We predict ground motions in the Salt Lake basin (SLB) during M 7 earthquakes on the Salt Lake City segment of the Wasatch fault (WFSLC). First we generate a suite of realistic source representations by simulating the spontaneous rupture process on a planar, vertical fault with the staggered-grid split-node finite-difference (FD) method. The initial distribution of shear stress is the sum of both a regional depth-dependent shear stress appropriate for a dipping, normal fault and a stochastically generated residual shear stress field associated with previous ruptures. The slip-rate histories from the spontaneous rupture scenarios are projected onto a detailed 3D model geometry of the WFSLC that we developed based on geological observations. Next, we simulate 0- to 1-Hz wave propagation from six source models with a 3DFD code, using the most recent version of the Wasatch Front Community Velocity model. Horizontal spectral accelerations at two seconds (2-s SAs) reveal strong along-strike rupture direction effects for unilateral ruptures, as well as significant amplifications by the low-velocity sediments on the hanging-wall side of the fault. For ruptures nucleating near the southern end of the segment, we obtain 2-s SAs of up to 1.4g near downtown SLC, caused by a combination of rupture-direction and basin-edge effects. Average 3-s SAs and 2-s SAs from the six scenarios are generally consistent with values predicted by four next-generation attenuation models.