The concept of "numerical Green's functions" (NGF or Green's function database) is developed. The basic idea is: a large seismic fault is divided into subfaults of appropriate size, for which synthetic Green's functions at the surface (NGF) are calculated and stored. Consequently, ground motions from arbitrary kinematic sources can be simulated, rapidly, for the whole fault or parts of it by superposition. The target fault is a simplified, vertical model of the Newport-Inglewood fault in the Los Angeles basin. This approach and its functionality are illustrated by investigating the variations of ground motions (e.g. peak ground velocity and synthetic seismograms) due to the source complexity. The source complexities are considered with two respects: hypocenter location and slip history. The results show a complex behavior, with dependence of absolute peak ground velocity and their variation on source process directionality, hypocenter location, local structure, and static slip asperity location. We concluded that combining effect due to 3-D structure and finite-source is necessary to quantify ground motion characteristics and their variations. Our results will facilitate the earthquake hazard assessment projects.