Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

Batac, Rene C.; Paguirigan Jr., Antonino A.; Tarun, Anjali B.; Longjas, Anthony G.

doi:https://doi.org/10.5194/npg-24-179-2017

Articles | Volume 24, issue 2

https://doi.org/10.5194/npg-24-179-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/npg-24-179-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 24, issue 2

Research article

|

27 Apr 2017

Research article |

| 27 Apr 2017

Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

Rene C. Batac, Antonino A. Paguirigan Jr., Anjali B. Tarun, and Anthony G. Longjas

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Final revised paper (published on 27 Apr 2017)
Preprint (discussion started on 02 Jun 2016)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'referee report - context building and precise definitions are needed', Francois Landes, 04 Jul 2016
- AC1: 'Reply to Referee 1 (F. Landes)', Rene Batac, 08 Sep 2016
RC2: 'Interactive comment on “Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes” by R. C. Batac et al.', Anonymous Referee #2, 05 Jul 2016
- AC2: 'Reply to Referee 2 (Anonymous)', Rene Batac, 08 Sep 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Rene Batac on behalf of the Authors (08 Sep 2016) Author's response Manuscript

ED: Referee Nomination & Report Request started (29 Oct 2016) by Richard Gloaguen

RR by Francois Landes (07 Nov 2016)

Suggestions for revision or reasons for rejection

I think the authors have substantially improved the paper. There are still a few points that need to be improved, but the overall quality is now much more satisfactory.

General comment:
Please use floating point notation (e.g. 1.5 instead of 3/2), when you have no prediction or argument for the expoenents to take these simple rational values. Otherwise it is misleading, as usually when an exponent is *exactly*U equal to a ratinal number, there is (relatively) simple argument explaining that result. In your paper I believe most exponents are irrational numbers.

1.0
Ok, I see you added some litterature, I haven't compared in detail but reading the whole paper I found it more clear.
I see you cited Landes and Lippiello 2016, this is nice but not very necessary: please do not feel like you should cite me because I'm refereeing. Cite if you truly believe it is relevant.
I think you would gain readership by further putting things into context in a precise way, comparing your results quantitatively with other model's, but that may also be for a separate publication, it's your choice. Now the reader is not lost, I think.

1.1
Ok, good.

1.2
Thank you for this nice discussion and adding these itneresting results.
You should add one or two tentative fits and their corresponding power-law exponents in Fig 4.

About your last comment on 1.2, a remark:
you say that V and A are equally representations of the energy .... but it's like saying that velocity v and kinetic energy E_k of a system are equally valid representations of its temperature: instead, we have |v|^2 ~ T ~ E_k, not |v|~T~E_k. Exponents change if you use a variable other than the correct one (or not proportional to it).
If P(A) ~ A^-1.6 and V~A^1.5 for instance, using P(A) dA = P(V) dV , you get (I think) P(V)~V^-((1.6-1.5+1)/1.5)=V^-1.4.
I do not think it is crucial for your results that the exponents match very well: the key result is that you have bimodal statistics in both space and time distributions which appear as a result of introducing p. So even if the exponent of fig 4 is not very close to the famous 5/3=1.6666666 you wish for, it's ok, your paper is worthwhile (amyway the "true" value of b is very debated).

1.3
Ok... So you elected to call M (and sometimes m) the magnitude and m (?) its threshold... why not use m always and m_th for the threshold ?

1.4
Ok, excellent, this point is now much clearer to me and clearer in the paper.

1.5
I appreciate your work, but cannot find this discussion in the revised paper. Where did you include (part of) this discussion?

Let me add a comment for you:
what I was trying to exaplain is that because of this effect (of Fig ii of your reply), your model may be described by "count", the y-axis of Fig ii, instead of the proba p. Let me call "count" C here. Using C as parameter is completely equivalent to using p.
Using C as control parameter, it becomes obvious that as soon as C > 10^5, i.e. 1000 times its baseline value, what you are actually doing is a quasi- extremal dynamics, since you are almost always picking this site.
For lower values of C (in the range p~0.007 I guess C is much closer to its baseline value), you are not doing extremal dyanmics, but since you load all sites at random almost equally, your loading protocol is in effect quite similar to uniform loading.

I just noticed this fact while reading your paper and I think one needs to study this matter carefully in order to compare with other loading protocols.

It is not necessary to have this discussion in full in your paper, a short comment to let the reader realize this fact will be enough.

1.6
OK

1.7
OK

1.8
OK

1.9
Thanks, this is now very clear when reading the paper, and furthermore one understands why it is important to threshold (relative to interevent time statistics). I learned something new, thank you !

1.10
OK

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RR by Stefan Hergarten (22 Nov 2016)

Suggestions for revision or reasons for rejection

Sorry for not taking part in the first round of review, although I was asked. Therefore my review mainly refers to the question whether the authors addressed the numerous concerns raised by the two first reviewers appropriately. I feel that they did in general, but in my opinion there are still two important points that require more clarification.

(1) Points 1.4, 2.2 and 2.6 of the original reviews refer to the role of the parameters used for calibrating the model and the relationship to established models in this field. If I understood the model correctly, $\nu = 0.25$ (at $p = 0$) should reproduce the original BTW sandpile model, while $\nu \to 0$ (at $p = 0$) should correspond to the OFC model in the conservative limit. Both cases are characterized by scaling exponents in the event size distribution lower than the values found in this manuscript, and those found here fit much better to real earthquakes. The finding of larger exponents between the two limiting cases is interesting and unexpected, but it should be shown clearly, perhaps with a figure showing the dependence on $\nu$. In this context it should also be made clear that the finding is not a
spurious effect of an exponentially decreasing event size distribution.

(2) The relationship to earthquake rupture area and seismic moment of the model properties (points 1.2 and 1.3) is still not very clear. $A$ should correspond to the rupture area, and $V$ to the seismic moment.

Provided that the authors can clarify these points and demonstrate that their results on the scaling exponents are nor a spurious effect, I think that the manuscript brings some progress into the understanding of such simples models in the context of earthquakes, so that I would recommend publication then.

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ED: Publish subject to minor revisions (further review by Editor) (04 Jan 2017) by Richard Gloaguen

AR by Rene Batac on behalf of the Authors (10 Jan 2017) Author's response Manuscript

ED: Publish as is (11 Jan 2017) by Richard Gloaguen

AR by Rene Batac on behalf of the Authors (17 Jan 2017) Author's response Manuscript

Short summary

The sandpile-based model is the paradigm model of self-organized criticality (SOC), a mechanism believed to be responsible for the occurrence of scale-free (power-law) distributions in nature. One particular SOC system that is rife with power-law distributions is that of earthquakes, the most widely known of which is the Gutenberg–Richter (GR) law of earthquake energies. Here, we modify the sandpile to be of use in capturing the energy, space, and time statistics of earthquakes simultaneously.