Results

GLACIAL ISOSTATIC ADJUSTMENT

5.5 Results

The set of models testing the influence of GIA on the North American stress field parallel those testing the influence of Farallon slab loading (Chapter 4) and use the same viscosity structures. The first model (GIA-A0) uses the 3D viscosity structure of model A0 in Chapter 4, which does not have any weak zones; the second (GIA- A1) uses the viscosity structure of model A1 in Chapter 4, which has weak zones placed at different depths depending on geophysical constraints for their respective locations; the third (GIA-A1b) uses the viscosity structure of model A1b in Chapter 4, which has weak zones placed at the same depth between 25-75 km; and the fourth (GIA-1D-3Davg) and fifth (GIA-1D-VM5a) models use a 1D viscosity structure from either the radial mean of the 3D viscosity structure of model GIA-A0 or VM5a (Peltier et al., 2015), respectively. Like in the mantle flow models, in all cases with weak zones, weak zone viscosities are a factor of 1000 times less viscous than the surrounding lithosphere.

𝑆_{𝐻 𝑚 𝑎𝑥} orientations induced solely by GIA stress are shown in Figure 5.1 a,b, which in comparison to Figure 5.1 c,d reveal the importance of including tectonic back- ground stress. The𝑆_{𝐻 𝑚 𝑎𝑥} directions in eastern North America exhibit a rotational pattern around the margin of the former Laurentide ice-sheet, with near E-W orien- tations in Texas and the central-eastern U.S. near New Madrid transitioning to N-NE orientations in southeast Canada. The inclusion of weak zones at the locations of the aulacogens or other structures leads to small improvements in the fit of the𝑆_{𝐻 𝑚 𝑎𝑥} direction in the central eastern U.S. but a reduction in the fit throughout much of the Charlevoix and Lower Saint Lawrence Seismic Zones (Figure 5.1 b). The addition of the tectonic background stress leads to an improvement in the fit throughout most of eastern North America, by as much as 20° in some places. The tectonic stress dominates such that the overall fit of the regional stress field is largely the same as that predicted through mantle flow. But even without the tectonic background stress, the majority of misfits across eastern North American are still less than∼28°.

There is a progressively counterclockwise stress rotation due to GIA moving north- eastwards across eastern North America (Figure 5.2). This gradation is even stronger

Figure 5.1: Changes in misfit between observed and modeled𝑆_{𝐻 𝑚𝑎 𝑥}for different GIA models using different viscosity input. a)𝑆_{𝐻 𝑚𝑎 𝑥}orientations induced by GIA only (i.e., no tectonic background stress) from model GIA-A0 colored by misfit (|modeled - observed|) to the observed stress orientations from the WSM of Heidbach et al. (2018) (light gray lines). b) Difference in the𝑆_{𝐻 𝑚𝑎 𝑥}misfit between model GIA-A1 and model GIA-A0 (i.e., between models with vs. without weak zones) for GIA only.

c) Difference in𝑆_{𝐻 𝑚𝑎 𝑥}misfit between model GIA-A0 + tectonic background stress and model GIA- A0 with GIA only. d) Difference in𝑆_{𝐻 𝑚𝑎 𝑥} misfit between model GIA-A1 + tectonic background stress and model GIA-A0 with GIA only.

when assuming a 1D viscosity profile (Figure 5.2 c). In this case, the rotations in- duced by GIA are mostly dependent on the ice-loading history, as there are no lateral viscosity variations to introduce strength contrasts in the lithosphere. The inclusion of weak zones at either variable depths (Figure 5.2 b) or the constant 25-75 km (Figure 5.2 c) results in subtle clockwise stress rotations in New Madrid and Eastern Tennessee, as well as parts of the Northern Appalachians and Western Quebec, while even stronger counter-clockwise rotations are observed in the LSLSZ. However, the rotations induced by GIA, with or without weak zones, are very small and at most within±5°. Thus, the spatial variations in stress orientations caused by GIA at the present day are insignificant compared to the observed variation of 𝑆_{𝐻 𝑚 𝑎𝑥} in the WSM, which can often vary by as much as 25°within a single seismic zone. Nev-

ertheless, the subtle transition from clockwise to counterclockwise rotation across eastern North American predicted by the GIA stresses alone produces a style of faulting at the present day that mirrors that observed from focal mechanism stress inversion, transitioning from predominantly strike-slip and normal faulting in the central-eastern U.S. to thrust faulting in southeastern Canada, as measured by the 𝐴𝜙parameter (Hurd and Zoback, 2012).

Figure 5.2: Rotation in 𝑆_{𝐻 𝑚𝑎 𝑥} induced by GIA for different viscosity inputs relative to tectonic background stress. a) Rotation in𝑆_{𝐻 𝑚𝑎 𝑥} orientation induced by GIA using 3D viscosity with no weak zones present (i.e., between model GIA-A0 with tectonic background stress and model A0).

Observed stress orientations from the WSM of Heidbach et al. (2018) are shown in the background as light gray lines. b) Rotation in𝑆_{𝐻 𝑚𝑎 𝑥}induced by GIA in the presence of weak zones (i.e., between model GIA-A1 with tectonic background stress and model A1). c) Rotation in𝑆_{𝐻 𝑚𝑎 𝑥}induced by GIA assuming a 1D viscosity structure (i.e., between model GIA-1D-3Davg with tectonic background stress and model A0). d) Rotation in𝑆_{𝐻 𝑚𝑎 𝑥} induced by GIA using 3D viscosity with weak zones all at depths of 25-75 km (i.e., between model GIA-A1b with tectonic background stress and model GIA-A1b.

The magnitudes of the stress perturbations associated with these rotations range from 5-15 MPa, with the highest deviatoric stress magnitudes centered over Hudson Bay, the site of the fastest present day uplift. Two pockets of high stress are situated over northern Virginia and Nova Scotia, separated by a region of little to almost no GIA induced deviatoric stress (Figure 5.3 c). The effect of 3D viscosity versus

1D viscosity is pronounced, however. Lithospheric variability introduces elevated deviatoric stress in Eastern Tennessee, western New York and Pennsylvania, New Hampshire and Vermont, and over the entirety of the LSLR, which exhibits some of the largest stress perturbations (Figure 5.3 e). Within GIA models with 3D viscosity, weak zones introduce an additional stress perturbation of only 2-5 MPa, with the strongest effects on stress magnitude concentrated closer to the former ice-margin.

The highest stress perturbations are located along the northwest margin of the LSLR, specifically along the boundary of the weak zone, rather than immediately above the weak zone (Figure 5.3 d,f), which is also where ancient rift-bounding faults are likely to be present. Interestingly, the presence of weak zones actually results in a stress drop in the vicinity of the most seismically active part of the Western Quebec Seismic Zone, though its north-westernmost end does exhibit higher stresses. Stress perturbations in New Madrid and Eastern Tennessee are only on the order of 2 MPa, though are slightly higher in New Madrid when the weak zone is placed at 25-75 km rather than deeper in the mantle lithosphere. Strong peaks in stresses are also present at the PA-NA plate boundary (Figure 5.3 a) due to the inclusion of low viscosity plate boundary weak zones.

While small, the stress rotations and magnitude perturbations that are invoked by GIA still have implications for fault stability in eastern North America. As in Chapter 4, the potential for fault reactivation in the New Madrid, Western Quebec, and Lower Saint Lawrence and Charlevoix Seismic Zones is explored by means of the Coulomb failure stress (CFS) in Figures 5.4, 5.5, and 5.6, respectively. Instead of the absolute CFS, we plot the change in CFS between the GIA models and their corresponding tectonic and dynamic background stress as calculated with CitcomS to highlight the degree to which GIA shifts faults closer to or farther from failure.

In this case, a positive change in Coulomb failure stress, like a positive CFS, means a more unstable fault or at least a move towards instability, and a negative change means more stable or a move towards stability. Mohr circles are still plotted at the same fault locations used in Chapter 4 using the full shear and normal stresses resolved on that fault.

In the NMSZ, the pattern of fault stability that GIA affects is opposite to that predicted from the mantle flow models shows in Figure 4.13. The addition of GIA shifts all SW-NE oriented faults within the NMSZ closer to failure. Those oriented NW-SE, including the Reelfoot Fault, actually move farther from failure, in contrast to the results of the mantle flow models, in which the Reelfoot Fault

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Figure 5.3: GIA induced stress magnitudes. a) Profiles of the second invariant of deviatoric stress from GIA only along line B-B’ for 3D viscosity input (light green lines) with no weak zones (solid line), weak zones at different depths (dashed line), weak zones at 25-75 km depth (dashed-dotted line), and 1D viscosity input (dark blue lines) from the radial average of model GIA-A0 (thick line) and from VM5a (thin line). New Madrid Seismic Zone (NMSZ) and Eastern Tennessee Seismic Zone (ETSZ) are labeled accordingly. Profile positions are labeled in panel (c); same transect as in Figures 4.4 and 4.11 in Chapter 4. Note: length of the profile is longer than map area (see Chapter 4, Figure 4.4 orthographic panel). b) Profiles of stress magnitude from GIA along line A-A’. Lines as in (a). New Madrid Seismic Zones (NMSZ), Western Quebec Seismic Zone (WQSZ) and Charlevoix Seismic Zone (CXSZ) are labeled accordingly. c) Map of GIA induced deviatoric stress magnitude for model GIA-A0 (3D viscosity but no weak zones). d) Perturbation to the stress in (c) by including weak zones (i.e., difference between models GIA-A1 and GIA-A0). d) Stress perturbation induced by the inclusion of 3D viscosity (i.e., difference between models GIA-A0 and GIA-1D-3Davg). f) Perturbation to the stress in (c) by placing all weak zones at 25-75 km depth (i.e., difference between models GIA-A1b and GIA-A0).

was the only fault to exhibit positive, and therefore unstable, CFS conditions. This flip in the observed pattern is a direct result of the slight clockwise rotation of the 𝑆_{𝐻 𝑚 𝑎𝑥} direction in the NMSZ towards a more E-W direction under the influence of GIA. Such an orientation places the region’s strike-slip faults in a more optimal position to be reactivated. Changes in CFS brought about by GIA are subtle, at most about 5 MPa – not enough to fully stabilize or destabilize a fault in terms of the total Coulomb failure stress, as distances between the resolved shear stress and the failure criterion can still be upwards of±100 MPa – but the changes do highlight the patterns of relative fault stability promoted by GIA that under different tectonic background stress regimes may bring a fault closer to failure. Changes in CFS are greatest overall in the case of shallower weak zones (Figure 5.4 c), and changes in CFS are both the least pronounced and the most stabilizing in the case of 1D GIA (Figure 5.4 d).

The changes in CFS are more variable in the Western Quebec Seismic Zone, which only exhibits higher stress perturbations towards its northwest end. In the case of 3D GIA without weak zones, GIA stresses lead to an increase in CFS by 0.5 to 1.5 MPa on faults that already breach the instability regime due to loading from the Farallon slab (Figure 4.14 a). Small changes (∼0.5 MPa) are observed on other WQSZ faults, but only those in the western half come closer to failure. The inclusion of shallow weak zones results in positive changes in CFS, upwards of 3-4 MPa on most faults in the western half, while those in the eastern half move towards stability. The 1D GIA model produces little to no change in the CFS on WQSZ faults, highlighting the role of lateral heterogeneities in governing the stress changes within this seismic zone rather than the ice history alone.

However, within the LSLSZ and CXSZ, even the 1D GIA model leads to notable increases in Coulomb failure stress by as much as 5 MPa (Figure 5.6 d). The lithosphere is thinner in the 1D models, and without lateral variability in the LAB depth, there is no thick craton under North America. Thus, for locations closer to the craton, such as the LSLR, the difference in deformation in response to the ice-load between the 3D and 1D cases will be enhanced, with the 1D model promoting a stronger response. Similar CFS changes are observed in the CXSZ for 3D GIA models with weak zones (Figure 5.6 b,c), which bring almost the entirety of the LSLRS faults closer to failure. The effects, however, are most pronounced specifically within the CXSZ rather than the Montreal Seismic Zone farther to the southwest, consistent with the concentration of seismicity in this part of the LSLRS

Figure 5.4: Mohr circles (main plot) and change in Coulomb failure stress (map inset) for faults in the NMSZ between models with GIA and the corresponding models without GIA presented in Chapter 4, calculated using𝜇=0.6. Fault locations from Thompson et al. (2020). Fault strike and dip information for the Axial Fault (strike=46°, dip=90°), the New Madrid North Fault (strike=29°, dip=72°), the Risco Fault (strike=92°, dip=82°), and the North Reelfoot Fault (strike=167°, dip=30°) are from Csontos and Van Arsdale (2008). Faults with unknown dip are assumed to have a dip of 90°. Mohr circles are drawn for New Madrid faults at the locations of the stars on the map using the fault’s strike and dip and the stress tensor at that location. Star colors correspond to Mohr circle colors. Star locations for the three northernmost stars correspond to the most likely epicenters of the 1811-1812 earthquake sequence (Delano et al., 2021). The cloud of points on each Mohr circle represent the shear vs. normal stress for all possible stress tensors in the inset region given that fault’s geometry. Black straight line is the Mohr-Coulomb failure criterion for𝜇=0.6; gray line is for𝜇 =0.4; and light-gray line is for𝜇 = 0.2. (a) Results from model GIA-A0 (no weak zones).

(b) Results from model GIA-A1 (weak zones at variable depths). (c) Results from model GIA-A1b (weak zones between 25-75 km depth). (d) Results from model GIA-1D-3Davg (radial viscosity, no weak zones).

compared to others. Again, while the changes in CFS are small relative to the absolute CFS plotted in Figure 4.15, for the case of the LSLRS, changes are large

Figure 5.5: Mohr circles (main plot) and change in Coulomb failure stress (map inset) for faults in the WQSZ between models with GIA and the corresponding models without GIA presented in Chapter 4, calculated using𝜇=0.6. Fault locations from Rimando and Peace (2021) and Lamontagne et al.

(2020). Fault strikes approximated using the best fitting great circle through the lineation. Unless otherwise specified, fault dips were assumed to be 56°(Bent et al., 2003; Rimando and Peace, 2021).

Dip of the fault associated with the Timiskaming 1935 earthquake (black star) and nearby faults are from Bent (1996) (strike=146°, dip=45°). Mohr circles are drawn for four faults, using the stress tensor at the location of the corresponding star on the map: The Timiskaming fault of the M 6.1 1935 earthquake, the Rapide-du-Cheval Blanc Fault near the epicenter of the M 6.3 1732 Montreal earthquake, the Lachute Fault (NE of Ottawa), and the Coulonge Fault (NW of Ottawa). Earthquake locations from Bent (2022) and Bent et al. (2003). Star colors correspond to Mohr circle colors. The cloud of points on each Mohr circle represent all possible stress tensors in the inset region given that fault’s geometry. Black straight line is the Mohr-Coulomb failure criterion for𝜇=0.6; gray line is for𝜇 =0.4; and light-gray line is for𝜇 = 0.2. (a) Results from model GIA-A0 (no weak zones).

(b) Results from model GIA-A1 (weak zones at variable depths). (c) Results from model GIA-A1b (weak zones between 25-75 km depth). (d) Results from model GIA-1D-3Davg (radial viscosity, no weak zones).

enough on some faults that coupled with even a very small reduction in the fault friction, faults that were stable in the case of only the tectonic and mantle flow induced stress would become unstable.

Figure 5.6: Mohr circles (main plot) and change in Coulomb failure stress (map inset) for faults in the LSLRS, including the CXSZ, between models with GIA and those without presented in Chapter 4, calculated using𝜇=0.6. Fault strikes approximated for each fault location using the best fitting great circle through the lineation. Fault dips assumed to be 53°, consistent with the values of steeply dipping rift bounding normal faults for the LSLRS as reported by Bent et al. (2003) and Bent (1992).

Mohr circles are drawn for the three faults closest to the epicenters of the 1663 M 7.0 and 1925 M 6.2 Charlevoix earthquakes and the M 6.3 1732 Montreal earthquake, using the fault’s strike and dip and the stress tensor at the location of the corresponding star on the map. Star colors correspond to Mohr circle colors. Earthquake locations from Bent (2022). The cloud of points on each Mohr circle represent the shear vs. normal stress for all possible stress tensors in the inset region given that fault’s geometry. Black straight line is the Mohr-Coulomb failure criterion for𝜇=0.6; gray line for𝜇 =0.4; and light-gray line is for𝜇 = 0.2. (a) Results from model GIA-A0 (no weak zones).

(b) Results from model GIA-A1 (weak zones at variable depths). (c) Results from model GIA-A1b (weak zones between 25-75 km depth). (d) Results from model GIA-1D-3Davg (radial viscosity, no weak zones).