Horizontal motions, bedrock incision, and the structure of relief in growing folds and orogens

Topographic divide asymmetry may arise from gradients in rock erodibility and orographic precipitation across a mountain belt, and/or tectonic displacement fields that uplift and translate rock horizontally during orogenesis. While simple models exploring relief in active orogens typically consider tectonic motions that are uniform and vertical, the displacement field at Earth's surface generated by slip on finite-length faults is inherently inhomogeneous and contains vertical and horizontal components, which may play an important role in divide asymmetry. In this study, we consider channel profiles that evolve according to the shear stress rule for bedrock fluvial erosion and that experience inhomogeneous horizontal and vertical components of tectonic motion. Dimensional analysis of our revised shear stress rule reveals a dimensionless coefficient that relates bedrock erodibility and basin geometry to slip rate on the underlying fault. We implement our model in a series of 1D non-dimensional numerical experiments that calculate river profile geometry on either side of a topographic divide that is free to advect through the model domain in response to horizontal motion. We drive the models with displacements calculated over a dipping, buried edge dislocation, and examine non-dimensional relief and divide asymmetry resulting from variations in fault dip, non-dimensional fault tip location and non-dimensional model extent. We find that asymmetry results from the full displacement field and from the vertical displacement field alone. Fault dip plays a strong role in the magnitude and direction of divide asymmetry, both in models that include the horizontal motions and those that neglect them. The greatest divide asymmetry resulting from the full displacement field is achieved over dislocations with shallow non-dimensional upper tip depths and small dip angles, although steeply-dipping faults produce asymmetry in the opposite direction. By setting the horizontal component of motion to zero, we find the greatest divide asymmetry resulting from the vertical component of motion alone to be caused by deeply-buried dislocations with low dip angles. Not surprisingly, non-dimensional model extent alters the magnitude of the asymmetry but not the way in which asymmetry varies with dip. Taken together, these results demonstrate the complexity of the surface response to heterogeneous strain and highlight the importance of considering the full deformation field in coupled tectonic and landscape analyses.