imposed. Varying *σ*_{0} produces the L-curve shown in Fig. S6. We select *σ*_{0} = 10^{−1.5} for our preferred inversion that yields the best trade-off between misfit and smoothness of the slip distribution. We invert the 15 ICs using the same parametrization for each IC and recombine them linearly.

We thus obtain the spatio-temporal evolution of slip deficit related to SSEs (*δ*_{deficit}(*p*, *t*)) with respect to the long-term slip deficit given by the locking ratio (see Sect. 4). In order to get a coherent slip deficit rate (\(\dot{\delta }_{deficit} \left( {p,t} \right)\)) time evolution (*t *= 1,…, *T*) on each sub-fault (*p* = 1, …, *P*), we take the time derivative of the low-pass filtered slip deficit. In particular, we apply an equiripple low-pass filter with passband frequency of 1/21 days^{−1}, stopband of 1/35 days^{−1}, passband ripple of 1 dB with 60 dB of stopband attenuation. If the slip deficit increases on a given patch (i.e. positive slip deficit rate), then that patch is accumulating strain, i.e. it is loading. When the slip deficit decreases (i.e. negative slip deficit rate), then the patch undergoes slip. SSEs thus correspond to time periods of negative slip deficit rate. A movie of the SSEs kinematics is available in the supplement (Movie S1). The sensitivity of the kinematic model to the regularisation parametrisation is also shown in the supplement (Movie S2, S3 and S4).

### 5.2 SSEs Spatial and Temporal Determination

*t*a given sub-fault

*p*is experiencing an SSE if \(\dot{\delta }_{\text{deficit}} (p,t) < V_{\text{thresh}} = -\, 40\) mm/year. For the specific epoch under exam, we identify all the sub-faults with slip rates below this threshold by applying a contour at

*V*

_{thresh}. The number of contours defines the number of SSEs occurring at time

*t.*We do the same at time

*t*+ 1 and verify which contours at time

*t*+ 1 overlap with the contours at time

*t*. If there is an overlap, we assume that they are the same SSE. For every SSE, we thus automatically select a starting and ending time (

*t*

_{ k}

^{in}and

*t*

_{ k}

^{fin}, with

*k*= 1, …,

*N*

_{SSEs}). Special cases can arise where an SSE splits itself or two SSEs merge together. In both scenarios, the SSEs at time

*t*and

*t*+ 1 are considered to be the same. With this procedure, we identify 119 potential SSEs between 2007 and 2017. From those 119, some involve only 1 or 2 sub-faults and are very short in time. We consider them as noise. We also remove any candidate under 60 km depth. Our final selection of SSEs gathers

*N*

_{SSEs}= 64 events shown in Fig. 8.

*k*-th event as the union of all the sub-faults participating to it, denoted by the set \(\left\{ {s_{k} } \right\} = \left\{ {p | \dot{\delta }_{{{\text{deficit}},k}} (p,t) < V_{\text{thresh}} {\text{for }}t_{k}^{\text{in}} \le t \le t_{k}^{\text{fin}} } \right\}\). However, the

*V*

_{thresh}parameter might truncate spatially and temporally our estimated SSEs. To relax slightly this constrain, we extend the spatial influence of each SSE to their neighbouring sub-faults and extend their time delimitation by 1 day before and after. Note that during and within the area of influence of each SSE, the slip deficit rate of sub-faults can be negative or positive depending on the SSE’s history of propagation. For one event, within its area of influence and time period, we calculate the moment rate function at time

*t*, \(\dot{M}_{0} \left( t \right)\), using equation:

*μ*is the shear modulus (here fixed to 30 GPa),

*S*

_{k}is the total number of sub-faults belonging to the

*k*-th SSE’s area of interest, \(A_{{s_{k} }}\) is the area of sub-fault

*s*

_{k}. The negative sign in front of the sum is added in order to have positive moment rates during SSEs, reference that we will keep for the rest of this study.

Applying this moment rate calculation methodology on the filtered *δ*_{deficit} described in Sect. 5.1 (passband frequency of 1/21 days^{−1}, stopband of 1/35 days^{−1}) results, however, in very smoothed moment rate functions. To retrieve more detailed moment rate functions, we perform instead a zero-phase digital filtering on the rough *δ*_{deficit} using a 8-days window, but focus only on the area and time period of each SSE as estimated before from the very smoothed data. The moment rate of each SSE acquired from the rougher version of *δ*_{deficit} is shown in Fig. 8. Those moment rates do not take into account interseismic loading during SSEs. To estimate the uncertainty on the SSEs moment rate function, we assume that it is represented by their short-term variability before filtering. The uncertainties represented in Fig. 8 are calculated based on the standard deviation of the mean on the rough version of \(\delta_{\text{deficit}}\) using a 16-day moving window centered in the epoch of interest.

### 5.3 SSEs Kinematics

Our SSE catalogue (Fig. 8) contains events with moment magnitude from 5.3 to 6.8 and duration between 14 and 106 days. Their propagation speed is of the order of ∼ 2000–4000 km/year (respectively, ∼ 5.5–11 km/day) (Fig. 9).

The combined moment rate of all the SSEs from our catalogue between 2007 and 2017 is shown in Fig. 11a. Two endmembers are shown, one assuming that interseismic loading is negligible during SSEs and the other assuming that the fault is loaded at the long-term plate rate during this period. They represent the two possible extremes of moment rate released by the SSEs from our catalogue. Bias in segment determination is introduced from the selection of *V*_{thresh}. For example, certain SSEs might not be detected or a same SSE could have been cut into pieces (e.g. events 28 and 30 in 2011). Increasing *V*_{thresh} to − 35 mm/year, we retrieve instead 81 SSEs, several events are merged (events 1,2 and 3 in 2007 or 28 and 30 in 2011), smaller events appear, but the global dynamics remains unchanged (Fig. S7). Additionally, increasing *V*_{thresh} also increases the risk of introducing noise.

### 5.4 Potential Biases and Limitations

The combination of the uncertainty on GPS measurements, the low-pass filtering, the value of *V*_{thresh} and the interpreted fault geometry, specifically in the North, hinders our possibility to retrieve small SSEs that remains within the noise level. In the most Northern part of the fault, our kinematic model is difficult to interpret due to the proximity of the fault’s border which is prone to noise from the inversion. The southern part of Cascadia seems more prone to having small SSEs, which are more difficult to detect. This can be due to the slower convergence rate of the region (27 mm/year) compared to the northern segments (45 mm/year). The spatial distribution of GPS stations plays also a role in that matter.

Two opposite effects may affect the duration estimation of the SSEs. The temporal slip deficit filtering tends to augment SSEs duration. On the other hand, the selection of small enough (i.e. large enough in absolute value, in order to limit the effects of noise) *V*_{thresh} cuts the onset (*t* _{ k} ^{in} ) and end (*t* _{ k} ^{fin} ) of SSEs. Moreover, it additionally impacts SSEs’ spatial extent, disregarding areas that do not slide fast enough. The value of the estimated peak slip during an SSE (Fig. 8) depends on the regularization of the inversion. The fact that the inversions are ill-posed and require regularization thus probably explains why different inversions can yield significantly different peak slip values. For example, the SSEs peak slip reported in our study (∼ 1.5 cm) are smaller than the peak slip indicated in Dragert and Wang (2011) (∼ 3–5 cm) for the May 2008 event.

There is also a possibility that the number of selected ICs used for the SSE model (Sect. 3.1.4) biases the kinematic description. In our case, 15 components were selected to describe the kinematics. However, the selection is initially based on a pool of 32 components with 17 components seemingly noise. Increasing or decreasing the total number of components produced by the vbICA changes slightly the number of ICs related to SSEs, but does not change qualitatively the dynamics observed in our model. On the contrary, by increasing the total number of ICs, the vbICA extracts further components estimated as local effects or noise. We tested up to 44 ICs.

The uncertainty on the position of the SSEs propagation front also depends on the factors mentioned above (i.e. GPS measurements, low-pass filtering, value of *V*_{thresh}, interpreted fault geometry and number of ICs). Additionally, the choice of the representative line of the average along-strike location of SSEs also plays a role, even though minor. Note that the initial phase of the SSEs front positions might represent more a shadow of the slip deficit rate of SSEs decreasing under *V*_{thresh} rather than the actual SSEs front propagation. The values of SSE front propagation rate estimated from our kinematic model are anyways similar to the ones estimated from tremor propagation since SSEs and tremors are most often correlated.

## 6 Implications and Conclusion

We determined the secular model of interseismic coupling on the megathrust (the time-average pattern of locking ratio) and the kinematics of SSEs from 2007 to 2017 in a consistent and coherent way. The vbICA has shown to be very effective at separating the SSEs from the various other sources of temporal variations in the position time series, such as those due to surface hydrology, post-seismic signals, local effects or common mode motion.

With our vbICA-based Inversion Method (vbICAIM), we were therefore able to describe the kinematics of fault slip on the Cascadia megathrust between 2007 and 2017 using 352 cGPS position time series. Our kinematic model provides the most comprehensive view of the SSEs along Cascadia. We were able to produce a catalogue of 64 events over the 2007–2017 time period. As already documented in previous studies of SSEs (e.g. Bartlow et al. 2011; Wech and Bartlow 2014), we find a remarkable systematic correlation in space and time between SSEs and tremors.

The zone of SSEs and tremors is relatively well resolved and, when compared with the interseismic coupling model (Fig. 12), clearly reflects a downdip segmentation of the mode of slip on the megathrust. This zone lies inland from the coastline and is clearly disconnected from the locked zone as already pointed out in some past studies (e.g. Gao and Wang 2017). In this transition zone, which spans between ~ 100 km and ~ 150 km away from the trench, fault creep is remarkably stationary resulting in a slip rate close to the long-term slip rate along the megathrust. This zone thus seems to act as a buffer isolating the seismogenic zone of the megathrust from the zone of SSEs. This buffering zone probably reduces the risk that an SSE triggers a large megathrust rupture (Segall and Bradley 2012).

The downdip segmentation of the mode of slip along megathrust has long been noticed and considered to reflect the influence of both temperature and lithology (Hyndman et al. 1997; Scholz 1998; Oleskevitch et al. 1999). These two factors could also explain the existence of two separate zones of unstable frictional sliding (Gao and Wang 2017). The one closer to the trench would correspond to a zone of rate-weakening frictional sliding controlled by the frictional properties of continental rocks. For quartzo-feldspathic rocks, friction indeed transitions from rate-weakening to rate-strengthening as temperature exceeds ~350 °C (Blanpied et al. 1995). In Cascadia, this temperature is reached at a depth shallower than the intersection with the forearc Moho, and therefore probably determines the downdip limit of the shallower zone of unstable sliding (Hyndman et al. 1997; Scholz 1998; Oleskevitch et al. 1999) (Fig. 12). The second region is instead located around the mantle wedge corner, where high-pore fluid pressure might result in low permeability of the serpentinized mantle (Wada et al. 2008). This hypothesis is consistent with the correlation between the zone of SSEs and tremors with the forearc Moho (red dots in Fig. 12) as proposed by Gao and Wang (2017).

## Notes

### Acknowledgements

We thank Kelin Wang for his constructive review of this manuscript. This study was partially supported by NSF award EAR-1821853 to JPA. We thank also Zachary E. Ross for his help. We thank Kristel Chanard for discussions and providing the times series predicted based on the surface mass variations derived from GRACE.

## Supplementary material

Supplementary material 2 (MP4 25386 kb)

Supplementary material 3 (AVI 5591 kb)

Supplementary material 4 (AVI 5342 kb)

Supplementary material 5 (AVI 5101 kb)

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