Finite-fault source inversions reveal the spatial complexity of earthquake slip or prestress distribution over the fault surface. In this paper we discuss a stochastic model that reproduces the spatial variability and the long-range spatial correlation of the slip distribution of the 1979 Imperial Valley earthquake. We have found that stochastic models based on non-Gaussian distributions are better suited to describe the spatial variability of the slip amplitude over the fault. We also show that a stochastic modeling of the slip amplitude based on a Gaussian distribution fails to reproduce the spatial variability observed in the original slip distribution. The stochastic models can be used to deduce ground motion from other earthquakes statistically similar to Imperial Valley.