the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Dec 2021
Postglacial strain rate – stress paradox, example of the Western Alps active faults
Abstract. The understanding of the origins of seismicity in intraplate regions is crucial to better characterize seismic hazards. In formerly glaciated regions such as Fennoscandia North America or the Western Alps, stress perturbations from Glacial Isostatic Adjustment (GIA) have been proposed as a major cause of large earthquakes. In this study, we focus on the Western Alps case using numerical modeling of lithosphere response to the Last Glacial Maximum icecap. We show that the flexural response to GIA induces present-day stress perturbations of ca. 1–2 MPa, associated with horizontal extension rates up to ca. 2.5 × 10−9 yr−1. The latter is in good agreement with extension rates of ca. 2 × 10−9 yr−1 derived from high-resolution geodetic (GNSS) data and with the overall seismicity deformation pattern. In the majority of simulations, stress perturbations induced by GIA promote fault reactivation in the internal massifs and in the foreland regions (i.e., positive Coulomb Failure Stress perturbation), but with predicted rakes systematically incompatible with those from earthquake focal mechanisms. Thus, although GIA explains a major part of the GNSS strain rates, it tends to inhibit the observed seismicity in the Western Alps. A direct corollary of this result is that, in cases of significant GIA effect, GNSS strain rate measurements cannot be directly integrated in seismic hazard computations, but instead require detailed modeling of the GIA transient impact.
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Interactive discussion
Status: closed
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RC1: 'Comment on se-2021-141 by Grosset et al.', Anonymous Referee #1, 25 Jan 2022
General comments
This study uses the thin elastic plate model software gFlex to calculate crustal deformation and corresponding stress changes due to ice loading in the Western Alps. Deformations are compared to GNSS data. Stress changes are then used to assess Coulomb failure stresses (CFS) and fault motion parameters at the locations of some major faults in the area. The authors find that observed vertical deformation can be explained by ongoing rebound after ice melt while observed horizontal motion can be much larger than the modelled result. Modelled fault motion does not fit observed parameters, thus the authors conclude that corresponding stresses due to ice unloading cannot explain the current seismicity pattern and rather inhibit fault motion.
I was looking forward reading this study. However, I must say that I am very disappointed now with this manuscript and its overall presentation. As far as I understand from a quick web search, this manuscript is part of a PhD study of the first author. While it looks, at first glance, well written with interesting figures, the reader easily spots a lot of irritating sloppiness when reading the text and looking more closely at the figures. Additionally, a more thorough literature search would have helped the authors putting their study and results in much better context. I will discuss my major concerns in more detail below.
As much as I would like to support and not disappoint a young student here, I am unfortunately left with a decision to reject this manuscript. You will see that my comments address the modelling performed here. The authors note occasionally that it is "simple", but from my perspective it is not appropriate for this type of research at all. At least, from what I can gather from the text. As it is presented, it is largely a black box which makes it impossible for the reader to repeat and confirm the calculations. Therefore, the conclusions must be questioned. Revising the manuscript thus goes beyond of major polishing of some parts.
Specific comments
L15ff - This statement is wrong. The references here and many related works by these authors and others explain seismicity at the end of the last glaciation with corresponding stresses due to glacial isostatic adjustment (GIA), not the recent seismicity. As far as I am aware of, only Brandes et al. (2015, 2019) suggest a potential link with historic and recent seismicity in northern Central Europe, but that it is due to stress build-up after previous stress release (Brandes et al. 2015) or deeper crustal stress changes (Brandes et al. 2019) in an area outside the formerly glaciated area. Please also have a look at Ojala et al. (2018) for phases of enlarged seismic activity in Fennoscandia and see further discussion of this subject in Olesen et al. (2021).
L19 - I do not understand these rapid decay times of 103-105 years and to what they relate. Please explain!
L20 - Where do these numbers come from? Please add reference, but also have a look at Arvidsson (1996) and Ojala et al. (2018).
L21 - This statement neglects the importance of stress migration due to the viscoelastic nature of the mantle, see e.g. Steffen et al. (2021). Even an icecap like the one previously covering the Alps has sensed the mantle - thus a thin plate model misses this contribution to the overall stress change.
L36 - The important studies by Sella et al. (2007), Peltier et al. (2015), Simon et al. (2016) and Robin et al. (2020) for North America seem much more appropriate for being cited here than the PhD thesis by Tarayoun (which is mainly written in French). You may also consider substituting Johansson et al. (2002) with very recent studies for Fennoscandia by Kierulf et al. (2021) or Lahtinen et al. (2022).
L47 - Please mark these earthquakes with a special symbol in Figure 2a.
L52 - Please mark these faults with names in Figure 2b.
L67 - Unclear to me why 150-200 km is appropriate. Please provide good reasoning for the reader. This comes out of nowhere. Looking at Fig. A2, 120 km Gaussian make it even smoother, so perhaps 100 or 105 km Gaussian radius would perhaps give a better fit to the model result.
L83ff - A thin plate method that uses elastic plate thickness Te is not appropriate for GIA investigations. Te describes a physical property (material parameter) of the lithosphere with the unit in km. Te characterizes the strength of the plate to long-term loading in terms of millions of years. GIA is a much shorter, though not a short-term loading process, and leads to a "dynamic" change in Te - so Te cannot be longer used as constant.
L88ff - Your model description is insufficient. All input parameters should be explained and a table should be added with all values.
L90 - Unclear how this ice load model is implemented: What is the resolution of the model in time and space? How do you account for the 3D ice thickness variation in your 2D planar model?
L91 - Unclear why you remove the ice instantaneously. Do you use the ice load model from Mey et al. (2016) or do you just use the LGM limits and put 2 km of ice in there, which you remove at once at 15 kyr BP? That would have nothing to do with the glaciation history and give you misleading results. Unclear why LGM is at 15 kyr BP? Mey et al. (2016) clearly state that maximum extent was at 21 kyr BP with rapid thinning thereafter. Please explain carefully what you did here, especially which ice load model was implemented in which form (time and space)!
L94 - This is not a GIA model. It is a thin plate model with a loading function. The important stress migration contribution from the mantle to the lithosphere is missing.
L102 - Please show the results of all parameter combinations, e.g. in the Appendix.
L113 - Stresses should be investigated at the depth of main seismicity, not at the plate top (surface) as GIA stresses are not constant with depth.
L118 - These stresses appear to be too big given the ice thicknesses indicated in Mey et al. (2016), which are in large parts much less than 1000 meters, and given your preferred decay rates. Based on them not much depression should be left and thus impounded flexural stresses must have almost ceased. Doesn't seem logical. Please provide a map of the horizontal and Coulomb failure stresses and selected graphs for some locations of interest (faults). Also guide the reader what these numbers represent so that they cannot be misunderstood. If the stress values you provide would be related to the Laurentian or Scandinavian ice sheets, their formerly glaciated areas would be scattered with faults - but they aren't.
L128 - Suggest rephrasing to 'would account'.
L130ff - Strongly suggest to rephrase to a very careful tone as all these conclusions are based on a very, very simple model not reflecting GIA.
L141f - Sentence does not make sense.
L146 - Equation is wrong. Either ΔCFS = Δτ - μ' Δσn or CFS = τ - μ' σn, but not mixed.
L152 - Wrong definition here. Switch < and > symbols.
L162 - near-vertical fault dips mean ca. 90° dip, which you did not test. Please rephrase.
L167 - rake is defined from -180° to +180°, so a rake of 180°±20° doesn't make sense. Please rephrase.
L183ff - You are discussing results based on a very, very simple model that actually does not reflect the process you aimed at investigating. In my view, there is no paradox at all. For a thorough discussion, you should show ΔCFS over time from before glaciation to today. Then you should be aware of the fact that when ΔCFS reaches instability, a pre-existing fault is likely to move if the fault orientations favor it (see e.g. Steffen & Steffen 2021). This will lead to a stress drop. I suppose this very likely happened to many faults in the Western Alps during and/or soon after deglaciation. Since then, most, if not all, fault activity is likely related to other processes than GIA. This is what is discussed in e.g. Olesen et al. (2021). Given the size, thickness and history of the Alpine Icecap it is very unlikely that such GIA-induced stress build-up as discussed in Brandes et al. (2015) happened here. This should be investigated in future, of course, but definitely not with a thin plate model. I also miss a discussion in view of the findings of Keiding et al. (2015), who compare strain rates and seismicity in Fennoscandia.
Figure 1 - this is only a very simple sketch. Stress is not constant with depth, among others. Please revise carefully, see e.g. Steffen et al. (2021).
Figures 4 & 5 - Please draw ice extent at LGM and of the last glaciation time step in 4a and 5a. Although I understand that the modeling results do not provide a large range of rakes, it'd be helpful if you show 4b and 5b for different µ. Please also show a plot where the ranges of different models are mapped.
I could not access the model code. The given link led to 404 error.
Technical corrections
- L2 - comma missing after Fennoscandia
- L34 - Network should be System
- L59 - Strange unit style. Use mm/yr, mm*yr-1 or mm yr-1.
- L63 and throughout ms - diacritical mark should by en-dash
- L85 - use correct font for wm
- L90 - LGM abbreviation not introduced yet
- L110 - 15 km (space missing)
- L156 - please explain BDFA
- L165ff - degree symbol (°) missing
- All figures - enlarge to page width
- Figure 3 - center scale for 3a (zero should be white, not 0.5).
References
- Arvidsson, R. (1996). Fennoscandian earthquakes: Whole crustal rupturing related to postglacial rebound. Science 274(5288), 744-746, doi:10.1126/science.274.5288.744.
- Brandes, C., Steffen, H., Steffen, R., Wu, P. (2015). Intraplate seismicity in northern Central Europe is induced by the last glaciation. Geology 43(7), 611–614, doi:10.1130/G36710.1.
- Brandes C., Plenefisch T., Tanner D.T., Gestermann N., Steffen H. (2019). Evaluation of deep crustal earthquakes in northern Germany – Possible tectonic causes. Terra Nova 31 (2), 83–93, doi:10.1111/ter.12372.
- Keiding, M., Kreemer, C., Lindholm, C.D., Gradmann, S., Olesen, O., Kierulf, H.P. (2015). A comparison of strain rates and seismicity for Fennoscandia: depth dependency of deformation from glacial isostatic adjustment. Geophys. J. Int. 202(2), 1021–1028, doi:10.1093/gji/ggv207.
- Kierulf, H.P., Steffen, H., Barletta, V.R., Lidberg, M., Johansson, J., Kristiansen, O., Tarasov, L. (2021). A GNSS velocity field for geophysical applications in Fennoscandia. J. Geodyn. 146, 101845, doi:10.1016/j.jog.2021.101845.
- Lahtinen, S., Jivall, L., Häkli, P., Nordman, M. (2022). Updated GNSS velocity solution in the Nordic and Baltic countries with a semi-automatic offset detection method. GPS Solut. 26, 9, doi:10.1007/s10291-021-01194-z.
- Mey, J., Scherler, D., Wickert, A., Egholm, D.L., Tesauro, M., Schildgen, T.F., Strecker, M.R. (2016). Glacial isostatic uplift of the European Alps. Nat. Commun. 7, 13382, doi:10.1038/ncomms13382.
- Ojala, A.E., Markovaara-Koivisto, M., Middleton, M., Ruskeeniemi, T., Mattila, J., Sutinen, R. (2018). Dating of paleolandslides in western Finnish Lapland. Earth Surf. Process. Landf. 43, 2449–2462, doi:10.1002/esp.4408.
- Olesen, O., Steffen, H., Sutinen, R. (2021). Future Research on Glacially Triggered Faulting and Intraplate Seismicity. In: Steffen, H., Olesen, O. & Sutinen, R. (eds.) Glacially-Triggered Faulting, Cambridge University Press, Cambridge, 419–428, doi:10.1017/9781108779906.032.
- Peltier, W.R., Argus, D.F., Drummond, R. (2015). Space Geodesy Constrains Ice Age Terminal Deglaciation: The Global ICE-6G_C (VM5a) Model. J. Geophys. Res. Solid Earth, 120, 450–487, doi:10.1002/2014JB011176.
- Robin, C.M.I., Craymer, M., Ferland, R., James, T.S., Lapelle, E., Piraszewski, M., Zhao, Y. (2020). NAD83v70VG: A New National Crustal Velocity Model for Canada. Geomatics Canada, Open File 62, 70 pp., doi:10.4095/327592.
- Sella, G.F., Stein, S., Dixon, T.H., Craymer, M., James, T.S., Mazzotti, S., Dokka, R.K. (2007). Observation of glacial isostatic adjustment in “stable” North America with GPS. Geophys. Res. Lett., 34, L02306, doi:10.1029/2006GL027081.
- Simon, K.M., James, T.S., Henton, J.A., Dyke, A.S. (2016). A glacial isostatic adjustment model for the central and northern Laurentide Ice Sheet based on relative sea level and GPS measurements. Geophys. J. Int. 205, 1618–1636, doi:10.1093/gji/ggw103.
- Steffen, R., Steffen, H. (2021). Reactivation of non-optimally orientated faults due to glacially induced stresses. Tectonics 40(11), e2021TC006853, doi:10.1029/2021TC006853.
- Steffen, R., Wu, P., Lund, B. (2021). Geomechanics of glacially triggered faulting. In: Steffen, H., Olesen, O. & Sutinen, R. (eds.) Glacially-Triggered Faulting, Cambridge University Press, Cambridge, 20–40, doi:10.1017/9781108779906.004.
Citation: https://doi.org/10.5194/se-2021-141-RC1 -
AC1: 'Reply on RC1', Juliette Grosset, 03 Feb 2022
Dear editor, dear colleagues,
We wish to provide a quick comment in response to review RC1. Although we recognize (and will address) many of the reviewer’s comments regarding the lack of details and specifics in our manuscript, we wish to rebut the main comment regarding the appropriateness of the model that we use here. This model (thin elastic plate over a uniform viscous medium) is indeed very simple, but contrary to the reviewer’s comment, we are convinced that it provides appropriate information and results for the Alpine GIA study. For several reasons:
- Such a model has already been used, including in recent publications for this kind of study (e.g., Mey et al., 2016; Sternai et al. 2019).
- Although it lacks the technical developments of more complex GIA models, the thin-plate model provides reasonable first-order predictions of deformation and stress that are enough to address the point made in our study (apparent opposition between extensive strain rates and compressive stress).
- The issue of stress migration pointed out by the reviewer is primarily a function of the sensitivity to mantle visco-elastic behavior. In the Western Alps, the small size of the icecap limits this sensitivity to the uppermost mantle, at most, and thus the potential stress migration issue is likely very small if not negligible (e.g., Steffen et al., 2015).
- Finally, on a more general note, we wish to point out that a model is as valid as any other models as long as it provides realistic testable predictions based on physically sound hypothesis. Simply stating that a contribution is “missing” does not render a model inappropriate.
We are in the process of running several finite-element models to show that, in this particular study, the thin-plate model provides useful predictions and that our conclusions are robust. Once these tests are done, we hope that we will have the opportunity to provide a detailed reply to the reviewer’s comments.
References
Mey, J., Scherler, D., Wickert, A. D., Egholm, D. L., Tesauro, M., Schildgen, T. F., and Strecker, M. R.: Glacial isostatic uplift of the European Alps, Nature Communications, 7, 1–9, https://doi.org/10.1038/ncomms13382, 2016.
Steffen, R., Steffen, H., Wu, P., and Eaton, D. W.: Reply to comment by Hampel et al. on “Stress and fault parameters affecting fault slip magnitude and activation time during a glacial cycle,” Tectonics, 34, 2359–2366, https://doi.org/10.1002/2015TC003992, 2015.
Sternai, P., Sue, C., Husson, L., Serpelloni, E., Becker, T. W., Willett, S. D., Faccenna, C., Di Giulio, A., Spada, G., Jolivet, L., Valla, P., Petit, C., Nocquet, J.-M., Walpersdorf, A., and Castelltort, S.: Present-day uplift of the European Alps: Evaluating mechanisms and models of their relative contributions, Earth-Science Reviews, 190, 589–604, https://doi.org/10.1016/j.earscirev.2019.01.005, 2019.
Citation: https://doi.org/10.5194/se-2021-141-AC1
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RC2: 'Comment on se-2021-141', Björn Lund, 22 Feb 2022
Please find enclosed my review of Grosset, Mazzotti and Vernant, "Postglacial strain rate - stress paradox, example of the Western Alps active faults". The manuscript analyzes the response of the Western Alps region to the deglaciation of the latest ice sheet covering the region. The authors use a simple model of glacial isostatic adjustment (GIA) to estimate stress and strain in the Earth and compare that to GNSS data and earthquake focal mechanisms. This is an interesting study which goes all the way to the slip directions in the earthquakes to compare how the stress induced by GIA affects current day seismicity. I think this a very worth while study, however, there are issues with the GIA modelling and the fault stability estimates that need further work. I therefore recommend major revision.
Björn Lund
Uppsala University
Main comments:
1. Modelling GIA stress and strain.
(a)The thin plate/viscous mantle approach used for the modelling is a significant simplification of the GIA modelling problem and does not take into account stress redistribution due to the mantle (e.g. Wu, 1992; Steffen et al. 2015). Even for a relatively small ice sheet, such as the Alpine in this study, the mantle will be invoked (e.g. Arnadottir et al., 2009 used a more complex GIA model for current deglaciation in Iceland), especially for the elastic plate thicknesses found in the manuscript, with a best fit Te of 10 - 20 km. How large this effect is depends on the ice sheet configuration, the elastic parameters including Te and the viscosity of the mantle, but also the depth of interest in the model. At seismogenic depths in a 10 km thin plate it is not unlikely that the mantle stress redistribution is rather important. The authors should evaluate this by comparing to a more realistic GIA simulation tool.(b) Write out the parameters used to calculate the flexural parameter and the relaxation time, i.e. Young's and shear modulus, viscosity etc. How large is the model domain and what are the boundary conditions, which are important for stress estimates?
(c) There is very little description of the ice model, it is not even included in its entirety in Figure 3. What is the temporal behaviour of the ice sheet (plot ice volume and maximum ice thickness through time) and how is it implemented in the model? Do you use the full ice sheet? How do you start the ice model? A full load in equilibrium at LGM will not capture the transient behaviour of the GIA response, as it is unlikely that the Earth is in flexural equilibrium at the LGM.
(d) Extracting the GIA induced stress field from the top of the elastic plate does indeed give you a maximum stress signal, but it is not very realistic as the earth model almost certainly is too stiff near the surface, not taking near-surface fracturing into account. Also, I guess earthquakes in the region rarely occur in the uppermost 1-2 kilometers? With best fitting GIA models of Te 10 - 20 km, and seismicity down to 15 km depth, it is unclear to me why the near-surface stress field should be the most appropriate to use. On the contrary, below 10 km in a 20 km elastic plate stresses go from compressive to tensile.
(e) The model domain contains significant topography, from the Mediterranean to Mont Blanc. Therefore probably also a significant root. I guess that affects the flexure of the area. It would be nice with some discussion of this.
2. GIA and fault stability.
The Coulomb Failure Stress, CFS, is widely used when estimating how a stress change affects faults, promoting or demoting stability. However, using the change in CFS (D_CFS) with shear and normal stresses estimated from some external process, like GIA in this case, may lead you wrong. Unless the shear and normal stress changes occur in the directions of the pre-existing shear and normal stresses, the full stress tensor has to be taken into account. As the GIA induced stresses are significantly smaller than the in-situ stress even at LGM, at depths of more than 1-2 km, it is unlikely that the GIA stresses change the directions of the in-situ principal stresses, so the effect of the combined stress field needs to be considered, see e.g. Lund et al. (2009). This is of course tricky if you do not know the what the stress field without the GIA component looks like. Since the present day GIA stresses are very small compared to the in-situ stress it would have been interesting to see the focal mechanisms, or even better a stress inversion of the focal mechanisms, to get an idea of the current stress field. This issue needs to be addressed, and discussed, as it affects the results of section 4. As an example, for the Belledonne fault GIA predicts reverse faulting while the mechanisms show strike-slip. So GIA does not drive seismicity on its own, but perhaps GIA adds that extra bit of stress that pushes the fault into instability? Such that the seismic activity is larger than it would have been without GIA. Or, oppositely lower?
Further, on line:15: Reference for "plate tectonics cannot be the main source of SCR seismicity." That is not generally correct.
16: Need to define "recent", as today's seismicity in Fennoscandia is very much tectonics driven (e.g. Bungum et al, 2010) whereas the late/end-glacial was very much influenced by GIA.
18: Add Wu et al., 1999 or Lund et al. 2009 for Fennoscandia.
19: "Rapid decay in 103 - 105 yr"? Please explain what you mean, and give a reference. The timing of the Fennoscandian postglacial earthquakes are very uncertain and associated with the time just be fore ice retreat from a location, during ice retreat and just after, at the various locations. This gives a span of at least 1,000 years for the about a dozen ruptures, perhaps more as the exact time of ice free conditions are uncertain.
20: The Pärvie earthquake may have bee as large as Mw 8.0 (Lindblom et al., 2015).
41: You should comment on Keiding et al. (2015) who did a similar study for Fennoscandia. And also had problems reconciling the GNSS data, GIA and seismicity.
62, 66: Not sure if there is a problem with my pdf-viewer, but there is a different sign than a decimal dot in 1.2. Aha, it should be a hyphen?
66: Figure 3a shows the vertical velocities, which is perhaps not a good indicator of the size and variation in horizontal velocities, making up the strain rate field. How large are the uncertainties in the velocities, and propagated to your strain rates?
85: "wm" ? OK, I see. Write it in italics.
116 and Fig 3: Please add the outline of the maximum ice sheet to Fig 3a as well. How well does the current vertical GNSS velocities agree with the ice edge and the concept of a forebulge?
118: 50 MPa of horizontal compression under a 2 km (18 MPa) thick ice? That is a very high number.
120: GIA in Fig 3C.
122: The difference between GNSS and GIA strain rates in Fig 3 could be shown with for example bow tie plots, which would make the comparison much easier.
139: Indicate that you discuss present time(?).
143: Maximum horizontal GIA stress?
146-147: With DeltaCFS you should use Delta_tau and Delta_sigma_n, and therefore also the change in shear stress and the change in normal stress.
158: "...predicted rates are compared..."
206-209: This sentence is a little unclear. The ice adds a large vertical stress, the lithosphere slowly flexes inducing horizontal stresses. The increase in average stress increases fault stability. The rapid melting of the ice, compared to the Earth's rebound, decreases vertical stress faster than horizontal stress, resulting in an induced reverse stress state. Combined with a pre-existing reverse stress state, in a similar direction as in Fennoscandia, the process destabilizes faults. See Lund et al. (2009). Then we have the added action of strain accumulation during 50 - 60 kyr of ice cover, which adds to the horisontal stress/strain.
Figures:
3) Indicate that this is present time for 3c. The arrows in 3c are virtually impossible to see, and even the ones in 3b are difficult in many areas. Perhaps have different scales in b and c, with a large legend and the caption pointing out the difference? A factor of 2 difference could make the comparison easier? As you show vertical velocities in 3a, perhaps point out that you show horizontal strain rates. Add a scale bar to the figures, as the text explicitly talks about 90 km half-width filtering and 150-200km wavelength signals.
4 and 5) Add that this is the present day stress field. It would be good to have the extent of the ice sheet on these maps as well.
A3) The symbols are very difficult to see, even at 300% magnification on my screen.
References
Arnadóttir, T., Lund, B., Jiang, W., Geirsson, H., Björnsson, H., Einarsson, P., Sigurdsson, T., 2009. Glacial rebound and plate spreading: results from the first countrywide GPS observations in Iceland. Geophys. J. Int. 177 (2), 691–716, doi: 10.1111/j.1365-246X.2008.04059.xBungum, H., Pascal, C., Olesen et al. (2010). To what extent is the present seismicity of Norway driven by postglacial rebound? Journal of the Geological Society of London, 167, 373–384, doi.org/10.1144/0016-76492009-009.
Lund, B., Schmidt, P. and Hieronymus, C. (2009). Stress Evolution and Fault Stability during the Weichselian Glacial Cycle. SKB Technical Report TR-09-15, Swedish Nuclear Fuel and Waste Management Co., Stockholm, 106 pp. https://www.skb.com/publication/1968408/TR-09-15.pdf
Keiding, M., Kreemer, C., Lindholm, C. D. et al. (2015). A comparison of strain rates and seismicity for Fennoscandia: depth dependency of deformation from glacial isostatic adjustment. Geophysical Journal International, 202, 1021–1028, doi.org/10.1093/gji/ggv207.
Lindblom, E., Lund, B., Tryggvason, A. et al. (2015). Microearthquakes illuminate the deep structure of the endglacial Pärvie fault, northern Sweden. Geophysical Journal International, 201, 1704–1716, doi.org/10.1093/gji/ggv112.
Steffen, R., Steffen, H., Wu, P., and Eaton, D. W. (2015) Reply to comment by Hampel et al. on “Stress and fault parameters affecting fault slip magnitude and activation time during a glacial cycle,” Tectonics, 34, 2359–2366, https://doi.org/10.1002/2015TC003992.
Wu, P. (1992). Viscoelastic vs. viscous deformation and the advection of pre-stress. Geophysical Journal International, 108, 35–51, doi.org/10.1111/j.1365-246X.1992.tb00844.x.
Wu, P., Johnston, P. and Lambeck, K. (1999). Postglacial rebound and fault instability in Fennoscandia. Geophysical Journal International, 139, 657–670, doi.org/10.1046/j.1365-246x.1999.00963.x.
Citation: https://doi.org/10.5194/se-2021-141-RC2
Interactive discussion
Status: closed
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RC1: 'Comment on se-2021-141 by Grosset et al.', Anonymous Referee #1, 25 Jan 2022
General comments
This study uses the thin elastic plate model software gFlex to calculate crustal deformation and corresponding stress changes due to ice loading in the Western Alps. Deformations are compared to GNSS data. Stress changes are then used to assess Coulomb failure stresses (CFS) and fault motion parameters at the locations of some major faults in the area. The authors find that observed vertical deformation can be explained by ongoing rebound after ice melt while observed horizontal motion can be much larger than the modelled result. Modelled fault motion does not fit observed parameters, thus the authors conclude that corresponding stresses due to ice unloading cannot explain the current seismicity pattern and rather inhibit fault motion.
I was looking forward reading this study. However, I must say that I am very disappointed now with this manuscript and its overall presentation. As far as I understand from a quick web search, this manuscript is part of a PhD study of the first author. While it looks, at first glance, well written with interesting figures, the reader easily spots a lot of irritating sloppiness when reading the text and looking more closely at the figures. Additionally, a more thorough literature search would have helped the authors putting their study and results in much better context. I will discuss my major concerns in more detail below.
As much as I would like to support and not disappoint a young student here, I am unfortunately left with a decision to reject this manuscript. You will see that my comments address the modelling performed here. The authors note occasionally that it is "simple", but from my perspective it is not appropriate for this type of research at all. At least, from what I can gather from the text. As it is presented, it is largely a black box which makes it impossible for the reader to repeat and confirm the calculations. Therefore, the conclusions must be questioned. Revising the manuscript thus goes beyond of major polishing of some parts.
Specific comments
L15ff - This statement is wrong. The references here and many related works by these authors and others explain seismicity at the end of the last glaciation with corresponding stresses due to glacial isostatic adjustment (GIA), not the recent seismicity. As far as I am aware of, only Brandes et al. (2015, 2019) suggest a potential link with historic and recent seismicity in northern Central Europe, but that it is due to stress build-up after previous stress release (Brandes et al. 2015) or deeper crustal stress changes (Brandes et al. 2019) in an area outside the formerly glaciated area. Please also have a look at Ojala et al. (2018) for phases of enlarged seismic activity in Fennoscandia and see further discussion of this subject in Olesen et al. (2021).
L19 - I do not understand these rapid decay times of 103-105 years and to what they relate. Please explain!
L20 - Where do these numbers come from? Please add reference, but also have a look at Arvidsson (1996) and Ojala et al. (2018).
L21 - This statement neglects the importance of stress migration due to the viscoelastic nature of the mantle, see e.g. Steffen et al. (2021). Even an icecap like the one previously covering the Alps has sensed the mantle - thus a thin plate model misses this contribution to the overall stress change.
L36 - The important studies by Sella et al. (2007), Peltier et al. (2015), Simon et al. (2016) and Robin et al. (2020) for North America seem much more appropriate for being cited here than the PhD thesis by Tarayoun (which is mainly written in French). You may also consider substituting Johansson et al. (2002) with very recent studies for Fennoscandia by Kierulf et al. (2021) or Lahtinen et al. (2022).
L47 - Please mark these earthquakes with a special symbol in Figure 2a.
L52 - Please mark these faults with names in Figure 2b.
L67 - Unclear to me why 150-200 km is appropriate. Please provide good reasoning for the reader. This comes out of nowhere. Looking at Fig. A2, 120 km Gaussian make it even smoother, so perhaps 100 or 105 km Gaussian radius would perhaps give a better fit to the model result.
L83ff - A thin plate method that uses elastic plate thickness Te is not appropriate for GIA investigations. Te describes a physical property (material parameter) of the lithosphere with the unit in km. Te characterizes the strength of the plate to long-term loading in terms of millions of years. GIA is a much shorter, though not a short-term loading process, and leads to a "dynamic" change in Te - so Te cannot be longer used as constant.
L88ff - Your model description is insufficient. All input parameters should be explained and a table should be added with all values.
L90 - Unclear how this ice load model is implemented: What is the resolution of the model in time and space? How do you account for the 3D ice thickness variation in your 2D planar model?
L91 - Unclear why you remove the ice instantaneously. Do you use the ice load model from Mey et al. (2016) or do you just use the LGM limits and put 2 km of ice in there, which you remove at once at 15 kyr BP? That would have nothing to do with the glaciation history and give you misleading results. Unclear why LGM is at 15 kyr BP? Mey et al. (2016) clearly state that maximum extent was at 21 kyr BP with rapid thinning thereafter. Please explain carefully what you did here, especially which ice load model was implemented in which form (time and space)!
L94 - This is not a GIA model. It is a thin plate model with a loading function. The important stress migration contribution from the mantle to the lithosphere is missing.
L102 - Please show the results of all parameter combinations, e.g. in the Appendix.
L113 - Stresses should be investigated at the depth of main seismicity, not at the plate top (surface) as GIA stresses are not constant with depth.
L118 - These stresses appear to be too big given the ice thicknesses indicated in Mey et al. (2016), which are in large parts much less than 1000 meters, and given your preferred decay rates. Based on them not much depression should be left and thus impounded flexural stresses must have almost ceased. Doesn't seem logical. Please provide a map of the horizontal and Coulomb failure stresses and selected graphs for some locations of interest (faults). Also guide the reader what these numbers represent so that they cannot be misunderstood. If the stress values you provide would be related to the Laurentian or Scandinavian ice sheets, their formerly glaciated areas would be scattered with faults - but they aren't.
L128 - Suggest rephrasing to 'would account'.
L130ff - Strongly suggest to rephrase to a very careful tone as all these conclusions are based on a very, very simple model not reflecting GIA.
L141f - Sentence does not make sense.
L146 - Equation is wrong. Either ΔCFS = Δτ - μ' Δσn or CFS = τ - μ' σn, but not mixed.
L152 - Wrong definition here. Switch < and > symbols.
L162 - near-vertical fault dips mean ca. 90° dip, which you did not test. Please rephrase.
L167 - rake is defined from -180° to +180°, so a rake of 180°±20° doesn't make sense. Please rephrase.
L183ff - You are discussing results based on a very, very simple model that actually does not reflect the process you aimed at investigating. In my view, there is no paradox at all. For a thorough discussion, you should show ΔCFS over time from before glaciation to today. Then you should be aware of the fact that when ΔCFS reaches instability, a pre-existing fault is likely to move if the fault orientations favor it (see e.g. Steffen & Steffen 2021). This will lead to a stress drop. I suppose this very likely happened to many faults in the Western Alps during and/or soon after deglaciation. Since then, most, if not all, fault activity is likely related to other processes than GIA. This is what is discussed in e.g. Olesen et al. (2021). Given the size, thickness and history of the Alpine Icecap it is very unlikely that such GIA-induced stress build-up as discussed in Brandes et al. (2015) happened here. This should be investigated in future, of course, but definitely not with a thin plate model. I also miss a discussion in view of the findings of Keiding et al. (2015), who compare strain rates and seismicity in Fennoscandia.
Figure 1 - this is only a very simple sketch. Stress is not constant with depth, among others. Please revise carefully, see e.g. Steffen et al. (2021).
Figures 4 & 5 - Please draw ice extent at LGM and of the last glaciation time step in 4a and 5a. Although I understand that the modeling results do not provide a large range of rakes, it'd be helpful if you show 4b and 5b for different µ. Please also show a plot where the ranges of different models are mapped.
I could not access the model code. The given link led to 404 error.
Technical corrections
- L2 - comma missing after Fennoscandia
- L34 - Network should be System
- L59 - Strange unit style. Use mm/yr, mm*yr-1 or mm yr-1.
- L63 and throughout ms - diacritical mark should by en-dash
- L85 - use correct font for wm
- L90 - LGM abbreviation not introduced yet
- L110 - 15 km (space missing)
- L156 - please explain BDFA
- L165ff - degree symbol (°) missing
- All figures - enlarge to page width
- Figure 3 - center scale for 3a (zero should be white, not 0.5).
References
- Arvidsson, R. (1996). Fennoscandian earthquakes: Whole crustal rupturing related to postglacial rebound. Science 274(5288), 744-746, doi:10.1126/science.274.5288.744.
- Brandes, C., Steffen, H., Steffen, R., Wu, P. (2015). Intraplate seismicity in northern Central Europe is induced by the last glaciation. Geology 43(7), 611–614, doi:10.1130/G36710.1.
- Brandes C., Plenefisch T., Tanner D.T., Gestermann N., Steffen H. (2019). Evaluation of deep crustal earthquakes in northern Germany – Possible tectonic causes. Terra Nova 31 (2), 83–93, doi:10.1111/ter.12372.
- Keiding, M., Kreemer, C., Lindholm, C.D., Gradmann, S., Olesen, O., Kierulf, H.P. (2015). A comparison of strain rates and seismicity for Fennoscandia: depth dependency of deformation from glacial isostatic adjustment. Geophys. J. Int. 202(2), 1021–1028, doi:10.1093/gji/ggv207.
- Kierulf, H.P., Steffen, H., Barletta, V.R., Lidberg, M., Johansson, J., Kristiansen, O., Tarasov, L. (2021). A GNSS velocity field for geophysical applications in Fennoscandia. J. Geodyn. 146, 101845, doi:10.1016/j.jog.2021.101845.
- Lahtinen, S., Jivall, L., Häkli, P., Nordman, M. (2022). Updated GNSS velocity solution in the Nordic and Baltic countries with a semi-automatic offset detection method. GPS Solut. 26, 9, doi:10.1007/s10291-021-01194-z.
- Mey, J., Scherler, D., Wickert, A., Egholm, D.L., Tesauro, M., Schildgen, T.F., Strecker, M.R. (2016). Glacial isostatic uplift of the European Alps. Nat. Commun. 7, 13382, doi:10.1038/ncomms13382.
- Ojala, A.E., Markovaara-Koivisto, M., Middleton, M., Ruskeeniemi, T., Mattila, J., Sutinen, R. (2018). Dating of paleolandslides in western Finnish Lapland. Earth Surf. Process. Landf. 43, 2449–2462, doi:10.1002/esp.4408.
- Olesen, O., Steffen, H., Sutinen, R. (2021). Future Research on Glacially Triggered Faulting and Intraplate Seismicity. In: Steffen, H., Olesen, O. & Sutinen, R. (eds.) Glacially-Triggered Faulting, Cambridge University Press, Cambridge, 419–428, doi:10.1017/9781108779906.032.
- Peltier, W.R., Argus, D.F., Drummond, R. (2015). Space Geodesy Constrains Ice Age Terminal Deglaciation: The Global ICE-6G_C (VM5a) Model. J. Geophys. Res. Solid Earth, 120, 450–487, doi:10.1002/2014JB011176.
- Robin, C.M.I., Craymer, M., Ferland, R., James, T.S., Lapelle, E., Piraszewski, M., Zhao, Y. (2020). NAD83v70VG: A New National Crustal Velocity Model for Canada. Geomatics Canada, Open File 62, 70 pp., doi:10.4095/327592.
- Sella, G.F., Stein, S., Dixon, T.H., Craymer, M., James, T.S., Mazzotti, S., Dokka, R.K. (2007). Observation of glacial isostatic adjustment in “stable” North America with GPS. Geophys. Res. Lett., 34, L02306, doi:10.1029/2006GL027081.
- Simon, K.M., James, T.S., Henton, J.A., Dyke, A.S. (2016). A glacial isostatic adjustment model for the central and northern Laurentide Ice Sheet based on relative sea level and GPS measurements. Geophys. J. Int. 205, 1618–1636, doi:10.1093/gji/ggw103.
- Steffen, R., Steffen, H. (2021). Reactivation of non-optimally orientated faults due to glacially induced stresses. Tectonics 40(11), e2021TC006853, doi:10.1029/2021TC006853.
- Steffen, R., Wu, P., Lund, B. (2021). Geomechanics of glacially triggered faulting. In: Steffen, H., Olesen, O. & Sutinen, R. (eds.) Glacially-Triggered Faulting, Cambridge University Press, Cambridge, 20–40, doi:10.1017/9781108779906.004.
Citation: https://doi.org/10.5194/se-2021-141-RC1 -
AC1: 'Reply on RC1', Juliette Grosset, 03 Feb 2022
Dear editor, dear colleagues,
We wish to provide a quick comment in response to review RC1. Although we recognize (and will address) many of the reviewer’s comments regarding the lack of details and specifics in our manuscript, we wish to rebut the main comment regarding the appropriateness of the model that we use here. This model (thin elastic plate over a uniform viscous medium) is indeed very simple, but contrary to the reviewer’s comment, we are convinced that it provides appropriate information and results for the Alpine GIA study. For several reasons:
- Such a model has already been used, including in recent publications for this kind of study (e.g., Mey et al., 2016; Sternai et al. 2019).
- Although it lacks the technical developments of more complex GIA models, the thin-plate model provides reasonable first-order predictions of deformation and stress that are enough to address the point made in our study (apparent opposition between extensive strain rates and compressive stress).
- The issue of stress migration pointed out by the reviewer is primarily a function of the sensitivity to mantle visco-elastic behavior. In the Western Alps, the small size of the icecap limits this sensitivity to the uppermost mantle, at most, and thus the potential stress migration issue is likely very small if not negligible (e.g., Steffen et al., 2015).
- Finally, on a more general note, we wish to point out that a model is as valid as any other models as long as it provides realistic testable predictions based on physically sound hypothesis. Simply stating that a contribution is “missing” does not render a model inappropriate.
We are in the process of running several finite-element models to show that, in this particular study, the thin-plate model provides useful predictions and that our conclusions are robust. Once these tests are done, we hope that we will have the opportunity to provide a detailed reply to the reviewer’s comments.
References
Mey, J., Scherler, D., Wickert, A. D., Egholm, D. L., Tesauro, M., Schildgen, T. F., and Strecker, M. R.: Glacial isostatic uplift of the European Alps, Nature Communications, 7, 1–9, https://doi.org/10.1038/ncomms13382, 2016.
Steffen, R., Steffen, H., Wu, P., and Eaton, D. W.: Reply to comment by Hampel et al. on “Stress and fault parameters affecting fault slip magnitude and activation time during a glacial cycle,” Tectonics, 34, 2359–2366, https://doi.org/10.1002/2015TC003992, 2015.
Sternai, P., Sue, C., Husson, L., Serpelloni, E., Becker, T. W., Willett, S. D., Faccenna, C., Di Giulio, A., Spada, G., Jolivet, L., Valla, P., Petit, C., Nocquet, J.-M., Walpersdorf, A., and Castelltort, S.: Present-day uplift of the European Alps: Evaluating mechanisms and models of their relative contributions, Earth-Science Reviews, 190, 589–604, https://doi.org/10.1016/j.earscirev.2019.01.005, 2019.
Citation: https://doi.org/10.5194/se-2021-141-AC1
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RC2: 'Comment on se-2021-141', Björn Lund, 22 Feb 2022
Please find enclosed my review of Grosset, Mazzotti and Vernant, "Postglacial strain rate - stress paradox, example of the Western Alps active faults". The manuscript analyzes the response of the Western Alps region to the deglaciation of the latest ice sheet covering the region. The authors use a simple model of glacial isostatic adjustment (GIA) to estimate stress and strain in the Earth and compare that to GNSS data and earthquake focal mechanisms. This is an interesting study which goes all the way to the slip directions in the earthquakes to compare how the stress induced by GIA affects current day seismicity. I think this a very worth while study, however, there are issues with the GIA modelling and the fault stability estimates that need further work. I therefore recommend major revision.
Björn Lund
Uppsala University
Main comments:
1. Modelling GIA stress and strain.
(a)The thin plate/viscous mantle approach used for the modelling is a significant simplification of the GIA modelling problem and does not take into account stress redistribution due to the mantle (e.g. Wu, 1992; Steffen et al. 2015). Even for a relatively small ice sheet, such as the Alpine in this study, the mantle will be invoked (e.g. Arnadottir et al., 2009 used a more complex GIA model for current deglaciation in Iceland), especially for the elastic plate thicknesses found in the manuscript, with a best fit Te of 10 - 20 km. How large this effect is depends on the ice sheet configuration, the elastic parameters including Te and the viscosity of the mantle, but also the depth of interest in the model. At seismogenic depths in a 10 km thin plate it is not unlikely that the mantle stress redistribution is rather important. The authors should evaluate this by comparing to a more realistic GIA simulation tool.(b) Write out the parameters used to calculate the flexural parameter and the relaxation time, i.e. Young's and shear modulus, viscosity etc. How large is the model domain and what are the boundary conditions, which are important for stress estimates?
(c) There is very little description of the ice model, it is not even included in its entirety in Figure 3. What is the temporal behaviour of the ice sheet (plot ice volume and maximum ice thickness through time) and how is it implemented in the model? Do you use the full ice sheet? How do you start the ice model? A full load in equilibrium at LGM will not capture the transient behaviour of the GIA response, as it is unlikely that the Earth is in flexural equilibrium at the LGM.
(d) Extracting the GIA induced stress field from the top of the elastic plate does indeed give you a maximum stress signal, but it is not very realistic as the earth model almost certainly is too stiff near the surface, not taking near-surface fracturing into account. Also, I guess earthquakes in the region rarely occur in the uppermost 1-2 kilometers? With best fitting GIA models of Te 10 - 20 km, and seismicity down to 15 km depth, it is unclear to me why the near-surface stress field should be the most appropriate to use. On the contrary, below 10 km in a 20 km elastic plate stresses go from compressive to tensile.
(e) The model domain contains significant topography, from the Mediterranean to Mont Blanc. Therefore probably also a significant root. I guess that affects the flexure of the area. It would be nice with some discussion of this.
2. GIA and fault stability.
The Coulomb Failure Stress, CFS, is widely used when estimating how a stress change affects faults, promoting or demoting stability. However, using the change in CFS (D_CFS) with shear and normal stresses estimated from some external process, like GIA in this case, may lead you wrong. Unless the shear and normal stress changes occur in the directions of the pre-existing shear and normal stresses, the full stress tensor has to be taken into account. As the GIA induced stresses are significantly smaller than the in-situ stress even at LGM, at depths of more than 1-2 km, it is unlikely that the GIA stresses change the directions of the in-situ principal stresses, so the effect of the combined stress field needs to be considered, see e.g. Lund et al. (2009). This is of course tricky if you do not know the what the stress field without the GIA component looks like. Since the present day GIA stresses are very small compared to the in-situ stress it would have been interesting to see the focal mechanisms, or even better a stress inversion of the focal mechanisms, to get an idea of the current stress field. This issue needs to be addressed, and discussed, as it affects the results of section 4. As an example, for the Belledonne fault GIA predicts reverse faulting while the mechanisms show strike-slip. So GIA does not drive seismicity on its own, but perhaps GIA adds that extra bit of stress that pushes the fault into instability? Such that the seismic activity is larger than it would have been without GIA. Or, oppositely lower?
Further, on line:15: Reference for "plate tectonics cannot be the main source of SCR seismicity." That is not generally correct.
16: Need to define "recent", as today's seismicity in Fennoscandia is very much tectonics driven (e.g. Bungum et al, 2010) whereas the late/end-glacial was very much influenced by GIA.
18: Add Wu et al., 1999 or Lund et al. 2009 for Fennoscandia.
19: "Rapid decay in 103 - 105 yr"? Please explain what you mean, and give a reference. The timing of the Fennoscandian postglacial earthquakes are very uncertain and associated with the time just be fore ice retreat from a location, during ice retreat and just after, at the various locations. This gives a span of at least 1,000 years for the about a dozen ruptures, perhaps more as the exact time of ice free conditions are uncertain.
20: The Pärvie earthquake may have bee as large as Mw 8.0 (Lindblom et al., 2015).
41: You should comment on Keiding et al. (2015) who did a similar study for Fennoscandia. And also had problems reconciling the GNSS data, GIA and seismicity.
62, 66: Not sure if there is a problem with my pdf-viewer, but there is a different sign than a decimal dot in 1.2. Aha, it should be a hyphen?
66: Figure 3a shows the vertical velocities, which is perhaps not a good indicator of the size and variation in horizontal velocities, making up the strain rate field. How large are the uncertainties in the velocities, and propagated to your strain rates?
85: "wm" ? OK, I see. Write it in italics.
116 and Fig 3: Please add the outline of the maximum ice sheet to Fig 3a as well. How well does the current vertical GNSS velocities agree with the ice edge and the concept of a forebulge?
118: 50 MPa of horizontal compression under a 2 km (18 MPa) thick ice? That is a very high number.
120: GIA in Fig 3C.
122: The difference between GNSS and GIA strain rates in Fig 3 could be shown with for example bow tie plots, which would make the comparison much easier.
139: Indicate that you discuss present time(?).
143: Maximum horizontal GIA stress?
146-147: With DeltaCFS you should use Delta_tau and Delta_sigma_n, and therefore also the change in shear stress and the change in normal stress.
158: "...predicted rates are compared..."
206-209: This sentence is a little unclear. The ice adds a large vertical stress, the lithosphere slowly flexes inducing horizontal stresses. The increase in average stress increases fault stability. The rapid melting of the ice, compared to the Earth's rebound, decreases vertical stress faster than horizontal stress, resulting in an induced reverse stress state. Combined with a pre-existing reverse stress state, in a similar direction as in Fennoscandia, the process destabilizes faults. See Lund et al. (2009). Then we have the added action of strain accumulation during 50 - 60 kyr of ice cover, which adds to the horisontal stress/strain.
Figures:
3) Indicate that this is present time for 3c. The arrows in 3c are virtually impossible to see, and even the ones in 3b are difficult in many areas. Perhaps have different scales in b and c, with a large legend and the caption pointing out the difference? A factor of 2 difference could make the comparison easier? As you show vertical velocities in 3a, perhaps point out that you show horizontal strain rates. Add a scale bar to the figures, as the text explicitly talks about 90 km half-width filtering and 150-200km wavelength signals.
4 and 5) Add that this is the present day stress field. It would be good to have the extent of the ice sheet on these maps as well.
A3) The symbols are very difficult to see, even at 300% magnification on my screen.
References
Arnadóttir, T., Lund, B., Jiang, W., Geirsson, H., Björnsson, H., Einarsson, P., Sigurdsson, T., 2009. Glacial rebound and plate spreading: results from the first countrywide GPS observations in Iceland. Geophys. J. Int. 177 (2), 691–716, doi: 10.1111/j.1365-246X.2008.04059.xBungum, H., Pascal, C., Olesen et al. (2010). To what extent is the present seismicity of Norway driven by postglacial rebound? Journal of the Geological Society of London, 167, 373–384, doi.org/10.1144/0016-76492009-009.
Lund, B., Schmidt, P. and Hieronymus, C. (2009). Stress Evolution and Fault Stability during the Weichselian Glacial Cycle. SKB Technical Report TR-09-15, Swedish Nuclear Fuel and Waste Management Co., Stockholm, 106 pp. https://www.skb.com/publication/1968408/TR-09-15.pdf
Keiding, M., Kreemer, C., Lindholm, C. D. et al. (2015). A comparison of strain rates and seismicity for Fennoscandia: depth dependency of deformation from glacial isostatic adjustment. Geophysical Journal International, 202, 1021–1028, doi.org/10.1093/gji/ggv207.
Lindblom, E., Lund, B., Tryggvason, A. et al. (2015). Microearthquakes illuminate the deep structure of the endglacial Pärvie fault, northern Sweden. Geophysical Journal International, 201, 1704–1716, doi.org/10.1093/gji/ggv112.
Steffen, R., Steffen, H., Wu, P., and Eaton, D. W. (2015) Reply to comment by Hampel et al. on “Stress and fault parameters affecting fault slip magnitude and activation time during a glacial cycle,” Tectonics, 34, 2359–2366, https://doi.org/10.1002/2015TC003992.
Wu, P. (1992). Viscoelastic vs. viscous deformation and the advection of pre-stress. Geophysical Journal International, 108, 35–51, doi.org/10.1111/j.1365-246X.1992.tb00844.x.
Wu, P., Johnston, P. and Lambeck, K. (1999). Postglacial rebound and fault instability in Fennoscandia. Geophysical Journal International, 139, 657–670, doi.org/10.1046/j.1365-246x.1999.00963.x.
Citation: https://doi.org/10.5194/se-2021-141-RC2
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