the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Jul 2025
Coseismic Surface Rupture Probabilities from Earthquake Cycle Simulations: Influence of Fault Geometry
Abstract. Earthquake surface ruptures are a significant hazard for critical infrastructure and society. Probabilistic Fault Displacement Hazard Analysis (PFDHA) tackles this hazard using empirical and numerical models to estimate the likelihood of surface ruptures. However, empirical datasets are often incomplete and limited to few geodynamic settings, reducing their accuracy for site-specific analyses. Moreover, existing models do not capture the influence of physical fault parameters, such as geometry, on surface rupture occurrence nor its spatial variability. We use the RSQSim rate-and-state earthquake simulator to simulate seismicity across twelve alternative geometries of a test fault that incorporate variations of fault connectivity at depth, dip and fault trace sinuosity, aiming for a systematic evaluation of their influence on the probability of primary surface rupture and its spatial variability. Our results show that fault geometry is key in controlling the probability of surface rupture. Models with fault connectivity at depth and greater fault trace sinuosity yield higher probabilities than their counterparts. Conversely, disconnected models limit rupture propagation across segments, reducing surface rupture capability in specific fault regions. This study demonstrates the importance of considering fault geometry when assessing seismic hazards and confirms that earthquake cycle simulators offer a robust tool for next generation PFDHA models.
Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-3135', Maria Francesca Ferrario, 04 Aug 2025
General comments:
The paper by Gómez-Novell et al investigates the role of fault geometry in the probability of surface rupture along a fault, using the RSQSim earthquake simulator. More specifically, the authors analyze how fault connectivity at depth and fault sinuosity both at surface and depth drives the magnitude frequency distribution, max magnitude and probability of surface rupture. The Mt. Vettore (Central Italy) area is taken as a test area, to run the models and compare the outputs with coseismic and long-term slip.
I enjoyed reading the paper and I want to congratulate the authors for putting together such interesting research. The text is properly organized, figures are illustrative and well-detailed in the text. The paper is of high significance, since it applies earthquake cycle simulators to the evaluation of surface rupture probability; to my knowledge, it is the first attempt in the literature, and the paper could pave the road for a wider application in PFDHA, by providing an alternative approach with respect to those more commonly applied. Given the above, I suggest accepting the paper following minor reviews.
Below I list some comments which I hope may be useful for the revision stage.
Specific comments:
- Lines 10-12: this sentence may benefit from rephrasing. The likelihood of surface rupture is just one of the several components needed to run a PFDHA. Overall, PFDHA estimates the likelihood of exceeding a given displacement value, usually expressed as annual frequency of exceedance.
- Introduction: consider to add the references to the recently published IAEA Tecdoc 2092 https://doi.org/10.61092/iaea.74us-dn4n and the paper by Valentini et al 2025 (10.1029/2024RG000875 )
- Lines 62-63: compared to many (most of?) other active faults worldwide, the Mt Vettore fault geometry is quite well-constrained. I would not say that data on the subsurface geometry is not available, given also that the fault was responsible for the widely studied 2016 earthquake sequence.
- Section 2.2. Can you provide a numerical measure of the different degrees of sinuosity in your models? Something like the sinuosity index of a river. It may help the reader to grasp the variability among models.
- Section 2.2. Why have you selected the “fault” level of the Central Apennine database instead of the “trace” level? Is it a matter of model resolution (i.e., the 300 m wide fault elements)?
- Section 2.3.3. Several slip rate estimates at surface are available for the fault segments from Cupi to Mt Vettore; they cover different time intervals (e.g., post-galcial; long-term geological). Since you need to define the slip distribution to run the model, I’m wondering if considering a distribution directly derived from the surface measurements along the entire 40-km long system (instead of the distribution detailed at lines 163-170) could make an impact on the obtained results.
- Line 225: I had some difficulty in understanding the meaning of Mmax in your condition rule. One needs to know that the Mmax obtained in the models is always lower than 6.6 (i.e., M2016 + 0.1), however this info is provided later in the text
- Line 229: delete one “them”
- Line 375 (figure 10): nice image, thanks for providing this figure. I found myself moving back and forth between figures 9 and 10, to compare the regressions and the along-strike variation in rupture probability. I found it quite interesting such comparison. For instance, in the connected constant models, the trace-linear configuration seems to have a higher probability in fig 10; however, in fig 9, at Mw 6.0 the trace-trace model lies above the trace-linear. Consider the possibility to add in figure 10 a label or colored dot representing, for each model, the probability of surface rupture at Mw 6.0 extracted from figure 9.
- Lines 380-385: the surface rupture probability depends on the fault area; in the disconnected model, this is proportional to fault length. In figure 10, Mt Bove shows the highest probability. Does this depend on the adopted Mw-area relation? I mean, using the Thingbaijam et al relation, a Mw 6.0 corresponds to roughly 200 km2; with the 12-km seismogenic thickness, it means a ca. 15-km long fault. Is this the size of Mt Bove segment? Is the Mt Porche area (disconnected linear-linear model) enough to generate a Mw 6.0 event?
- Line 469: here you highlight the importance of constraining fault traces at surface. In some cases, different interpretations may be present. For instance, the CAD fault database is the result of a big effort in data harmonization by several groups which may have mapped the fault traces in a slightly different manner. Do you have any hint on how to incorporate such uncertainty into the modeling setup?
- Line 494: typo in broadest
- Lines 536-540: another factor at play to explain the lower probabilities obtained by empirical models could be the role of local properties and in particular near-surface materials. Loose sediments or weak rocks favor an accommodation of slip by tilting/warping rather than brittle fracturing.
- I acknowledge that it is beyond the scope of the paper, but as a side note I think it may be interesting to investigate the amount of surface slip in your surface rupturing events, and to see to which extent retaining only events with slip higher than (say) 5 cm moves the regressions toward higher magnitudes.
- Line 593: in figure 8 you consider earthquakes with Mw > 4.0; in figure 10 Mw > 6; in figure 12 Mw > 5.5. I understand the reasoning behind such choices, but explaining this aspect earlier in the manuscript could enhance clarity.
- Section 4.5. I agree that earthquake simulators can overcome some of the limitations of empirical datasets. However, the method applied in this paper requires quite detailed site-specific data, which may not be always available: do you think this aspect can limit the applicability of earthquake simulators for PFDHA studies? For instance, the earthquake approach in PFDHA is much more used than the displacement approach (Youngs et al 2003).
- Lines 643-644: Fault-specific analyses in PFDHA are better addressed with the displacement approach rather than the earthquake approach.
Francesca Ferrario, 4 August 2025.
Citation: https://doi.org/10.5194/egusphere-2025-3135-RC1 -
RC2: 'Comment on egusphere-2025-3135', Anonymous Referee #2, 21 Aug 2025
The probability that an earthquake becomes a surface-rupturing event is a key ingredient in probabilistic displacement hazard analysis. Robust estimates of these probabilities are limited by the scarcity of surface rupturing events. Understanding how different fault properties, such as geometry, connectivity at depth, or sinuosity, affect this probability, is hampered by the lack of detailed observations at depth. Gomez-Novell et al. bring an innovative approach to this data gap. They use rupture simulators to test the effect of different fault geometries at depth on the probability that an event becomes a surface rupturing one on the Mt Vettore fault in Italy. Their study highlights how geometry influences the probability of surface rupture and offers a pathway to incorporate inferences from simulators into PFDHA. The contribution is original and useful and I support eventual publication.
I have some minor comments that are mostly focused on improving the clarity of the article:
- Figure 2: the segmentation and smoothness degrees the authors test are very reasonable but I find the trace-trace trace-smooth etc. wording to be very confusing. I think the suite of geometries may be captured by two constraints: a segmentation (n of separate segments) constraint, and a roughness (for example, RMS roughness as used in fault roughness studies). These would describe the suite of geometries quantitatively and remove the confusion infused by the naming choices.
- Line 229 typo in extra them
- Figure 7 - I don’t understand why the connected listric would produce larger magnitude events than the connected constant - isn’t the listric geometry quite unfavorable for slip propagating into those regions?
- Figure 8 - telling these models apart visually is a bit hard. Can the authors fit a logistic regression to highlight the differences between the two end-member models? Should be easy to do since the authors do it anyway to provide the parameters in the next table and have the regressions in Fig 9.
- Line 327 - the authors point out that a and b are not the rate and state friction coefficients but the intercept and slope of the logistic fits. This is a useful consideration. They should also point out that a and b are not the parameters in the magnitude-frequency distribution, since this is another possible source of confusion given the nature of the article.
- Figure 10 - consider not using a divergent color map, since the probabilities go from 0 to 1.
- I appreciate how this article weaves the modeling results with the results from empirical studies in the literature.
- The authors could refer to Valentini et al. (2025)’s call for more model-driven advances to supplement current PFDHA approaches as part of the justification for this work.
Citation: https://doi.org/10.5194/egusphere-2025-3135-RC2 -
RC3: 'Comment on egusphere-2025-3135', Anonymous Referee #3, 22 Aug 2025
Dear editor,
Thanks for the opportunity to review “Coseismic Surface Rupture Probabilities from Earthquake Cycle Simulations: Influence of Fault Geometry” by Gomez-Novell et al. I enjoyed reading the paper; it is well written and makes some interesting points, and in my opinion is worth publishing.
I have a few high-level comments that — if addressed — could help significantly improve the paper:
- This isn’t the first paper to consider RSQSim as a useful tool for PFDHA… The authors should check out Daglish et al. (2025). The present study is much more local in focus and considers impacts of fault geometry, which Daglish et al. do not consider. However, some of the discussion by Daglish et al. may be useful to the authors, especially in the light of my other comments.
- The manuscript is overwhelmingly positive about the potential of earthquake simulators for PDFHA… Some detailed discussion of limitation (at least 1-2 paragraphs) would give a more balanced view. For example, I think it’s important to discuss uncertainties in trace location, distributed off-fault deformation and the challenges associated with identifying a primary trace.
- The authors are quite evangelical about RSQSim as a simulator and could (ideally) tone down their language slightly throughout the manuscript. I agree that RSQSim does a surprisingly good job generating realistic-looking populations of synthetic earthquakes considering how much it simplifies earthquake physics, but it is only a simple model and is definitely missing some aspects of realistic earthquake slip distributions. The authors should include discussion of the limitations of RSQSim, especially for generating earthquakes.
- I know the focus is on the influence of fault geometry, but I think the study should be expanded significantly to understand the sensitivity of surface rupture probabilities to prescribed slip distribution and rake, and the relative importance of those factors compared with fault geometry. For example, I think that the assumed — and largely unconstrained — slip-rate distribution will potentially influence the modelled earthquakes more than geometry. I couldn’t find any indication of what rakes the authors specified, but I assume pure normal… Setting a constant horizontal azimuth of extension and adjusting rakes to match that azimuth could also make a big difference to modelled earthquakes. I think those factors are really worth exploring… It is a bit of work but I think it’s important and not enough for a separate paper.
- I’m worried by the way slip-rate distributions are specified… Delogkos et al. (2023) tapered slip towards the edges of each fault segment, whereas this study tapes across the whole fault segment. I think that combined with the loading scheme, this approach will potentially lead to nucleation of very large (unrealistic) numbers of small earthquakes close to fault edges. That effect may be negated in the analysis by the minimum of 10 patched that the authors impose, but it is important to provide better visualisation of where earthquakes nucleate in the model, either in the main paper or supp info.
Thanks again for the opportunity to review.
References
Daglish, J. M.; Stahl, T.; Howell, A.; Wotherspoon, L. Advancing Regional Analysis of Road Infrastructure Exposure to Fault Displacement Hazard: A New Zealand Case Study. International Journal of Disaster Risk Reduction 2025, 105440. https://doi.org/10.1016/j.ijdrr.2025.105440.
Delogkos, E.; Howell, A.; Seebeck, H.; Shaw, B. E.; Nicol, A.; Mika Liao, Y.-W.; Walsh, J. J. Impact of Variable Fault Geometries and Slip Rates on Earthquake Catalogs From Physics-Based Simulations of a Normal Fault. Journal of Geophysical Research: Solid Earth 2023, 128 (11), e2023JB026746. https://doi.org/10.1029/2023JB026746.
Citation: https://doi.org/10.5194/egusphere-2025-3135-RC3
Data sets
RSQSim catalogues for the Monte Vettore Fault System (Central Italy) Octavi Gómez-Novell, Francesco Visini, José A. Álvarez-Gómez, Bruno Pace, Julián García-Mayordomo https://doi.org/10.5281/zenodo.15470924
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