Integrating field observations and fracture mechanics models to constrain seismic source parameters for ancient earthquakes

Most of our understanding of earthquake rupture comes from interpretation of strongground-motion seismograms; however, near-rupture-tip fields of stress and particle motions are difficult to resolve. In particular, the decay of frictional resistance from a peak value at the leading tip of the rupture to a residual kinetic value and subsequent healing characterizes the earthquake process, yet the nature of this evolution in situ is still unclear. Knowledge of this coseismic frictional constitutive behavior has been supplemented by laboratory experiments, yet scaling laboratory experiments to natural faults is non-trivial because these experiments do not exactly reproduce the boundary conditions governing natural earthquakes. Field investigations of exhumed faults provide the spatial resolution needed to integrate remote seismological observations, laboratory experiments, and numerical models of the rupture process for natural ruptures. Here we build on previous work that showed that the orientation of pseudotachylyte injection veins found along the Gole Larghe fault zone in granitoid rocks of the Italian Alps can be used to infer rupture directivity and velocity. We demonstrate that the length of these veins can be used to further constrain the rupture size, slip weakening distance, stress drop, and fracture energy. The results are consistent with seismological observations and recent friction experiments incorporating rapid accelerations, placing constraints on coseismic frictional evolution in granitoid rocks. INTRODUCTION Most seismic source parameters, including stress and strength drop, fracture energy G, slip distance S, and rupture velocity vII, are routinely estimated using seismology. Earthquake rupture requires frictional resistance on a fault to drop from a peak value equal to the static fault strength to a smaller residual value (i.e., strength drop) with slip, a process described as “slip weakening”. The fracture energy G(S), defined as the area under the shear stress–versus–slip curve between the peak and residual stresses, is a robust seismological measure; however, absolute stress values before and after slip, and the slip weakening distance Dc, are difficult to resolve (Abercrombie and Rice, 2005). During the past two decades, laboratory friction experiments conducted in different configurations have been employed to investigate coseismic frictional constitutive behavior of rocks and analog materials at or near seismic slip speeds (e.g., Yuan and Prakash, 2008a, 2008b; Di Toro et al., 2011). These studies provide valuable insight into the evolution of friction stress during slip, yet the broad validity of laboratory-derived frictional constitutive laws, particularly at fast slip rates, remains unclear. An obvious source of discrepancy comes from the fact that many of these experiments are conducted at normal stress and slip velocity that may not reflect conditions during natural seismic fault ruptures (Niemeijer et al., 2012; Rowe and Griffith, 2015). Given the difficulty of resolving near-tip stress and velocity fields of earthquake ruptures and replicating natural seismic slip conditions in the laboratory, in the present study we use coseismically formed fault structures exposed along exhumed faults to characterize transient near-tip stress fields associated with ancient earthquakes. This approach builds off the work of Di Toro et al. (2005a) in which orientation and spatial distribution of pseudotachylyte injection veins along the Gole Larghe fault zone cutting tonalite in the southern Italian Alps were used to infer earthquake rupture velocity and directivity. We extend this approach by using the measured injection vein lengths to further constrain earthquake source parameters, including dynamic stress and strength drops, rupture pulse length, G, and Dc, using the pulse-like rupture model of Rice et al. (2005), an analytical model for the two-dimensional (2-D) stress field around a moving slip pulse of length L with a slip-weakening zone of length R behind the rupture tip. Figure 1 shows a schematic of the slip pulse propagating along a pre-cut interface in a laboratory specimen (Xia et al., 2004; Griffith et al., 2009). The model uses a moving coordinate system with the origin at the rupture tip and the positive x-axis in the direction of rupture (Fig. 1). Within the slip-weakening zone, shear stress experiences a spatially linear decay from peak tp to a residual value tr at the trailing edge of the slip weakening zone (x = –R). Slip occurs along the entire slip patch of length L, and the strength is assumed to recover at the trailing edge (x = –L). This decay has an exponential relationship with slip, i.e., t(S) = (tp – tr)ec + tr , where Dc is a characteristic slip distance (Rice et al., 2005). Using this form, fracture energy G can be estimated by integrating over the first term on the right-hand side of this equation, yielding G = (tp – tr) Dc for Dc < S. Note that this definition relationship differs from the commonly applied relationship ( ) = τ − τ G D 2 p r c in which the relationship between stress and slip is assumed to be linear and no weakening occurs beyond the slip Dc (e.g., Abercrombie and Rice, 2005). It is assumed that the fault strength heals to its original value such that final fault strength syx = s0 yx for x < –L. The pulse model for earthquake rupture is convenient for the present application because the ratio of the dynamic stress drop (s0 yx – tr) to the strength drop (tp – tr) is constrained by L/R, reducing the number of free variables (Rice et al., 2005, their equation 8). The model does not require knowledge of the frictional constitutive behavior a priori, and due of the relationship between L, R, and s0 yx – tr , only a few combinations of these parameters can match the total slip magnitude constrained in the lab or field. GEOLOGY, September 2015; v. 43; no. 9; p. 1–4 | Data Repository item 2015260 | doi:10.1130/G36773.1 | Published online XX Month 2015 © 2015 eological Society of A erica. For permission to copy, contact [email protected]. R