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• W1504709504 abstract "Steffen et al. [2014b; hereafter referred to as Steffen et al.] report the results of two-dimensional finite element models, which they performed to decipher the response of preexisting faults to changes in surface loads induced by the growth and melting of continental ice sheets and the associated glacial isostatic adjustment (GIA). Having worked on the response of faults to glacial-interglacial changes in ice and water loads on Earth's surface since 2004 [Hetzel and Hampel, 2005; Hampel and Hetzel, 2006; Hampel et al., 2007, 2009, 2010a, 2010b; Karow and Hampel, 2010; Turpeinen et al., 2008; Ustaszewski et al., 2008], we are disconcerted to realize (1) that Steffen et al. describe our modeling approach in a misleading way, (2) that they do not mention the specific results (e.g., regarding the amount and timing of fault slip) of our studies anywhere in their article despite the similarity of the topic of their article, and (3) that the content and layout of Steffen et al.'s Figure 1 closely resembles two figures previously published in our studies, but they do not cite the source (they, however, introduced conceptual errors concerning the glacial-interglacial stress evolution into their figure). In the following, we address these three points in more detail. Concerning point 1, the following inadequate and erroneous description of our modeling approach is given by Steffen et al.: “A similar approach was developed by Hampel and Hetzel [2006] and numerous thrust-fault results were presented in Turpeinen et al. [2008], but their models simplify the effects of GIA stress and neglect the effect of the viscoelastic mantle. However, the mantle is the driving force of the viscoelastic behavior of GIA, and without the mantle, only an elastic GIA effect is taken into account. Furthermore, fault slips in their models are a result of the combined effects of a stress related to GIA and a converging horizontal displacement boundary condition.” These statements on our models are misleading in several aspects and require a detailed response. First, Steffen et al.'s description gives the reader the impression that our models did not contain viscoelasticity at all, which is wrong. In fact, all our models did include a viscoelastic lithospheric mantle as part of the model domain and also a viscoelastic asthenosphere, which was implemented by boundary conditions. Except for the earliest models [Hetzel and Hampel, 2005; Hampel and Hetzel, 2006], our models even included a viscoelastic lower crust. In our parameter studies [Hampel and Hetzel, 2006; Hampel et al., 2009, 2010b; Turpeinen et al., 2008], we demonstrated that the viscosity of the lower crust and lithospheric mantle exerts a fundamental control on the fault slip behavior. It is therefore erroneous when Steffen et al. state that we only took into account the “elastic GIA effect,” because the effect of the viscoelastic layers is clearly recognizable in our results [e.g., Turpeinen et al., 2008; their Figures 4 and 5]. In this context, we point out that Steffen et al. employ a 160 km thick, purely elastic model lithosphere. Hence, they ignore that the presence of viscoelastic layers in the lithosphere affects not only the fault slip evolution—as shown by our models—but also the GIA stress evolution, as shown by other workers [e.g., Klemann and Wolf, 1999]. Furthermore, Steffen et al. use a density for the crust of 3256 kg/m3. This value is geologically implausible and, in our view, also not supported by the Preliminary Reference Earth Model of Dziewonski and Anderson [1981] to which Steffen et al. refer. Dziewonski and Anderson [1981, their Tables II to IV] provide the following values: For the depth intervals 0–3.0 km, 3.0–15.0 km, and 15.0–24.4 km, constant densities of 1020, 2600, and 2900 kg/m3 are given. Between 24.4 and 40.0 km, the density slightly decreases from 3380.76 kg/m3 to 3379.06 kg/m3. Based on these values, it remains unclear, how Steffen et al. derived a density of 3256 kg/m3 for their 40 km thick model crust. Concerning the interaction between postglacial rebound and tectonic background deformation, Steffen et al. claim that “The advantage of this new model [Steffen et al., 2014a] is that the role of GIA-induced stress is explicitly included and not mixed in with the effect of plate motion.” This statement leaves the reader with the impression that models like ours, which do consider the plate tectonic setting, are inferior to models that neglect plate tectonic motion. As the plate motion is unarguably present in nature—even if the resulting deformation rates are as low as in Scandinavia [Milne et al., 2001]—it is important to consider this parameter if results are to be applied to natural case studies as done by Steffen et al. and ourselves [e.g., Turpeinen et al., 2008]. The importance of this parameter was also underlined by the results of our parameter studies [Hampel and Hetzel, 2006; Turpeinen et al., 2008]. With respect to point 2, we note that Hetzel and Hampel [2005] were the first to include discrete fault planes in finite element models to investigate the response of faults to glacial-interglacial changes in surface loads and to actually compute the amount of postglacial fault slip. Earlier studies by other workers merely analyzed stress changes by means of Mohr diagrams using so-called “fault-stability margins” (i.e., the difference between the Mohr circle of stress and the failure envelope) but were not able to derive any values for postglacial fault slip [e.g., Johnston, 1987; Johnston et al., 1998; Wu et al., 1999; Wu and Johnston, 2000]. Our models represented a major step forward, because apart from making quantitative predictions on fault displacement, they were able to explain why earthquakes were triggered by the melting of ice sheets and by the regression of lakes. Between 2006 and 2010, we published a series of articles including comprehensive parameter studies as well as applications to faults in Scandinavia, the Basin and Range Province in North America, and the European Alps [Hampel and Hetzel, 2006; Hampel et al., 2007, 2009, 2010a, 2010b; Turpeinen et al., 2008; Ustaszewski et al., 2008; Karow and Hampel, 2010]. In particular, our models could explain the postglacial earthquakes in Scandinavia [Turpeinen et al., 2008] and the hitherto enigmatic postglacial slip rate increase on the Wasatch and Teton normal faults [Hetzel and Hampel, 2005; Hampel et al., 2007]. In their study, Steffen et al. investigate the effect of a number of parameters (e.g., friction coefficient and fault dip) and apply their results to faults in Scandinavia. Neither in their introduction nor in the discussion, do Steffen et al. mention the results from our publications despite the obvious similarity between the studies (which were performed using the same finite element software, ABAQUS). In our parameter studies, we used both two- and three-dimensional models with one or more normal and thrust faults to explore the effect of various parameters on the glacial-interglacial slip behavior, including (a) the spatial dimensions and temporal evolution of the load, (b) fault dip, friction coefficient, and fault position relative to the surface load, and (c) rheological parameters of the lithosphere and asthenosphere [Hampel and Hetzel, 2006; Hampel et al., 2009, 2010a, 2010b; Turpeinen et al., 2008]. Steffen et al. have chosen a similar range of parameters for their models but their discussion does not even mention our results, although they calculate the amount and timing of fault slip as we did in our studies. Similarly, Steffen et al. discuss the effect of the fault position relative to the surface load in their two-dimensional model without mentioning that we have analyzed the same parameter using a three-dimensional model [Hampel et al., 2009]. One may, of course, always argue that numerical models are never completely identical and hence their results are not fully comparable. In the case of Steffen et al. and our studies, however, the topic and the parameter ranges explored are so strikingly similar that it would have been straightforward to mention the results of our studies. Such references to earlier work on the same topic would have enabled the reader to compare the results obtained by both author teams and to evaluate the actual importance of the differences between the model domains (i.e., the consideration of the sublithospheric mantle versus consideration of the viscoelastic layers of the lithosphere). Differences also exist between some aspects of the modeling technique, for example, regarding the use of the approach of Wu [2004] by Steffen et al. and our approach to consider buoyancy forces at material boundaries. Concerning the latter point, we note that Hampel et al. [2009, their Appendix A] presented a comparison between these two modeling approaches, which showed that the differences in the calculated rebound are minor, as acknowledged by Patrick Wu, who was one of the reviewers of our article. Finally, Steffen et al. apply their results to the ~150 km long Pärvie Fault in northern Scandinavia. The Pärvie Fault is the largest among several postglacial faults in the Lapland Fault Province and is characterized by a well-preserved ~15 m high fault scarp, which formed ~9000 years ago [Lagerbäck, 1992] presumably during a Mw ≈ 8.2 earthquake [Arvidsson, 1996]. Again, Steffen et al. do not mention anywhere in their paper that a quantitative comparison between modeled fault displacements and postglacial displacements on faults in the Lapland Fault Province was carried out before by Turpeinen et al. [2008]. In their discussion, these authors presented a two-dimensional model with a thrust fault (their Figure 10), in which the ice sheet width, the ice loading history, and the tectonic deformation rate were adjusted to Scandinavia [Talbot, 1999; Milne et al., 2001]. The timing and magnitude of the modeled postglacial fault slip compared well with the paleoseismological record from faults in the Lapland Fault Province, even though parameters like fault dip or friction coefficient were not adjusted (because they are not well constrained by data) and lateral variations in the structure of the Scandinavian lithosphere were not considered. Concerning the causal relationship between postglacial earthquakes and the melting of the Fennoscandian ice sheet, Turpeinen et al. [2008] arrived at similar conclusions as Steffen et al., although Turpeinen et al. [2008] compared the total postglacial displacement with the reported fault scarp heights, whereas Steffen et al. compare the earthquake magnitude (which they calculated from the modeled amount of fault displacement) in model and nature. Also, both author teams showed that after a short period of intense faulting, slip accumulation and hence seismic activity decreased markedly in Scandinavia, which is in agreement with paleoseismological and seismological records [e.g., Mörner, 1978; Lagerbäck, 1979; Lagerbäck, 1992; Dehls et al., 2000; Mörner, 2005; Bungum et al., 2010]. With respect to point 3, we would like to draw the reader's attention to Steffen et al.'s Figure 1 (Figure 1a). Regarding both content and layout, Steffen et al.'s Figure 1 appears to be a simplified version of our figures about the stress evolution on normal faults (Figure 1b) [Hampel and Hetzel, 2006, Figure 1] and on thrust faults (Figure 1c) [Turpeinen et al., 2008, Figure 9]. However, none of our studies is cited in their figure caption. Although the stress evolution in all three figures starts with a stress state close to the Mohr-Coulomb failure envelope, we argue that the subsequent evolution as depicted by Steffen et al. contains significant conceptual errors. According to the Mohr circle in part (b) of Steffen et al.'s figure, the principal stresses σ1 and σ3 increase by the same amount during glaciation (i.e., the diameter of the Mohr circle and hence the differential stress is the same before and during glaciation). As—regardless of the tectonic setting—the change of the vertical principal stress is mainly governed by the load, whereas the horizontal principal stress is influenced by the flexure of the lithosphere, an increase of both principal stresses by the same amount would be an improbable coincidence (i.e., this scenario is not the general case). Rather than being a subtle detail, the notion that the differential stress—depicted by the size of the Mohr circle—changes during glacial loading is of fundamental importance for fault slip. In most cases, the combined effect of loading, flexure, and viscous flow in the lithospheric layers leads to a decrease in the differential stress, which explains why fault slip is suppressed during the presence of ice/water loads for both normal and thrust faults (as schematically shown in Figures 1b and 1c) [Hampel and Hetzel, 2006; Turpeinen et al., 2008]. In some cases, however, the net effect of loading, flexure, and viscous flow can also be an increase in the differential stress, which promotes slip on faults during glaciation [Hampel et al., 2010b]. In this context we note that Steffen et al. incorrectly cite Johnston [1987] as reference for the statement that “flexure of the lithosphere induces horizontal bending stresses as well, which change all components of the stress tensor.” In his simple analysis, Johnston [1987] did not consider flexure-induced horizontal stress changes at all. For contractional tectonic settings, he argued that earthquakes on thrust faults are suppressed beneath large ice sheets, which provides an explanation for the low seismicity beneath the Greenland and Antarctica ice sheets. However, Johnston [1987] also argued that slip on normal faults should be promoted by the presence of loads, as the load increases the vertically oriented maximum principal stress σ1. Our numerical models demonstrated that this statement is generally not correct because the effects of flexure and the associated horizontal stress changes are neglected [Hetzel and Hampel, 2005; Hampel et al., 2006; Hampel et al., 2010b]. Finally, we note that in part (c) of Steffen et al.′s figure (Figure 1a), the Mohr circle crosses the Mohr-Coulomb failure envelope. This does not comply with the concept of the Mohr analysis of stress, in which failure and fault slip occur as soon as the Mohr circle for stress touches the Mohr-Coulomb failure envelope [e.g., Jaeger and Cook, 1979]. Between 2006 and 2013, funding was provided by the German Research Foundation within the framework of an Emmy-Noether project entitled “The response of seismogenic faults to natural and human-induced changes in loads on Earth's surface” to A. Hampel (HA 3473/2-1)." @default.
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• W1504709504 title "Comment on “Stress and fault parameters affecting fault slip magnitude and activation time during a glacial cycle” by Steffen et al." @default.
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