the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 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
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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
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