Peer review of: The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence (2020)

Reviewers' Comments: 
 
Reviewer #1: 
Remarks to the Author: 
Nature Communications manuscript NCOMMS-20-01427, “The influence of the brittle-ductile 
transition zone on aftershock and foreshock occurrence" by G. Petrillo et al. 
 
 
The manuscript builds on a 2 layer cellular automaton to mimics the changes of rheological 
behavior of the crust with increasing depth, from velocity weakening to velocity strengthening. The 
model succeeds in reproducing the observed statistical features of both aftershocks and 
foreshocks. The most impressive outputs lie in the b value change in foreshocks as compared to 
aftershocks distribution, respectively. This latter result, which reinforces the intensely debated 
robustness of possible observed foreshocks is missing to be explicitly described in the current 
abstract version. When the overall manuscript is of high quality, i suggest reshaping parts of the 
manuscript will enhance its impacts. This task is an low-risk high gain recommendation that should 
be quickly fulfilled by the author group skills. 
 
First, the mapping of the model hypothesis on the current seismicity challenges and context is not 
clear enough. As example, when pointing on the key role of afterslip in earthquake triggering, the 
authors appear to bound the seismicity in the 5-15 km range. Such a depth statement is only true 
for the "continental" earthquakes, it does not apply for subduction zone seismicity. However, 
several cases discussed in the text and the referenced literature focus on subduction zone quakes. 
Accordingly, the authors should clarify the database they use all along the manuscript to calibrate 
the model outputs. 
Second, the comparison with previous spring-blocks model should (i) be accessible to a broader 
audience and (ii) comprehensively review the current knowledge. As an example, Pelletier (2000) 
and Jagla et al. model both reproduce the submitted manuscript results closely. More focused text 
on which control parameters support advances relative to previous simulations should be included 
in a revised version. More technically, it is known (e.g., the review by Arcangelis et al. 2016) that 
some models fail to reproduced observations for the whole scale of earthquake size. Why are the 
simulation results bounded to Mmax=4 should be discussed (a few lines and figure(s) in 
supplementary materials are welcome)? Which are the largest/smallest possible event in the 
10000x100000 lattice size the authors use should be discussed? 
Third, from the result section, figure 3-5 demonstrates there is a limited range of theta and sigma 
parameter values that reproduces the observed scaling laws for aftershocks and foreshocks. It 
contradicts the abstract result described as "recovered at a quantitative level without any fine-
tuning." 
 
Specific comments: 
p3, All the sentences on foreshocks are specific to rare cases. The text should be tampered down 
accordingly. 
p3, two (over 3) reference for before-shock-slow-slip apply for subduction cases. How does the 
model works for these cases is not clear when authors describe the universality of aftershocks and 
foreshocks patterns for shallows seismicity solely? 
p3, the reference to Gulia and Wiemer is very controversial and nonuniversal at all. First, the 
authors suggest that the observed pattern is deterministic rather than statistical. Second, only two 
cases are analysed by Gulia and Wiemer, with different space-time-magnitude window for each 
event, without justification (e.g. Brodsky, E. E. (2019). Determining whether the worst earthquake 
has passed) 
p9 top, "have earthquakes as large as the whole system, something that happens in observational 
data." 
The authors must specify what the "system" that is supposed to correspond to observational data 
is. Because earthquake size remains non-predictable, observational data are related to a given 
seismic network for which no system can be isolated from each other. Furthermore, is it not the 
"coupling at different scales" the basis of the author's primary hypothesis ("The organization in 
time, space and energy of aftershocks is characterized by scaling behaviors with exponents which 
are quite universal"). In such a context, "earthquake as large as the system size" must be 
clarified. Note here that on the result section, the Mmax is bounded to M=4 without information on 
the simulated system size? 
p9 comparison with previous spring-blocks model: 
- magnitude definition and Mmax Mo=f(slip) versus M=f(Sliding block)? 
The model of Pelletier 2000 presents seismic activity consistent with the GR law for small events 
whereas the large magnitude behavior changes from supercritical behavior, for large seismic 
couplings, to a GR distribution with a magnitude cutoff, for low seismic couplings. Similarly (De 
archangels et al. 2016 points on "BK models implementing state–rate friction laws have also been 
widely studied. Results show that the magnitude distribution is strongly affected by the friction 
parameters. Under the condition of so-called 'strong friction instability' a GR behavior is found at 
small magnitudes with b ≃ 1, followed by an almost flat behavior reminiscent of the peak structure 
found in the super-critical regime. A double peak distribution is conversely observed in the 
opposite condition of 'weak friction instability' These references question the ability of the author 
model to reproduce the full range of magnitude. Why are distribution results bounded to M1-4 
range ? Which are the largest/smallest possible event in the 10000x100000 lattice the authors 
use? 

Results 
- Figure5-7: there is an indication for neither theta nor sigma values that are used for these 
simulations? 
-Figure 6: the number of fore-aftershocks should not be the same, as pointed in the text and on 
(inset) figure 5? 
-p13 aftershock location: 
"First of all, we observe that most aftershocks occur close to the border of the mainshock's 
fractured area…. . This scenario is strongly supported by recent observations of the aftershock 
organization after big mainshocks 59.” 
Most of the #59 reference earthquakes are subduction zone earthquakes below 15 km depth (see 
p2). Are the patterns of "universality" classes still stable with depth, is not discussed? Some recent 
papers point the others way (e.g., Hainzl et al. JGR 2019) 
-A modified figure 2 to present the results the same way as cited in #59 reference is more than 
welcome? 
 
 
 
Reviewer #2: 
Remarks to the Author: 
This work, based on a novel geophysical numerical model, shows that a combination of two 
rheological behaviors, velocity weakening and velocity strengthening, is a mechanism generating 
the statistical features of aftershocks and foreshocks. These features include a smaller b-value for 
foreshocks and aftershock regions scaling with main shock magnitude. To my knowledge, these 
results are original. Reproducing complex statistical spatio-temporal features of seismicity with a 
model devised from physical laws and quite simplified (to a justified level) is remarkable. 
 
The text is well written (see however points below) and scientifically sound. The results are very 
interesting and the claim of this work is important. In my opinion there are the ingredients for 
publishing in Nat. Comm., provided that the following points are addressed convincingly by the 
Authors. 
 
 
1. By the notation in text (one-dimensional indices “i” and “j”), and by looking at figure 1, the 
impression is that one deals with a 2xN model. The sentence ending with “organized on a 
rectangular lattice (see Fig. 1)” seems to confirm this interpretation. However, figure 2 shows a 
square lattice with sides Lx and Ly not introduced in the main text. Only in the Methods this 
becomes clear. The text should be improved to better describe the geometry of the model. 
 
Having settled that the model is composed by two 2d carpets on top of each other, it becomes less 
clear how this is related to the depth in the crust. The Authors argue that the changing with depth 
of rheological properties of the crust is the feature that justifies the introduction of both velocity 
weakening and velocity strengthening. How is this represented in the model? Is it a model of a 
single fault or of a tectonic region? 
 
The excellent performance of the model invites to think of some alternative interpretation: Is it 
possible that weakening and velocity strengthening are both taking place at the two sides of a fault 
(in different measure) at every depth? 
 
 
2. The “without any fine-tuning” claim in the abstract should be better explained. In the text it is 
not obvious if the third parameter epsilon (for dissipation) is exactly set to zero or is kept at an 
arbitrarily small value. The readers should be able to find all information for reproducing the 
results. 
 
At page 12 “ Results do not depend on the specific values of Θ and σ, thus we only present them 
for intermediate values: Θ = 0.5, σ =5.” should be better justified. 
The range of variability for the disorder is chosen by the authors and sigma=5 seems rather at its 
top than at intermediate range. 
 
Theta=0.5 gives the better Gutenberg-Richter law in figure 3 and indeed it becomes the value over 
which the Authors focus in other figures. I do not understand the mismatch in cutoff between the 
curves for Theta=0.5, sigma=5 in the inset (orange data) of figure 3 and in its main panel 
(magenta). They should be the same curve, I believe. 
 
 
3. At page 9 there is a hint at the BTW model. This seems a bit limited. The introduction should 
include a broader perspective giving the proper credit to the mechanism of self-organized criticality 
as the origin of avalanches with power laws. 
 
 
4. In the Methods, it is not clear if the model is updated sequentially or in parallel. There would be 
no difference if the model were Abelian as the BTW model, which is probably requiring a hard 
mathematical proof. The statement “The precise synchronization of the updates does not matter” 
makes sense only if the model is Abelian. 
 
 
Minor points: 
 
* The caption of figure 4 does not comment on its inset. 
 
* Sometimes Theta becomes theta in the text and figures. 
 
* Caption 1: “: each fault modeled as” → “: each fault is modeled as” 
 
* Page 13: “largest mainshock magnitude mM do we have a sufficient number” → we do have 
 
* Page 21: “ Indeed, the ui are subject to a velocity-weakening rheology”, should be strengthening 
 

Marco Baiesi, 
Dipartimento di Fisica e Astronomia "Galileo Galilei", 
Universita' di Padova, 
Italy