the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Sep 2024
The Size Distributions of Faults and Earthquakes: Implications for Orogen-Internal Seismogenic Deformation
Abstract. Pre-existing geological discontinuities such as faults represent structural and mechanical discontinuities in rocks which influence earthquake processes. As earthquakes occur in the subsurface, seismogenic reactivation of pre-existing fault networks is difficult to investigate in natural settings. However, it is well-known that there exists a physical link between both faults and earthquakes since an earthquake’s magnitude is related to the ruptured fault area and therefore fault length. Furthermore, faults and earthquakes exhibit similar statistical properties, as their size distributions follow power laws.
In this study, we exploit the relation between the size distributions of faults and earthquakes to decipher the seismic deformation processes within the exhumation-related orogen-internal setting of the Southwestern Swiss Alps, which due to its well-monitored seismic activity and the excellent outcrop conditions provides an ideal study site. Characterizing the size distribution of exhumed fault networks from different tectonic units based on multi-scale drone-based mapping, we find that power law exponents of 3D fault networks generally range between 3 and 3.6. Comparing these values with the depth-dependent exponents of estimated earthquake rupture lengths, we observe significantly larger values of 5 to 8 for earthquake ruptures at shallow depths (< 3 km below sea level (BSL)). At intermediate crustal depths (~3 to 9 km BSL), the power law exponents of faults and earthquakes appear to be similar. These findings imply depth-dependent differences in the seismogenic reactivation of pre-existing faults in the study region: while partial rupturing is the prevailing deformation mechanism at shallow depths, faults are more likely to rupture along their entire length at intermediate crustal depths. Therefore, the present-day near surface differential stresses are likely insufficient to rupture entire pre-existing faults seismogenically. Our findings have direct implications for seismic hazard considerations, as earthquakes that rupture along entire faults appear to become less likely with decreasing depth.
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RC1: 'Comment on egusphere-2024-2975', Francesco Iezzi, 13 Nov 2024
The manuscript presents a thorough study on the relationships between the distribution of fault sizes and of earthquake rupture sizes. This is used for understanding fault activation processes within the brittle crust.
The work is rigorous and precise, especially in the statistical treatment of the data.
My main concern lies on how fault segmentation was dealt during the mapping of faults at multiple scales. Faults can be formed by multiple close segments, hence what can appear as a single fault at 1:1000 scale may appear as multiple smaller segments at 1:100 scale. I believe it is important to clarify this passage as this could bias the results.
I have attached a pdf with other comments on the paper.
Kind regards
Francesco Iezzi
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RC2: 'Comment on egusphere-2024-2975', Anonymous Referee #2, 29 Nov 2024
Review of a manuscript by S. Truttmann et al. (2024), Ms No.: egusphere-2024-2975,
“The Size Distributions of Faults and Earthquakes: Implications for Orogen-Internal Seismogenic Deformation”
- General comments
The manuscript by Sandro Truttmann et al. examines the relationship between fault size distributions and earthquake rupture patterns within the western Central Alps of Switzerland. They combined mapping of pre-existing discontinuities across multiple spatial scales (from outcrop to map scale; 1:10 to 1:1000) from UAV-based photogrammetry (for the outcrop scale) as well orthophotos and DEM’S available from Swisstopo (for the map scale) with earthquake data from the Swiss seismological network. After a statistical analysis of the fracture network (focusing on the fractal dimensions of the fracture network), and the earthquakes, they explored the statistical link between these independently obtained datasets and their implications for seismogenic deformation in the study area (Central Swiss Alps, characterised by pronounced post-collisional shortening, numerous highly strained tectonic nappes involving both Palaeozoic crystalline basement and Mesozoic-Paleogene sedimentary successions, and very moderate present-day seismicity and rather negligible horizontal motions as suggested by GNSS).
Their findings suggest depth-dependent differences in fault reactivation, highlighting the reduced likelihood of complete fault ruptures at shallow depths due to lower differential stresses. These insights are relevant for assessing the likelihood of induced seismicity in future geothermal energy exploration in the frontal Swiss Alps.
The paper is already very well structured and well written. Kudos to the authors for clearly elaborating their approach and methods with great detail, e.g., explain what kind of advantages the choice of a circular counting window for extracting fracture orientations and lengths has over an e.g., square counting window. The statistical analyses of the fracture network with the derivation of fractal dimensions using power-law distributions also appears very robust and reveal a large degree of details.
Overall, the study is very original and deserves publication pending minor revisions.
I have, however, a very minor comment pertaining to the nomenclature of a pivotal term in their study: the authors persistently call the discontinuities in the database they derived from the multiscale mapping approach “faults” rather than, more neutrally “fractures” (which would include all extensional discontinuities (joints, veins)).
- Specific comments
- Specific comments on the main text
line 15 ff: “we find that…”: I find this statement unclear. Which parameters around 3D fault networks show a power law behaviour? Pls clarify.
line 79: “(…) enhanced (…)”: My concern is a bit that “enhanced” might be misunderstood in terms that the events were induced, which is not what you mean to say, I guess (?).
I suppose you attempt saying that activity (i.e., frequency of events in a given timespan) is “above average” in the study area. But perhaps it’d be best to simply omit the word.
I think it’d be more important to elaborate whether all the events (with M as small as 0-1) are natural earthquakes, with e.g., quarry blasts or mining-induced events removed.
line 133: “mode I fractures“: I’d suggest to simply say “extensional fractures” instead of mode I. You have nowhere introduced mode II and III fractures for shear fractures, i.e. faults s. str. either. In my opinion, the definition of mode I, II and III has no particular relevance beyond the rock mechanical community. In structural geology it usually suffices to discriminate between extensional and shear fractures.
line 137: “slickensides”: sorry for being an ultra-picky knowitall, but a slickenside per se does not form a kinematic indicator yet. It merely tells us that - assuming Bott’s paradigm - it formed parallel to the maximum resolved shear stress acting upon a plane. But it requires extra information from asymmetric structures along those slickensides (slickenfibres, slickolites, …) to tell the slip sense.
Cetero, “i.e.” (id est) implies that you’d consider kinematic indicators and slickensides synonymous terms or at least along same hierarchical categories, which is not the case.
line 202 ff: part of the analysis to obtain the mapped fracture’s fractal dimension D involved a Maximum Likelihood estimation (MLE) that was used for fitting datasets that were normalized with the area term L^D to a power law. Was this normalization done on the previously post-processed dataset with “truncated” and “censored” fractures below and above certain thresholds removed?
line 205: “faults” should be in plural form.
line 252: please see my comment to Fig. 1, caption, below, referring to this text: Please also refer to the strike directions of dominant fracture sets in the caption, not only here.
line 285ff: Question: what if the alpha_F and the dimensionless fault density term c were calculated separately for different bedrock lithologies? Perhaps one would discern some control of the lithology after all?
lines 312 ff: Please explain that this range of values for alpha_R results from your analysis regardless which of the three scaling laws were used (L14, T17 and WC94).
I could not find a value of 3.88 for alpha_R in any of the plots for subdomains A to D in Fig. 8 at first, until I realised that there are numbers in very delicate light grey font in each bottom left panel. Some visually impaired people might find that difficult to read. Please think of improving contrasts!
Please also consider my comment left in the caption to this figure 8 below.
line 391 to 393: “active planes” and “active nodal planes”: in lines 391 and 393, you mention “active planes” and “active nodal planes”. I guess that you mean the same in both cases, i.e., the active fault plane as one of the two mutually perpendicular nodal planes of a fault plane solution. If so, please clarify that you refer to the fault plane and use the terms consistently.
line 406: don’t you simply want to say “directions”? Directivity is sthg else.
line 408: “(…) indicating a link across lithologies”: better perhaps to say more explicitly: “(…) indicating a link across various structural levels and different lithologies”.
line 414: “insensitivity of alpha_f to lithological variations”: again here, I’d suggest to insert that you refer to lithological variations across different structural levels (i.e. basement - cover separation) and not to any along-strike facies changes (N.B. even if unlikely, someone with a more stratigraphic background might erroneously assume so).
line 422: “ranges” instead of “is ranging”.
line 435: “brittle-viscous”: hello, the ultra-picky knowitall reviever is back…. ahem, perhaps better say “frictional-viscous” in my view, because this refers more to the physical deformation mechanisms in both cases, whereas “brittle” is description for the degree of spatial localisation of deformation, i.e. only deformation style rather than physically underlying principles.
- Specific comments on figures
Fig. 1: Since you refer a lot to differently oriented nodal planes and actually rupturing fault planes, as well as their kinematics (left-lateral, right lateral, etc) in the discussion of your study (5.3), it would be very worthwhile to have ideas about the prevalent stress field in the study area. Refer to e.g. the work of U. Kastrup 2004 or Houlié et al 2018*. You already cited Kastrup et al, 2004 anyway, but perhaps some synoptic representation of her main results of stress direction determinations (and their variations) on the scale of your map would be helpful.
Fig. 3: imho, you should indicate that your orientation histograms show strike directions of fractures. Please note that in the corresponding text (lines 250 ff, section 4.1.1.) you refer to the dip directions of fracture sets A_Im A_II AND A_III rather than referring to strike directions.
Fig. 8: (See also comment to text lines 312 ff)
Please explain that this range of values for alpha_R results from your analysis regardless which of the three scaling laws were used (L14, T17 and WC94).
I could not find a value of 3.88 for alpha_R in any of the plots for subdomains A to D in Fig. 8 at first, until I realised that there are numbers in very delicate light grey font in each bottom left panel. Some visually impaired people might find that difficult to read. Please think of improving contrasts!
Fig. 10: What is the separation between shallow and intermediate depth earthquake hypocenters based on? Is it a geological reason or a seismological one? Also, I suggest adding the abscissa labels for depth BSL (km) in all sub-plots a, b, c, as this will increase their legibility and emphasise their importance as “stand-alone” figures.
Fig. 11: as this is your final and concluding figure summarizing what I think is your most important finding, namely the fact that you consider that shallow crustal faults down to c. 3-4 km depth are less likely to rupture along their entire length in contrast to deeper faults (depths 5 to 9 km). In view of this, I recommend to again explain to the reader the meaning of the terms alpha_r and alpha_f. What is the parameter n(l) on the ordinate axis again? Also, be more explicit in explaining that white are pre-existing fractures and red the seismically active patches along these.
- Technical aspects
Should the authors consider my comments on Fig. 1b relevant (adding more info about the current stress state to more rapidly understand the focal mechanisms and which faults are possible active at present), they might think of adding this reference.
Houlié, N., Woessner, J., Giardini, D., & Rothacher, M. (2018). Lithosphere strain rate and stress field orientations near the Alpine arc in Switzerland. Scientific Reports, 8(1), 2018. https://doi.org/10.1038/s41598-018-20253-z
Sincerely and best wishes,
an anonymous but happy reviewer ;-)
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