The nature of geometric and topological information contained in statistical correlation functions was investigated systematically using simulated porous media, generated by the level-cut of Gaussian random fields. Pore space partitioning techniques based on multiorientation scanning were implemented to determine the pore and neck size distributions, coordination number distribution, and genus of a number of model porous media. These results were correlated with the statistical properties (porosity and correlation function) of the microstructure, revealing for the first time the extent of morphological diversity of a broad class of stochastically reconstructed porous media. It was found that the dominant factor explaining microstructural variability among the media studied is the dimensionless length of spatial correlation. Accordingly, the resolution at which the void space is discretized during simulation was shown to affect significantly the resulting pore and neck size distributions and specific genus. It was also found that the average coordination number of simulated porous media is independent of correlation length, but decreases slightly with decreasing porosity.