the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Sep 2026
How much of a regional Coulomb stress map survives its own uncertainty? An audit with forecast-skill validation for Türkiye
Abstract. Static Coulomb stress transfer is increasingly automated over open catalogues and fault databases rather than built by hand for single events. We ask how much of such a result survives its own inputs. For Türkiye we resolve the stress imparted by 46 Mw ≥ 6 earthquakes between 1990 and 2026 onto 6,970 sub-segments of the mapped active-fault network, screening each across 25 parameter combinations. Three silent failure modes emerge. First, 44 records of the GEM Global Active Faults Database store a central rake 180° from the circular midpoint of their own bounds; all lie in two source compilations, one being the principal North Anatolian Fault strand south of Istanbul, where it reverses the stress change from −0.029 to +0.251 MPa. Second, anchoring ruptures on catalogue centroids rather than mapped traces displaces them by a median of 18.4 km; across 27 testable events this flips the sign on a median of 11.9 % of segments against 2.0 % for a rake ±15° and dip ±10° perturbation, and is the larger of the two in 20 of them. Third, sign stability rises from 74.3 % to 89.5 % between 1 and 50 kPa. A pseudo-prospective test against subsequent seismicity gives a segment-weighted AUC of 0.711 for Mw < 7 sources, but clustering leaves an effective sample of 42, one event supplies 38 % of it, an event-equal estimate gives 0.589 ± 0.112, and distance matching leaves 0.655 with an interval spanning 0.5. Screening improves the estimate by +0.016 (95 % paired bootstrap [+0.001, +0.051]; one-sided p = 0.020). The forecast evidence is suggestive rather than strong; the two input-integrity findings do not depend on it. Coulomb maps should be published with an explicit statement of which parts are interpretable.
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CC1: 'Comment on egusphere-2026-5171', Yunus Doğan, 21 Oct 2026
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AC1: 'Reply on CC1', Mehmet Sait Vural, 22 Oct 2026
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Thank you for your question, which highlights an important distinction between input consistency and parameter sensitivity. The main implication is that robustness to parameter variation should be assessed alongside the consistency of the underlying inputs. A calculation may remain stable across the tested parameter combinations despite an inconsistency in its reference inputs. The rake correction documented in this study illustrates this distinction: input-consistency checks and parameter-sensitivity screening provide complementary evidence for determining which parts of a regional Coulomb stress map can be meaningfully interpreted.
Citation: https://doi.org/10.5194/egusphere-2026-5171-AC1
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AC1: 'Reply on CC1', Mehmet Sait Vural, 22 Oct 2026
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CC2: 'Comment on egusphere-2026-5171', Dr. Ranjit Das, 23 Oct 2026
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The manuscript does not adequately address the limitations of conventional earthquake magnitude scales Mw and M or provide a clear justification for the consistent use of these scales throughout the analysis. In particular, the manuscript uses both Mw and M, yet these scales are not technically the same and should be clearly distinguished. Mw and M differ by approximately 0.03 magnitude units, and therefore their interchangeable use may lead to ambiguity. The authors should explicitly define the meaning of each magnitude notation and specify which parameter is used in event selection, statistical analyses, and the interpretation of results.
Furthermore, recent studies have highlighted mathematical and theoretical limitations associated with conventional magnitude Mw formulations, particularly for earthquakes below approximately magnitude 7.5 (Das et al., 2025, and references therein). In addition, Matsu'ura (2025) discussed theoretical limitations of the scale and raised issues regarding its mathematical formulation and physical interpretation. Despite the direct relevance of these studies to earthquake characterization, they are not considered or discussed in the manuscript.
The authors should provide a scientifically justified explanation for selecting (Mw) (or (M), as used in the manuscript) rather than the Das magnitude scale (Mwg). The justification cannot be based solely on the widespread use of (Mw); instead, it should demonstrate why the selected magnitude scale is more appropriate for the specific objectives and methodology of this study. This issue is particularly important because the study applies a magnitude threshold for event selection and investigates magnitude-dependent forecasting performance. The authors should therefore discuss whether the choice of magnitude scale could influence event selection, forecasting results, and the robustness of the conclusions.
References:Das, R., Das, A., Choudhury, D., Meneses, C., Barrera, F. G., Wason, H. R., & Alam, M. A. (2025). Updated probabilistic seismic hazard assessment using Mwg (Das magnitude scale) to address moment magnitude (M) scale inaccuracies below 7.5: A case study from Northeast India. Scientific Reports, 15(1), 43502.
Matsu’ura, M. (2025). A theoretical basis of the moment magnitude scale. Earth, Planets and Space, 77(1), 151.
Citation: https://doi.org/10.5194/egusphere-2026-5171-CC2 -
AC2: 'Reply on CC2', Mehmet Sait Vural, 27 Oct 2026
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Dear Dr. Das,
Thank you for your comment. It raises a point on which the manuscript was not explicit enough: the role of the magnitude scale in the analysis. Below, each point of your comment is answered in turn, followed by the changes we will make to the manuscript. The results of five sensitivity runs of the complete pipeline are given in the attached supplement (Fig. S1, Table S1).
- “The manuscript does not adequately address the limitations of conventional magnitude scales or justify their consistent use.”
We agree that this should be stated explicitly. The magnitude enters the analysis in five places only, and in none of them as the object of the conclusions:
(a) Event selection. The 46 source events are the GCMT solutions with Mw >= 6.0 in the study box.
(b) Source model. The slip is computed from the GCMT scalar moment, D = M0/(mu A), so the physical input is M0 and not a magnitude. Rupture length and width follow Wells and Coppersmith (1994), whose regressions are expressed in terms of moment magnitude; for four events the mapped surface-rupture length replaces the regression.
(c) Strata. The skill results are reported for sources with Mw < 7 and Mw >= 7 (GCMT Mw).
(d) Seismicity catalogue for the skill test. AFAD ML and Md are converted to Mw with relations fitted to matched GCMT, USGS and ISC solutions (Table 2) so that one completeness threshold (Mw 2.5) can be applied; the test compares counts before and after each source event, so only the threshold, not the absolute scale, matters.
(e) The downstream hazard and siting demonstration (Sects. 3.8 and 4.6), which inverts the Wells and Coppersmith relations to obtain characteristic magnitudes; it is a demonstration, and none of the three conclusions rests on it.The three conclusions of the paper are comparisons made inside one calculation (a corrected versus an uncorrected rake record; a position perturbation versus a mechanism perturbation; screened versus unscreened segments). They do not rest on the absolute value of a magnitude. This is why the choice of scale can matter only through (a) to (d), and we have tested each (point 5).
- “Mw and M differ by about 0.03 and are used interchangeably; define each notation and say which one is used for selection, statistics and interpretation.”
Mw always denotes the GCMT moment magnitude, Mw = (2/3)(log10 M0 - 16.1) with M0 in dyn cm, which is the same as (log10 M0 - 9.1)/1.5 with M0 in N m. We believe the difference of about 0.03 that you mention is the difference between this constant and that of Hanks and Kanamori (1979), who give 16.05; the two definitions differ by 0.033 for every earthquake. Because we compute the slip from M0 directly, this offset does not enter the stress calculation. It would move the selection threshold by 0.033 and add four events (GCMT Mw 5.976, 5.976, 5.989 and 5.998), and it is covered by the threshold runs below.
The unsubscripted “M” appears in the manuscript in four places and should not: (i) the counts of USGS events “of M >= 5” in Sect. 2.1 and Table 1; (ii) “M >= 6, AFAD versus USGS” in Table 1; (iii) the probability “of M > 7.3” quoted from Murru et al. (2016); and (iv) the titles of cited papers. In (i) and (ii) the quantity is the preferred magnitude of the catalogue concerned: of the 55 USGS events of magnitude 6 or more, 53 are Mww, Mwc, Mw or Mwb and 2 are mb; of the 38 AFAD events of magnitude 6 or more, 18 are Mw, 11 Md, 8 ML and 1 Ms. We will state this in the text and replace the unsubscripted M by the catalogue and the magnitude type. For the 46 selected events, the USGS preferred magnitude is a moment magnitude in all 46 cases and differs from the GCMT value by -0.022 on average (standard deviation 0.073; range -0.20 to +0.08), which gives a measure of the agency-to-agency scatter that any choice of scale has to live with.
- “Das et al. (2025) and Matsu’ura (2025) are not considered.”
Thank you; we will cite and discuss both. As we read them:
Das et al. (2025), building on Das et al. (2019), use the scale Mwg = log10 M0/1.36 - 12.68 (M0 in dyn cm) and argue that the standard Mw relation is not appropriate below about M 7.5, because the energy-magnitude relation on which it rests was derived for Ms of about 7 and below. Mwg is a linear function of log10 M0 and therefore of Mw: for the GCMT convention Mwg = 1.103 Mw - 0.84. It is lower than Mw by 0.22 at Mw 6.0, 0.12 at Mw 7.0 and 0.04 at Mw 7.8, and coincides with it near Mw 8.2 (Fig. S1a).
Matsu’ura (2025) argues that the energy-moment relation used to justify the standard moment magnitude is questionable, because the radiated energy depends on the dynamics of the rupture while the moment depends on its final state, and derives a corrected scale M’w = Mw + 2 log10(vr/Vs) + 0.2 from a self-similar crack model. For rupture velocities of 0.7 to 0.9 of the shear velocity this is a constant offset between -0.11 and +0.11.
Both proposals relabel the same scalar moment M0, one by a monotone linear function of Mw and the other by a constant. Neither changes which event is larger than which, nor the moment that enters our slip calculation. The scale also remains under discussion in the literature (for example, Gasperini and Lolli, 2024, comment on Das et al., 2019), and we do not take a position on which scale describes radiated energy better. What we can and should show is that our conclusions do not depend on the choice.
- “Justify the use of Mw rather than Mwg; widespread use is not sufficient.”
We agree that wide use is not a justification, and we do not claim that Mw is a better measure of earthquake size than Mwg. The reasons for retaining Mw are specific to what this study does:
(a) The quantity that propagates into the result is M0 from the GCMT catalogue. The magnitude is used for labelling, for the selection threshold, and as the argument of an empirical scaling law.
(b) The Wells and Coppersmith (1994) regressions were calibrated against moment magnitude. Evaluating them at Mwg without recalibration would be inconsistent with their derivation; we therefore did so only as a sensitivity test (S1 below), not as the primary analysis.
(c) The seismicity catalogue (about 579,000 AFAD events, almost all ML or Md) can be converted only through magnitudes shared with an external reference. The three external catalogues used here (GCMT, USGS, ISC) report Mw. An Mwg catalogue would need a regional calibration of ML and Md against Mwg for Türkiye; Das et al. (2025) provide such regressions for Northeast India, but none exists for Türkiye, and we would not wish to extrapolate them.
(d) The findings are differences within one calculation, so a smooth relabelling of the magnitude axis cannot reverse them; this is what the tests below show.- “Could the choice of scale influence event selection, forecasting results and the robustness of the conclusions?”
We re-ran the complete pipeline (source model, cumulative Coulomb stress change, position-versus-mechanism comparison, pseudo-prospective skill test) for five alternatives. S1: Wells and Coppersmith evaluated at Mwg (computed from the GCMT moment) for all 46 events. S2: S1 plus selection at Mwg >= 6.0, which is equivalent to Mw >= 6.20 (31 events). S3: completeness threshold of the seismicity catalogue raised from Mw 2.5 to Mw 3.06, the Mw equivalent of Mwg 2.5. S4 and S5: selection at Mw >= 5.9 (55 events) and Mw >= 6.1 (39 events), which brackets the offset of plus or minus 0.1 of the Matsu’ura correction. The stratification boundary needs no run: Mwg 7.0 corresponds to Mw 7.11, and no selected event lies between Mw 6.99 (Samos 2020) and Mw 7.13, so the Mw < 7 stratum is identical.
Source geometry and the stress map. Using Mwg shortens the modelled ruptures (median length 24.9 km to 20.0 km) and raises the mean slip (0.59 m to 0.84 m), because the moment is conserved. The cumulative stress-change map is nevertheless nearly unchanged: Spearman correlation 0.975 with the baseline, and the sign agrees on 99.4 % of the 2,085 segments with an absolute stress change above 5 kPa (S2: 0.955 and 98.0 %; S4 and S5: at least 0.98 and 99.4 %).
Position versus mechanism. Rupture position remains the larger source of uncertainty in every variant. The median fraction of segments whose sign flips is 11.9 % for position against 2.0 % for mechanism in the baseline, and 19.9 % against 2.6 % (S1), 13.4 % against 2.6 % (S2), 11.9 % against 2.0 % (S3), 11.9 % against 2.0 % (S4) and 11.9 % against 2.2 % (S5). Position flips more signs in 20 of 27 events in the baseline, 23 of 30 (S1), 18 of 24 (S2), 20 of 27 (S4) and 19 of 26 (S5); paired two-sided Wilcoxon p between 0.00007 and 0.0009.
Forecast skill. Across the variants the pooled AUC for Mw < 7 sources ranges from 0.659 to 0.701 (baseline 0.694), the event-equal AUC from 0.551 to 0.621 (0.608), the distance-matched AUC from 0.625 to 0.652 (0.646), and the screening gain from +0.016 to +0.026 (+0.016). The lower bounds of the event-clustered intervals of the pooled AUC lie between 0.44 and 0.52, the distance-matched estimates remain unconvincing (one-sided p between 0.064 and 0.161), and the lower bound of the paired interval for the screening gain lies between -0.005 and 0.000 in all variants. The skill result was reported in the manuscript as suggestive rather than established; no choice of scale changes that statement, and none turns it into a strong result.
In short: the two input-integrity findings (the rake record and the position of the rupture) do not depend on the magnitude scale, and the skill result is as marginal under Mwg or a shifted threshold as it is under Mw.
Note on the baseline. The comparison uses a clean end-to-end re-run of the pipeline as baseline. It reproduces the position-versus-mechanism results of the preprint exactly (27 events; 11.9 % and 2.0 %; 20 of 27 and 24 of 27), but the skill statistics differ slightly from those in the preprint (pooled AUC 0.694 against 0.711; event-equal 0.608 against 0.589; distance-matched 0.646 against 0.655; screening gain +0.016 with an interval of [-0.001, +0.046] against [+0.001, +0.051]). The skill table of the preprint was computed from an intermediate file that predates the final update of the magnitude-conversion relations and the source model. We will regenerate all skill statistics from the final pipeline in the revised manuscript and report the updated values; the qualitative reading is unchanged, but the lower bound of the screening-gain interval then includes zero, and we will say so.
Changes to the manuscript
- Sects. 2.1 and 3.1: a paragraph defining Mw (GCMT; formula and constant), the catalogue magnitudes (ML, Md, Mw, Ms, mb) and the conversion to Mw, with the statement that the unsubscripted M is no longer used.
- A new table, “Where the magnitude enters the analysis” (points (a) to (e) of our answer 1).
- Replacement of every unsubscripted M by the catalogue and magnitude type (Sect. 2.1, Table 1, Sect. 4.4).
- A new subsection in the Discussion, “Sensitivity to the magnitude scale”, summarising S1 to S5, with Table S1 and Fig. S1 in the supplement, and a sentence on the limits of Mw in the limitations paragraph.
- New references: Hanks and Kanamori (1979); Bormann and Di Giacomo (2011); Das et al. (2019, 2025); Matsu’ura (2025); Gasperini and Lolli (2024).
- The scripts of the five variants will be added to the Zenodo record.
Yours sincerely,
Mehmet Sait VuralReferences cited in this reply
Bormann, P. and Di Giacomo, D.: The moment magnitude Mw and the energy magnitude Me: common roots and differences, J. Seismol., 15, 411-427, https://doi.org/10.1007/s10950-010-9219-2, 2011.
Das, R., Sharma, M. L., Wason, H. R., Choudhury, D., and Gonzalez, G.: A seismic moment magnitude scale, Bull. Seismol. Soc. Am., 109, 1542-1555, https://doi.org/10.1785/0120180338, 2019.
Das, R., Das, A., Choudhury, D., Meneses, C., Barrera, F. G., Wason, H. R., and Alam, M. A.: Updated probabilistic seismic hazard assessment using Mwg (Das magnitude scale) to address moment magnitude (M) scale inaccuracies below 7.5: a case study from Northeast India, Sci. Rep., 15, 43502, https://doi.org/10.1038/s41598-025-06642-1, 2025.
Gasperini, P. and Lolli, B.: Comment on “A Seismic Moment Magnitude Scale” by Ranjit Das, Mukat Lal Sharma, Hans Raj Wason, Deepankar Choudhury, and Gonzalo Gonzalez, Bull. Seismol. Soc. Am., 114, 2270-2274, https://doi.org/10.1785/0120230230, 2024.
Hanks, T. C. and Kanamori, H.: A moment magnitude scale, J. Geophys. Res., 84, 2348-2350, https://doi.org/10.1029/JB084iB05p02348, 1979.
Matsu’ura, M.: A theoretical basis of the moment magnitude scale, Earth Planets Space, 77, 151, https://doi.org/10.1186/s40623-025-02278-7, 2025.
Wells, D. L. and Coppersmith, K. J.: New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. Seismol. Soc. Am., 84, 974-1002, 1994.Citation: https://doi.org/10.5194/egusphere-2026-5171-AC2 -
AC3: 'Supplement to AC2', Mehmet Sait Vural, 27 Oct 2026
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Supplement to AC2. The attached file contains Fig. S1 (the relation between Mwg and Mw, and the results of the five sensitivity runs S1 to S5) and Table S1 (summary of all variants), which are referred to in my reply to CC2 above.
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CC3: 'Reply on AC2', Dr. Ranjit Das, 29 Oct 2026
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The authors have scientifically addressed most of the concerns. However, while noting that “the scale also remains under discussion in the literature,” they cite Gasperini and Lolli (2024), whose arguments include several inaccuracies. Therefore, the authors should also cite the reply paper by Das and Das (2026) for the readers’ benefit.
Reference
Das, R., & Das, A. (2026). Limitations of Mw and M scales: Compelling evidence advocating for the das magnitude scale (Mwg)—A critical review and analysis. Indian Geotechnical Journal, 56(2), 979-997.
Citation: https://doi.org/10.5194/egusphere-2026-5171-CC3 -
AC4: 'Reply on CC3', Mehmet Sait Vural, 30 Oct 2026
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We thank Dr Das for reading our reply and for the additional reference. We agree that readers should be able to see both sides of the exchange. In the revised manuscript, the sentence that notes that the magnitude scale remains under discussion will cite the comment by Gasperini and Lolli (2024) together with the review by Das and Das (2026), which answers it, and we will leave the assessment of the two arguments to the reader; as stated in AC2, we take no position on which scale describes radiated energy better, because the conclusions of our audit do not depend on the choice (sensitivity runs S1–S5 in the supplement to AC2).ReferenceDas, R. and Das, A.: Limitations of Mw and M scales: compelling evidence advocating for the Das magnitude scale (Mwg), a critical review and analysis, Indian Geotech. J., 56, 979–997, https://doi.org/10.1007/s40098-024-01147-6, 2026.Citation: https://doi.org/
10.5194/egusphere-2026-5171-AC4
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AC4: 'Reply on CC3', Mehmet Sait Vural, 30 Oct 2026
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AC2: 'Reply on CC2', Mehmet Sait Vural, 27 Oct 2026
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Data sets
Data, code and supplementary materials for "How much of a regional Coulomb stress map survives its own uncertainty? An audit with forecast-skill validation for Türkiye" Vural, M. S. https://doi.org/10.5281/zenodo.22134495
Model code and software
Analysis code for "How much of a regional Coulomb stress map survives its own uncertainty? An audit with forecast-skill validation for Türkiye" Vural, M. S. https://doi.org/10.5281/zenodo.22134495
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Your findings reveal a distinction between the consistency of input data and parameter uncertainty. What is the primary implication of this distinction for the interpretation of regional Coulomb stress maps?