Recent studies have shown that a useful scheme to characterize subsurface heterogeneity is to use fractional Brownian motion (fBm) and fractional Gaussian noise (fGn). Commonly used techniques to detect these fractal distributions include rescaled range, spectral, and semivariogram analyses. Although rescaled range analysis is considered to be superior to spectral or semivariogram techniques, it cannot be used to clearly discriminate fGn and fBm from a given data set in some cases. On the basis of the fact that both adjusted range and rescaled range analyses, for a true fGn data set, should yield the same slope value in the relevant log-log plots, a simple scheme is developed to discriminate fGn and fBm using a combination of the two analyses. The usefulness of the proposed scheme is evaluated with one-dimensional computational experiments and by an application to a data set of observed air permeability logs. Lack of clear discrimination may have contributed to inconsistent past results, and it is recommended that old data sets be reanalyzed. ¿ American Geophysical Union 1996