This research is to invert near-source waveforms of the Loma Prieta earthquake to determine the temporal and spatial behavior of fault slip. These data will be supplemented with records from intermediate and teleseismic distances. The methodology proposed here is a frequency domain inversion method using a new norm minimization constraint that produces slip models characterized by having the most nearly constant rupture velocity, and spatial slip amplitude distribution, that are consistent with the data. Source parameters such as hypocenter location, source time function, rupture front geometry and direction of propagation are not predetermined, but solved for. This research is a component of the National Earthquake Hazard Reduction Program.