Three different aspects of estimating properties from seismic data are treated in this thesis: (1) Deterministic processing of a high resolution shallow seismic data set with good geologic control, (2) traveltime estimation from complicated models described statistically, and (3) estimation of a the vertical autocorrelation length of such models. The first part of this thesis is the processing and interpretation of a shallow seismic dataset collected in an open pit copper mine near Tyrone, New Mexico. The seismic image is compared with the outcrop in the open pit mine wall along which the seismic line was collected, and with drill data obtained from the mine operators. Specific features imaged by the experiment include the base of the overlaying sediment, the base of the leached capping, and fractures and shear zones that control local ground water flow. The features in the migrated section compare well with outcrop and drill data. The second part of the thesis studies the systematic bias of velocities estimated from first arrival travel times measured from a class of very complicated velocity models. Traveltimes were computed for statistically described velocity models with anisotropic von Karman correlation functions. The results of a finite difference eikonal solver, corresponding to very small wavelength experiments, are compared to results from picking first arrivals of full wavefield finite difference simulations. The eikonal solver results show the largest systematic bias, corresponding to the ray theoretical limit, and the results from the full wavefield experiments are smaller, but with very similar dependence on aspect ratio of the anisotropic correlation function. The third part defines two methods to obtain the vertical correlation length from seismic data approximated by the primary reflectivity series, which conventionally is used as the ideal result of seismic imaging. The first method is based on fitting a theoretical power spectrum based on the known source spectrum and fractal dimension to the average vertical power spectrum of the seismograms. This method works for a range of conditions where the correlation length is relatively small compared to the wavelength. Larger correlation lengths can be estimated by a second method based on deconvolving and integrating the seismogram to obtain an approximation of a vertical slice of the velocity model.