Summary A deterministic inversion of band-limited seismic data produces smooth models which are devoid of high frequency variations observed in well logs. Stochastic inversion methods often based on Gaussian priors can produce high frequencies in the desired model. In this paper, we propose a new stochastic prestack inversion algorithm where fractal models constructed from well logs are used to generate a prioi models. Angle stack data are used in the inversion in which a suitably chosen objective function is minimized using a nonlinear optimization method called ‘very fast simulated annealing.’ We demonstrate the effectiveness of our method with application to a field dataset.