Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

Cavers, M. S.; Vasudevan, K.

doi:https://doi.org/10.5194/npg-22-589-2015

Articles | Volume 22, issue 5

https://doi.org/10.5194/npg-22-589-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/npg-22-589-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 22, issue 5

Brief communication

|

09 Oct 2015

Brief communication |

| 09 Oct 2015

Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

M. S. Cavers and K. Vasudevan

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Final revised paper (published on 09 Oct 2015)
Preprint (discussion started on 24 Feb 2015)

Interactive discussion

Status: closed

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

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- Supplement

RC C80: 'Nonlinear analysis of time series', Anonymous Referee #1, 21 Mar 2015
- AC C124: 'Initial response to the anonymous referee 1', Michael S. Cavers, 21 Apr 2015
RC C147: 'Interesting work, but needs some methodological clarification', Reik Donner, 15 May 2015
- AC C245: 'Initial response to the referee 2', Michael S. Cavers, 20 Jun 2015

Peer-review completion

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

AR by Michael S. Cavers on behalf of the Authors (20 Jun 2015) Author's response Manuscript

ED: Referee Nomination & Report Request started (24 Jun 2015) by Ilya Zaliapin (deceased)

RR by Anonymous Referee #1 (29 Jun 2015)

RR by Reik Donner (30 Jul 2015)

Suggestions for revision or reasons for rejection

The authors have made a great step forward by addressing much of the concerns raised by the reviewers of the original discussion paper. The manuscript is much clearer now in terms of its methodological approach and results. However, before final publication in NPG, there are some further minor aspects to be addressed and/or clarified:

• p.5, l.2: “…for one Delta t or for successive Delta t’s” – Delta t is used in the paper as describing the sampling interval, not the time index; so this part should read “for one or more time steps”
• p.5, l.4: please add a reference for the presence of intermittency
• At many points throughout the manuscript, the authors use a very sloppy language by just skipping some important words. For example, on p.7, l.6, “the number of occurrences from state I to state j” should read “the number of occurrences of transitions from…” I recommend careful proofreading of the whole manuscript regarding this aspect prior to delivering the final version to the publisher.
• p.7, ll.11-13 and 14-16: literal repetition due to a copy-paste error
• p.7, ll.19-20: Requirement 2 is not clear from the text, please phrase more clearly
• p.7, l.21: The authors use the state numbering that is only introduced on p.8 – please rearrange the material in this section accordingly
• p.9, ll.4-5: Do you mean “within the spatial distance d_ij between I and j around I”? Please specify.
• p.10: Given the actual contents of Section 3, I recommend changing the section title to “Analysis methods and results”.
• Section 3.1: The advantage of EEMD in comparison with classical EMD still does not become fully obvious. Please add one sentence or so to make this point explicit.
• p.12, l.22: Is there any argument justifying this assumption?
• p.13, ll.2-4: It is still not fully clear what is done here. Previously, the authors take the EQ catalog data, compute time series of transition frequencies between all states and sum them up. I assume that at this point, the summation is skipped, and EEMD is performed to the transition frequency time series for all pairs of states first, and then the corresponding IMFs are summed up – is this correct? If so, please write this more clearly; otherwise explain what you are actually doing. I agree that due to the additivity imposed in both the EMD and total weight calculation, both steps would commute. However, I am wondering if the natural time-scales of the IMFs for each pair of states are always the same. The author state elsewhere that EMD provides a dyadic decomposition – in my personal experience, this is not necessarily the case. Is there something special about the implementation of EMD used in this work?
• p.13, ll.16-18: It would be good if the authors could explicitly refer to certain times (calendar dates) here. If I interpret this sentence correctly, the authors mean a certain time period of enhanced activity at the end of the record (“bursts” in Fig. 2a) – if so, it is not surprising that such a bursty (intermittent) behavior shows up at various time scales of the decomposition (you would expect something similar in other time series decomposition techniques as well). In this spirit, the broad signal across various scales is not too surprising from the original data. I feel that this aspect should be mentioned briefly.
• p.14, l.1: From the context, it is not clear why the authors speak of a “periodic trend” here.
• p.14, l.2: Please give calendar dates instead of numbers of sampling intervals.
• Figure captions: The captions of Fig. 3 and Fig. 6 could be drastically reduced by combining repeated contents. For example, in Fig. 3, you do not need to explicitly count the IMFs. In Fig. 6, the text describing the contents of panels (a,b) and (c,d) could be easily combined.
• In general, I strongly recommend to redraw several of the figures replacing the rather arbitrary time axis by calendar dates as values (Figs. 2a, 3, 4,6).

Although this is a list with quite some items, I think that addressing these points only requires minor amendments to the text, so that I can actually recommend publication of this work without further review. In addition to the specific points raised above, an additional careful proofreading is recommended.

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ED: Publish subject to minor revisions (further review by Editor) (30 Jul 2015) by Ilya Zaliapin (deceased)

AR by Michael S. Cavers on behalf of the Authors (19 Aug 2015) Author's response Manuscript

ED: Publish as is (05 Sep 2015) by Ilya Zaliapin (deceased)

AR by Michael S. Cavers on behalf of the Authors (11 Sep 2015)

Short summary

We introduced a new modified Markov chain model to generate a time series of the earthquake sequences from a global catalogue with an optimum time sampling of 9 days. Here, we subject the time series to a known analysis method namely an ensemble empirical mode decomposition to study the state-to-state fluctuations in each of the intrinsic mode functions. Also, we establish the power-law behaviour of the time series with the Fano factor and Allan factor used in time-correlative behaviour studies