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| 27 Nov 2024
Topographic stresses affect stress changes caused by megathrust earthquakes and condition aftershock seismicity in forearcs: Insights from mechanical models and the Tohoku-Oki and Maule earthquakes
Abstract. Aftershocks of megathrust earthquakes at subduction zones may be driven by stresses arising from the topography of the forearc. However, the effect of topographic stresses on aftershock triggering is quantitatively not well understood and has been neglected in Coulomb failure stress models that assess whether the stress change caused by an earthquake promotes or inhibits failure on nearby faults. Here we use analytical and numerical models to examine the importance of topographic stresses on stress changes caused by megathrust earthquakes in the forearc. We show that the superposition of topographic and tectonic stresses leads to a dependence of the stress change on the stress state of the forearc. The dependence on the forearc stress state largely determines the coseismic stress change induced by a megathrust earthquake and must be considered when calculating Coulomb failure stress changes. We further show that increases in Coulomb failure stress promoting widespread failure in the forearc are only possible if topographic stresses dominate the regional stress field after the megathrust earthquake. Applying our modelling approach to the 2011 Mw 9.0 Tohoku-Oki and 2010 Mw 8.8 Maule megathrust earthquakes shows that the effect of topographic stresses caused Coulomb failure stress changes of up to ~40 MPa, which promoted the majority of aftershocks in the Japanese and Chilean forearcs. The model results further reveal that the spatial distribution of aftershocks was influenced by local differences in pre-earthquake stress states, fault strength and megathrust stress drop. Our analysis highlights the significance of topographic stresses in Coulomb failure stress calculations, enabling a better estimation of seismic hazard at subduction zones.
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RC1: 'Comment on egusphere-2024-3592', Kelin Wang, 18 Dec 2024
This paper presents mechanical analyses to make the point that surface topography is an important factor in affecting stress and earthquake-induced stress change and, particularly from subduction zone forearcs, should be considered in Coulomb stress modelling. It is a very useful contribution deserving publication. The Coulomb wedge modelling is illuminating. The numerical model results are not very easy to understand because of the way they are presented, but they make intuitive sense and I believe are correct. To improve readability, I suggest that the authors make a moderate effort to clarify and simplify arguments and presentation.
The logic of the study is simple but the writing sometimes makes it convoluted and unnecessarily complicated. The worst example is the first paragraph of the Conclusions. Besides being unclear whether “stress state” refers to the state before or after the earthquake, or both, what is said here is incorrect at face value. In the linear system considered in this study, stress change is uniquely determined by fault stress drop, with no relation with the absolute state of stress before or after the event. If by “stress state” you actually mean "Coulomb stress", then nothing new is being said here, as Coulomb stress is always known to depend on pre-earthquake stress state. This paragraph should be deleted. There are similar situations in other parts of the paper. I leave it to the authors to check them out.
I think the discussion in Section 2.2 is unnecessarily detailed and thus distracting. Much of it (with figures) should be moved to the Supplement. The practical difference between the two definitions is very small, and I am not sure if the new definition has actual scientific advantage (see specific comment on line 230-231 below).
It is difficult to understand the finite element model results given the way they are presented. For example, in Fig. 9d, presumably the positive Coulomb stress in the lower crust in 200 – 280 km distance is for normal faulting, because Fig. 9a shows a steepening of sigma_1. But such steepening can also indicate less compressive stress instead of extensional stress. I am sure that the rigidity contrast across the model Moho is responsible for the lower-crust positive Coulomb stress, but I cannot tell how. It is not possible to understand the results based on the information shown in these plots (see specific comments on Fig. 9 below).
Other comments by line numbers:
58-- requires to account for -> requires accounting for
79-- alpha is slope angle, not slope.
102-- I know that the author understands this but is trying to avoid bringing up more complications. Unfortunately, it cannot be avoided. Because Dahlen's lambda_b is a small-taper approximation, so is his mu_b', and therefore his solution is not exact (as explained in Wang et al., 2006 GRL). Only if mu_b' is properly defined, will the solution be exact.
138-- Because “dynamic weakening processes” is used to describe processes under high rate friction today, it is better to say “coseismic weakening” here.
168-170. It is incorrect to use the absolute value operator here. For example, if tau flips direction such that tau_post = -tau_pre, this equation would incorrect yields a delta(tau) = 0 instead of 2*tau_pre. One just has to specify that tau is in the direction favouring slip as in King et al. (1994), then -tau will resist slip.
Fig. 4. The plots in (a) and (b) are switched by mistake and therefore contradict their headings at the top.
230-231. Not a valid argument. The conventional definition does not require the knowledge of pre-existing weakness and stress anisotropy either.
314-- I am curious how the code prevents numerical instability at large (e.g. 250 km) depths if gravity is applied as a body force. Because of the very large lithostatic stress, differences between principle stresses are beyond computer precision.
385-389. I suspect the large mu_b’=0.2 adds much push against the upper plate. Without it, would mu_b’ for the rest of the fault be larger than 0.015 to 0.022?
Fig. 9a. I find it difficult to understand the model results because the display contains no information on shear stress and stress magnitude. Is it possible to plot stress crosses scaled with stress magnitude?
Fig. 9c. Differential stress without direction misses important information. How do we know whether the change promotes compressive or extensional failure?
Fig. 9e. Are the observed earthquakes in 200 – 280 km distance normal-faulting events? Presumably the positive Coulomb stress in the lower crust in this region shown in Fig. 9d is for normal faulting, because Fig. 9a shows a steepening of sigma_1. But such steepening can also indicate less compressive stress instead of extensional stress. I am sure that the rigidity contrast across the model Moho is responsible for the lower-crust positive Coulomb stress, but I cannot tell how.
415-- If it was extensional also before 2011 as said later in the text, it should be explained here. The figure only shows events after 2011. Nakamura et al. (2016) showed a mixture of reverse and normal events before 2011 in this area.
427-- The small mu_b-pre values used here may be needed to keep the stress drop low so that is does not exceed the values shown in Fig. 10b. However, there was large shallow afterslip in this area, and the total stress drop responsible for the aftershocks is larger than the coseismic stress drop shown in Fig. 10b. Iinuma used GPS over a much shorter time window that reflects mostly coseismic change, but the aftershocks are affected by the afterslip which continues to relieve stress on the megathrust over a longer time.
511-512. The second point is not very useful. More fundamental is the plunge which shows tension vs. compression.
514 onward. Poor writing. Reverse the sequence by first saying flat surface can only allow compression, both before and after an earthquake…
521-522. can promote … only if …
540-- There should be a distinction between pervasive and local failure. See discussion in Section 4.4 of Wang et al. (2019). In my view, the lack of recognition of potentially very large, multi-scale heterogeneity is the biggest shortcoming of Coulomb stress analysis as is commonly conducted. I do not ask the authors to solve this problem in this work, but some qualitative discussion will be useful.
576-- cause -> would necessitate
589-590. I have a hard time finding what mu value was used for all the other models. Was it 0.7? It should be prominently stated somewhere, and the reader should be reminded here again.
Citation: https://doi.org/10.5194/egusphere-2024-3592-RC1 -
RC2: 'Comment on egusphere-2024-3592', Romain Jolivet, 15 Jan 2025
In this article, Dielforder et al provide an attempt at exploring the effect of several parameters usually not accounted for on the Coulomb failure stress resulting from large earthquakes in subduction zones. They first explore an analytical solution showing that topography has an influence on whether some faults will be brought closer to or away from failure. They then build numerical models to show the importance of topography, geometry and rheological contrasts between the crust and the mantle wedge on the same quantities, comparing various cases and showing the potential for explaining the distribution of aftershocks in such cases.
I have not found major flaws in the paper or in the reasoning (if I understood it well), the text is nicely written and the figures are quite clear. However, I concur with Pr Wang’s review about the general clarity of the paper. Several elements are explained in a quite convoluted way and the actual objectives are not necessarily clearly exposed. In particular, it took me quite some time to figure out what was the difference with what had been proposed earlier, while it seems to me that it is the core of the paper. I describe below what I mean by that. I believe that this paper will make a nice contribution to our field of research and I look forward to read an amended and clearer version of it.
Main Comments:
- While the focus of the introduction is clearly the role of topography on the pre-stress conditions, it seems to me that it is not the case for the whole paper. The first part indeed focuses on topography, from a simple analytical perspective which I like very much, but the modeling part introduces additional complexities (rheological, geometry) which are not necessarily clearly introduced in the first place. Furthermore, the limits on the sources of pre-stress are not necessarily discussed which makes the whole description of the objectives not that clear to me. For instance, the remanence of stresses from previous earthquakes or previous cycles is not discussed while it could be of similar orders of magnitude of the other sources mentioned currently.
- There is no comparison between the potential to explain the location of aftershocks using the classic coulomb approach (semi-elastic half space following King et al 1994) with the various refinements proposed here. While the authors state that topography is a “first order” contribution, there no elements in the paper supporting that assertion. The first order contribution to aftershocks is not the pre-stress but the earthquake itself and it would be great to be able to quantify the effect of each of the improvements brought to the calculations. One way would be to simply turn off gravity in the models, but also see what happens without the rheological heterogeneities and quantify the performance of the different models. If the parameterization proposed by the authors is indeed of importance, it should definitely greatly improve the overlap between the positive CFS regions and the aftershock distributions. I am asking this because simple CFS seems to work to some extent for strike slip earthquakes where topography does not play a major role, compared to subduction zones.
- I havent found in the paper the notion of attribution of the earthquakes to a sequence of aftershocks. I guess the authors have carefully taken care of this aspect but are all the events used here really aftershocks and how is the selection performed? Is it simply over a given time period after the mainshocks and if so, is the duration of that period of importance? I know that there is no time dependent processes in the CFS calculation but there is a time dependency in the aftershock distribution and over a long time, some “interseismic seismicity” should show up in the dataset, polluting the interpretation in this case.
Minor points:
- There is two sections 2.2
- Point P1 (figure 2) is not indicated on figure 1
- I am not convinced by the need for figure 4 since it simply explains what CFS is. It certainly is a nice textbook figure, but I don’t see how it brings new elements to the discussion. In general, removing elements that are known or separating them clearly from what is new would certainly help clarifying the objectives of the paper.
- Line 515: Some words are missing in this sentence
- Line 525: Some words are also missing here.
- The first sentence of the conclusion is quite awkward. The stress change does not depend on the initial stress since it only depends on the stress drop. If you mean the CFS, then yes, but please clarify.
I have to say that since I am late a writing my review, I have read the comments from Pr Wang and while I would have written myself some of his questions and concerns, I fully support his review. I hope these comments will help the authors improving this nice manuscript.
Cheers,
Romain JolivetÉcole normale supérieure, Paris, France
Citation: https://doi.org/10.5194/egusphere-2024-3592-RC2
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