A simple model for faceted topographies at normal faults based on an extended stream-power law

Abstract

Abstract. Faceted topographies at normal faults have been studied for more than a century. Since the dip angle of the facets is typically much lower than the dip angle of the fault, it is clear that the facets are not just the exhumed footwall, but have been eroded considerably. It has also been shown that a constant erosion rate in combination with a constant rate of displacement can explain the occurrence of planar facets. Quantitatively, however, the formation of faceted topographies is still not fully understood. In this study, the shared stream-power model for fluvial erosion and sediment transport is used in combination with a recently published extension for hillslopes. As a major theoretical result, it is found that the ratio of the tangent of the facet angle and the dip angle of the fault as well as the ratio of baseline length and horizontal width of perfect triangular facets mainly depends on the ratio of the horizontal rate of displacement and the hillslope erodibility. Numerical simulations reveal that horizontal displacement is crucial for the formation of triangular facets. For vertical faults, facets are rather polygonal and much longer than wide. While the sizes of individual facets vary strongly, the average size is controlled by the ratio of hillslope erodibility and fluvial erodibility.