Seismic data do not contain some low- and high-frequency information because of the band-limited nature of the source wavelet. A deterministic inversion of such band-limited seismic data produces smooth models which are devoid of high-frequency variations observed in well logs. Stochastic inversion methods often based on random Gaussian priors can have a limitation of producing high frequencies in the desired model particularly the frequency band not constrained by the input seismic data. In this paper, we propose a new stochastic poststack inversion algorithm where fractal models constructed from statistical properties of well logs are used to generate a priori models. This provides a high-resolution model without injecting spurious high-frequency estimates in model space. Stacked seismic data are used in the inversion in which a suitable objective function is minimized using a nonlinear optimization method called 'very fast simulated annealing'. We demonstrate the effectiveness of our method for the estimation of acoustic impedance with the application to a field dataset.