material would flow extremely slowly similarly to a brittle material. The shear zone

Size: px

Start display at page:

Download "material would flow extremely slowly similarly to a brittle material. The shear zone"

Godwin Knight
5 years ago
Views:

1 GSA DATA REPOSITORY Hayman and Lavier Supplementary model description: Lavier et al. (213) showed that formation or reactivation of mixed mode fractures in ductile shear zones might generate variations in creep rate over a wide range of time scales (seconds to thousands of years). In the model, the creep transients are produced in a two layer model in which a viscoelastic plate (upper plate or hanging wall) of thickness, is coupled to a layer (shear zone) of thickness,. may vary from a few millimeters to kilometers. Lavier et al. (213) took the velocity at the top of the upper plate as, and the bottom of the shear zone as moving at a constant velocity,, assuming that flow may be occurring below the shear zone in the ductile lower crust or lower plate. may be constant or equal to zero. The upper plate was modeled as a Maxwell viscoelastic solid of shear modulus, and of viscosity, approaching values where the material would flow extremely slowly similarly to a brittle material. The shear zone itself behaves as a viscous material with viscosity,. For the Beagle Channel rocks, we take to range from Pa.s, consistent with quartz flow laws (e.g., Kronenberg and Tullis, 1984) that describe the deformation preserved in the microstructure (Fig. DR1). In the original (Lavier et al., 213) approximation, creep events or transients are generated when plastic failure occurs in a single fracture or a network of fractures at the interface between the upper plate and ductile shear zone. The main difference between that approximation and the one we make in this effort is that we envision that stronger blocks within the shear zone localize the fractures. Therefore, in our effort we assigned another viscosity term,, taken to be equivalent to, which describes stronger lenses within the shear zone. For the Beagle Channel rocks, an =1 23 Pa.s is consistent with plagioclase flow laws (e.g., Rybacki and Dresden, 24) that describe the deformation preserved in the microstructure (Fig. DR2). The stress drop generated by plastic failure is concurrent with the creep, S in the shear zone. The brittle fracture is modeled as a dislocation of radius w and shear modulus, μ (Chinnery, 1969; Dietrich, 1986). Stress continuity at the interface perturbed by the stress change caused by the dislocation result in the following formulation: where, (1) and. The decay constant, D and natural period, of the oscillator depend on the effective elastic and viscous structure of the crust. In addition, the natural periodicity is determined by the shear modulus, the shear zone thickness, and the radius of the characteristic shear fracture. The right hand side term in equation (1) has the dimensions of force per

2 unit length and represents an external force applied to the oscillator system due to the tectonic forcing. Two characteristic time scales T u and T c control the nature of the slip events. The time scale T u is the decay time related to the resistance of the shear zone to flow. Note that 2 Dif the creep is under or critically damped and 2 4 if the creep is over damped. The natural period, T c of the oscillator is given by 2 1. The natural period is dependent on the shear zone effective stiffness K e is therefore dependent on the aspect ratio of the shear zone thickness to the effective radius of the fractured region or damage zone,, as well as on the shear modulus of the zone of fractures. Another way of envisioning the factor is that it basically represents how efficiently shear is transmitted through the whole ductile shear zone thickness. The presence of a large and efficient fracture network allows for more creep. A single isolated fracture is very inefficient and leads to very little creep, and potentially leads to oscillations (explained below). A thin layer with a small value for has a small effective stiffness and, consequently, a long period. In contrast, a thick shear zone has a small effective stiffness and, consequently, a small period. The model predicts 4 main creep behaviors (Lavier et al., 213): (1) Steady creep at a very damaged and weak brittle ductile transition. In that case and is very small and the shear zone can creep freely. In this case, the shear zone creeps at a rate close to the tectonic rate. (2) Slow creep events occur when. The shear zone is soft and experiences extended periods of creep at rates larger than the tectonic rate before returning to a jammed state. (3) Critical slow creep events occur when. This corresponds to the state for which the shear zone creeps before returning to steady state (jammed) in the shortest amount of time. (4) Oscillations occur when and is large. The stiffness in the shear zone is such that damping cannot diffuse creep efficiently. This last behavior occurs for very stiff shear zones (i.e., = 1) with a very low contrast in viscosity between the weak and strong phases (i.e., = 1 15 ), and thus the creep events are underdamped. Such under damped behavior is expressed as decaying, sinusoidal oscillations, which do not resemble any geodetically observed behavior except for perhaps some intraplate strain transients (Wernicke et al., 28). In Figures DR1&2 we show examples of the microstructure of the Beagle Channel rocks that illustrate the grain scale deformation mechanisms of veining and ductile creep. In Figures DR3 5 we show the creep amount and rates for a range of apparent stiffness controlled by the parameter, shear zone viscosity, depths, and corresponding to the range of conditions discussed in the main text. The shear zone thickness, is 1 m. All other parameters are held the same as in Figure 3 in the main text. The results shown in figure 1 to 3 demonstrate the robustness of the model to simulate creep events across a wide range of depth and shear zone viscosities. The aspect ratio which controls the apparent stiffness of the shear zone has a strong effect on the events. If the shear zone is thin and wide

3 (large network of connected fractures) it is soft and acts as a good lubricant and creep events last longer and slip slower. If the shear zone is thick and narrow (small network of fractures) it is stiff and creep events are short and slip faster. References for Supplementary Materials Chinnery, M. A., 1969, Theoretical fault models, in A Symposium on Processes in the Focal Region, 37, edited by K. Kasahar and A. E. Stevens, pp , Publ. Dom. Obs., Ottawa. Dieterich, J. H., 1986, A model for the nucleation of earthquake slip, in Earthquake Source Mechanics, Geophys Monogr. Ser., vol. 37, edited by S. Das, J. Boatwright, and C. H. Scholz, pp , AGU, Washington, D. C. Kronenberg, A., and Tullis, J., 1984, Flow strengths of quartz aggregates Grain size and pressure effects due to hydrolytic weakening: Journal of Geophysical Research, v. 89(NB6), p , doi:1.129/jb89ib6p4281. Lavier, L.L., Bennett, R.A., Duddu, R., 213, Creep events at the brittle ductile transition: Geochemistry Geophysics Geosystems, v. 14, p , doi:1.12/ggge Rybacki, E., and Dresen, G., 24, Deformation mechanism maps for feldspar rocks: Tectonophysics, v. 382, p , doi:1.116/j.tecto Wernicke, B., Davis, J.L., Niemi, N.A., Luffi, P., and Bisnath, S., 28, Active megadetachment beneath the western United States: Journal of Geophysical Research, v. 113, doi: 1.129/27JB5375.

4 Figure Captions: Figure DR1: Photomicrographs of quartzofeldspathic gneiss from Bahia Pia (54 43 S W), Beagle Channel, from the outcrop featured in Figure 2 of the main text. (a) thin section scan illustrating the distribution of biotite (brown bladed crysts), sillimanite, and mixtures of quartz and feldspar (clear with some blue birefringence due to polarizing filter used with scanner). (b) photomicrograph in plane polarized light of an area in a illustrating that even where biotites (brown) appear to define an interconnected foliation, they in fact are mixed with other aluminosilicate minerals such as sillimanite (colorless, bladed crysts with high relief). (c) Same area as in b but in cross polars, illustrating the mixture of completely, dynamically recrystallized quartz and partly dynamically recrystallized feldspar (note twinning in grains with irregular grain boundaries). (d) the edge of the vein featured in Figure 2 in the main text. Note the blocky quartz grains and sharp vein walls. Altogether we interpret a d to indicate that strain was predominantly accommodated by dislocation creep (dislocation climb in quartz and grain boundary migration in plagioclase) and fracturing that led to fluid filled (quartz precipitating) veins. Figure DR2: Photomicrographs from the mafic lens featured in Figure 2 of the main text, adjacent to the area in Figure DR1. (a) thin section scan from the mafic lens, illustrating highly foliated amphibole (brown and green crysts) and plagioclase (clear crysts with some blue birefringence), cut by a thin quartz vein (smaller than the vein featured in Figure 2). (b) photomicrograph from an area in a in planepolarized light. (c) same area as in b in cross polarized light (d) closeup of an area in c illustrating the highly strained nature of plagioclase grains which we interpret to have accommodated strain primarily through crystal plastic grain boundary migration. Figure DR3: a) and b) For low viscosity (1 11 Pa.s) and 25 km depth the total amount of creep is mainly dependent and the initial slip = 1 m. The creep rate is highly dependent on the stiffness of the shear zone determined by. b) For a larger depth (4 km) the creep rates are higher and the durations lower. c) For high viscosity (1 15 Pa.s) are not significantly different although the creep rates is lower and some oscillations occur at = 1. d) For high viscosity and greater depth (4 km), the events are similar for the same range of, although at high viscosity the events experience more oscillations at = 1. The creep events show very little dependence on viscosity. Oscillations may be an artifact of our formulation. Overall the events similarities are very robust across a wide range of conditions. The main controlling parameter is the stiffness of the shear zone that is dependent on and the shear modulus of the brittle material. To obtain creep events similar to slow slip events the apparent stiffness of the shear zone has to be of the high ( = 1).

5 Figure DR4: We analyze the effect of event depth and stiffness on the size and duration of the events. Repeating creep events for shear zone with high stiffness, = 1 (a) and (c) and low stiffness, = 1 (b) and (d). For the same shear zone viscosity (1 13 Pa.s) a shallower event has a longer duration. For high stiffness the duration is 5 weeks at 25 km (a) and 2 weeks at 4 km (c). For low stiffness the duration is ~8 weeks at 25 km and ~5 weeks at 4 km. Figure DR5: We analyze the effect of shear zone viscosity and stiffness on the size and duration of the events. The parameter is a strong control on the duration of the events as in Figure 2 of the main text, and seen when comparing (a) to (b) and c) to d). For = 1 when the viscosity increases from 1 11 Pa.s (a) to 1 15 Pa.s (c) the creep rate decreases from 4 m.yr 1 to 2 m.yr 1. For = 1 the effect is similar. An increase in viscosity from 1 11 Pa.s (b) to 1 15 Pa.s (d) decreases the creep rate slightly. The shear zone viscosity has more control on the behavior of the shear zone when the apparent stiffness is higher.

6 a b.5 cm.5 mm c d.5 mm.2 mm Figure DR1

7 a b.5 cm.5 mm c d.5 mm.2 mm Figure DR2

8 a) H b = 25 km, η w = 1 11 Pa.s, H w = 1 m. b) H b = 4 km, η w = 1 11 Pa.s, H w = 1 m c) H b = 25 km, η w = 1 15 Pa.s, H w = 1 m. γ = 1 γ = 1 γ = γ = 1 γ = 1 γ = γ = 1 γ = 1 γ = d) H b = 4 km, η w = 1 15 Pa.s, H w = 1 m γ = 1 γ = 1 γ = Figure DR3

9 a) H b = 25 km, η w = 1 13 Pa.s, H w = 1 m, γ = 1. b) H b = 25 km, η w = 1 13 Pa.s, H w = 1 m.,γ = c) H b = 4 km, η w = 1 13 Pa.s, H w = 1 m.,γ = d) H b = 4 km, η w = 1 13 Pa.s, H w = 1 m.,γ = Figure DR4

10 a) H b = 4 km, η w = 1 11 Pa.s, H w = 1 m.,γ = b) H b = 4 km, η w = 1 11 Pa.s, H w = 1 m.,γ = c) H b = 4 km, η w = 1 15 Pa.s, H w = 1 m.,γ = d) H b = 4 km, η w = 1 15 Pa.s, H w = 1 m.,γ = Figure DR5

Supplement of Pinch and swell structures: evidence for strain localisation by brittle viscous behaviour in the middle crust

Supplement of Solid Earth, 6, 1045 1061, 2015 http://www.solid-earth.net/6/1045/2015/ doi:10.5194/se-6-1045-2015-supplement Author(s) 2015. CC Attribution 3.0 License. Supplement of Pinch and swell structures: