Materials and Methods The deformation within the process zone of a propagating fault can be modeled using an elastic approximation. In the process zone, stress amplitudes are poorly determined and much lower than an elastic model predicts, but strains and the principal axes of strain are more or less correct (1). The form of the strain tensor can consequently be used together with a simple Coulomb-like failure criterion (2) to define the orientations and mechanism of predicted faulting. In this work, the shear zone or fault is modeled as a rectangular dislocation in an elastic half-space (3). A Young's Modulus of 1.0 and a Poisson's ratio of 0.5 are adopted. With these values the results can then be interpreted in terms of strain, with the Coulomb strain being numerically equivalent to the Coulomb stress. The calculations are carried out using an effective friction of 0.4. Because the model uses a non-zero friction, the failure planes associated with Coulomb strain are not orthogonal and a standard seismic focal mechanism representation of the predicted fault planes is not correct. The convention adopted to denote the faults uses a simplified stereonet representation of the fault geometry and kinematics (Figs. 1d. and 2e). For each fault mechanism a blue or red line shows the intersection of the fault with the plane of the model. The rake for each fault is indicated by a red or blue dot showing the intersection of the slip vector with a hemisphere behind the modeled plane. To aid in discriminating relative motions, blue lines represent apparent clockwise (or right-lateral) motion, while red lines indicate apparent anticlockwise (or left-lateral) motion. For all of the models, Coulomb strain is plotted as a function of master fault slip. This allows the relative activity of different parts of the slip-partitioned system to be estimated. The figures use simplified representations of the master faults consistent with the known form of the fault system. Three segments (SA1 to 3) are used to model the San Andreas fault (Fig. 2b) and four (HA1 to 4) to model the Haiyuan fault (Fig. 2d). The locations of the faults within the figures are shown by green lines. Strains are calculated for 1 meter of horizontal slip in both cases. The direction of this slip is taken to be parallel to the mean orientation of the central San Andreas (Fig. 2b, segment SA1) and to the mean orientation of the Haiyuan west of the modeled area (Fig. 2d, segment
HA1). The slip is resolved onto the other segments to give appropriate strike-slip and dip-slip components. For both models the master faults extend from 30 km to 1000 km (infinite) depth. The coordinates of the segment ends for the San Andreas model are:- Segment SA1 dip 90 : 54.8300 N, -158.345 E to 34.9734 N -119.487 E; Segment SA2 dip 80 N: 34.9734 N, -119.487 E to 33.8646 N, -116.272 E; Segment SA3 dip 90 : 33.8646 N, -116.272 E to -13.5670 N, -82.2496 E. Segments 1 and 3 are pure strikeslip. The coordinates of the fault ends for the Haiyuan model are:- Segment HA1 dip 90 : 37.7293 N, 80.3217 E to 38.2828 N, 99.5088 E; Segment HA2 dip 70 S: 38.2828 N, 99.5088 E to 37.3872 N, 102.152 E; Segment HA3 dip 80 S: 37.3872 N, 102.152 E to 37.4510 N, 105.725 E; Segment HA4 (Gulang fault) dip 80 S: 37.3872 N, 102.152 E to 36.4163 N, 125.298 E. For segments HA3 and HA4 the horizontal component of slip is 70% on HA3, 30% on HA4. The conversion from geographic to Cartesian co-ordinates is carried out using a stereographic projection. For the San Andreas model the pole is at 34 N, -108 E. For the Haiyuan model it is at 38.0 N, 101.0 E.
DipofMainFault=30 Cross-Section Map-View Reverse Component = 1.0 m Strike-Slip Component = 0.0 m Reverse Component = 1.0 m Strike-Slip Component = 0.2 m Reverse Component = 1.0 m Strike-Slip Component = 0.4 m Reverse Component = 1.0 m Strike-Slip Component = 0.6 m Reverse Component = 1.0 m Strike-Slip Component = 0.8 m Reverse Component = 1.0 m Strike-Slip Component = 1.0 m
Reverse Component = 0.8 m Strike-Slip Component = 1.0 m Reverse Component = 0.6 m Strike-Slip Component = 1.0 m Reverse Component = 0.4 m Strike-Slip Component = 1.0 m Reverse Component = 0.2 m Strike-Slip Component = 1.0 m Reverse Component = 0.0 m Strike-Slip Component = 1.0 m -1x10-5 strain 1x10-5 Figure S1. Slip partitioning resulting from strain on a 30 dipping oblique fault. Left side of figure shows strain distribution and optimal failure planes in a cross-section perpendicular to the fault. Right side shows strain distribution and optimal failure planes in map view. Blue mechanisms indicate clockwise relative displacement in cross-section and right-lateral motion in map view. Red symbols indicate counter-clockwise motion in cross-section and left-lateral motion in map view. See Fig. 1d for explanation of symbols in crosssection and Fig. 2e for explanation of symbols in map view.
Dip of Main Fault = 45 Cross-section Map View Reverse Component = 1.0 m Strike-Slip Component = 0.0 m Reverse Component = 1.0 m Strike-Slip Component = 0.2 m Reverse Component = 1.0 m Strike-Slip Component = 0.4 m Reverse Component = 1.0 m Strike-Slip Component = 0.6 m Reverse Component = 1.0 m Strike-Slip Component = 0.8 m Reverse Component = 1.0 m Strike-Slip Component = 1.0 m
Reverse Component = 0.8 m Strike-Slip Component = 1.0 m Reverse Component = 0.6 m Strike-Slip Component = 1.0 m Reverse Component = 0.4 m Strike-Slip Component = 1.0 m Reverse Component = 0.2 m Strike-Slip Component = 1.0 m Reverse Component = 0.0 m Strike-Slip Component = 1.0 m -1x10-5 strain 1x10-5 Figure S2. Slip partitioning resulting from strain on a 45 dipping oblique fault. Left side of figure shows strain distribution and optimal failure planes in a cross-section perpendicular to the fault. Right side shows strain distribution and optimal failure planes in map view. Blue mechanisms indicate clockwise relative displacement in cross-section and right-lateral motion in map view. Red symbols indicate counter-clockwise motion in cross-section and left-lateral motion in map view. See Fig. 1d for explanation of symbols in crosssection and Fig. 2e for explanation of symbols in map view.
Dip of Main Fault = 60 Cross-Section Map View Reverse Component = 1.0 m Strike-Slip Component = 0.0 m Reverse Component = 1.0 m Strike-Slip Component = 0.2 m Reverse Component = 1.0 m Strike-Slip Component = 0.4 m Reverse Component = 1.0 m Strike-Slip Component = 0.6 m Reverse Component = 1.0 m Strike-Slip Component = 0.8 m Reverse Component = 1.0 m Strike-Slip Component = 1.0 m
Reverse Component = 0.8 m Strike-Slip Component = 1.0 m Reverse Component = 0.6 m Strike-Slip Component = 1.0 m Reverse Component = 0.4 m Strike-Slip Component = 1.0 m Reverse Component = 0.2 m Strike-Slip Component = 1.0 m Reverse Component = 0.0 m Strike-Slip Component = 1.0 m -1x10-5 strain 1x10-5 Figure S3. Slip partitioning resulting from strain on a 60 dipping oblique fault. Left side of figure shows strain distribution and optimal failure planes in a cross-section perpendicular to the fault. Right side shows strain distribution and optimal failure planes in map view. Blue mechanisms indicate clockwise relative displacement in cross-section and right-lateral motion in map view. Red symbols indicate counter-clockwise motion in cross-section and left-lateral motion in map view. See Fig. 1d for explanation of symbols in crosssection and Fig. 2e for explanation of symbols in map view.
Dip of Main Fault = 75 Cross-Section Map View Reverse Component = 1.0 m Strike-Slip Component = 0.0m Reverse Component = 1.0 m Strike-Slip Component = 0.2 m Reverse Component = 1.0 m Strike-Slip Component = 0.4 m Reverse Component = 1.0 m Strike-Slip Component = 0.6 m Reverse Component = 1.0 m Strike-Slip Component = 0.8 m Reverse Component = 1.0 m Strike-Slip Component = 1.0 m
Reverse Component = 0.8 m Strike-Slip Component = 1.0 m Reverse Component = 0.6 m Strike-Slip Component = 1.0 m Reverse Component = 0.4 m Strike-Slip Component = 1.0 m Reverse Component = 0.2 m Strike-Slip Component = 1.0 m Reverse Component = 0.0 m Strike-Slip Component = 1.0 m -1x10-5 1x10-5 strain Figure S4. Slip partitioning resulting from strain on a 75 dipping oblique fault. Left side of figure shows strain distribution and optimal failure planes in a cross-section perpendicular to the fault. Right side shows strain distribution and optimal failure planes in map view. Blue mechanisms indicate clockwise relative displacement in cross-section and right-lateral motion in map view. Red symbols indicate counter-clockwise motion in cross-section and left-lateral motion in map view. See Fig. 1d for explanation of symbols in crosssection and Fig. 2e for explanation of symbols in map view.
References 1. A. Hubert-Ferrari et al., Geophys. J. Int., 153, 111 (2003). 2. G.C.P.King, M. Cocco. Advances in Geophysics, 44, 1 (2001). 3. Y. Okada, Y. Bull. seism. Soc. Amer. 75,1135 (1985).