A Laboratory Earthquake-Based Stochastic Seismic-Source-Generation Algorithm for Strike-Slip Faults and Its Application to the Southern San Andreas Fault

**Source-Model-Generation Algorithm Validation: 2004 M_{w} 6.05 Parkfield-Like Earthquake on Southern San Andreas Fault**

The validation exercise to ensure that the ground motions produced by the stochastic source models are similar to those produced by finite-source inversion models is repeated for an *M _{w}* 6.05 earthquake. As was done for the

The statistical comparison of peak ground velocity (see Figs. S5 and S6) and the displacement resulting from the two source models indicates significant differences. This can be attributed primarily to the strength of the slip asperity in the stochastic source compared to that in the finite-source inversion. The reason for this may be the magnitude–area relation that suggests a rupture area of just 10 km × 10 km for an *M _{w}* 6.0 earthquake, whereas the finite-source inversion for the Parkfield earthquake points to a significantly larger area and smaller slips as a result. The comparison of attenuation of ground motion (median peak average horizontal velocity) with distance from source between stochastic and Parkfield models is shown in Figure S7. The median peak horizontal velocity and displacement (and median ± 1 standard deviation) and the spectral acceleration (at 3 s) as a function of distance from the source simulated at sites in the greater Los Angeles region that are within 100 km of the median stochastic source model (

**Figure S1.** (a) Stochastic median source model with slip (in meters) for an *M _{w}* 6.05 earthquake on the San Andreas fault. (b) Finite-source inversion model for the

Figure S2**.** Rupture scenarios: (solid lines) median peak ground velocity (PGV) computed at 636 sites in southern California from 10 rupture scenarios (5 rupture locations along the southern San Andreas fault × 2 rupture directions) using each of five stochastic source realizations and (dashed lines) the corresponding median PGV from all fifty scenario earthquakes. All earthquakes are of magnitude *M _{w}* 6.05.

**Figure S3.** East–west (EW) and north–south (NS) components of PGV (cm/s) from a north-to-south propagating rupture at location 3 on the southern San Andreas fault: (a) and (b) *M _{w}* 6.05 stochastic median source model and (c) and (d)

**Figure S4.** EW and NS components of peak ground displacement (PGD; cm) from a north-to-south propagating rupture at location 3 on the southern San Andreas fault: (a) and (b) *M _{w}* 6.05 stochastic median source model; (c) and (d)

Figure S5. Five *M*_{w} 6.05 north-to-south rupture scenarios (at locations 1–5) on the San Andreas fault using **(a)–(e)** the stochastic median model and **(f)–(j)** the *M _{w}* 6.0 Parkfield earthquake finite-source inversion model: histograms and best-fit lognormal probability density function (PDFs; insets) of PGV at 636 stations in southern California. The product of the listed scaling factor and the normalized histogram ordinate at a specific peak velocity gives the total number of stations for that velocity.

Figure S6. Five *M _{w}* 6.05 south-to-north rupture scenarios (at locations 1–5) on the San Andreas fault using

Figure S7**.** Median peak average horizontal velocity (m/s) (+, stochastic model; x, Parkfield model) as a function of source-to-site distance in southern California due to an *M*_{w} 6.05 earthquake occurring along the southern San Andreas fault. The shaded region corresponds to median ± 1 standard deviation. A total of 10 rupture scenarios (5 rupture locations × 2 propagation directions) are considered.

**Figure S8.** (a) Median peak horizontal velocity (m/s) and (b) median peak horizontal displacement (m) as a function of source-to-site distance for 10 *M*_{w} 6.05 earthquake scenarios on the southern San Andreas fault (5 rupture locations × 2 rupture directions) using the median stochastic source model (+, simulations; CB08, predictions by the Campbell–Bozorgnia Next Generation Attenuation [NGA] relation). The shaded region corresponds to median ± 1 standard deviation.

Figure S9**.** Spectral acceleration (*g*) at *T* = 3 s (SA^{3s}) as a function of source-to-site distance for 10 *M*_{w} 6.05 earthquake scenarios on the southern San Andreas fault (5 rupture locations × 2 rupture directions): + and o are the simulated east–west and the north–south SA^{3s} components at the greater Los Angeles sites using the median stochastic source model, respectively, and x shows the predictions by the Campbell–Bozorgnia NGA relation. The shaded region corresponds to median ± 1 standard deviation.

Ji, C. (2004). Slip history of the 2004 (*M _{w}* 5.9) Parkfield earthquake (single-plane model), available at http://www.tectonics.caltech.edu/slip_history/2004_ca/parkfield2.html (last accessed December 2014).

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