Stochastic models for the crystalline crust produce synthetic seismograms that compare well with recorded data for a variety of crustal ages and tectonic environments. In this paper, we explore the parameter space describing such stochastic models as a basis for formulating the inverse problem; that is, we wish to estimate the parameters which define a stochastic model from the recorded backscattered wave field. We base the estimation on approximate relations between the primary reflectivity series, which is the ideal wave field response of a medium, and various seismic gathers. A two-dimensional lateral correlation method is used to investigate the sensitivity of synthetic wave fields to horizontal characteristic length. A derived empirical relationship relates the scale length to the half width of the correlation coefficient. A horizontal wavenumber-time domain spectral analysis successfully estimates the horizontal characteristic length (ax) and the fractal dimension (D) of the stochastic medium from which the wave field was backscattered. We employ a Monte Carlo based optimization scheme to fit the observed spectral values to a one-dimensional von K¿rm¿n function and simultaneously estimate values for ax and the Hurst number &ngr;. The method yields consistent results when tested on synthetic data. Application of this technique to data sorted into different domains shows that zero-offset sections yield the best estimate. We also present results of our estimates using this method on a Program for Array Seismic Studies of the Continental Lithosphere (PASSCAL) dynamite source shot gather and a vibroseis-source Consortium for Continental Reflection Profiling (COCORP) data set recorded in the Basin and Range Province.¿ 1997 American Geophysical Union