The generation of seismicity catalogs on synthetic fault networks holds the promise of providing key inputs into probabilistic seismic-hazard analysis, for example, the coefficient of variation, mean recurrence time as a function of magnitude, the probability of fault-to-fault ruptures, and conditional probabilities for foreshock-mainshock triggering. I employ a seismicity simulator that includes the following ingredients: static stress transfer, viscoelastic relaxation of the lower crust and mantle, and vertical stratification of elastic and viscoelastic material properties. A cascade mechanism combined with a simple Coulomb failure criterion is used to determine the initiation, propagation, and termination of synthetic ruptures. It is employed on a 3D fault network provided by Steve Ward (unpublished data, 2009) for the Southern California Earthquake Center (SCEC) Earthquake Simulators Group. This all-California fault network, initially consisting of 8000 patches, each of ~12 square kilometers in size, has been rediscretized into ~100;000 patches, each of ~1 square kilometer in size, in order to simulate the evolution of California seismicity and crustal stress at magnitude M ~ 5-8. Resulting synthetic seismicity catalogs spanning 30,000 yr and about one-half million events are evaluated with magnitude-frequency and magnitude-area statistics. For a priori choices of fault-slip rates and mean stress drops, I explore the sensitivity of various constructs on input parameters, particularly mantle viscosity. Slip maps obtained for the southern San Andreas fault show that the ability of segment boundaries to inhibit slip across the boundaries (e.g., to prevent multisegment ruptures) is systematically affected by mantle viscosity.