## 4 Implications for Friction Analysis  
The experimental setup developed in [1; 3], which combines ultra-high-speed photography with digital image correlation, enables us to observe displacements, velocities, and stresses close to the interface. For the field of view shown in Figure 1, these quantities can be measured up to 25 \(\upmu\)m (0.5 pixels) from the interface using the \"fill boundary\" algorithm of Vic-2D. This enables studying the evolution of friction, defined by the ratio \(f=\sigma_{12}{}^{0}/\sigma_{22}{}^{0}\), at any point along the interface, as well as its dependence on variables such as slip (relative displacement across the interface) and slip rate [1]. As a first approach to enforce traction continuity on the interface, the tractions \(\sigma_{12}{}^{0}\) and \(\sigma_{22}{}^{0}\) were calculated in [1] by averaging the stresses at the pixels immediately above and below the interface. Because of the anti-symmetric and symmetric patterns in the stress changes \(\Delta\sigma_{22}\) and \(\Delta\sigma_{12}\), respectively, the normal stress on the interface \(\sigma_{22}{}^{0}\) was inferred to be nearly constant, as expected during the propagation of a dynamic shear rupture along a planar interface, and the shear stress \(\sigma_{12}{}^{0}\) had a smoother evolution than the individual components \(\sigma_{12}{}^{0}\) and \(\sigma_{12}{}^{0}\) above and below the interface. The averaging enabled us  
Figure 7: The effect of parameter \(n_{x2,cnt}\) on the stress field. (**a–d**) Full-field maps of normal (left) and shear (right) stresses for \(n_{x2,cnt}=7\) and 19. (**e–h**) Normal (left) and shear (right) stresses vs position along paths perpendicular to the interface at \(x_{1}=170\) and 220 pixels (grey lines in (**c**)) for different values of \(n_{x2,cnt}\). The circles on the curves correspond to \(n_{x2,inter}\), while the filled diamonds correspond to \(n_{x2}\). The stresses calculated with the “fill boundary” algorithm of Vic-2D without the traction continuity algorithm are also shown, where the black diamonds correspond to the centers of the subsets above and below the interface. In all the cases shown in this figure \(n_{x1}=7\) and \(n_{x2,inter}=10\). to study friction, despite large differences between the normal stresses immediately above and below the interface [1], but it is important to examine whether those average values actually correspond to the tractions at the interface computed with the continuity condition. In general, the averaged normal stresses (without TC enforcement) agreed with the normal stresses computed with TC enforcement for the pixels immediately above and below the interface (Figure 8a), with some small deviations. Note that, because we enforced the continuity at the interface, the stresses obtained with TC enforcement for the pixels located 0.5 pixels above and below the interface did not completely overlap, with a maximum difference of 0.3 MPa. Because of its symmetry with respect to the interface, the discontinuity in shear stress across the interface for the original Vic-2d results (Figure 8b) was significantly smaller than in the normal stress. Overall, there was a good agreement between the shear tractions obtained by the averaging procedure and those obtained with TC enforcement, again, with some minor differences. Interestingly, the differences were consistently smaller in the cohesive zone (the zone where the shear traction drops from a maximum to a residual value), with a maximum difference of about 1 MPa at \(x_{1}=9\) mm. This is also shown locally in Figure 5h. Because the stresses were computed from displacement gradients, small changes in the displacements were enough to enforce the traction continuity on the interface, and there were only minor differences between the interface-parallel displacements and velocities obtained with TC enforcement and those obtained without TC enforcement (Figure 8c,d). The small differences in stresses resulted in some differences in the evolution of local friction with slip and slip rate (Figure 8e,f).