Simple statistics for complex Earthquake time distributions

Matcharashvili, Teimuraz; Hatano, Takahiro; Chelidze, Tamaz; Zhukova, Natalia

doi:https://doi.org/10.5194/npg-25-497-2018

Articles | Volume 25, issue 3

https://doi.org/10.5194/npg-25-497-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/npg-25-497-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 25, issue 3

Research article

|

10 Jul 2018

Research article |

| 10 Jul 2018

Simple statistics for complex Earthquake time distributions

Teimuraz Matcharashvili, Takahiro Hatano, Tamaz Chelidze, and Natalia Zhukova

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Final revised paper (published on 10 Jul 2018)
Preprint (discussion started on 19 Jan 2018)

Interactive discussion

Status: closed

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

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RC1: 'RC: Referee comment', Anonymous Referee #1, 23 Jan 2018
- AC1: 'Interactive comment on “Simple statistics for complex Earthquakes’ time distribution” by Teimuraz Matcharashvili et al.', Teimuraz Matcharashvili, 14 Mar 2018
- AC3: 'Revised Manuscript', Teimuraz Matcharashvili, 14 Mar 2018
- AC5: 'Revised manuscript', Teimuraz Matcharashvili, 15 Mar 2018
- AC7: 'revised version of manuscript with track changes', Teimuraz Matcharashvili, 19 Mar 2018
- AC9: 'Comments to revision', Teimuraz Matcharashvili, 19 Mar 2018
RC2: 'A mere statistical exercise', Anonymous Referee #2, 31 Jan 2018
- AC2: 'Interactive comment on “Simple statistics for complex Earthquakes’ time distribution” by Teimuraz Matcharashvili et al.', Teimuraz Matcharashvili, 14 Mar 2018
- AC4: 'Revised Manuscript', Teimuraz Matcharashvili, 14 Mar 2018
- AC6: 'Revised manuscript', Teimuraz Matcharashvili, 15 Mar 2018
- AC8: 'revised version of manuscript with track changes', Teimuraz Matcharashvili, 19 Mar 2018
- AC10: 'Comments to revision', Teimuraz Matcharashvili, 19 Mar 2018
SC1: 'Revised manuscript sent 14 Mar 2018', Teimuraz Matcharashvili, 15 Mar 2018

Peer-review completion

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

AR by Teimuraz Matcharashvili on behalf of the Authors (01 Apr 2018) Author's response Manuscript

ED: Referee Nomination & Report Request started (04 Apr 2018) by Norbert Marwan

RR by Anonymous Referee #2 (18 Apr 2018)

RR by Anonymous Referee #1 (19 Apr 2018)

Suggestions for revision or reasons for rejection

Even though the authors took large effort to respond to all comments, they could not dispel my major concern about the appropriateness of the introduced IDT measure to describe the degree of randomness. The complete paper is based on the assumption that for random sequences sum_[i=1..N] DT(i) → 0, for large N. This needs to be proofed. Referring to a paper in preparation or stating “ logically, for any random sequence, the sum of the deviation times should approach zero, when “ (revised version, page 2, last paragraph) is not sufficient. The sentence needs mathematical background. I assume the authors have something like the law of large number in mind, but this is not valid in their application, since it requires independent identical distributed data. Yet, DT(i) is not independent from DT(i-1).
Also the presentation of a matching example (as the analysis of colored noise) is not sufficient to proof the concept. In fact, Fig. 5a) contradicts the authors assumption, since IDTs for shorter time series (e.g. N = 5000) are smaller than IDTs for longer time series (N=34020) and consequently do not converge to zero for large N.
Moreover, a deterministic time-series with equidistant time steps contradicts the authors assumption that the IDT for more random-like time series is closer to zero, than for deterministic time series (even though a equidistant time series is not in the interest of the study). I could think of several other deterministic time series, where this is the case.

Further, several conclusions are not well founded. E.g.

revised paper, page 7: “From this figure [fig. 6] we see that IDT values goes closer to zero when the extent of order decreases. Besides, it also becomes clear that even for short data sets IDT calculation is useful to detect differences in considered data sets.”
Figure 6 only shows, that the distributions for low orders are more narrow than for higher orders. Yet, the mean seems to be the same for all distributions and differs from zero (~0.8?). Since sequences of high order magnitude also have good chances to be close to zero, the usefulness of IDT to detect differences is questionable. Several changes will be undetected.
On top, neither Figure 6 nor any other analyses shows, how IDT reacts to changes in the regularity of the time series. For all synthetic data sets the spectral exponent stays constant.

Revised paper, page 9: “Increasing the threshold to M3.6, M4.6, and M5.6 leads to following IDT values: 71.7, 6.7, -0.87 accordingly. Two important things can be underlined here: first, the increase of the magnitude threshold makes the time distribution of remained EQs more random and second, according to our conjecture to the more random EQ distribution should corresponds the closer to zero IDT value, what indeed is shown above. “
The IDT values depend on the number of events in the time series. Consequently the IDTs for the different threshold magnitudes are not comparable and can not be used to support the given conclusions.

Revised paper, page 10: “Thus, comparing the average of integral deviation times, calculated for the entire length of randomized catalogues, with the IDT value of the original SC catalogue, we see that the last one is two orders of magnitude larger.”
Comparing the average IDT of randomized catalogues to the original catalogue is not meaningful comparison, since the average value can be expected to be closer to zero in any case. It would be reasonable to instead show the IDT of the original catalogue in Fig 7, which gives the distribution of IDTs of randomized time series.

Revised paper, page 11: “the strongest earthquakes never occurred in periods, when IDT curve comes close to zero value or crosses abscissa line” …
This is not very surprising, since only 6 of the 3500 time windows correspond to the large magnitude earthquakes. It is quite unlikely to hit one those time windows.
Revised paper, page 12: “As we see in Fig. 9, analysis carried out on shorter catalogues, confirm the result obtained for the entire period of observation (1975-2017) and convinces that the curve of IDT values crosses abscissa at periods of relatively decreased seismic energy release.”.
Still it is unlikely to hit one of the high magnitude EQ windows. Fig. 9 also shows that the crossing of the abscissa strongly depends on the starting point of the studied period (e.g. the points for 1980 differ strongly compared to 1985). Consequently, I doubt there is a meaningful interpretation of the crossing points.

There are several other issues that are confusing and not very consistent. Due to the general problems with the introduced concept and the drawn conclusions, I refer only to a few of these issues in the following.

In general, it is difficult to compare the IDT values you provide, since some are not normalized, some are normalized to the span of window (e.g. Fig. 5), some to number of events (e.g. Fig 9). A uniform presentation should be used. E.g. it is difficult to compare the IDT of the original SC catalogue (not normalized) with the distribution of IDTs for randomized catalogues (normalized to span of window).

The results of Fig. 5b do not match with Fig. 6. The mean values for high orders are larger in Fig 5b compared to the means in Fig. 6.

I still don’t understand the authors' concept of randomized time series, since a shuffling of occurrence times will not change anything. Maybe the authors mean a shuffling of waiting times.

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ED: Reconsider after major revisions (further review by editor and referees) (25 Apr 2018) by Norbert Marwan

AR by Teimuraz Matcharashvili on behalf of the Authors (04 Jun 2018) Author's response

ED: Referee Nomination & Report Request started (12 Jun 2018) by Norbert Marwan

RR by Anonymous Referee #1 (13 Jun 2018)

ED: Publish as is (13 Jun 2018) by Norbert Marwan