In general, inversion algorithms rely on good starting models to produce realistic earth models. A new method, based on a fractional Gaussian distribution derived from the statistical parameters of available well logs to generate realistic initial models, uses fractal theory to generate these models. When such fractal-based initial models estimate P- and S-impedance profiles in a prestack stochastic inversion of seismic angle gathers, very fast simulated annealing — a global optimization method — finds the minimum of an objective function that minimizes data misfit and honors the statistics derived from well logs. The new stochastic inversion method addresses frequencies missing because of band limitation of the wavelet; it combines the low- and high-frequency variation from well logs with seismic data. This method has been implemented successfully using real prestack seismic data, and results have been compared with deterministic inversion. Models derived by a deterministic inversion are devoid of high-frequency variations in the well log; however, models derived by stochastic inversion reveal high-frequency variations that are consistent with seismic and well-log data.