Characterization of the structure of river-bed gravels using two-dimensional fractal analysis

This paper is concerned with the application of fractal analysis to underst and the structure of water-worked gravel-bed river surfaces. High resolutio n digital elevation models, acquired using digital photogrammetric methods, allowed the application of two-dimensional fractal methods. Previous grave l-bed river studies have been based upon sampled profiles and hence one-dim ensional fractal characterisation. After basic testing that bed elevation i ncrements are Gaussian, the paper uses two-dimensional variogram surfaces t o derive directionally dependent estimates of fractal dimension. The result s identify mixed fractal behavior with two characteristic fractal bands, on e associated with the subgrain scale and one associated with the grain scal e, The subgrain scale characteristics were isotropic and sensitive to decis ions made during the data collection process. Thus, it was difficult to dif ferentiate whether these characteristics were real facets of the surfaces s tudied. The second band was anisotropic and not sensitive to data collectio n issues. Fractal dimensions were greater in the downstream direction than in other directions suggesting that the effects of water working are to alt er the level of surface organisation, by increasing surface irregularity an d hence roughness. This is an important observation as it means that water- worked surfaces may have a distinct anisotropic signal, revealed when using a fractal type analysis.