Yannick Canivena, Stéphane Domingueza Roger Solivaa, Michel Peyreta, ... critical slip distance Dc used in the rate and state friction laws (Dieterich, 1972a;.
Supplementary material for
Relationships between along-fault heterogeneous normal stress and fault slip patterns during the seismic cycle : Insights from a strike-slip fault laboratory model Earth and Planetary Science Letters Yannick Canivena, Stéphane Domingueza Roger Solivaa, Michel Peyreta, Rodolphe Cattina, Frantz Maertenb a - University of Montpellier, Géosciences Montpellier Laboratory, France b - Schlumberger, Information Solutions Division, Montpellier, France Corresponding author: Y. Caniven, UMR-5243 - Géosciences Montpellier Laboratory, University of Montpellier, CC.60, 34095 Montpellier cedex 5, France
e-mail : yannick.caniven@gm.univ-montp2.fr
Journal : Earth and Planetary Science Letters.
These supplementary materials contain editable tables of data presented figures 3 and 5. A supplementary Figure S1 shows the good repeatability of our results detailed in the present paper. Finally, a short note recalls the theoretical concepts that govern the condition of slip stability and detailed estimates of important parameters in the model. This data set contains surface deformation kinematics data that has been recorded in seismic cycle experiments. They were processed using a sub-pixel spectral correlation algorithm developed by Van Puymbroeck (2000) and treated with GMT software (Global Mapping Tools) using bash codes. 1. Table_Fig3.xlsx : Data for Figure 3 Labels of colums are the same as for the figure and described in corresponding captions. 2. Table_Fig5_Table.xlsx : Data for Figure 5 Labels of colums are the same as for the figure and described in corresponding captions.
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3. Figure S1 : Results from another experiment performed using a different initial normal stress distribution.
Figure S1 : Results from another experiment performed using a different applied normal stress distribution. a) Up : Dashed black line shows σyy distribution along the fault trace.
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Down : Red curves shows 93 fault slip profiles (fault parallel component of horizontal surface displacements) that were detected among 300 successive measurements extracted from a 2h-long period of the experiment (2h, i.e ~100 Kyrs in nature). Blue vertical bars and yellow stars indicate the location of maximum displacement for each slip profile. b) Dmax along the fault vs Time. c) Recurrence-time of SC events.
Comments on the Figure S1 : As for the presented experiment in the paper, most of strong microquakes are characterized by a maximum coseismic slip located close to one of the normal-stress peaks (stress asperity zone). Slip events associated with slow aseismic fault creep were not filtered from this dataset and are probably included among the lowest slip events visible below 0.05 mm in the graph (a). Slip events types were not differentiated here because the purpose of this figure is only to show the relationship between the location of maximum displacements and that of stress asperities. Note here that the amplitudes of stress asperities are lower (~100 Pa maximum) and the normal stress distribution along the fault appears then more homogenous. Clustering sequences presented in Caniven et al., (2015) and discussed in the present paper were recorded during this experiment. The recurrence-times of SC events (c) extend on a larger range of values implying that the seismic cycle is more regular in that case.
4. Note on the slip stability in the experiments : Similarity between model and natural faults in slip stability needs to be established before one could extrapolate laboratory results to earthquake behavior. The stability of slip in a system depends on the normal stress σn applied to the fault plane, the system stiffness K and fault material frictional parameters such as (a-b) and the critical slip distance Dc used in the rate and state friction laws (Dieterich, 1972a; Ruina, 1983; Scholz, 1998). Estimate of frictional parameters conducts to determine the critical length Lc of the slipping region above which instability occurs, i.e. the socalled nucleation size, which is the minimum size of unstable events. At first order, the model scaling is considered to be correct if (a-b) is conserved between model and nature (dimensionless) and Dc and Lc imply consistent natural equivalents using the geometric factor L*. !
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The frictional parameter (a-b) describes the velocity dependence of friction, usually determined experimentally by measuring the frictional response to step changes of slip rate. For (a-b) ≥ 0, the material is «velocity strengthening» and the system is intrinsically stable. For (a-b) ≤ 0, the material is «velocity weakening» and the system become unstable at a critical value of the normal stress σc with !.!"
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For our experiments, we estimate (a-b) using the stress drop associated with stickslip events, the normal stress applied to the fault, and a velocity step increase from stable slip to coseismic slip (Caniven et al., 2015). Based on these data, (a-b) can be estimated to about -0.017 which is very close to the -10−2 value determined for rocks in the velocity weakening domains, depending on temperature, normal stress and shear rates (Stesky et al., 1974; Marone et al., 1990; Blanpied et al., 1991; Marone, 1998; Scholz, 1998). Estimate Dc is also important because it controls the nucleation processes of earthquakes and the dynamic rupture history. In fact, Dc is the slip amount necessary for friction to change in response to a velocity variation. For the presented analog model, we estimated Dc from the Eq.1, considering a critical normal stress σc of about 100 Pa (stick-slip is inhibited when σn < 100 Pa ) and a shear stiffness K such as !
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with E the Young modulus, ν the Poisson ratio and L the slipping region length. Using the values of these parameters presented earlier in this section and a maximum rupture length L of 1 m for the great analog earthquakes (see section 3.2), Dc ~ 30 µm. Consistent with the used L*, for natural earthquakes, Dc is proposed to be in the order of decimeters to several meters by laboratory experiments with high velocity frictional tests (e.g, Di Toro et al., 2011 and references therein) or by numerical and seismological estimates (e.g, Fukuyama and Suzuki, 2016 and references therein).
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Assuming an in-plane (Mode II) crack model (Andrews, 1976), we estimated the critical length Lc in the model with :
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Eq. (3)
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In the range of the applied normal stress along the analog fault, we found Lc ~ 1 mm, consistent with our L* and typical Lc values for natural earthquakes being in the order of hectometers to kilometers (e.g, Kaneko et al., 2016; Ohnaka, 2013 among many others).
Supplemental reference list : Andrews, D.J. (1976). Rupture velocity of plane strain shear cracks. J. Geophys. Res. 81, 5679–5687. Blanpied, M.L., Lockner, D.A., and Byerlee, J.D. (1991). Fault stability inferred from granite sliding experiments at hydrothermal conditions. Geophysical Research Letters 18, 609– 612. Caniven, Y., Dominguez, S., Soliva, R., Cattin, R., Peyret, M., Marchandon, M., Romano, C., and Strak, V. (2015). A new multilayered visco-elasto-plastic experimental model to study strike-slip fault seismic cycle. Tectonics 2014TC003701. Dieterich, J.H. (1972). Time-dependent friction in rocks. Journal of Geophysical Research 77, 3690–3697. Fukuyama, E., and Suzuki, W. (2016). Near-fault deformation and Dc during the 2016 Mw7.1 Kumamoto earthquake. Earth Planets Space 68, 194. Kaneko, Y., Nielsen, S.B., and Carpenter, B.M. (2016). The onset of laboratory earthquakes explained by nucleating rupture on a rate-and-state fault. J. Geophys. Res. Solid Earth 121, 2016JB013143. Marone, C. (1998). Laboratory-derived friction laws and their application to seismic faulting. Annual Review of Earth and Planetary Sciences 26, 643–696. Marone, C., Raleigh, C.B., and Scholz, C.H. (1990). Frictional behavior and constitutive modeling of simulated fault gouge. J. Geophys. Res. 95, 7007–7025. Ohnaka, M. (2013). The Physics of Rock Failure and Earthquakes (Cambridge University Press).
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Van Puymbroeck, N., Michel, R., Binet, R., Avouac, J.P., and Taboury, J. (2000). Measuring earthquakes from optical satellite images. Applied Optics 39, 3486–3494. Ruina, A. (1983). Slip instability and state variable friction laws. Journal of Geophysical Research: Solid Earth 88, 10359–10370. Scholz, C.H. (1998). Earthquakes and friction laws. Nature 391, 37–42. Stesky, R.M., Brace, W.F., Riley, D.K., and Robin, P.-Y.F. (1974). Friction in faulted rock at high temperature and pressure. Tectonophysics 23, 177–203.
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