The fractal properties of topography as controlled by the interactions of tectonic, lithological, and geomorphological processes

Landscape topography widely exhibits fractal structure. Because of the complexity of relief geometry this structure is not homogeneous in space, and the study of its spatial characteristics represents a powerful method for investigating the interrelationships between landforms and underlying processes. We explore these interrelationships using the digital elevation model (DEM) of an area located in central Italy, where landscape topography is strongly linked to its geological evolution, being characterized by alternating intermountain basins and mountain ranges trending NW–SE. A modified version of the method based on the standard deviation of relief elevations is used to evaluate the fractal parameters of relief after tiling the DEM in spatial units characterized by homogeneous fractal geometry, and statistical methods in conjunction with spatial analysis techniques are applied to the resulting terrain datasets. Both the lowest and (to a lesser extent) the highest values of fractal dimension are found to follow the ridge-andvalley trend. Low fractal dimension is observed in the mountain ranges characterized by massive strata of limestone, and along the fault scarps defining the contact between the intermountain basins and the surrounding slopes, where sediment deposition prevails. High fractal dimension is observed in regions characterized by highly erodible terrigenous lithology, and in areas where tectonic activity favors erosional processes mainly by rivers. The analysis of the (fractal) power law parameters also suggests that each major lithological complex has its own characteristic fractal signature. These results provide new insights into the link between the fractal properties of topography and the tectonic, lithological, and geomorphological features of the area, and show that the analysis approach proposed is useful to depict key aspects about the geomorphological and geological setting of an area, using only a DEM.