# Statistical modelling of co-seismic knickpoint formation and river response to fault slip

Most landscape evolution models adopt the paradigm of constant and uniform uplift. It results that the role of fault activity and earthquakes on landscape building is understood under simplistic boundary conditions. Here, we develop a numerical model to investigate river profile development subjected to fault displacement by earthquakes and erosion. The model generates earthquakes, including mainshocks and aftershocks, that respect the classical scaling laws observed for earthquakes. The distribution of seismic and aseismic slip can be partitioned following a spatial distribution of mainshocks along the fault plane. Slope patches, such as knickpoints, induced by fault slip are then migrated at a constant rate upstream a river crossing the fault. A major result is that this new model predicts a uniform distribution of earthquake magnitude rupturing a river that crosses a fault trace and in turn a negative exponential distribution of knickpoint height for a fully coupled fault, i.e. with only co-seismic slip. Increasing aseismic slip at shallow depths, and decreasing shallow seismicity, censors the magnitude range of earthquakes cutting the river towards large magnitudes and leads to less frequent but higher-amplitude knickpoints, on average. Inter-knickpoint distance or time between successive knickpoints follows an exponential decay law.

Using classical rates for fault slip (15 mm yearinline-formula−1) and knickpoint retreat (0.1 m yearinline-formula−1) leads to high spatial densities of knickpoints. We find that knickpoint detectability, relatively to the resolution of topographic data, decreases with river slope that is equal to the ratio between fault slip rate and knickpoint retreat rate. Vertical detectability is only defined by the precision of the topographic data that sets the lower magnitude leading to a discernible offset. Considering a retreat rate with a dependency on knickpoint height leads to the merging of small knickpoints into larger ones and larger than the maximum offset produced by individual earthquakes. Moreover, considering simple scenarios of fault burial by intermittent sediment cover, driven by climatic changes or linked to earthquake occurrence, leads to knickpoint distributions and river profiles markedly different from the case with no sediment cover. This highlights the potential role of sediments in modulating and potentially altering the expression of tectonic activity in river profiles and surface topography. The correlation between the topographic profiles of successive parallel rivers cutting the fault remains positive for distance along the fault of less than half the maximum earthquake rupture length. This suggests that river topography can be used for paleo-seismological analysis and to assess fault slip partitioning between aseismic and seismic slip. Lastly, the developed model can be coupled to more sophisticated landscape evolution models to investigate the role of earthquakes on landscape dynamics.

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Steer, Philippe / Croissant, Thomas / Baynes, Edwin / et al: Statistical modelling of co-seismic knickpoint formation and river response to fault slip. 2019. Copernicus Publications.

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