Measuring fractal trends in rock surface roughness at the outcrop scale

ABSTRACT: The evolution of dynamical systems formed by the complex interaction of distinct processes over time has been offered as an explanation for the existence of the many temporal and spatial fractal signals evident in nature. This theoretical framework provides a useful context for understanding the role of gradual and catastrophic processes such as rockfalls, landslides and other mass movements in geomorphology, and their contribution to landforms which approach fractal roughness over broad scaling ranges. The main purpose of this study is to investigate techniques for modeling scale dependent roughness using terrestrial laser scanning (TLS) point cloud data, namely multiresolution analysis by the discrete wavelet transform. The Huckleberry Creek Reservoir spillway in Russellville, Arkansas was selected as a test site for the fractal roughness analysis. The spillway walls, excavated from Pennsylvanian age fluvial Hartshorne sandstone in 1994, were scanned at 2-5 cm point spacing. Point clouds were segmented and interpolated over 2.5D grids for anisotropic roughness analysis by the discrete wavelet transform. The limited spatial extent and inconsistent resolution of the data impose upper and lower bounds on viable measurement scale, but provide the means to bridge the gap between small scale profilometric and coarse scale airborne derived geometric datasets in broad bandwidth surface morphology studies. The implementation of multiresolution analysis presented here provides a novel means for quantitative representation of morphological features useful for characterization and interpretation of distinct rock units.