On 16 September 2015, a Mw 8.3 earthquake occurred near the city of Illapel in central Chile. It ruptured part of a locked segment of the south American subduction zone that is surrounded by two areas of relatively low coupling . Thanks to the Centro Sismológico Nacional (CSN) of the University of Chile, this region was heavily instrumented with GNSS stations at the time of the earthquake . Thus, we have access to 15 high-rate GNSS stations that are located < 350 km from the earthquake epicenter (Fig. ). To investigate the first 12 h following the mainshock, we first need to obtain sub-daily position time series. For that, we used the 30 s 3-component kinematic position time series starting just 5 min after the origin time of the mainshock from . To reduce the high-frequency noise, a Kalman filter, which was tuned to be suitable for detecting slow processes over timescales of hours to days , was used during the processing of the GNSS data. Then, these time series were post-processed by applying a sidereal filter constructed in such a way that it can remove periodic noise without removing the post-seismic signal . Finally, we disregarded the vertical component because its noise level is too large (∼ 2 times that of the horizontal components). An example illustrating the post-processing can be found in Fig. .

Over the first 12 h that followed the Illapel earthquake, two large aftershocks were reported in the Global Centroid Moment Tensor (GCMT) catalog. The first one (Mw 7.1) occurred ∼ 23 min after the mainshock, while the second one (Mw 6.8) occurred ∼ 5.25 h after it. To quantify later in the discussion the impact of these large aftershocks on the post-seismic slip, we calculate their static offsets from the position time series. Because of the Kalman filter, these offsets are smoothed over time and thus are not accommodated instantaneously but instead over a certain duration (Tkalman). That duration can be estimated by the following formula: AΔtk, where A is the expected amplitude of the static offset at the stations, Δt is the sampling interval of the time series, and k is the parameter of the Kalman filter (3.0×10-7 km s-2). We estimate A by computing the expected offsets using Okada's formulas inside an homogeneous half-space (μ=39 GPa for the rigidity and ν=0.25 for the Poisson's ratio) and using the nodal plane with the shallower dipping angle as well as the hypocenter location reported by the GCMT catalog. The expected width and length of the fault plane is determined using the empirical relationship for subduction-interface events obtained by . From the estimated Tkalman, we extract the static offsets of these two aftershocks from the position time series by choosing a pre-earthquake position at t=origin time-Tkalman and a post-earthquake position at t=origin time+Tkalman. We center the offset on the origin time of each earthquake to account for the fact that the Kalman filter is applied both forward and backward. We show in Supplement S1 two tables that summarize the computed offsets at each station for both aftershocks. An example of a corrected time series is presented in Fig. .

The kinematic position time series, even after applying a sidereal filter, remain relatively noisy. The standard deviation calculated over the 6 d of data prior to the mainshock ranges from 2.45 to 3.98 mm. Thus, we choose to favor noise reduction over the rate of positioning. Every hour, from the 1st to the 12th hour after the mainshock, we calculate the average position using a 1 h window centered on the time of interest. Thus, we obtain hourly position time series that show the cumulative surface displacement since the mainshock. The errors associated with these new observations are set to the standard deviation of the time series measured prior to the mainshock. Figure illustrates for one station the different steps that we perform to obtain the hourly position time series (see Supplement S2 for similar figures for all the stations). The orange dots in Fig.  represent the hourly positions that we use to obtain the spatiotemporal evolution of very early afterslip. Because of strong spurious signals that are not of tectonic origin, we disregard the first two hours for station LVIL and hours 2 and 3 for station OVLL.

Using the observations described above, we attempt to obtain the hourly spatial distribution of afterslip on a planar fault that is 600 km long along the strike and 300 km long along the dip (Fig. ). Our assumed fault geometry has a strike of 3∘ N and is adjusted such that its upper edge coincides with the trench. The fault dip is chosen to be 17∘, which corresponds to the average dip of the slab at this location calculated from the Slab1.0 model from . Then, the fault is divided into 450 sub-faults, 30 along the strike and 15 along the dip, with the slip amplitude and rake angle evaluated at their centers. We use the approach by to compute the static response of each sub-fault in a tabular medium obtained from the CRUST1.0 database . For a given source model, the surface displacements at each receiver are computed by summing the contribution of each sub-fault.

We search for the spatial distribution of slip amplitude and rake angle independently for each time step. For the slip amplitude, we limit the search to values between 0 and 1 m, thus ensuring the positivity of slip. For the rake angle, we only explore values that are plus or minus 15∘ from the rake angle of the mainshock given by the GCMT catalog (i.e., 109∘). Both parameters are drawn from a uniform prior. The spatial distribution of the source parameters is obtained using an optimization procedure similar to that of . We use a heat-bath simulated annealing algorithm, an evolution of the Metropolis–Hastings that lowers the rejection rate by computing the relative probabilities from a set of trial models before a random move is made . To measure the difference between the observed (o) and calculated (c) surface displacements, we use the cost function of to which we add a smoothing constraint: 1ε=1N∑i=1N(oi-ci)/ei2∑i=1Noi2+ωΛ, where N is the number of observations (2 horizontal components × number of receivers), e is the error associated with the observation, Λ is the Laplacian of the slip distribution and ω is the weight given to the Laplacian (0.1 in this study – see Supplement S3 for a discussion on how the value is chosen).

Similarly to , we keep track of the model after each iteration. For each time step, we run the algorithm 100 times, each time with a different random seed, which leads to a slightly different outcome after each run. Thus, we end up for each time step with an ensemble of 40 000 models along with their misfit values. We use this ensemble of models to build an average one along with its standard deviation. Both are computed by weighting the models by the inverse of their misfit, thus giving more weight to best fitting models. Hereafter, we set to zero the sub-faults that have a mean slip amplitude that is smaller than its standard deviation.

One of the first points we aim to assess is the relationship in space and time between aftershocks and post-seismic slip right after the mainshock, here during the first 12 h. For that, we compare the spatiotemporal evolution of slip and aftershocks using the catalog compiled by (see Fig. ). Although it is possible that some of these aftershocks are not on the subduction interface, based on the focal mechanisms obtained by we can make assumptions at least for regions where we observe afterslip. We find that afterslip and aftershocks show large similarities. Over the first 2 h, most of the seismic activity occurs south of the rupture area, just as does the post-seismic slip. To the north, very little activity is seen during these first 2 h but it then progressively intensifies just like the post-seismic slip. After the first 12 h of the post-seismic phase, we see a pattern where post-seismic slip and aftershocks strongly overlap, both surrounding the co-seismic rupture area. The same observation can be made when we use the independently obtained aftershock catalog by (see Supplement S7).

The strong similarity between these two spatiotemporal evolutions could be due to the fact that the cumulative contribution of aftershocks is not removed from the position time series, thus contributing to the estimated fault slip. For instance, this is what has been proposed to explain the pre-seismic slip pattern prior to the 2014 Iquique, Chile, earthquake . This naturally leads to the question of the partitioning between seismic and aseismic slip during the very early post-seismic phase. To investigate this question, we compare the geodetic moment from the post-seismic slip models with the seismic moment released by aftershocks. To estimate the latter, we use the GCMT catalog for the two largest earthquakes and the catalog from the Centro Sismológica Nacional (CSN) of the University of Chile for the smaller earthquakes, restricting to those with available moment magnitude estimates. Thus, over the whole fault plane considered in this study, there are 38 aftershocks with magnitudes ranging from 4.5 and up to 7.1. That leads to a seismic moment released by the aftershocks of 9.5 × 1019 Nm. This estimate is slightly larger than the geodetic moment of afterslip (8.3 × 1019 Nm), which we will discuss next. But the fact that the seismic moment released by aftershocks is rather close to the geodetic moment of afterslip would suggest that the post-seismic slip that we have obtained can be imputed to seismic slip rather than aseismic slip. However, we find that there is a very large spatial discrepancy : ∼ 95 % of the seismic moment released by the aftershocks is done in the southern patch, ∼ 0.1 % in the northern patch and ∼ 4.9 % elsewhere on the fault plane.

To investigate that in more detail, we have looked at the temporal evolution of the geodetic moment compared to that of the seismic moment released by aftershocks for each patch (see Fig. ). To the north (Fig. a), we find that the time evolution of the geodetic moment does not follow the time evolution of the moment released by aftershocks. Moreover, we see that the latter is much smaller (3.5 × 1017 Nm) than the geodetic moment (1.8 × 1019 Nm). This indicates that the slip in this region is more likely to be largely aseismic slip. Instead, to the south (Fig. b), we find that the time evolution of the geodetic moment follows rather well the time evolution of the seismic moment. That would indicate that the slip in this region is rather caused by seismic slip from the aftershocks. But we find that the seismic moment is larger than the geodetic moment by about a factor of 2. This might suggest that we cannot accurately recover all the seismic slip that occurs in this area. However, several explanations can be proposed to explain such a discrepancy. First, the seismic moment of the two largest aftershocks given by the GCMT catalog are obtained using the Preliminary Earth Model PREM – , a model that differs from the one we use in this study (CRUST1.0). Also, it has been noted that PREM might over-estimate the rigidity especially at shallow depths . Then, the Kalman filter used to process the GNSS has been tuned to properly recover slow processes such as afterslip. Consequently, it might not be suited to recover large and sudden static offsets, which can distort the recovery of the real ground motion . Thus, it is possible that we underestimate the static offsets caused by the largest aftershocks. Finally, as pointed out by , there is also a moment-dip trade-off when near-field geodetic data are used. As our fault plane only approximates the real geometry of the slab, our model could have a lower moment because of our approximation of the dip angle.

Hence, to better isolate aseismic slip, we use corrected position time series, of which the contribution of the two largest aftershocks is removed, to obtain hourly images of the post-seismic slip. The results can be seen in Fig. . Our models show that post-seismic slip is now only observed north of the co-seismic rupture area and that the patch to the south has completely vanished. Therefore, it supports even further the fact that post-seismic slip south of the mainshock rupture area is likely the result of seismic slip only from the aftershocks. On the contrary, post-seismic slip to the north is likely aseismic as the contribution of aftershocks (3.5 × 1017 Nm) is small compared to the geodetic moment of this patch (1.7 × 1019 Nm). We note that the geodetic moment of the northern patch remains similar to the previous estimate obtained using the non-corrected position time series. This illustrates that this patch is stable, regardless of the dataset used.

As a next step, we analyze the temporal evolution between the amount of aseismic afterslip and the number of aftershocks in the northern patch (Fig. , and Supplement S7 for the same comparison using the catalog of ). First, we find that the cumulative afterslip exhibits a logarithmic trend. Similarly to other studies carried out in Ecuador and Japan respectively, we do not observe the acceleration phase of afterslip predicted by . Indeed, before reaching the steady state, under a rate-and-state friction law, slip is expected to accelerate transiently before it starts to expand quasi-statically. Thus, our results suggest that for this earthquake also, the steady state is reached very quickly after the mainshock (< 1 h). When we make the comparison with the cumulative number of aftershocks, we find that the two curves do not follow the same trend. This seems at odds with observations made on the early times of the post-seismic phase by and . As these two studies do not specifically focus on the first 12 h but rather on the trend over a couple of days, it would be very interesting to investigate in detail what happens during the very early stage of the post-seismic phase for these two examples.

Based on theoretical arguments, suggest that if afterslip is driving the generation of aftershocks, we should expect a similar time evolution between the cumulative number of aftershocks and the cumulative afterslip. Their analysis assumes that the deformation from aftershocks should be small compared to that of afterslip and that steady state is reached, and both criteria seem to be met here. But the fact that we do not observe such a relationship is not incompatible with the fact that afterslip drives aftershocks even just after the mainshock. For instance, following the Parkfield Earthquake in California, showed that there could be a deviation from that expected relationship, especially at the beginning of the post-seismic sequence, even when hypothesizing that afterslip drives aftershocks. The way aftershocks respond to stress changes may be quite complex, especially when considering the full rate-and-state friction law e.g.,. It is also possible that very early aftershocks are triggered by the mainshock static stress changes and that it is only later that afterslip starts to drive aftershocks . Other processes could also be candidates as the driving mechanism for aftershock generation e.g., fluid flow,. We also cannot rule out the fact that the earthquake catalog might still be incomplete, thus missing aftershocks at the very early stage of the post-seismic phase.

To summarize, we find here that post-seismic slip can arise from distinct frictional properties on the fault. To the south, slip is essentially seismic, which can be usually associated with a velocity-weakening regime under the rate-and-state friction law framework. Instead, to the north, slip is almost purely aseismic, which is more in line with a velocity-strengthening regime. We can hypothesize regarding the causes of that bimodal behavior. For instance, suggest that fracture zones enclose the mainshock rupture area favoring fluids circulation at these places. Differences in the pore-fluid pressure between the north and the south could be why we observe distinct behaviors. The nature of the plate interface could also be invoked to explain the bimodal behavior of afterslip. For instance, provide evidence of strong lithological contrast at the region of the Illapel earthquake, likely explained by materials being dragged down by the erosive Chilean margin. This could generate high variability of the plate interface roughness. also propose that plate interface rugosity plays a role in controlling the spatial pattern of longer-term Illapel's aftershocks (the first 24 h). Thus, roughness of the plate interface could explain the heterogeneity of the slip modes in this area. We also find that the southern patch is associated with a high coupling of the plate interface while the one to the north is at a transition zone between high and low coupling . This could explain why one region favors seismic slip (south) while the other favors aseismic slip (north). Still, the fact that we can very early on suggest that the fault is divided into regions of distinct frictional properties can prove to be useful for forecast the spatial pattern of aftershocks.

Most of the physics-based models of aftershock sequences used for forecasting do not include information about post-seismic slip, although the study by shows that it could have a positive impact on the forecast.

In the case of the Illapel earthquake, we show that the surface observations carry enough information to image the spatiotemporal evolution of post-seismic slip very early after the mainshock. We also see that the slip pattern inferred at this very early stage does not evolve much over time. This is not an isolated example as made a similar inference for the 2016 Pedernales, Ecuador, earthquake, with the slip patches imaged over the first 72 h persisting after 30 d. provides another example of such behavior following the 2016 Kumamoto, Japan, earthquake. Thus, post-seismic slip from the first hours after the mainshock can help characterize longer-lasting post-seismic slip. Finally, we also show that differences in frictional behavior can be revealed from the very first stage of the post-seismic phase. Thus, imaging the very early post-seismic slip with little time latency could provide valuable additional information to help forecasting the spatial pattern of aftershocks.

Getting images of the slip distribution is not the main challenge as the problem is linear and computationally rather fast. The challenge lies more in the ability to obtain GNSS position time series rapidly with a low-enough noise level. Thanks to the growing number of GNSS networks worldwide, along with the improvement of the processing techniques, we find an increasing number of examples showing that it is possible to accurately monitor in near-real-time various geophysical processes, whether these processes involve seismic slip and/or aseismic slip. For instance, such monitoring is done for the rapid study of earthquakes e.g.,, or to monitor volcanic activities e.g.,, but with an accuracy of only a few centimeters.

To the best of our knowledge, the Nevada Geodetic Laboratory (NGL) has provided open access since 2019 to 5 min position time series with a 1 h latency (so-called ultra-rapid solutions), and for a significant number of GNSS stations worldwide (see , for details about the data available at the NGL). However, the short latency at which these solutions are made available is associated with an increase in the noise level compared to the solution used in this study. Therefore, we first have to assess if the noise level of these observations is low enough to infer information about the very early post-seismic slip.

Thus, we compare the noise level of the position time series from the two stations of our study which are also available from the NGL, CERN, and SANT. We choose the period of July 2019 as there are no significant earthquakes reported nearby in the GCMT catalog. The average standard deviation of the ultra-rapid NGL time series is 0.95 and 1.31 cm for the east and north components, respectively, which is higher than for the post-processed time series used in this study (0.26 and 0.30 cm for the east and north components, respectively). But we note that 5 out of 15 stations that we use show surface displacements that are larger than 1.31 cm after just 1 h. Thus, given the 1 h latency before the NGL ultra-rapid position time series are made available, it would have been possible to obtain an image of the first hour of the post-seismic slip ∼ 2 h after the occurrence of the mainshock. This preliminary conclusion is promising in the prospect of including information about very early post-seismic slip for the forecasting of aftershock locations. Of course, some tests will be necessary to assess the impact of adding such information for the forecast of aftershocks and to evaluate whether or not this could ever be implemented operationally.