the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Apr 2026
Constraints on the Lithospheric Structure and Rheology of Northern Chile from 8-year Post-Seismic Deformation following the Mw8.1 Iquique Earthquake
Abstract. Understanding and modeling the deformation following large earthquake is essential for characterizing the rheological structure and processes that release post-seismic stress. Here, we measured postseismic deformation over an 8-year period following the 2014 Mw8.1 Iquique earthquake using Sentinel-1 InSAR and GNSS time series in northern Chile and Bolivia. We jointly modeled the surface displacements caused by afterslip and viscoelastic relaxation using a two-dimensional finite element model. The combination of GNSS and InSAR data allows us to continuously map the temporal and spatial variations of the displacement field, especially in the vertical component, providing valuable constraints for modeling the rheological structure of the continental plate from the slab to the Altiplano. The amplitude of the uplift pattern claims for a weak zone below the western part of the Altiplano, where the volcanic arc is fed by partial melting. To reproduce the temporal evolution of post-seismic uplift, this weak zone must be governed by a Burgers rheology, combining a transient Kelvin body with a viscosity ηKwz = 2 × 1018 Pa.s and a Maxwell body with a viscosity ηMwz = 2 × 1019 Pa.s. To the west, our preferred model includes a cold nose rooting into the slab at a slab-mantle decoupling depth of dCN = 84 km. This near-trench elastic wedge, predicted by thermal models, drives mantle flow and generates surface uplift during post-seismic relaxation. By characterizing the post-seismic deformation field following the Iquique earthquake, our results refine the rheological structure below the Central Andes and define its response to stress changes down to short time scales.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-2003', Jeff Freymueller, 19 May 2026
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AC1: 'Reply on RC1', Anne Socquet, 02 Jul 2026
We would like to thank the reviewer for his positive feedbacks and suggestions, and for highlighting the added value of this study, notably the importance of the vertical deformation by combining GNSS and InSAR.
We agree with the reviewer that 3D models would be more correct, but that the choice of sticking to 2D models allows us to explore the parameters’ space and different trade-offs, which would not be possible in such an exhaustive manner with a 3D model. We also agree that the main outcome of the paper -- the existence of a weak zone below the volcanic arc -- would hold with a 3D model. A 3D model would likely improve the fit to the far field deformation, that is anyway very poorly constrained with sparse and noisy GNSS observations. We are therefore grateful that the reviewers supports our positioning to go for a 2D model instead of a 3D one.
The reviewer suggests to call ‘mantle wedge’ what we call the ‘weak zone’. We however disagree here because an important part of this weak zone is composed by the thick (70-80 km) and hot continental crust. We will make sure to describe this more clearly in the text of the revised version, to avoid any misunderstanding.
We agree that we explore a large range of parameters. This has the advantage of exploring the trade-offs within the parameters’ space, but makes the paper a bit ‘indigest’. We will do our best to improve the readability of the paper in the revised version, by following the reviewer’s suggestion of adding a road map at the beginning of section 5. We may also consider putting some of the tests in electronic supplement.
Thanks a lot for the list of typo. We will carefully proofread the revised version!
Citation: https://doi.org/10.5194/egusphere-2026-2003-AC1
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AC1: 'Reply on RC1', Anne Socquet, 02 Jul 2026
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RC2: 'Comment on egusphere-2026-2003', Sabrina Metzger, 28 May 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2003/egusphere-2026-2003-RC2-supplement.pdf
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AC2: 'Reply on RC2', Anne Socquet, 02 Jul 2026
We would like to thank very much the reviewer for her very detailed and extensive review, and for the constructive suggestions provided that will help improve significantly the revised version of the paper.
Thanks a lot for highlighting the added value of the paper, both on synthesis of geodetic data and on the visco-elastic modelling and parameter’s space exploration. Because of this exploration, we understand and acknowledge that the paper might be difficult to read. This has been raised by reviewer #1 as well, and we will do our best to improve the ‘flow’ of the revised version (including in the wording and descriptions), and better highlight the geologic importance and the key findings for non-experts. We agree that the geographic locations should be introduced in a map or removed from the text. More generally we are very thankful to the reviewer for providing numerous detailed comments. We will carefully polish the text of the revised version.
The reviewer wonders how the fit to InSAR and GNSS data is weighted relatively in order to choose the best model. THe simple answer is that we do not have a ‘recipe’. We evaluate separately the chi squared for all different data sets (GNSS horizontal, vertical, InSAR ascending and descending), and we chose the preferred model as being the ‘best’ compromise, explaining most of the data.
Finally, we agree that a discussion about the role of pore-pressure diffusion following large earthquakes, as suggested by recent studies, should be added.
Citation: https://doi.org/10.5194/egusphere-2026-2003-AC2
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AC2: 'Reply on RC2', Anne Socquet, 02 Jul 2026
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RC3: 'Comment on egusphere-2026-2003', Anonymous Referee #3, 01 Jun 2026
This paper combines 8 years of GNSS time series with 5 years of InSAR to characterize post-seismic deformation of a Mw8.1 earthquake Authors jointly inverted afterslip and viscoelastic relaxation using a 2D FEM that explored several parameters: afterslip geometry, structure of a weak upper plate, cold-nose decoupling depth, oceanic mantle viscosities. Authors preferred an elastic cold nose reaching slab-mantle decoupling depth and Burgers rheology for the weak zone.
This study has significant importance in understanding the deformation after a megathrust earthquake. They explored the particular time interval of an earthquake cycle that connects the short-term coseismic and long-term interseismic periods, which is often the most difficult time period to model and characterize. This paper has reasonably dealt with this difficulty. There are a few other strong points of this paper:
- The dataset is valuable; the longer observation window is a genuine advance
- The core conclusions are plausible and reasonably supported, especially the cold-nose result and weak-zone Burgers rheology result
However, several methodological choices warrant stronger justification.
- There is a 7-month InSAR gap, which means the early uplift signal that the paper argues requires a Kelvin body is dependent only on GNSS. The authors should state this limitation explicitly at the point where the Burgers conclusion is drawn, not only in the data section.
- I got a little confused with referencing InSAR with GNSS mentioned in section 3.1. Then, in section 6.3, authors state that GPS reference issue will propagate into InSAR flattening. Also, in section 5.3, authors note that the ascending InSAR track brings the “strongest constraint” on the optimal location of the cold nose limit. These statements seem contradictory, and I am having a hard time distinguishing an independent InSAR constraint from the one inherited through referencing. Shouldn’t a GNSS-only or InSAR-only fit, shown side by side, strengthen the argument?
- The parameter exploration (section 4.3) in this paper varies individually around a preferred model instead of jointly sampling the parameter space. If these parameters are coupled, few would definitely show trade-offs (such as afterslip amplitude/width vs near-field viscosity, dcn vs h vs Xcraton). Therefore, the sequential search in the paper risks settling in a local minimum and underestimating uncertainties. The authors should at minimum, in section 4.3, (i) state if and where joint exploration was performed, (ii) justify the order of parameter exploration, (ii) report uncertainties around preferred values rather than listing optimal point values (the reader cannot judge whether dcn = 84 km is meaningfully distinct from 80 or 88 km). The afterslip amplitude-width grid search is the right idea and should be extended to the parameters that most strongly trade off.
- One of the major limitations of the current methodology is how the geodetic signal is partitioned. From my reading (and please correct me if I am wrong), the partitioning is built into the model rather than derived from it. I see that depth, width, amplitude, and time function of afterslip are prescribed. I wonder how this mechanical decoupling between co-seismic viscoelastic run and afterslip would affect the final interpretation. In a self-consistent model, co-seismic and afterslip stresses both should load the viscoelastic medium, and the relaxation should modify the stress that drives the afterslip. Summing two independent runs neglects this coupling. The authors should at least argue why this is acceptable over a decadal window. This seems important since the afterslip is allowed to extend to the very depth range where the weak zone and decoupling begin to matter. The claim "the early uplift requires a transient Burgers rheology" is only as robust as the imposed afterslip vertical signature.
Minor comments:
- Line 8 (abstract): “The amplitude of the uplift pattern claims for a weak zone”. Replace the word “claims for” with “requires” or “calls for”.
- In the first paragraph of the introduction, fix the citation formats (currently: "?e.g.>[] pollitz2006post, panet2010upper, suito2017importance, Li2017PostseismicRheology, boulze2022post")
- Define what you mean by ‘weakened zone’ in the first paragraph of the introduction so that readers will understand the reason behind this characterization.
- Second from the last sentence in introduction reads,The use of a simple 2D model, rather than a 3D model, allows us to test 50 various configurations against the data.’ Authors should add another line after this that justifies their choice of isolated parameter testing in a 2D setting rather than doing co-evolution of parameters in a 3D setting.
- Can you the numbers such as 1.10^(20) to a consistent pattern of 1 * 10^(20). I mistook this for a decimal point first.
- Fix the section 5.1 heading. The wording does not make sense at all.
- In Figure B2, I see the x-axis titled ‘afterslip depth’ goes from 75-100. But Table 1 shows the exploration range of afterslip depth goes from 30-50 km. This is confusing and should be made internally consistent.
- A Kelvin rigidity of 136 GPa for the weak zone seems unusually high. Please provide a physical justification or clarify that this is an effective parameter rising from Burgers to Maxwell transposition
- The Luo and Wang (2021a) and (2021b) appear to be the exact same paper.
Citation: https://doi.org/10.5194/egusphere-2026-2003-RC3 -
AC3: 'Reply on RC3', Anne Socquet, 02 Jul 2026
We thank very much the reviewer for their review and relevant and useful comments. Notably, we appreciate that the reviewer acknowledges the added value of the dataset, with a long observation window, as well as the relevance of the core conclusions, notably the cold-nose geometry and the necessity for a weak-zone with a Burgers rheology.
We agree with the reviewer that the need for a Kelvin body essentially relies on the GNSS data. We do not find however that this is a strong limitation as the GNSS data in the early period and in near field are of pretty good quality, including for the vertical, and the fit of the model with a Burgers viscosity is significantly improved compared to the model with a Maxwell viscosity.
We agree that explaining the referencing of InSAR with GNSS is never straightforward and can be confusing for non experts. Indeed InSAR is a relative measurement that should be offset and tilted onto the GPS. However, with the NSBAS processing that we use, the curvature of the INSAR is NOT inherited from GNSS and is a strong independent constraint for our models. In our case, this peak in the InSAR data is beautifully colocated with the peak of GNSS data, and we find a model that reproduces the location (and the amplitude) of the peak, that depends on the location (and amplitude) of the viscosity contrast at depth
We agree with the reviewer that the parameter exploration section is somewhat difficult to follow, as also pointed out by the two other reviewers. We agree with the reviewer that we should explain better our positioning and how the exploration is performed. We do not aim at providing the ultimate best model, in the least square sense, but we want to reach a ‘prefered’ reasonable model that fits our complete data set, with a reasonable compromise between horizontal and vertical, and that also makes sense on the geological point of view.
We agree that there are some trade-offs between parameters. The important parameters that we found to be affected by some tradeoff are :
- the crustal thickness, that changes slightly the wavelength and the amplitude of the deformation signal
- the maxwell viscosity in the weak zone, that changes the amplitude of long term signal associated with viscous relaxation, notably on the vertical
Although it surely exists, the trade-off between these two parameters is pretty small as the elastic thickness does not affect the deformation signal very much.
Other important parameters without major trade-off are:
- the location of the coldnose border, that controls the location of the maximum uplift
- the continental viscosity, that does not induce changes at short time scale, but changes the amplitude of the viscoelastic deformation at long times scales, notably in far field
- the kelvin viscosity in the weak zone, that changes the short-term (and the long-term) signal associated with the viscoelastic relaxation. In that case, a small tradeoff with the prescribed afterslip exists, but to obtain the observed vertical deformation in short-term, a significant contribution of the transient Kelvin viscosity in the weak zone is needed.
Finally, the following parameters are less impactful and without much trade-off. We will therefore move those tests to the electronic supplement in the revised version:
- the craton border, that slightly modifies the amplitude in far field, and that is not critical in this model
- the oceanic viscosity, that does not infer any change at short time scale, but changes amplitude of the vertical in the forearc at long time-scale.
In this paper we do not aim at performing any inversion nor doing a full parameter space exploration. We only want to evaluate the effect of each parameter on the resulting deformation, and compare it with the geodetic data, which is something that is rarely done for viscoelastic models with this level of detail. In several papers, including some of the most impactful, only one parameter is discussed, without a lot of data to constrain it. Here we explore a few parameters associated with the geometry and the rheology of the weak zone. Our ambition is to evidence the first order structure, not to explore a fully complex 3D structure, that our data would not be able to constrain (even though we have the most complete geodetic data set to date for this earthquake).
Finally, the reviewer understood correctly, the partitioning is built into the model and the afterslip is prescribed. We do not model a stress driven afterslip, because we were mostly interested in assessing the rheology of the overriding plate, and the geometry of the weak zone. We agree that it would be more elegant and correct to load the viscoelastic medium with both the co-seismic and the afterslip stresses. However, in our case the slip ratio co-seismic / afterslip is 7m/40cm, so a ratio of about 20. The stress loading by the afterslip is therefore negligible as it represents only 5 to 10% of added stress. This was confirmed by test simulations that we have run, and for simplicity in the model handling, we have decided to neglect the retroaction mechanism.
Citation: https://doi.org/10.5194/egusphere-2026-2003-AC3 -
AC4: 'Reply on RC3', Anne Socquet, 02 Jul 2026
We thank very much the reviewer for their review and relevant and useful comments. Notably, we appreciate that the reviewer acknowledges the added value of the dataset, with a long observation window, as well as the relevance of the core conclusions, notably the cold-nose geometry and the necessity for a weak-zone with a Burgers rheology.
We agree with the reviewer that the need for a Kelvin body essentially relies on the GNSS data. We do not find however that this is a strong limitation as the GNSS data in the early period and in near field are of pretty good quality, including for the vertical, and the fit of the model with a Burgers viscosity is significantly improved compared to the model with a Maxwell viscosity.
We agree that explaining the referencing of InSAR with GNSS is never straightforward and can be confusing for non experts. Indeed InSAR is a relative measurement that should be offset and tilted onto the GPS. However, with the NSBAS processing that we use, the curvature of the INSAR is NOT inherited from GNSS and is a strong independent constraint for our models. In our case, this peak in the InSAR data is beautifully colocated with the peak of GNSS data, and we find a model that reproduces the location (and the amplitude) of the peak, that depends on the location (and amplitude) of the viscosity contrast at depth
We agree with the reviewer that the parameter exploration section is somewhat difficult to follow, as also pointed out by the two other reviewers. We agree with the reviewer that we should explain better our positioning and how the exploration is performed. We do not aim at providing the ultimate best model, in the least square sense, but we want to reach a ‘prefered’ reasonable model that fits our complete data set, with a reasonable compromise between horizontal and vertical, and that also makes sense on the geological point of view.
We agree that there are some trade-offs between parameters. The important parameters that we found to be affected by some tradeoff are :
- the crustal thickness, that changes slightly the wavelength and the amplitude of the deformation signal
- the maxwell viscosity in the weak zone, that changes the amplitude of long term signal associated with viscous relaxation, notably on the vertical
Although it surely exists, the trade-off between these two parameters is pretty small as the elastic thickness does not affect the deformation signal very much.
Other important parameters without major trade-off are:
- the location of the coldnose border, that controls the location of the maximum uplift
- the continental viscosity, that does not induce changes at short time scale, but changes the amplitude of the viscoelastic deformation at long times scales, notably in far field
- the kelvin viscosity in the weak zone, that changes the short-term (and the long-term) signal associated with the viscoelastic relaxation. In that case, a small tradeoff with the prescribed afterslip exists, but to obtain the observed vertical deformation in short-term, a significant contribution of the transient Kelvin viscosity in the weak zone is needed.
Finally, the following parameters are less impactful and without much trade-off. We will therefore move those tests to the electronic supplement in the revised version:
- the craton border, that slightly modifies the amplitude in far field, and that is not critical in this model
- the oceanic viscosity, that does not infer any change at short time scale, but changes amplitude of the vertical in the forearc at long time-scale.
In this paper we do not aim at performing any inversion nor doing a full parameter space exploration. We only want to evaluate the effect of each parameter on the resulting deformation, and compare it with the geodetic data, which is something that is rarely done for viscoelastic models with this level of detail. In several papers, including some of the most impactful, only one parameter is discussed, without a lot of data to constrain it. Here we explore a few parameters associated with the geometry and the rheology of the weak zone. Our ambition is to evidence the first order structure, not to explore a fully complex 3D structure, that our data would not be able to constrain (even though we have the most complete geodetic data set to date for this earthquake).
Finally, the reviewer understood correctly, the partitioning is built into the model and the afterslip is prescribed. We do not model a stress driven afterslip, because we were mostly interested in assessing the rheology of the overriding plate, and the geometry of the weak zone. We agree that it would be more elegant and correct to load the viscoelastic medium with both the co-seismic and the afterslip stresses. However, in our case the slip ratio co-seismic / afterslip is 7m/40cm, so a ratio of about 20. The stress loading by the afterslip is therefore negligible as it represents only 5 to 10% of added stress. This was confirmed by test simulations that we have run, and for simplicity in the model handling, we have decided to neglect the retroaction mechanism.
Citation: https://doi.org/10.5194/egusphere-2026-2003-AC4
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This paper presents a suite of 2D viscoelastic models for the postseismic deformation following the 2014 Iquique earthquake. The key finding is for a low viscosity weak zone (mantle wedge), which is required to explain the postseismic vertical displacements in particular. I think the paper is very well done, and the model they present represents a substantial improvement over past studies. They find that the vertical displacements are especially important in constraining elements of the model, because there are some much stronger tradeoffs within the model parameters when only the horizontal displacements are considered. (I think this is generally true for subduction zone postseismic studies).
The models are 2D rather than 3D. The advantage is that this makes the computational time much shorter, allowing a fuller exploration of the (multi-parameter) parameter space. But the cost is that the model becomes a bit inaccurate far from the trench, because in a 3D model the far field locations will “see” the edges of the rupture but in the 2D case there is no edge to the rupture as it is infinitely long. So the 3D model deformation would likely go to zero a bit closer to the trench than in the 2D model used here. I think in this case the use of a 2D model is OK because the main features that are being modeled and interpreted are close enough to the trench. It is possible that some optimal parameters values might change a bit in the case of a 3D model, but the basic structure they find should not change.
The authors consider a variety of geometric parameters for the viscoelastic structure, and systematically vary these values to find the optimal values. Their final model seems very sensible to me, and I think the basic geometry of an elastic cold nose and a low viscosity mantle wedge is a substantial improvement over previous studies. The “weak zone” that the authors identify really is the mantle wedge. I think it will be more clear to simply refer to it as the mantle wedge.
There are a lot of potential tradeoffs to explore in the model, starting with the contributions of afterslip vs viscoelastic relaxation, and also including potential variations of the viscoelastic geometry. It is a bit hard to keep track of all of the tests shown in Figures 7-15; this is a challenge for all such papers because there simply are so many things to test. I think the authors could help the reader a bit by providing a paragraph or two at the start of section 5 that would serve as a kind of “road map” to the rest of the section.
Line 124. “Therefore, we fixed tau to 45 days”. Based on what? The GNSS? You later get a different value for the GNSS. I suspect that it does not make much difference because you are modeling only the total deformation in the InSAR, but why the difference in time constant?
Figure 4, inset. I suggest using black rather than green. The green could set up an issue for colorblind readers, and black will be at least as clearly visible.
Minor corrections
Line 2. Change earthquake to earthquakes
Lines 8. I don’t know what you mean to say by “claims for a weak zone”. The verb is wrong.
Lines 20-21. Errors in references.
Line 30. Add “is” before “substantially”
Line 67. Change “is” to “was” at the start of the line
Line 97. Add SAR after interferometric
Line 129. Change cumulated to cumulative. Change from to for
Line 131. Change miss to lack
Line 134. Change cumulated to cumulative
Line 147. Change Bi-frequency to Dual-frequency.
Line 148. Change inverted to estimated
Line 149. Add the before VMF1. Add “mapping functions” after VMF1
Line 150. Change keep to estimate
Line 156. Add the before eight
Line 164. Change developped to developed.
Line 206. Change “As for” to “As with”
Line 251. Change is to are. Change parameter to parameters
Line 270. Add a comma after rheology
Line 271. Change transposed to translated
Line 353. Change “The afterslip” to “Afterslip”
Line 364. Change “add up” to “add constructively”
Line 370. Change “show that the” to “showed that”
Line 389. Change constraints to constrained
Line 393. Add “any” before “cold nose”
Line 399. Delete the comma after parameters